reservoir fluid mechanics lab

PE 4521 Experiment 1: Measurements of Oil Density, API Gravity and Viscosity 1. Objectives.

• To determine density and viscosity of three liquid hydrocarbons as a function of

temperature and to examine if any correlation exists between the liquid density and viscosity

• To determine viscosity of three inverse emulsions and to examine the effect of changing water/oil volume ratio on the emulsion rheology

2. Discussion.

Detailed analysis of a crude oil using its complex chemical composition is very difficult if not impossible. Therefore, crude oils are classified according to their physical properties. Density (specific gravity or API gravity) and viscosity are the most important ones. Measurement of API gravity and viscosity is simple, yet essential in the petroleum industry. The specific gravity of a crude oil is defined as the ratio of the density of the liquid to the density of pure water, both measured at specified conditions of pressure and temperature. (Density of pure water is given in Table 3-28.) Dynamic viscosity of a crude oil can be loosely defined as the internal resistance of the oil to flow. Viscosity appears in the mobility coefficient of Darcy’s law during the description of flow of phases in porous medium. The latter is the characteristic fluid flow parameter that controls the rate at which fluid can be produced under an applied potential gradient. Density, on the other hand, is important when the flow takes place under the influence of gravity; hence it appears as the coefficient of depth gradient in Darcy’s equation. An emulsion is a fluid system containing two liquid phases, one of which is dispersed as droplets in the other. The liquid which is broken up into droplets is termed the dispersed phase, whilst the liquid surrounding the droplets is known as the continuous phase or dispersing medium. The two liquids, which must be immiscible or nearly so, are frequently referred to as the internal and external phases, respectively. There are two types of emulsions, direct emulsions and invert emulsions. In direct emulsions, oil droplets are dispersed in water, which were also called oil-in-water emulsion (o/w). In invert emulsions, the opposite is true, since the water droplets are dispersed in oil, which is also called water-in-oil emulsion (w/o). Generally invert emulsions are preferred when a large amount of oil is desired. Emulsions are formed using two phases (such as oil and water) in the presence of an emulsifying agent, i.e., emulsifier. The most common emulsifiers are surfactants. A surfactant, or surface active agent, is a macromolecule with a polar (hydrophilic) head and a long non-polar hydrocarbon (hydrophobic) tail. A good analogy for the surfactant molecules would be lollypops. These molecules locate themselves at the water-oil interface and give an elastic behavior to the dispersed droplets in the emulsion system and, hence, create a thermodynamically stable emulsion. Crude oil emulsions are generally of the water-in-oil type, which are more viscous than either of their constituents. On the other hand, oil-in-water emulsions have lower viscosity than that of the oil phase. Measuring the emulsion viscosity is one of the objectives of this experiment.

Figure 1 Dyed mineral oil mixed with water to produce a pink-colored emulsion.

Figure 2. Appearance of emulsion with its dispersed and continuous phases under the microscope.

Figure 3. A water-in-oil emulsion droplet shown at a microscopic level.

3. Equipment. 25 ml pycnometer, electronic balance, Cannon-Fenske viscometers, API hydrometers, graduated cylinders, electronic balance, stopwatch, latex gloves, lab coat and safety goggle

4. Materials.

Various crude oils, water and an emulsifying agent. 5. Procedure.

To measure the API gravity and density of oil at room temperature using hydrometer: a) Dip the API hydrometer in the graduated cylinder containing the liquid at room

temperature. Spin the hydrometer gently and allow it to come to rest. Note the API gravity reading on the stem of the hydrometer

b) Calculate the specific gravity γo=141.5/(131.5+oAPI) c) Calculate apparent molecular weight of the crude oil using MW=42.43 γo / (1.008-γo) d) Calculate the oil density ρoil = γo ρwater (g/cc) of the crude oil at room temperature.

Here the water density is read from the attached pure water table

To measure the density of oil at room temperature using pycnometer: a) Wash the pycnometer by water, clean it, and let it dried using oven b) Measure the weight of the empty pycnometer using electronic balance c) Fill the pycnometer with one of the oils used in hydrometer experiments above, put

the cover, and allow the excessive liquid to come out through the capillary tube in the cover

d) Weight the filled pycnometer, using electronic balance e) Record the difference in the weight of the pycnometer between the filled and

the empty. f) The density of the liquid is the ratio of the difference in the weight of

pycnometer to the volume of pycnometer. g) Repeat the measurement of density for the other oil samples used in hydrometer

experiments above

To measure oil viscosity: a) See the attached instructions for Cannon-Fenske viscometer. Fill the viscometer as

indicated in step 4. It will turn out that when the viscometer is inverted the liquid will fill about half of the bulb in the bigger arm. Apply suction to draw the liquid from the big arm so that it is in the bulb above the upper etched mark. Allow the liquid to fall freely down past the lower etched mark. Note the time required for the liquid meniscus to pass from the upper to the lower mark. You will want to replicate this step at least one more time to find the average flow time

b) Repeat at several temperatures c) Calculate the kinematic viscosity from the average time and the viscometer constant. d) Repeat the measurements at three other temperatures. Make sure that the viscometer is

kept in the temperature bath for sufficient long time for the liquid to come to the temperature of the bath

e) Use density values obtained from step ‘b’ to find the dynamic viscosity values at three temperatures

f) Clean all equipment and the work area

To measure w/o emulsion viscosity: a) Prepare the invert emulsions at varying emulsifying agent concentration. Place a

suitable volume of diesel oil into a mixer. Add the required volume of emulsifying agent to diesel oil in the mixer slowly and mix the mixture. Finally, add the suitable volume of distilled water and mix it about 20-30 minutes

b) Measure the emulsion viscosity using the Cannon-Fenske viscometer as explained above for the oil

c) Repeat the steps using emulsions with two changing water/oil volume ratios and hence two different volumes of continuous phase

6. Report

a) In the introduction part of your report discuss the significance and practical applications of density, API gravity and viscosity measurements in oils and oil field emulsions

In the discussion part of your report: b) Compare the values of oil density and API gravity estimated using hydrometer and

pycnometer. c) Examine and comment on the temperature dependence of viscosity for the various

fluids you considered d) Compare the emulsion viscosity with the viscosity of the oil phase. Discuss the impact

of water/oil volume ratio on the viscosity e) Comment on controllable measurement error and its impact on calculated results

DENSITY OF PURE WATER (FROM PERRY’S CHEMICAL ENGINEERING HANDBOOK, ON PAGES 375 AND 376)

continue next page…

Unit Conversion: To convert kilogram per cubic meter to pounds per cubic foot, multiply by 0.06243 oF=9oC/5+32

PE 4521 Experiment 2 Measurement of Gas Viscosity using Molecular Dynamics Simulation 1. Objective. To predict the viscosity of a mixture of gas with known composition using molecular dynamics (MD) simulation along with Einstein’s equation 2. Discussion. Accurate prediction of gas viscosity using instrumentation is difficult and often not reliable. Here we learn to use molecular simulation as the method of predicting gas viscosity at a particular pressure and temperature. Einstein’s equation to predict the viscosity (Pa-s) of any fluid is given as:

( ) ( )[ ]230

02

10=−

∆×

=−

tGtGtTk

VB

gasµ ……………………………………………………eqn (1)

where V is the volume of a cubic computational cell with a 40 Å length, kB the Boltzmann constant equal to1.3806E-23 J/K, T the temperature (273.0K) and ∆t the time step for the simulation, which is 10sec in this case. The term in the bracket is known as the “canonical ensemble” average square mean displacement of the molecules with G(t) described as:

( ) ( )tmrV

tGN

iii∑

=

=1

1βα

Here, N is the number of gas molecules in the computational cell, riα is the position of molecule i in the α-direction, and miβ the momentum of the same molecule in the β-direction at time t. 3. Equipment. DL-POLY, parallel computing using LINUX cluster at the OU Supercomputing Center for Education & Research.

Figure 1. A snap shot from the MD simulation showing the location of gas molecules in a slit-shape pore.

4. Procedure. Below, the square mean displacement of the molecules is given at 10 second intervals for a number of gas molecules at 273.0K temperature and 1.028MPa pressure.

[G(t)-G(0)]2 (Pa-sec)2

[G(t)-G(0)]2 (Pa-sec)2

172.06 172.08 172.09 172.04

172.1 172.24 172.08 172.04 172.15 172.09 172.04 172.08 172.06 172.12 172.11 172.03 172.04 172.09 172.12 172.02

Take the average value of these and use it in equation (1) to estimate the gas viscosity 5. Report Report the estimated viscosity in centipoises (cp) 6. Bibliography.

1. Allen, M.P. and Tildesley, D.J. (2007) “Computer Simulation of Liquids,” Oxford University Press, London

2. Frenkel, D. and Smit B. (2002) “Understanding Molecular Simulation – From Algorithms to Applications,” Academic Press, Computational Science Series, San Diego

PE 4521 Experiment 3: Statistical Analyses of Core Data 1. Objective: The goal of this study is to use data that can be obtained from core analyses and/or well logs to determine statistical measures for distributions of reservoir properties (e.g., porosity, water saturation and permeability) and determine whether the properties can be spatially correlated. 2. Discussion: The volumetric estimation of original oil in-place is conceptually simple; see Craft et al. (1990), and Tiab and Donaldson (1996). The fundamental estimate is the reservoir bulk volume occupied by the liquid and/or vapor hydrocarbon phases. However, there are other parameters in the equation shown below. These include porosity, net to gross and phase saturation. In this exercise you will examine the character of these properties measured on cores believed to be from the same reservoir.

( ) ( )STB 7758 1bulk wi G oN V S N Bϕ= −

In practice engineers normally use average quantities for porosity, φ and water saturation, Swi. Unfortunately, they usually just calculate the averages without subjecting them to statistical analyses. The confidence with which the averages could be used would be much greater if the engineer understood how much statistical confidence could be placed in them. The goal of this lab experience is for you to develop insight into the use of statistics to understand core data. In addition, current trends in reservoir engineering are to use simulators for reservoir analysis and management. For some problems, it is important to examine the effects of reservoir heterogeneity, namely the values of reservoir parameters such as porosity and permeability are developed as functions of position within the reservoir. Consequently, it is convenient to identify if relationships exist between the parameters or if they are independent distributions. It seems appropriate to consider this experiment in two parts. First, examine core reports to identify correlated sections for all wells. Then check those sections, see if the porosity and water saturation frequency distributions appear to be from the same population. You will also check to see if they follow a normal distribution. Many people believe that they do (e.g. Amyx et al.1960). If the two cores are drawn from the same population, the sample frequency diagrams should be quite similar. Similarity would indicate that the two cores are from parts of the same reservoir that were formed by the same geologic processes. If the frequency diagrams are different you might conclude that they might be formed by different processes or at different times. If the frequency diagrams are the same, calculating average porosity and water saturation for the reservoir should be done using the combined frequency distributions, particularly since you will have proven that they are from the same population. If the distributions follow the normal or standard distribution (bell shaped curve), there are specific tests, such as the t-test; you can use to establish confidence limits that the measures of

central tendency and dispersion for the two cores were drawn from the same population. If they do not follow a normal distribution, you will need to use more words and more complicated analysis (thinking) to show how you determined the average values. The second part of the experiment does not directly impact on estimating the quantity of hydrocarbons originally in the reservoir. Rather it has to do with identifying relationships between reservoir parameters that can be used for scaling or assigning parameter (permeability) values to parts of the reservoir in a reservoir simulator. In this section, you will look for relationships between the parameters. It is reasonable to hypothesize that porosity is the fundamental parameter and connate water saturation and permeability could be functions of porosity. It would be reasonable to plot water saturation versus porosity to see if there is an identifiable relationship. (See Chapra and Canale, chapter 17 Regression.) Many people believe that permeability is log normally distributed. That means that the logarithm of permeability is normally distributed. Check your data to see if it confirms this belief. Plot permeability (and log-permeability) versus porosity and saturation to identify any relationship. You should report the results of your regression analysis with measures of quality. 3. Equipment: Core reports for two wells. These core sections are thought to be from the same unit. Use porosity, measured water saturation and maximum K [md] as data for your statistical analysis. 4. Procedure: Use the data, to estimate representative values of porosity and permeability. Also identify relationships that may exist between porosity, water saturation and permeability. This will “go more easily” in a spreadsheet since they have sort functions, graphical capability and some statistical analysis capability. (Make sure you know what the Excel functions mean and do.) 5. Report: Be sure to include your porosity and permeability histograms. It would be useful to have the histograms for all wells on the same figure (also the combined histogram if the data warrant it). Also include the cross-plots of water saturation and permeability versus porosity. Put the statistical calculations in the appendix. 6. References: Amyx, J.W., D.M. Bass, Jr and R.L. Whiting, Petroleum Reservoir Engineering, Physical Properties, McGraw-Hill, Inc., pp 536—560, 1960. Chapra, S.C. and R.P. Canale, Numerical Methods for Engineers, 3rd Edition, McGraw-Hill Publishing Company, Part 5 and Chapter 17, 1998. Craft, B.C., M. Hawkins and R.E. Terry, Applied Petroleum Reservoir Engineering, 2nd Edition, Prentice-Hall, pp. 69-76, 148-150, 1991. Tiab, D. and E.C. Donaldson, Petrophysics, Gulf Publishing Co., pp. 118-122, 1996. i.y.a. 2012

PE 4521 Experiment 4 Volumetric estimation of OOIP 1. Objective. The goal of this project is to determine the original oil in place using volumetric method. 2. Discussion. The volumetric estimation of original oil in place is conceptually simple; see Craft et al. (1990). The basic estimate is the estimate of the reservoir bulk volume occupied by the liquid and/or vapor hydrocarbon phases. Petroleum reservoirs are irregularly shaped bodies. To properly determine the volume one should integrate the irregular functions between the limits that bound the reservoir and its separation into distinct phase regions.

bVoo dzdydxzyxBSN ),,(/

That means determining the bounding top and bottom surface functions and the horizontal limits of the formation. Since these are not simple functions, integration must be approximate rather than analytic, Chapra and Canale (1998). Historically, geoscientists have determined structure maps from seismic imaging. They have then converted those maps to isopachous maps of the oil and gas zones using oil-water and gas-oil contact data where available. Graphical methods are generally used to contour areas of constant saturated thickness and a numerical method is used to integrate the volume, Vb, contained in the reservoir as mapped. The actual formula used is simple, Craft et al. (1991). N = C Vb (1-Sw) / Bo In oilfield units for liquid hydrocarbon saturated reservoirs, C is 7758 rb/ac-ft, Vb is in ac-ft, and Bo is in rb/stb and N is in stb. Porosity and water saturation is expressed in fraction. Even though the formula is simple there are several sources of errors. An excellent discussion on uncertainty estimation in volumetrics determination is given by Floris and Peersmann (1998). 3. Equipment. Planimeter or another graphical integration device. 4. Procedure. Use the data in Attachment 1, particularly the structural map and the isopach map of the pay zone thickness, excerpted from Andrews, et al. (1995 or 1996), to prepare a net oil sand isopachous map. Integrate the areas within contours using a planimeter and using

an appropriate numerical method to find the volume of the reservoir filled with hydrocarbons. There are three ways to calculate the volume: trapezoidal rule, Simpson’s rule and equation for the volume of the frustum of a pyramid. Trapezoidal rule: h is fixed = 10 ft

nnnn ataaaaahVolume )2...........22(21

1210 Simpson rule:

nnnnn ataaaaaaahVolume )42.......424(31

123210

where h = contour interval (ft) ao = area enclosed by zero contour ( at oil water contact) (acres) a1 = area enclosed by first contour an = area enclosed by nth contour tn = average formation thickness above the top contour Simpson rule is the more accurate of the two for irregular curves. However, either will usually give satisfactory results. Simpson’s rule is slightly more tedious and has the limitation that an even number of contour intervals (odd number of contours) must be used. The equation for the frustum of a pyramid can be expressed by:

)(31

00 nn aaaahVolume Do the calculation of the bulk volume associated with this reservoir Find the OOIP and compare with the one from the Booch Play where a0 = area enclosed by the lower contour in section (acres) an = area enclosed by upper contour in section (acres) Use the volume described by your map and other data from the table of reservoir engineering data to estimate the original oil in place by all three methods. (For the Booch reservoir, you will notice that a fault is mapped between the Hall #1 discovery well and other wells in the reservoir. The results of the reservoir simulation study suggest that the fault is a seal. Compare your estimate of original oil in place with the value reported in Attachment 1. 5. Report: Be sure to include your isopach map of the oil zone. Include calculations as part of the appendix material. Performing calculations in a spreadsheet would be helpful.

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6. Questions: a) One of the figures in Attachment 1 is the type log for the field; it shows the information used to determine the top and bottom of the pay zone interval. How precise do you think the thickness can be measured? What impact can that have on the estimate of original oil and gas in place? b) What are the various sources of errors in volumetric calculations? How will you minimize them? 7. References: Andrews, R.D., Northcutt, R. A., Knapp, R. M. and Yang, X. H. 1995. Fluvial-Dominated Deltaic (FDD) Oil Reservoirs in Oklahoma: The Booch Play, Oklahoma Geological Survey, Special Publication 95-3, 67 pp. Andrews, R.D., Rottman, K., Knapp, R. M., Bhatti, Z. N. and Yang, X. H. 1996. Fluvial-Dominated Deltaic (FDD) Oil Reservoirs in Oklahoma: The Skinner and Prue Plays, Oklahoma Geological Survey, Special Publication 96- 2, 106 pp. Chapra, S.C. and Canale, R. P. Numerical Methods for Engineers, 1998. 3rd Edition, McGraw-Hill Publishing Company, Chapter 21. Craft, B.C., Hawkins, M. and Terry. R. E. 1991, Applied Petroleum Reservoir Engineering, 2nd Edition, Prentice-Hall, pp. 69-76, 148-150. Floris, F. J. T., and Peersmann, M. R. H. E. 1998. Uncertainty estimation in volumetrics for supporting hydrocarbon exploration and production decision-making, Petroleum Geosciences, 4, pp. 33-40. iya2012

PE 4521 Experiment 5 Hydrocarbon Phase Behavior 1. Objective Study the pressure-volume behavior of hydrocarbon fluids and CO2–water mixture to determine experimental values for i) bubble point, ii) gas solubility, iii) formation volume factor, and iv) isothermal compressibility. 2. Discussion Crude oil physical properties such as gas solubility Rso, and formation volume factor Bo are function of pressure, temperature and composition (McCain, 1990). For a given hydrocarbon, the reservoir depletion can be approximated as an isothermal process and as such the above properties can be considered to be a function of pressure alone. In this experiment you will be determining bubble point, Rso, Bo and compressibility of a selected number of hydrocarbon fluids and CO2–water mixture at room temperature. Bubble point is the pressure Pb at which the bubbles of free gas first appear. Gas solubility, Rso, is the number of standard cubic feet of gas that will dissolve in one stock-tank barrel of oil at reservoir temperature and pressure, [scf/stb]. Henry’s law states that the solution of gas within a liquid is directly proportional to the pressure exerted by the gas above the liquid. However, this is an ideal law that only applies in limited circumstances. Standing’s correlation, equation 1.26 in Craft et al. 1991, corrects for the real nature of reservoir fluids by using an exponent of 1.204 rather than 1.000. Standing’s correlation is an approximation and may not be appropriate for specific oils and gas systems. When gas is forced into solution in crude oil by pressure there is an increase in the total liquid volume. This increase in liquid volume is described by the oil formation volume factor, Bo, and is based on stock tank volume. The formation volume factor may be defined as the volume in barrels at reservoir conditions occupied by one stock-tank barrel of oil plus the dissolved gas, [rb/stb]. Isothermal compressibility is a measure of change in volume as the pressure is changed. It can be calculated experimentally using the following equation:

−−−

=21

211PPVV

Vco

where V1 and V2 are volumes at pressures P1 and P2. V is the reference volume generally assumed to be average of the two volumes. 3. Equipment PVT cells, hydrocarbons, water and CO2, latex gloves, and safety goggles.

4. Procedure Briefly, the experiment consists of measuring pressure and volume of hydrocarbon and gas mixture in a PVT cell at room temperature. You will be using three PVT cells. Detailed instructions on how to operate the two cells will be provided to you in the laboratory. As you decrease the pump pressure in 500 psig increments down to the bubble point, read the pump displacement corresponding to each pressure stage. Check the cell inspection window during each pressure reduction. The appearance of small bubbles indicates that the saturation (bubble point) pressure has been reached. Expand the system below the bubble point in several increments (3-5) using the remaining pump displacement. Agitate the cell after each expansion to establish equilibrium before reading exact system pressure and volume. Use the data collected to determine the bubble point pressure by plotting system volume versus pressure. Above the bubble point all gas is in solution and you are directly measuring volume changes with pressure. Below the bubble point you are measuring the volume occupied by the liquid (oil plus dissolved gas) and the vapor phase volume occupied by the gas that has come out of solution. This is often referred to as the two phase or total formation volume factor, Bt. The liquid has volume N*Bo and the vapor has volume N*Bg (Rsoi – Rso). Use the ‘form’ of the correlations listed in Craft et al. 1991, along with your data to develop the PVT suite of Bo and Bg, Bt and Rso. You will need to make some assumptions. You can make good use of equations (1.26), p. 33, (1.28), p. 35, (1.29), p 37 and (1.1, 1.31), p. 38 in Craft et al. 1991. Note- you do not use them exactly as they are written but rather use their forms and use values at the bubble point pressure to solve for coefficients so that you preserve the forms while adjusting the correlations for your experimental results. 5. Report

a) Graphs (experimental points clearly indicated) for all the liquids and gas combinations: i. Cell pressure versus sample volume. ii. Two phase formation volume factor, Bt and Bo, versus cell pressure. iii. Solution gas, Rso, versus cell pressure. iv. Compressibility of liquids vs. pressure.

b) Report bubble point for the studied hydrocarbons. c) Show sample calculation for all the above parameters for one hydrocarbon.

7. References 1. Craft, B.C., Hawkins, M., and Terry, R. E.1991. Applied Petroleum Reservoir Engineering, 2nd Edition, Prentice-Hall, pp.31-44. 2. McCain, Jr., W. 1990. The Properties of Petroleum Fluids, 2nd edition, PennWell Books, Tulsa, OK.

IYA 2012

PE 4521 Experiment 6 Interfacial Tension, Contact Angle & Capillary Pressure Measurements 1. Objectives. To perform high pressure mercury injection experiment on three samples – two sandstones and one limestone; from the collected data, to calculate air-brine capillary pressure curve, pore throat size distribution, permeability and J-function. To measure solid-air-brine (with and without surfactant) interfacial tensions (IFTs), contact angles using Du Nuoy tensiometer and contact angle meter. 2. Discussion. Several techniques such as porous plate method, centrifuge method, and high-pressure mercury intrusion are used to obtain capillary pressure (see Amyx et al. 1960; Tiab and Donaldson 1996 etc.). Of all these methods, high pressure mercury injection is the most common one. Capillary pressure, IFT and contact angle data is very important to reservoir engineers as it is used to predict water saturation, calculate free water level, evaluate rock quality (e.g., wettability), calculate and interpret relative permeability curves, predict pore size distribution, develop residual hydrocarbon saturations etc. 3. Equipment. Rock samples, electronic scale, mercury injection high pressure porosimeter, DuNouy tensiometer (to measure interfacial tension) and contact angle measurement apparatus. See the attached supplementary notes for the equipment. Detailed directions on how to use the porosimeter, tensiometer and contact angle meter will be handed out in the laboratory. Caution: In this experiment you will be using mercury. Be very careful; at all times wear gloves. As in the other laboratory sessions, no eating and drinking is allowed in this lab. 4. Data and report. The basic data that you will be using consist of pressure and mercury intrusion volume. From the data do the following: 1) plot intrusion pressure versus Hg saturation, 2) calculate and plot pore throat size histogram, 3) convert and plot Hg-air data to air-brine capillary pressure, 4) estimate R35 and calculate permeability using Windland equation, and weighted geometric mean approach, 5) plot J-function versus wetting phase saturation and 6) discuss which of the three samples will be a better reservoir and why? 5. Bibliography: Amyx, J. W., Bass, D. M., and Whiting R. L.1960. Petroleum Reservoir Engineering: Physical Properties, McGraw Hill Book Co., NY, 610pp. Tiab, J. and Donaldson E. 1996. Petrophysics-Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties, Gulf Publishing Co. Houston, 706pp. Vavra, C. L., Kaldi, J. G., and Sneider, R. M. 1992. Geological Applications of Capillary Pressure: A review, AAPG Bull. 76, 840-850. Dastidar, R, Sondergeld, C. H. and Rai, C. S. 2007 An Improved Permeability Estimator from Mercury Injection for Tight Clastic Rocks, Petrophysics, 48, 186-190. iya2012

rCPc

θγ cos2=

( )( ) )(

)()()( cos

cos

Hgair

brineairHgaircbrineairc PP

−

−−− =

θγθγ

)cos(2)/(2166.)(

2/1

θγφKPSJ c

w =

Winland’s Equation:

φLogLogKLogR 864.0588.0732.035 −+=

351 245 1 469 1 701LogK . . Log . Log(R )= − + φ + 2 51 3 06 1 64 wgmLogK . . Log . Log(R )= − + φ +

where Pc: capillary pressure in psi θ : contact angle (130o for air-Hg, take 0o for air-brine)

γ : interfacial tension in dynes/cm (485 for air-Hg; you will determine in the lab for air-brine using tensiometer)

r : capillary radius in microns C : conversion constant (0.145) K : permeability in millidarcy φ : porosity (%) R35 :pore radius in microns at 35 percentile non wetting phase saturation Rwgm: weighted geometric mean radius

Supplementary Notes for Du Nouy Tensiometer

Du Nouy Tensiometer No 70545

Correction factor for surface and interfacial tension

Supplementary Notes for CAM-PLUS MICRO Contact Angle Meter

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Filtration – Pore size, pore volume, poreshape, and pore tortuosity are of interest tofilter manufacturers. Often, pore shape hasa more direct effect upon filtration thanpore size because it strongly correlates withfiltration performance and fouling.

Construction Materials – Diffusion, permeability, and capillary flow play important roles in the degradation processes in concrete, cement, and other construction materials.

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Data Reduction

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WATERFLOODING AND ENHANCED OIL RECOVERY PE 4521 Experiments 7, 8 and 9 Fall 2011 1. Objectives A) To become familiar with the application of core (sand pack) evaluation tests to predict

recovery factors from waterflooding, surfactant flooding and gas flooding. B) To determine petrophysical and multi-phase flow properties of the sand pack such as

porosity, permeability, irreducible water saturation, residual oil saturation and ‘end-point’ relative permeability for each recovery system.

2. Discussion

Primary production seldom depletes an oil reservoir. Common practice has been to water flood partially depleted reservoir after an initial primary production. The series of experiments you are scheduled to perform will help you to create a porous medium using mixtures of sands, to saturate a sand pack to establish oil saturation at connate water saturation and to flood. The latter stage also involves determination of the efficiency values of imbibition during water displacement, surfactant flooding and gas drive.

Surface tension at the oil-water interface of a reservoir system has a major influence upon residual oil saturation in the immiscible flooding of a porous medium. The displacement efficiency of a flood system increases as the interfacial tension decreases. Part of this net effect from a change in surface tension can be attributed to a change in wettability that also influences the residual oil saturation (see Craft et al. 1991, Figure 9.19, p. 381). One method of decreasing the interfacial tension between the displacing fluid and crude oil is by adding surfactant to the displacing fluid. When interfacial tension is sufficiently reduced, oil recovery can approach 100 per cent of the oil remaining after water flooding. Performance of a surfactant flood depends on several factors such as 1) pore geometry, 2) interfacial tension, 3) wettability or contact angle, and 4) pressure gradient. A number of factors, including brine composition, have major effect on interfacial tension. Many parameters must be considered in the design of a surfactant flood process. Gas drive is one of the techniques used to recover additional oil when recovery from primary energy becomes uneconomic. A gas flood is applicable in reservoirs with high permeability and high relief. Gravity segregation may occur in a gas drive system. Under some conditions segregation can result in high recovery factors. In other cases, low recovery may occur when gas overrides a zone of high oil saturation. Gas may also be used for pressure maintenance. In this case the recovery process is more complex. As a pressure maintenance agent it can also be useful for reservoirs with low permeabilities (see Craft et al. 1991, section 9.3.2, pp. 353—360).

3. Equipment Flow experiment assembly, Lucite sand pack tube, graduated cylinders, electronic balance, pycnometer, stopwatch, latex gloves and safety goggles. You will be working with dyed brine that may stain clothes. In general keep the pressure difference across the sand pack relatively low; a few psi (never more than 10 psi); this will give you enough time to watch what happens and to record data.

4. Materials

Mineral oil, NaCl brine, sand, sulfonate surfactant mixture (10% by volume in deionized water) and laboratory compressed air.

5. Procedure Waterflooding a) Build sand pack using 100 mesh quartz sand (grain density = 2.65 gm/cc). Prior to

making the sand pack weigh all empty tube and all other necessary parts those are needed to make full sand pack assembly. Start preparing the sand pack. Tap the side of the Lucite tube while filling to ensure a tight pack with minimum voids. After filling, put the tube in the metallic holder. Measure dimensions of the sand pack. Obtain the dry weight of the sand pack. Calculate pore volume and dry porosity of the pack. The porosity should not be more than 27%. If it is more, repeat the packing till you get porosity <27%. This is to ensure that the pack has reasonable permeability for you to do flow through experiments.

b) Install sand pack on the waterflood apparatus. Evacuate the sand pack to remove all the air and any moisture, then saturate with brine. Recover at least one pore volume of brine to ensure that the pack is fully brine saturated with no air left inside the tube. Disconnect and weigh. Calculate the saturated porosity. The difference between dry and saturated porosity should not be more than 3 porosity units.

c) Establish a flow rate with brine and determine absolute permeability. (Use brine viscosity and density measured earlier in the semester)

d) Flood the sand pack with oil until no water is produced. Measure displaced water. Determine irreducible water saturation and initial oil saturation. Determine effective (relative) oil permeability at irreducible water saturation [Craft et al. 1991]. Weigh the sand pack at this point to confirm saturations using a mass balance.

e) Waterflood sand pack with 2-3 pore volumes of water. Catch oil displaced in graduated cylinder. (If you do this slowly enough, you may be able to plot cumulative oil production (Np) versus amount of water injected (Wi). This is the fundamental ‘performance plot’ for waterflooding. You can record Np+Wp (water produced), Np (or Wp), versus time. Determine residual oil saturation to waterflood. Establish steady flow rate of brine and measure effective (relative) permeability to water at residual oil saturation. Weigh core at residual oil saturation to confirm water and oil saturations using a mass balance.

Surfactant Flooding a) Flood the sand pack with oil until no more water is produced. Measure displaced water.

Calculate starting oil and water saturation. Then flood the sand pack with surfactant solution. Catch effluent in graduated cylinders. 250 cc graduated cylinders are provided in the lab. Break through of the surfactant solution should occur between 50 and 100 cc. You will be able to see this by color of the effluent. You may take the density of the surfactant 1g/cc and the viscosity 0.96cst.

b) During the last 1-2 pore volumes, determine the effective permeability to the surfactant solution.

c) Allow the cylinders to set so that the oil and water will separate. Measure the oil and water recovered. It is useful to do this in a plot of Np versus Wi. You can also determine WORs for the separate cylinders and on a cumulative basis.

d) Clean all equipment including the sand packs and the work area. Gas Flooding a) For this experiment you will have to prepare a new sand pack, measure its properties, flow brine and oil to bring the sand pack to irreducible water saturation. (Plan to prepare the sand pack while other members of your team are doing the surfactant expt.) b) Flow oil through the sand pack so as to reach original hydrocarbon saturation. Check this by weight measurements. c) Displace oil from the sand pack with compressed air at constant pressure. Measure oil

production as a function of time. Record gas injection rate at the same times you measure oil production. You can use this data to determine injected gas. Continue flooding until oil production is zero.

6. Report results: a) Pore volume, porosity and absolute permeability of sand pack. b) Initial oil saturation, connate water saturation and Kro (Swc). c) Residual oil saturation and Krw (Sor). d) Recovery factor at the end of the water flood, surfactant flood and gas flood. See

displacement efficiency, Ed[Craft et al. 1991]. e) Mobility ratio for the water flood. f) Determine oil saturation, water saturation after the surfactant flood and Krw (Sor) g) Efficiency of the surfactant flood in terms of the oil in the core at the beginning of the

surfactant flood. h) The final oil saturation for the sand pack after surfactant flooding. i) Oil recovery factor for the gas flooding experiment. j) The final oil saturation for the sand pack after surfactant flooding. k) Np versus injected gas. 7. Things to keep in mind when writing the report (You may want to address these points in your report) a) What special safety concerns are there about these experiments? b) What factors might reduce the water flood recovery factor? Why? c) What properties of the reservoir rock or fluids could cause those factors to change? Why? d) Does the water flooding process seem efficient? Why? f) What factors might reduce the surfactant flood recovery factor? Why?

g) Does the surfactant flooding process seem efficient? Why? h) What are special economic concerns to monitor / overcome in surfactant flooding? j) Does the gas flooding process seem efficient? Why? (You might want to compare to your

water flooding results.) 8. References and Bibliography Craft, B.C., M. Hawkins and R.E. Terry, 1991. Applied Petroleum Reservoir Engineering, 2nd Edition, Prentice-Hall, pp.148—153 and 335-360, and 380-386. iya2012

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Experiment 1 & 2

Measurements of Oil Density, API Gravity and Viscosity

Measurement of Gas Viscosity using Molecular Dynamics Simulation

PE 4521 002—Reservoir Fluid Mechanics Laboratory

Team 002E

Role Name Performance Score Signature

Manager Axel Hannenberg 1.0

Researcher Lemmy Oshenye 1.0

Technician Lucas Gurgel De Carvalho 1.0

Analyst Nor Ashraf Norazman 1.0

Academic Integrity Statement

On my honor, I affirm that I have neither given nor received inappropriate aid in the completion of

this exercise.

Name: _________________________________ Date: _____________________________

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Abstract

An emulsion is a dispersion (droplets) of one liquid in another immiscible liquid. The viscosity of

emulsion depends on several factors such as viscosities of oil and water, volume fraction of water

dispersed, droplet-size distribution, temperature, shear rate, and amount of solids present (Kokal 2006, I-

538).

The oil densities obtained from hydrometer and pycnometer are 0.858-, 0.843-, 0.825-g/cm3 and 0.887-,

0.890-, 0.863-g/cm3 for crude oil 1, crude oil 2, and diesel respectively. The results are relatively similar

to each other. The API gravity values acquired from hydrometer and pycnometer are 33-, 35.9-, 39.5-

°API and 33.7-, 38.4-, 40-°API for crude oil 1, crude oil 2, and diesel respectively. The API gravity of

each samples measured from hydrometer are slightly lower than what are given due to equipment

sensitivity to temperature. Temperature has a significant effect on viscosity.

At 23°C, the dynamic viscosities for crude oil 1, crude oil 2, and diesel are 5.25-, 3.34-, 1.31-cP. At 33°C,

the dynamic viscosities for crude oil 1, crude oil 2, and diesel are 19.9-, 7.71-, 2.58-cP. At 60°C, the

dynamic viscosities for crude oil 1, crude oil 2, and diesel are 11.72-, 5.94-, 2.31-cP. The kinematic and

dynamic viscosities decrease as temperature increases. At room temperature, the kinematic viscosities of

crude oil 1, crude oil 2, diesel, emulsion 1, and emulsion 2 are 23.3-, 9.28-, 3.14-, 118.45-, 143.8-cSt. The

kinematic viscosity for the emulsion is higher compared to the crude oils and diesel.

Accurate prediction of gas viscosity using instrumentation is difficult. Molecular simulation method is

used to predict gas viscosity at a particular pressure and temperature. The average square mean

displacement of molecules is 172.1 (Pa·s)2. The calculated gas viscosity is 0.000146 cP.

Both the density and viscosity are inversely related to temperature. The measurement of the viscosity and

density of reservoir fluid could be a simple procedure but nonetheless an important aspect in the

economics of the well.

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Introduction

Although determining density and viscosity of petroleum fluids is simple, it is very important. For

instance, the heaviest oils may contain a high percentage of contaminant or nonhydrocarbon molecules,

resins and asphaltenes. The economic importance of understanding these high contaminant percentages is

demonstrated in the additional cost occurred in the processing time. Extra chemical separation means

special equipment is required and that contribute to greater cost. The lighter oils are easier to deal with

chemically because they require less exhaustive refinement. The viscosity is important because it affects

the pressure losses when the fluid is being transported or produced and it affects the cost. Density and

viscosity vary with temperature, pressure, and composition. Temperature causes the major variations in

these properties. Thus, it is important to study how these properties change with temperature. In the

petroleum industry, the density is measured in API gravity. A hydrometer can be used to measure API

gravity and density. The fluid composition will dictate whether the density will increase or decrease.

When temperature increases, the oil expands and its lightest fractions that were previously dissolved leave

the solution. For gas, as temperature increases, it expands and hence the density decreases. When

temperature increases, the viscosity can decrease nonlinearly (Fig. 1). On the other hand, the viscosity of

the gas increases with the increase of temperature due to the increase of the intermolecular collisions.

Some enhanced oil recovery (EOR) methods exploit these temperature/pressure concepts. For example,

steam injection and in-situ combustion are used to increase the reservoir temperature in order to lower the

oil viscosity so it will be easier to produce. The increase in temperature seen in the EOR methods adds

more energy to the reservoir. Fig. 1 shows that the greater the viscosity is, the greater it decreases with the

increase of temperature. Many petroleum reservoirs are linked to an aquifer. In many cases, reservoir

water is also produced along with the oil. Water is a polar substance and the oil is apolar, meaning they

are immiscible in nature. Since oil and water do not mix, there is an interfacial tension between the two

liquids. To reduce this interfacial tension, an emulsifier can be added to form an emulsion which is more

stable. However, the emulsion has completely different properties.

Fig. 1—Viscosity vs. temperature for three different oils (Tarcilio 2011).

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Experimental Procedure

Experiment 1

Hydrometer, pycnometer and Cannon-Fenske routine viscometer are used for this experiment (Fig. 2).

Dip the API hydrometer in the cylinder containing the oils at ambient temperature. Spin the hydrometer

and let it stabilize before taking the API gravity reading on the stem of the hydrometer. Calculate the

density of oil from the API gravity reading. Use electronic balance to record the pycnometer filled with

oil. Calculate the difference between an empty pycnometer and filled pycnometer. Take note of the

volume of the pycnometer to calculate the density of the oil. The Cannon-Fenske viscometer is designed

to measure viscosity of Newtonian liquids from of 0.5 to 20,000 cSt (Viswanath et al. 2007, 18). The

viscometer is kept in a beaker containing water. The water is heated to achieve the desired temperatures.

Apply suction to the tube until the oil in the viscometer is above the upper mark on the tube. Start the

stopwatch once the oil passes the upper mark and stop it once the oil reaches the lower mark. Multiply the

efflux time by the viscometer constant to obtain the kinematic viscosity. Repeat measurements several

times for different oils and temperatures.

Diesel, emulsifying agent and water are mixed into a mixer. To measure the water/oil emulsion viscosity,

use the Cannon-Fenske viscometer after preparing the invert emulsion. Use the stopwatch to record the

time for the emulsion to reach the lower mark. Repeat the steps using emulsions with different water/oil

volume ratios. The mixture contains 150 mL of diesel, 150 mL of water, and 2 mL of emulsifier. It is

assumed that the water/oil ratio is 50/50 from the relative volumes.

Fig. 2—From left to right: Pycnometer and electric balance; hydrometer to measure API gravity; and Cannon-Fenske

routine viscometer used to measure oil viscosity.

Experiment 2

The viscosity of gas with known composition is determined by using molecular dynamics simulation

together with Einstein’s equation. The simulation is set at 273K temperature and 1.028 MPa pressure. The

square mean displacement of the molecules is provided at 10-second intervals. Accurate gas viscosity is

important to understand the composition of the fluid within the reservoir.

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Results

Experiment 1

TABLE 1—OIL DENSITY VALUES OBTAINED FROM TWO METHODS

ρoil (g/cm3)

Crude oil 1 Crude oil 2 Diesel

Hydrometer 0.858 0.843 0.825

Pycnometer 0.887 0.890 0.863

TABLE 2—API GRAVITY VALUES OBTAINED FROM TWO METHODS

API°


Hydrometer 33 35.9 39.5

Pycnometer 33.7 38.4 40

Fig. 3—Oil density vs. temperature. Density of oil decreases with increase in temperature.

0.805

0.810

0.815

0.820

0.825

0.830

0.835

0.840

0.845

0.850

0.855

0.860

20 30 40 50 60 70

Oil

de

nsi

ty, ρ

, g/c

m3

Temperature, °C

Crude oil 1

Crude oil 2

Diesel

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Fig. 4—Kinematic viscosity vs. temperature. Viscosity of oil decreases with increase in temperature.

Fig. 5—Dynamic viscosity vs. temperature. Viscosity of oil decreases as temperature increases.

0

5

10

15

20

25

20 30 40 50 60 70

Kin

em

atic

vis

cosi

ty, ν,

cSt

Temperature, °C

Crude oil 1

Crude oil 2

Diesel

0

5

10

15

20

25

20 30 40 50 60 70

Dyn

amic

vis

cosi

ty, μ

, cP

Temperature, °C

Crude oil 1

Crude oil 2

Diesel

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Fig. 6—Oil density vs. dynamic viscosity. The rate of change for viscosity is dependent upon the oil density as a function

of temperature. The higher the oil density, the lower the API gravity, brings greater change in density with temperature.

TABLE 3—KINEMATIC VISCOSITIES OF EMULSION & OIL PHASES

Crude oil 1 Crude oil 2 Diesel Emulsion 1 Emulsion 2

ν (cSt) 23.29 9.28 3.14 118.45 143.80

Experiment 2

The average square mean displacement of molecules is 172.1 (Pa·s)2. The calculated gas viscosity is

0.000146 cP.

Discussion of Results

Experiment 1

The oil densities obtained from hydrometer and pycnometer methods are relatively similar to each other

(Tables 1 and 2). The results of differences may be due to the sensitivity of the equipment. Each of the

equipment has its own unique uncertainty. The uncertainty of the hydrometer could be contributed by

parallax error. The API gravity of each sample measured from hydrometer is slightly lower than the API

gravity measured from pycnometer due to equipment sensitivity to temperature.

For the Cannon-Fenske equipment, the constant of each station has to be interpolated or extrapolated by

assuming it has a linear relationship with temperature. The kinematic and dynamic viscosities have

similar correlations to temperature change. Viscosity decreases as temperature increases. This could be as

a result of the intermolecular attraction getting weaker. As temperature increases, the volume of oil

increases, the density of oil decreases (Fig. 3). The change in viscosity is largest for crude oil 1 followed

by crude oil 2 and diesel. Figs. 4 and 5 show that there is a trend that the smaller the API gravity, the

larger the change in viscosity (Fig. 6). The change in temperature can be related to the conditions in the

subsurface. As hydrocarbon fluid is being produced, the temperature decreases until it reaches the surface

0.805

0.810

0.815

0.820

0.825

0.830

0.835

0.840

0.845

0.850

0.855

0.860

0 5 10 15 20 25

Oil

de

nsi

ty, ρ

, g/c

m3

Dynamic viscosity, µ, cP

Crude oil 1

Crude oil 2

Diesel23°C

23°C

33°C

33°C

33°C

60°C

60°C60°C

23°C

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temperature. Understanding the dynamics of the fluid properties such as viscosity, density, and API

gravity can help the production team in designing the well for similar fields or for well intervention

purposes.

The kinematic viscosity for the emulsion is higher compared to the oil phase. The emulsion kinematic

viscosity is five times higher than crude oil 1, 12 times higher than crude oil 2, and 38 times higher than

diesel at room temperature of 23°C (Table 3). The small quantity of emulsifier contributes to the change

of the properties of the immiscible phases. The surface interfacial tension is reduced and then reaches

thermodynamic equilibrium. This means that there is lower energy required to increase the surface area of

two phases. The emulsion viscosity is substantially greater than the oil phase because emulsion shows

non-Newtonian behavior. This behavior is the result of droplet crowding or structural viscosity (Kokal

2006, I-538). The emulsion viscosity shows a similar behavior to the viscosity of the oil phase with

changes in temperature.

Determination of the fluid viscosity could aid reservoir fluid engineers in running simulations for wells

with similar properties to predict future production.

Experiment 2

The gas viscosity is calculated using the Einstein’s equation. The gas viscosity determination can tell the

quality of the gas produced from the reservoir.

Conclusion and Recommendation

The viscosity and temperature are inversely related in a nonlinear behavior. This is also true for density.

Gas viscosity can be determined from the combination of molecular dynamics simulation and Einstein’s

equation. There is a trend that the smaller the API gravity, the larger the change in viscosity. However,

there is no exact correlation about this trend. Determining the viscosity and density of reservoir fluid is an

important aspect in the economics of the producing wells.

of 11

References

Kokal, S.L. 2006. Petroleum Engineering Handbook, Vol. 1, I-533–I-538. Richardson, Texas, SPE.

Tarcilio Viana Dutra Junior, Petrobras.

Viswanath, D.S., Ghosh, T.K., Prasad, D.H.L. et al. 2007. Viscosity of Liquids: Theory, Estimation,

Experiment, and Data. Dordrecht, The Netherlands: Springer.

Appendices

𝑦 = 𝑦0 +(𝑥−𝑥0)(𝑦1−𝑦0)

𝑥1−𝑥0, ..............................(1)

𝛾𝑜 =141.5

131.5+°𝐴𝑃𝐼, ..............................(2)

𝑀𝑊 =42.43𝛾𝑜

1.008−𝛾𝑜, ..............................(3)

𝜌𝑜𝑖𝑙 = 𝛾𝑜𝜌𝑤𝑎𝑡𝑒𝑟, ..............................(4)

𝜇 = 𝜌𝜈, ..............................(5)

𝜇𝑔𝑎𝑠 =𝑉×10−30

2𝑘𝑏𝑇∆𝑡⟨[𝐺(𝑡) − 𝐺(𝑡 = 0)]2⟩, ..............................(6)

𝐺(𝑡) =1

𝑉∑ 𝑟𝑖𝛼𝑚𝑖𝛽(𝑡)𝑁𝑖=1 , ..............................(7)

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Raw Data

TABLE 4—SQUARE MEAN DISPLACEMENT OF MOLECULES AT 10 SECONDS INTERVAL AT 273.0K TEMPERATURE AND 1.028 MPA

PRESSURE

Square mean displacement of molecules

(Pa·s)2

172.06

172.08

172.09

172.04

172.1

172.24

172.08

172.04

172.15

172.09

172.04

172.08

172.06

172.12

172.11

172.03

172.04

172.09

172.12

172.02

Station 6 60°C Crude oil 1 Crude oil 2 Diesel

U909 T375 Z753

Size

100 100 50

Constant @ 40°C mm2/s2 (cSt/s) 0.01584 0.01609 0.004141


Time

1 6:47:04 4:21:60 6:20:19

2 6:21:68 4:06:15 6:32:00

API Gravity (°API) 33.7 38.40

Station 1 23°C (Ambient temp) Crude oil 1 Crude oil 2 Diesel

J276 P242 U166

Size

200 200 100 Constant @ 40°C mm2/s2 (cSt/s) 0.1107 0.09521 0.01548 Constant @ 100°C mm2/s2 (cSt/s) 0.1102 0.09474 0.01541

Time

1 3:30:72 1:36:72 3:21:49 2 3:29:44 1:37:91 3:24:14 API Gravity (°API) 33.7 38.40

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Station 4 33°C Crude oil 1 Crude oil 2 Diesel

M178 G505 U920

Size

200 200 100



Time

1 2:31:19 1:02:99 3:09:94

2 2:31:12 1:03:20 3:09:43

API Gravity (°API) 33.7 38.40 40.00

23°C (Ambient temp) Diesel Water Emulsifier

Volume mL 150 150 2

Emulsion Time

1 1:38:40 1:38:41

2 1:59:90 1:59 1:59:50

Equipment Constant

Equipment size

Constant @ 40°C mm2/s2 (cst/s) 1.202 400

Constant @ 100°C mm2/s2 (cst/s) 1.196

API Experiment (Hydrometer)

Crude oil 1 Crude oil 2 Diesel Water

°API 33 35.9 39.5 10.4

Weight Measurement (Each pycnometer is 10 mL)


Dry weight 16.5 16.4 16.3

Measured weight

1 25.3 25.3 25

2 25.4 25.3 24.9

3 25.4 25.3 24.9

Experiment 3

Statistical Analyses of Core Data


Team 002E


Manager Lemmy Oshenye 1.0

Researcher Lucas Gurgel De Carvalho 1.0

Technician Nor Ashraf Norazman 1.0

Analyst Axel Hannenberg 1.0



this exercise.

Name: _________________________________ Date: _____________________________

of 21

Abstract

Statistical analyses are an integral part of modern reservoir analysis; yet engineers frequently use only the

average quantities for porosity and connate water saturation to estimate the oil in place volume of the

reservoirs.

Statistical core analyses allow the team to correlate values of permeability, porosity, and water saturation

values among themselves. Histograms and cross plots of permeability and water saturation vs. porosity

are plotted to interpret whether the data from both cores indicates similar formation origins or not. Data

analysis shows that:

1. For both wells, the average values for permeability, porosity, and water saturation are unique

according to their zones. For each zone, there is a different trend for each parameter.

2. XAN 5 has a significant frequency of larger pore spaces with limited connectivity. The water and

oil saturation distributions are compared with each other in the results. XAN 5 has a higher

frequency of high oil saturation and low water saturation. XAN 12 has a significant frequency of

intermediate size pore spaces with a noticeable numbers of small pore spaces. The small pore

spaces have high connectivity between the pores, which may indicate the pore throats connect the

smaller pores.

3. The cross plots saturation, permeability and porosity seem to indicate a positive relation between

saturation and permeability. Permeability is not necessarily to be log-normally distributed.

The porosity and water saturation frequency distributions do not appear to be from the same population.

The team’s recommendation is to conduct a seismic survey to analyze the type of formation for the wells.

With the absence of relative permeability curves, it is hard to determine whether the formations are water-

wet or oil-wet rocks.

of 21

Introduction

Oftentimes statistical analyses are done improperly, or even worse, neglected in the petroleum industry.

For example, engineers frequently use only the average quantities for porosity and connate water

saturation to estimate the oil in place volume of the reservoirs. This simplification of data can be due to

the lack of time, the lack of data, economic reasons and so on.

Statistical analyses can be very important to give a more precise understanding about the reservoir

properties, thus providing companies with more certainty when making critical production decisions. For

instance, statistical analysis can provide necessary input data for numerical modeling, or it can be

implemented in subsequent analysis such as reservoir analyses and management using simulators.

Simulations are the current trend in reservoir engineering and the use of statistical data will only increase

as companies wish to exploit more complicated reservoirs. Therefore, it is very important for engineers to

develop an insight into the use of statistics in petroleum engineering.

It is very common that the reservoir exhibit heterogeneity and anisotropy, especially the unconventional

reservoirs. When reservoirs do not exhibit heterogeneity and anisotropy, it becomes very important to

examine the effects and the problems that this may cause to producing the reservoir. Some companies

offer rock analyses for characterization of reservoirs which includes statistical analyses. Basically,

analysis starts with taking core samples of different wells within a predefined area and then measuring

their degree of similarity by analyzing the statistical distributions of rock properties. Relationships are

then defined between the parameters if they are dependent, and develop functions of the properties with

respect to the position within the reservoir. Finally, a reference model can then be used for any well

within a certain range. This model will be continuously compared with other samples taken from other

wells to quantify the overall confidence of this previous model. Typically, the model may start with only

a few wells and have a high degree of confidence limited to the neighborhood of the cored wells. As new

samples are obtained, they might update the model to increase the region of confidence (Schlumberger

2011; Trudgen and Hoffmann 1967).

Core data of two wells are analyzed. The team looks to verify if the data indicated of the two wells are

from the same reservoir by analyzing the frequency distributions. In addition, relationships between the

parameters were drawn by applying regression techniques to add additional credence to the inferences

made from frequency distributions.


Use data from the core reports for two wells to estimate representative values of porosity and

permeability. Plot the porosity, permeability, water and oil saturations frequency distributions and analyze

the figures. Plot the natural logarithm of permeability vs. porosity and water saturation vs. porosity. Use

suitable regression techniques in finding the relationship between the parameters.

of 21

Results

Fig. 1—Histogram showing the maximum permeability distribution for XAN 5 and XAN 12 wells. Both of the wells display

skewed right distribution.

Fig. 2—Histogram showing the porosity distribution for XAN 5 and XAN 12 wells. Both of the wells display slightly skewed

left distribution. XAN 12 has a noticeable frequency of small pores.

0

5

10

15

20

25

30

35

40

45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Fre

qu

en

cykair,max Histogram XAN 5

XAN 12

0

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Fre

qu

en

cy

φ HistogramXAN 5

XAN 12

of 21

Fig. 3—Histogram showing the oil saturation distribution for XAN 5 and XAN 12 wells. XAN 5 shows skewed left

distribution and XAN 12 shows slightly skewed right distribution.

Fig. 4—Histogram showing the water saturation distribution for XAN 5 and XAN 12 wells. XAN 5 shows skewed right

distribution and XAN 12 shows a normal distribution.

0

10

20

30

40

50

60

1 2 3 4 5 6

Fre

qu

en

cy

Soil Histogram XAN 5

XAN 12

0

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 10

Fre

qu

en

cy

Swater Histogram XAN 5

XAN 12

of 21

Fig. 5—Exponential regression technique is used for both wells. The coefficient of determination R2 which relates to the

goodness of fit of data is not close to 1.0. The statistical model fits better for XAN 12 well compared to XAN 5 well.

y = 20.561e0.098x

R² = 0.0567

1

10

100

1,000

10,000

5 7 9 11 13 15 17 19

k air

,max

, md

φ, %

XAN 5: φ-kair,max

y = 2.7469e0.1234x

R² = 0.1173

0

0

0

1

10

100

1,000

10,000

-3 2 7 12 17 22

k air

,max

, md

φ, %

XAN 12: φ-kair,max

of 21

Fig. 6—Linear regression technique is used for both wells. The coefficient of determination R2 which relates to the

goodness of fit of data is not close to 1.0. The statistical model fits better for XAN 12 well compared to XAN 5 well.

y = -0.4039x + 19.457R² = 0.0466

0

5

10

15

20

25

30

35

5 7 9 11 13 15 17 19

S wat

er,

%

φ, %

XAN 5: φ-Swater

y = 0.9685x + 36.786R² = 0.0584

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20

S wat

er, %

φ, %

XAN 12: φ-Swater

of 21

Fig. 7—Linear regression technique is used for both wells. The statistical model fits better for XAN 12 well compared to

XAN 5 well. The oil saturation shows an upward trend for XAN 5 and a downtrend for XAN 12.

y = 0.9778x + 20.982R² = 0.0878

0

10

20

30

40

50

60

5 7 9 11 13 15 17 19

S oil,

%

φ, %

XAN 5: φ-Soil

y = -1.0828x + 24.055R² = 0.2341

0

5

10

15

20

25

30

35

40

45

50

-3 2 7 12 17 22

S oil,

%

φ, %

XAN 12: φ-Soil

of 21

Fig. 8—Lorenz plots for both wells to determine the heterogeneity of the formations. The Lorenz coefficients are 0.76 and

0.75 for XAN 5 and XAN 12, respectively. Both of the wells might be highly heterogeneous formations.


The permeability distribution is compared with the porosity distribution for both wells (Figs. 1 through

4). XAN 5 has a significant frequency of larger pore spaces with limited connectivity. The water and oil

saturation distributions are compared with each other. XAN 5 has a higher frequency of high oil

saturation and low water saturation. The analysis indicates there are more hydrocarbons with low connate

water saturation trapped within the unconnected large pore spaces. It is recommended that the engineers

fracture the reservoir to connect the pores and then produce the hydrocarbons economically. XAN 12 has

a significant frequency of intermediate size pore spaces with a noticeable numbers of small pore spaces.

The small pore spaces have high connectivity between the pores, which may indicate the pore throats

connect the smaller pores. By comparing the water and oil saturations, XAN 12 has higher frequency of

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

No

rmal

ize

d Σ

kh

Normalized Σφh

XAN 5: Lorenz Plot

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

No

rmal

ize

d Σ

kh

Normalized Σφh

XAN 12: Lorenz Plot

of 21

high water saturation and low oil saturation. The analysis indicates that the well has most of the pore

spaces containing water with low oil saturation. It is recommended that the drilling and production team

drill and complete the well with caution to avoid fracturing or damaging the reservoir. Fracturing of the

reservoir has the potential to cause high water production. Without relative permeability curves, it is

difficult to definitively determine whether the formations are water-wet or oil-wet rocks. More data and

further analysis are needed if the reservoir engineers are to determine the feasibility of waterflooding. The

porosity and water saturation frequency distributions do not appear to be from the same population.

The location of both wells is Guatemala. However, the histograms of different properties of both wells

show different frequency diagrams. The formation of both wells might be formed by different geologic

processes or at different times. The team is recommended to conduct a seismic survey to analyze the type

of formation for the wells.

The plotted porosity and permeability for both wells show there is a relationship between the two

parameters (Figs. 5 through 7). By using exponential regression, the coefficient of determination R2 of

XAN 5 is 0.0567, which does not truly indicate an accurate model to determine the relationship. The

model predicts the permeability (md) is a function of porosity (%) for XAN 5 by the following equation:

ln(𝑘) = 0.098𝜙 + 3.0234, ..............................(1)

Similar regression technique with R2 value of 0.1173 is used for XAN 12 and the relationship between

permeability and porosity is shown by the following equation:

ln(𝑘) = 0.1234𝜙 + 1.0105, ..............................(2)

The permeability used in the equations is the maximum permeability at the direction of the maximum

permeability. The direction of maximum permeability can be obtained by solving the horizontal and

vertical permeabilities using vector analysis. The goodness of fit of the models shows that the

permeability is not necessarily log-normally distributed.

The porosity and water saturation for both wells are related using a linear regression model. The R2 value

is 0.0466 for XAN 5 and the model (in percentages) shows the relationship is as follows:

𝑆𝑤𝑎𝑡𝑒𝑟 = −0.4039𝜙 + 19.457, ..............................(3)

The R2 value for XAN 12 is 0.0584 and the porosity and water saturation are related from the following

equation:

𝑆𝑤𝑎𝑡𝑒𝑟 = 0.9685𝜙 + 36.786, ..............................(4)

For XAN 5, water saturation decreases as the pore size increases. XAN 12 shows an opposite trend, in

which the water saturation increases as the pore sizes increases.

A simple linear regression technique is used to determine the general trend of oil saturation with porosity.

Fig. 7 displays an upward trend for XAN 5 but XAN 12 has a downward trend for oil saturation with

increase in porosity. There is more probability of the bigger pore spaces containing more organics for

XAN 5 but there is more probability of smaller pore spaces containing more organics for XAN 12.

of 21

However, interpretation of the probability should be used carefully since the coefficient of determination

R2 values are not close to 1.0.

The relationships developed from the models should be used with caution while performing reservoir

simulation for both wells. The coefficient of determination R2 is used to indicate the quality of the results

when running the simulation from the predicted models.

To quantify the reservoir heterogeneity, Lorenz coefficient is determined from Fig. 8. The permeability is

arranged from highest to the lowest, and the normalized flow capacity is plotted against the normalized

the fraction of total volume. The Lorenz coefficient can range from zero for a homogeneous formation to

one for a completely heterogeneous formation. Both of the wells might be highly heterogeneous with 𝐿 =

0.76 for XAN 5 and 𝐿 = 0.75 for XAN 12. The limitation of this method is that the Lorenz coefficient is

not uniquely related to the permeability distribution (Craig Jr. 1970, 1239). Information about the

heterogeneity of the reservoir can help the engineers to consider the nonuniform nature of the reservoir

while estimating recovery during an immiscible displacement.

Analysis of permeability, porosity, water and oil saturations interactions are done at respective depths by

superimposing two plots containing two different parameters in one figure. The intention of

superimposing the plots is to observe similarities and anomalies with each parameter at specific range of

depths for both wells. For XAN 5, significant anomalies are observed at depths of 7,620 to 7,630 ft. At

these depths, the formation has high permeability with low oil saturation and high water saturation. The

porosity varies from 6 to 12%. The small pore spaces with high permeability might indicate pore throats.

The high water saturation within the pore throats might indicate that the particular zone is a water-wet

formation.

Between 7,630 ft and 7,670 ft, the average porosity is approximately 15%, and the oil saturation varies

from 19.8 to 46.9% with an average of 36.9%. The average permeability is approximately 102 md and

average water saturation is 13%. This might indicate that the formation in the zone has larger pores that

contain mainly hydrocarbons with good connectivity. From 7,670 to 7,685 ft, there is a noticeable drop in

porosity, oil saturation, and a decline in permeability with an increase in water saturation. This might

related to the water-wet formation in this zone. Between 7,685 ft and 7,710 ft, all the parameters show

high variations; this might be due to the presence of anhydrites in the formation.

For XAN 12, between 7,714 ft and 7,722 ft, the presence of asphalt might contribute to low porosity and

high oil saturation. Within this zone, high grain density values are observed. Substantial amounts of clay

might be present within this zone; however, water saturation is relatively low compared to oil saturation.

The team could not determine what causes the increase in grain density. At 7,772 ft, there is a sudden

drop in porosity and water saturation. From 7,796 to 7,819 ft, the porosity drops to an average of 2.33%

with average oil saturation close to 19%. At depths from 7,742 to 7,790 ft, the formation has high water

saturation low oil saturation. It is best to avoid perforating in this zone because the well will produce

water which is not favorable for the operating company.

of 21

Conclusion

Statistical analysis of core data shows that air permeability measurements as practiced in the industry

have a systematic negative bias that must be addressed to improve overall core analysis results (Thomas

and Pugh 1989).

Reservoir rock properties are a sample of quantitative statistical observations that can be condensed and

represented by frequency distributions which may be described by calculated statistical parameters

(Trudgen and Hoffmann 1967).

Based on analysis, the team concludes that:

1. Correlations involving water saturation, porosity, and permeability are enhanced when their

distributions are known and accounted for.

2. Permeability is not necessarily log-normally distributed.

3. The porosity and water saturation frequency distributions do not appear to be from the same

population.

4. The average values for permeability, porosity, and water saturation are unique according to

position in the formation. For each zone, there is a different trend for each parameter.

of 21

References

Craig Jr., F.F. 1970. Effect of Reservoir Description on Performance Predictions. Journal of Petroleum

Technology: 1239–1245. SPE-2652-PA. http://dx.doi.org/10.2118/2652-PA.

Schlumberger. 2011. Terratek Tight Rock Analysis,

http://www.slb.com/~/media/Files/core_pvt_lab/product_sheets/terratek_tight_rock_analysis_

overview_ps.pdf (downloaded 16 September 2012).

Thomas, D.C. and Pugh, V. J. 1989. A Statistical Analysis of the Accuracy and Reproducibility of

Standard Core Analysis. The Log Analyst 30 (2): 71–77. SPWLA.

Trudgen, P. and Hoffmann, F. 1967. Statistically Analyzing Core Data. J. Pet Tech 19 (4): 497–503.

SPE-1574-PA. http://dx.doi.org/10.2118/1574-PA.

Appendices

Equations

𝑘𝑎𝑣𝑒 =∑ 𝑘𝑖ℎ𝑖

𝑛𝑖=1

∑ ℎ𝑖𝑛𝑖=1

, ..............................(5)

𝜙𝑎𝑣𝑒 =∑ 𝜙𝑖ℎ𝑖

𝑛𝑖=1

∑ ℎ𝑖𝑛𝑖=1

, ..............................(6)

𝑆𝑎𝑣𝑒 =∑ 𝜙𝑖ℎ𝑖𝑆𝑤𝑖

𝑛𝑖=1

∑ 𝜙𝑖ℎ𝑖𝑛𝑖=1

, ..............................(7)

∑ 𝑘ℎ𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 =∑ 𝑘𝑖ℎ𝑖

𝑛𝑖=1

∑ 𝑘ℎ𝑡𝑜𝑡𝑎𝑙

, ..............................(8)

∑ 𝜙ℎ𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 =∑ 𝜙𝑖ℎ𝑖

𝑛𝑖=1

∑ 𝜙ℎ𝑡𝑜𝑡𝑎𝑙

, ..............................(9)

𝐴𝑎𝑏𝑜𝑣𝑒 𝑙𝑖𝑛𝑒𝑎𝑟 𝑙𝑖𝑛𝑒 = 𝐴𝑢𝑛𝑑𝑒𝑟 𝑐𝑢𝑟𝑣𝑒 − 𝐴𝑢𝑛𝑑𝑒𝑟 𝑙𝑖𝑛𝑒𝑎𝑟 𝑙𝑖𝑛𝑒, ..............................(10)

𝐿 =𝐴𝑎𝑏𝑜𝑣𝑒 𝑙𝑖𝑛𝑒𝑎𝑟 𝑙𝑖𝑛𝑒

𝐴𝑢𝑛𝑑𝑒𝑟 𝑙𝑖𝑛𝑒𝑎𝑟 𝑙𝑖𝑛𝑒, ..............................(11)

�̅� =1

𝑛∑ 𝑥𝑖

𝑛𝑖=1 , ..............................(12)

𝜎2 =1

𝑛−1∑ (𝑥𝑖 − �̅�)2𝑛

𝑖=1 , ..............................(13)

𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 =∑(𝑥−�̂�)3

(𝑁−1)𝜎3, ..............................(14)

𝐾𝑢𝑟𝑡𝑜𝑠𝑖𝑠 =∑(𝑥−�̂�)4

(𝑁−1)𝜎4, ..............................(15)

of 21

Supplemental Figures and Tables

0

5

10

15

20

25

30

35

0

5

10

15

20

25

7,620 7,640 7,660 7,680 7,700 7,720

S wat

er,

%

φ, %

Depth, ft

XAN 5: φ-Swaterφ

Swater

0

10

20

30

40

50

60

0

5

10

15

20

25

7,620 7,640 7,660 7,680 7,700 7,720S o

il, %

φ, %

Depth, ft

XAN 5: φ-Soilφ

Soil

1

10

100

1,000

10,000

0

5

10

15

20

25

7,620 7,640 7,660 7,680 7,700 7,720

k air

,max

, md

φ, %

Depth, ft

XAN 5: φ-kair,maxφ

Kair,max

of 21

2.77

2.79

2.81

2.83

2.85

2.87

0

5

10

15

20

25

7,620 7,640 7,660 7,680 7,700 7,720

ρgr

ain

, g/c

m3

φ, %

Depth, ft

XAN 5: φ-ρgrainφ

ρgrain

0

5

10

15

20

25

30

35

0

10

20

30

40

50

60

7,620 7,640 7,660 7,680 7,700 7,720

S wat

er, %

S oil,

%

Depth, ft

XAN 5: Soil-SwaterSoil

Swater

1

10

100

1,000

10,000

0

10

20

30

40

50

60

7,620 7,640 7,660 7,680 7,700 7,720

k air

,max

, md

S oil,

%

Depth, ft

XAN 5: Soil-kair,maxSoil

Kair,max

of 21

1

10

100

1,000

10,000

0

5

10

15

20

25

30

35

7,620 7,640 7,660 7,680 7,700 7,720

k air

,max

, md

S wat

er,

%

Depth, ft

XAN 5: Swater-kair,maxSwater

Kair,max

1

10

100

1,000

10,000

0

10

20

30

40

50

60

70

7,620 7,640 7,660 7,680 7,700 7,720

k air

,max

, md

S o+w

, %

Depth, ft

XAN 5: So+w-kair,maxSo+w

Kair,max

0

10

20

30

40

50

60

70

0

5

10

15

20

25

7,620 7,640 7,660 7,680 7,700 7,720

S o+w

, %

φ, %

Depth, ft

XAN 5: φ-So+wφ

So+w

of 21

0

20

40

60

80

100

120

0

5

10

15

20

25

7,670 7,720 7,770 7,820

S wat

er,

%

φ, %

Depth, ft

XAN 12: φ-Swaterφ

Swater

0

10

20

30

40

50

0

5

10

15

20

25

7,670 7,720 7,770 7,820

S oil,

%

φ, %

Depth, ft

XAN 12: φ-Soilφ

Soil

1

10

100

1,000

10,000

0

5

10

15

20

25

7,670 7,720 7,770 7,820

k air

,max

, md

φ, %

Depth, ft

XAN 12: φ-kair,maxφ

Kair,max

of 21

2.77

2.79

2.81

2.83

2.85

2.87

0

5

10

15

20

25

7,670 7,720 7,770 7,820

ρgr

ain

, g/c

m3

φ, %

Depth, ft

XAN 12: φ-ρgrainφ

ρgrain

0

20

40

60

80

100

0

10

20

30

40

50

7,670 7,720 7,770 7,820

S wat

er, %

S oil, %

Depth, ft

XAN 12: Soil-SwaterSoil

Swater

1

10

100

1,000

10,000

0

10

20

30

40

50

7,670 7,720 7,770 7,820

k air

,max

, md

S oil,

%

Depth, ft

XAN 12: Soil-kair,maxSoil

Kair,max

of 21

1

10

100

1,000

10,000

0

20

40

60

80

100

7,670 7,720 7,770 7,820

k air

,max

, md

S wat

er,

%

Depth, ft

XAN 12: Swater-kair,maxSwater

Kair,max

1

10

100

1,000

10,000

0

20

40

60

80

100

7,670 7,720 7,770 7,820

k air

,max

, md

S o+w

, %

Depth, ft

XAN 12: So+w-kair,maxSo+w

Kair,max

0

20

40

60

80

100

0

5

10

15

20

25

7,670 7,720 7,770 7,820

S o+w

, %

φ, %

Depth, ft

XAN 12: φ-So+wφ

So+w

of 21

1

10

100

1,000

10,000

0

5

10

15

20

25

30

35

0 5 10 15 20 25

k air

,max

, md

S wat

er,

%

φ, %

XAN 5: Cross PlotWater Saturation

Air Permeability

0.00

0.01

0.10

1.00

10.00

100.00

1,000.00

10,000.00

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

k air

,max

, md

S wat

er, %

φ, %

XAN 12: Cross PlotWater SaturationAir Permeability

of 21

TABLE 1—DESCRIPTIVE STATISTICS OF PERMEABILITY, POROSITY, OIL AND WATER SATURATIONS FOR XAN 5

Parameter kair,max φ Soil Swater

Mean 262.0 13.3 34.0 14.1

Standard Error 86.1 0.4 1.2 0.7

Median 75 13.7 35.9 13.4

Mode 61.5 12.8 39.4 20.1

Standard Deviation 774.8 3.2 10.4 5.9

Sample Variance 600,322.3 9.9 108.3 34.8

Kurtosis 28.9 -0.6 1.1 -0.1

Skewness 5.2 -0.3 -1.0 0.3

Range 5,128.36 13.8 50.2 28.6

Minimum 8.64 5.4 2.5 2.5

Maximum 5137 19.2 52.7 31.1

Sum 21,223.4 1,080.8 2,756.4 1,139.5

Count 81 81 81 81

Confidence Level (95.0%) 171.3 0.7 2.3 1.3

TABLE 2—DESCRIPTIVE STATISTICS OF PERMEABILITY, POROSITY, OIL AND WATER SATURATIONS FOR XAN 12

Parameter kair,max φ Soil Swater

Mean 71.2 11.6 11.4 48.1

Standard Error 27.2 0.5 1.2 2.1

Median 12.8 12.5 8.5 47.7

Mode 6.68 11 1.3 29.8

Standard Deviation 264.8 5.2 11.5 20.7

Sample Variance 70,139.8 26.6 133.0 426.7

Kurtosis 42.1 -0.6 0.4 -0.8

Skewness 6.1 -0.5 1.1 0.2

Range 2,131.995 20.1 46.1 80.8

Minimum 0.005 1.5 0.5 12.1

Maximum 2132 21.6 46.6 92.9

Sum 6,764.5 1,106.3 1,087.3 4,566.2

Count 95 95 95 95

Confidence Level (95.0%) 54.0 1.1 2.3 4.2

Experiment 4

Volumetric Estimation of OOIP


Team 002E


Manager Lucas Gurgel De Carvalho 1.0

Researcher Nor Ashraf Norazman 1.0

Technician Axel Hannenberg 1.0

Analyst Lemmy Oshenye 1.0



this exercise.

Name: _________________________________ Date: _____________________________

of 10

Abstract

The calculation of a reservoir’s original oil in place (OOIP) is a vital task in determining a reservoir’s

value and potential. There are many different ways to approach calculating a reservoir’s OOIP, and it can

be useful to utilize a combination of these. In this experiment, the team uses both deterministic and

stochastic approaches to estimate OOIP in the Booch play, discovered in 1961 in Hughes County,

Oklahoma. The Booch oil reservoir is a channel sand formed from fluvial deposition.

In the deterministic approach, trapezoidal, Simpson’s, and pyramidal frustum methods are used to

calculate the OOIP. Trapezoidal method yields the highest estimated OOIP compared to Simpson’s and

pyramidal frustum methods. Pyramidal frustum overestimated the OOIP compared to Simpson’s rule but

underestimated the OOIP compared to trapezoidal rule. The approaches used are made under the

assumption that the Booch reservoir is fairly homogeneous. However, fluvial reservoirs are often very

heterogeneous due to their discontinuity and facies changes during the depositional process. Inaccurate

modeling and various sources of error may have contributed to the large differences between the data

provided and the three methods values, which is approximately 0.7 million STB.

Human error can cause random error to occur when using the planimeter. Taking measurements using the

planimeter requires high skill and precision. The error of the measurements is amplified when converting

the unit from in.2 to ft2 to acre. The magnified error is then carried in the volumetric calculations. Random

error can be minimized by repeating the measurements and then averaging the values. Human error aside,

numerical approaches are utilized to obtain an accurate OOIP estimate.

The uncertainties in geological and geophysical data have an impact in the estimation of reserves. The

team needs to obtain the original geophysical and geological data of the play to track the major

contributor of the overall uncertainty to get a more accurate estimate of OOIP.

of 10

Introduction

The determination of the amount of fluid existing in petroleum fields is essential for the correct

implementation of an exploratory project. The basic concepts of volumetric estimation of OOIP are

simple, yet imprecise. For instance, if the reservoir had a simple square shape, a defined thickness and

constant values for all the parameters, the volumetric estimation would be done using Eq. 1. Volumetric

calculations are made less accurate because of the complex reservoir shapes, as well as changes in the

values of parameters needed such as water saturation, oil saturation and porosity.

Unconventional reservoirs are more likely to have complex shapes and the parameters are not likely to

always be constant. In order to analysis more sophisticated reservoirs volumetric estimation should be

done through integrations of the functions of the reservoir shapes. Since these functions are virtually

impossible to determine, estimates are by default only numerical approximations.

The volumes of oil or gas of the reservoir may be computed in different ways. One of them is when the

geoscientists prepare a geological map from the subsurface data; for example, from seismic imaging and

core analysis. These maps are known as isopach maps. Contours of the hydrocarbon rich areas are made

from the top to the bottom of the reservoir, which allows for better indications of the corresponding

thicknesses of these areas. The water-oil contacts are also shown. The areas are then measured with a

planimeter, converted to the real scale of the reservoir, and finally the volume is estimated by numerical

integration (Garb 1985).

The most common numerical methods are the trapezoidal rule, which is less accurate, the Simpson’s rule,

which is more accurate but requires an even number of contoured areas, and the frustum of a pyramid.

These three methods are used to calculate the volume of OOIP of a reservoir and the values obtained are

compared with each other and with the original reservoir data provided.

Additionally, volumes of oil or gas can be estimated through material balance equations (MBE). These

equations depend on the drive mechanisms acting in the reservoir, and allow for how a reservoir fluids

mass balance changes with pressure (Rosa 2011). MBEs are written in terms of the rock properties and

the fluid behavior as a function of pressure, rock-fluid properties, and production history.


Use a planimeter for this experiment. The planimeter is used to trace along the boundary of a given

contour line on the net pay isopach map. When using the planimeter, pick a point on the desired interval

and carefully trace along the boundary of that interval clockwise. The planimeter finds the areas between

the isopach contours (Dean 2007). With a conversion in the map legend, convert the square inches given

by the planimeter to acres. Once the acreages of the different levels are known along with the heights, use

one of several numerical methods to calculate the volume. Use frustum of a pyramid, Simpson’s rule, or

the trapezoidal rule to calculate a volume which can be used in the volumetric equation along with values

for porosity, water saturation and formation volume factor to get an estimate for the volume of stock-tank

barrels (STB) in place.

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Fig. 1—The planimeter. The view glass is the piece on the far right and is used to follow the contour lines of the isopach

map. The wheels across the back on the left side provide stability when tracing along the contour horizon.

Results

TABLE 1—ESTIMATED BULK VOLUME AND ORIGINAL OIL IN PLACE

Vb N

Method acre-ft million STB

Trapezoidal 4,602 2.545×106

Simpson’s 4,549 2.516×106

Pyramidal Frustum 4,551 2.518×106

Data Provided No data 3.200×106

Fig. 2—Trapezoidal method presents the highest estimated OOIP. Estimated OOIP values for Simpson’s and pyramidal

frustum method are relatively similar to each other.

2.500

2.505

2.510

2.515

2.520

2.525

2.530

2.535

2.540

2.545

2.550

Trapezoidal Simpson Pyramidal Frustum

N, S

TB

Mill

ion

s

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Fig. 3—The estimated OOIP for the three methods are relatively similar with each other compared the data provided in the

engineering table. The three methods underestimate the OOIP compared to the data provided.


Trapezoidal method presents the highest estimated OOIP compared to Simpson’s and pyramidal frustum

methods. Pyramidal frustum overestimated the OOIP compared to Simpson’s rule but underestimated the

OOIP compared to trapezoidal rule.

However, the difference in the estimated OOIP values from the three methods are insignificant compared

to the OOIP provided from the engineering data. The difference between the three methods values to data

provided is approximately 0.7 million STB.

Craft et al. (1991) stated that whenever the ratio of the areas of any two successive isopach lines is less

than 0.5, then pyramidal frustum is applied. However, if it is more than 0.5, then trapezoidal rule is

applied. From the above statement, the team recommends the application of pyramidal frustum from the

60 to 50 ft contour interval because the ratio of the areas is smaller than 0.5. The team also recommends

applying Simpson’s rule on other intervals because the ratios are larger than 0.5 and Simpson’s rule is

usually more accurate than trapezoidal rule for irregular curves.

Based on the representative electric log for the Booch oil reservoir, the thickness can be measured

precisely at 10 ft intervals. The height interval impacts the volume calculations and thus affects the

estimated OOIP. It is assumed that the area is uniform throughout each of the 10 ft interval. The

uncertainty decreases if lower thickness interval is used.

There are various sources of errors that contribute to cumulative error in the volumetric calculations.

Human error can cause random error to occur when using the planimeter. Taking measurements using the

planimeter requires high skill and precision. Since the measurement is recorded in in.2, the error is

amplified when converting the unit from in.2 to ft2 to acre. The magnified error is then carried in the

volumetric calculations. Random error can be minimized by repeating the measurements and then

averaging the values.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Trapezoidal Simpson PyramidalFrustum

Data Provided

N, S

TB

Mill

ion

s

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Uncertainties in geophysical data have an impact on the geological data, which leads to uncertainties in

the estimated OOIP. It is very important to track the source with the largest uncertainty because that

would have the largest impact on the overall uncertainty in the volumetric calculations (Floris and

Peersmann 1998). Although the estimated OOIP is calculated using the provided porosity, water

saturation, and formation volume factor values, the uncertainties in these data are not considered at all in

the volumetric calculations. The largest source of uncertainty could be contributed from any of these

parameters or the calculated bulk volumes from the numerical methods. At this point, the team needs to

obtain the original geophysical and geological data of the play to track the major contributor of the overall

uncertainty to get a more accurate estimate of OOIP.


Trapezoidal method presents the highest estimated OOIP followed by pyramidal frustum and Simpson’s

methods. However, the difference in the estimated OOIP values from the three methods are insignificant

compared to the OOIP provided from the engineering data.

The uncertainties in geological and geophysical data have an impact in the estimation of reserves. The

team needs to obtain the original geophysical and geological data of the play to track the major

contributor of the overall uncertainty to get a more accurate estimate of OOIP.

of 10

References

Andrews, R.D., Northcutt, R. A., Knapp, R. M. and Yang, X. H. 1995. Fluvial-Dominated Deltaic (FDD)

Oil Reservoirs in Oklahoma: The Booch Play, Oklahoma Geological Survey, Special Publication

95-3, 1–67.

Craft, B.C., Hawkins, M. and Terry, R.E. 1991, Applied Petroleum Reservoir Engineering, 2nd Edition,

New Jersey: Prentice-Hall, 71.

Dean, L. 2007. Volumetric Estimation. Reservoir Engineering for Geologists: 11–14.

Floris, F.J.T., and Peersmann, M.R.H.E. 1998. Uncertainty estimation in volumetrics for supporting

hydrocarbon exploration and production decision-making, Petroleum Geosciences 4 (1): 33–40.

http://dx.doi.org/10.1144/petgeo.4.1.33.

Garb, F.A. 1985. Oil and Gas Reserves Classification, Estimation, and Evaluation. Distinguished Author

Series, J Pet Technol 37 (3): 373–390. SPE-13946-PA. http://dx.doi.org/10.2118/13946-PA.

Rosa, Adalberto Jose. 2011. Engenharia de Reservatorios de Petroleo, Rio de Janeiro, RJ, Brazil.

Appendices

Equations

𝑁 =𝐶𝑉𝑏𝜙(1−𝑆𝑤)

𝐵𝑜, ..............................(#)

Where 𝐶 = 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 (7758),𝑟𝑒𝑠 𝑏𝑏𝑙

𝑎𝑐𝑟𝑒‐𝑓𝑡

𝑉𝑏 = 𝑏𝑢𝑙𝑘 𝑣𝑜𝑙𝑢𝑚𝑒, 𝑎𝑐𝑟𝑒‐ 𝑓𝑡

𝜙 = 𝑝𝑜𝑟𝑜𝑠𝑖𝑡𝑦, 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛

𝑆𝑤 = 𝑤𝑎𝑡𝑒𝑟 𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛, 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛

𝐵𝑜 = 𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑣𝑜𝑙𝑢𝑚𝑒 𝑓𝑎𝑐𝑡𝑜𝑟,𝑟𝑒𝑠 𝑏𝑏𝑙

𝑆𝑇𝐵

𝑁 = 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑜𝑖𝑙 𝑖𝑛 𝑝𝑙𝑎𝑐𝑒, 𝑆𝑇𝐵

𝑉𝑡𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑𝑎𝑙 𝑟𝑢𝑙𝑒 =1

2ℎ(𝑎0 + 2𝑎1 + 2𝑎2 + ⋯ + 2𝑎𝑛−1 + 𝑎𝑛) + 𝑡𝑛𝑎𝑛, ..............................(#)

𝑉𝑆𝑖𝑚𝑝𝑠𝑜𝑛′𝑠 𝑟𝑢𝑙𝑒 =1

3ℎ(𝑎0 + 4𝑎1 + 2𝑎2 + 4𝑎3 + ⋯ + 2𝑎𝑛−2 + 4𝑎𝑛−1 + 𝑎𝑛) + 𝑡𝑛𝑎𝑛, ..............................(#)

Where ℎ = 𝑐𝑜𝑛𝑡𝑜𝑢𝑟 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙, 𝑓𝑡

𝑎0 = 𝑎𝑟𝑒𝑎 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝑏𝑦 𝑧𝑒𝑟𝑜 𝑐𝑜𝑛𝑡𝑜𝑢𝑟 (𝑎𝑡 𝑜𝑖𝑙 𝑤𝑎𝑡𝑒𝑟 𝑐𝑜𝑛𝑡𝑎𝑐𝑡), 𝑎𝑐𝑟𝑒𝑠

𝑎1 = 𝑎𝑟𝑒𝑎 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝑏𝑦 𝑓𝑖𝑟𝑠𝑡 𝑐𝑜𝑛𝑡𝑜𝑢𝑟, 𝑎𝑐𝑟𝑒𝑠

of 10

𝑎𝑛 = 𝑎𝑟𝑒𝑎 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝑏𝑦 𝑛𝑡ℎ 𝑐𝑜𝑛𝑡𝑜𝑢𝑟, 𝑎𝑐𝑟𝑒𝑠

𝑡𝑛 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑎𝑏𝑜𝑣𝑒 𝑡ℎ𝑒 𝑡𝑜𝑝 𝑐𝑜𝑛𝑡𝑜𝑢𝑟, 𝑓𝑡

𝑉 = 𝑏𝑢𝑙𝑘 𝑣𝑜𝑙𝑢𝑚𝑒, 𝑎𝑐𝑟𝑒‐ 𝑓𝑡

𝑉𝑓𝑟𝑢𝑠𝑡𝑢𝑚 𝑜𝑓 𝑎 𝑝𝑦𝑟𝑎𝑚𝑖𝑑 =1

3ℎ(𝑎0 + 𝑎𝑛 + √𝑎0𝑎𝑛), ..............................(#)

Where 𝑎0 = 𝑎𝑟𝑒𝑎 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑙𝑜𝑤𝑒𝑟 𝑐𝑜𝑛𝑡𝑜𝑢𝑟 𝑖𝑛 𝑠𝑒𝑐𝑡𝑖𝑜𝑛, 𝑎𝑐𝑟𝑒𝑠

𝑎𝑛 = 𝑎𝑟𝑒𝑎 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑐𝑜𝑛𝑡𝑜𝑢𝑟 𝑖𝑛 𝑠𝑒𝑐𝑡𝑖𝑜𝑛, 𝑎𝑐𝑟𝑒𝑠

Supplemental Figures and Tables

Some of the following tables and figures are taken from the Oklahoma Geological Survey 1995, Special

Publication 95-3, Fluvial-Dominated Deltaic (FDD) Oil Reservoirs in Oklahoma: The Booch Play.

Fig. 4—Isopach map of net Booch oil sand (pay sand), Booch oil reservoir, Greasy Creek field, Hughes County, Oklahoma.

of 10

Fig. 5—Representative electric log for the Booch oil reservoir, Greasy Creek field, Hughes County, Oklahoma, showing log

patterns for spontaneous potential, resistivity, and conductivity measurements. Perforated interval is marked.

TABLE 2—GEOLOGICAL/ENGINEERING DATA FOR THE BOOCH OIL RESERVOIR, GREASY CREEK FIELD, HUGHES COUNTY, OKLAHOMA

Reservoir size 140 acres

Well spacing (oil) 10 acres

Oil/water contact -1,555 ft below mean sea level

Gas/oil contact none

Porosity 15%

Permeability 35 md

Initial water saturation 45%

Thickness (net sand in reservoir) 40 ft average

Reservoir temperature 103°F

Oil gravity 39.5°API

Initial reservoir pressure 940 psia

Initial formation volume factor 1.157

Original oil in place (volumetric) 3.2 million STB

Cumulative primary production 692,315 BO

Recovery efficiency 22%

Cumulative gas no data

of 10

Raw Data

TABLE 3—AREAS RATIO AND AVERAGE DATA

Reading 1 Reading 2 Average Areas Ratio

in.2 in.2 in.2

0.356501 0.3720007 0.3642507 0.511111

0.697501 0.6820013 0.6897513 0.454545

1.534503 1.519003 1.526753 0.572254

2.681505 2.681503 2.681504 0.689244

3.8905 3.7975075 3.84400375 0.715098

5.440511 5.2390104 5.3397606 0.764707

7.1145 6.9905139 7.05250695 0.794118

8.959 8.7265 8.84275 average

0.643011

TABLE 4—CALCULATED STANDARD DEVIATIONS

Vb N

Method acre-ft STB

Trapezoidal 4,601.51 2,545,484.80

Simpson 4,548.69 2,516,268.36

Pyramidal Frustum 4,551.18 2,517,646.21

δVb δN

29.80 16,484.77

TABLE 5—ESTIMATED BULK VOLUME AND ORIGINAL OIL IN PLACE

Vb N

Method acre-ft million STB

Trapezoidal 4,602 ± 30 2.545×106 ± 1.6×104

Simpson’s 4,549 ± 30 2.516×106 ± 1.6×104

Pyramidal Frustum 4,551 ± 30 2.518×106 ± 1.6×104

Data Provided No data 3.200×106

Experiment 5

Hydrocarbon Phase Behavior


Team 002E


Manager Nor Ashraf Norazman 1.0

Researcher Axel Hannenberg 1.0

Technician Lemmy Oshenye 1.0

Analyst Lucas Gurgel De Carvalho 1.0



this exercise.

Name: _________________________________ Date: _____________________________

of 16

Abstract

It is important to determine the pressure-volume relationship of reservoir fluids because it helps to obtain

the bubblepoint pressure. Knowing the bubblepoint pressure is significant in understanding the phase

behavior of reservoir fluids by calculating integral parameters such as gas solubility, formation volume

factor (FVF), and coefficient of isothermal compressibility.

The evaluation and proper production of oil and gas reserves depends heavily on the knowledge of

reservoir fluid properties. These properties can either be obtained from laboratory experiments or

empirical correlations.

In this study, experimental measurements and empirical correlations are incorporated to determine values

of bubblepoint, gas solubility, FVF, and coefficient of isothermal compressibility. The gas solubility,

FVF, and coefficient of isothermal compressibility are plotted as function of pressure at a constant

temperature to observe the changes of each parameter with respect to pressure change. Data analysis

shows that:

1. The bubblepoint pressures for the 32°API oil, 38°API oil, and CO2-water mixture are 807.2-,

597.6-, and 874.6-psi respectively.

2. At pressures below the bubblepoint, the coefficient of isothermal compressibility is higher due to

the presence of the free gas. Once the gas is in solution, coefficient of isothermal compressibility

varies only slightly with increasing pressure because liquids are slightly compressible.

3. The solution GOR above and at the bubblepoint for the 32°API oil, 38°API oil, and CO2-water

mixture are 144.53-, 125.47-, 203.08-scf/STB. Solution GOR is constant at pressures above the

bubblepoint because all gas is in solution. At pressures below the bubblepoint, solution GOR

decreases because there is now free gas that has evolved out from the solution.

4. At pressures above the bubblepoint, the total FVF and FVF of liquid have the same value. The

FVF of liquid decreases at pressures below the bubblepoint but the total FVF increases

significantly.

It is recommended to perform hydrocarbon analysis on both crude oils to have a better understanding of

the compositional changes during the phase transition at pressures below the bubblepoint.

of 16

Introduction

Phase behavior is the behavior of vapor, liquid, and solids as a function of pressure, temperature, and

composition (Whitson and and Brule 2000).

As oil and gas are produced from the subsurface, they undergo changes of temperature, pressure and

composition. Such changes affect the volumetric and transport behavior of the fluids directly impacting

the surface volumes and quality of produced oil and gas (Devegowda 2011).

Some physical properties such as gas solubility, formation volume factor, bubblepoint and coefficient of

isothermal compressibility exist to help the study of hydrocarbon phase behavior. To determine these

properties, experiments are usually performed on fluid samples using PVT cells and data is collected.

PVT cells basically consist of a cylinder containing mercury in which the liquid sample to be studied is

placed.

The change from single-phase to two-phase affects the physical properties. There are two basic types of

gas liberation: flash and differential (Rosa 2011).

Flash liberation is when the gas that comes out of solution due to reduction in pressure is kept in contact

with the liquid. Likewise, gas is said to be differentially liberated when the gas coming out of solution is

removed from contact with the liquid. In this experiment, flash liberation is conducted for two different

samples of oils and for a mixture of water and CO2.

PVT analysis is integral in the calculation of reserves, production forecasts, and the efficiency of

enhanced oil recovery methods. It is also useful for surface separator design and to calculate flow in pipe

(Whitson and Brule 2000).


The temperature is set to 60°F. Set the pressure at approximately 2,000 psig for all samples. Reduce the

pressure in 200 psig increments before reaching the bubblepoint and in 100 psig increments or lower

when the pressure is close to the anticipated bubblepoint. For each reading, the pressure is allowed to

stabilize for 3 minutes before recording the pressure and volume. Pressure is plotted against volume and

the pressure at which the slope changes is the bubblepoint pressure. This experiment is performed using

CO2-water mixture, 32°API crude oil, and 38°API crude oil. The bubblepoint pressure and the

corresponding volume are observed and recorded and used as a reference volume (Ahmed 2001).

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Results

Fig. 1—The bubblepoint for 32°API oil is 807.2 psi at 148.5 mL at 60°F temperature.

Fig. 2—The bubblepoint for water with dissolve carbon dioxide is 874.6 psi at 140.3 mL at 60°F temperature.

y = -284.96x + 43132

y = -4.6454x + 1497.2

0

500

1,000

1,500

2,000

2,500

142 144 146 148 150 152 154 156

Pre

ssu

re, p

sig

Volume, mL

Pressure-Volume for 32°API Oil

y = -282.85x + 40564

y = -3.3361x + 1342.7

0

500

1,000

1,500

2,000

2,500

136 137 138 139 140 141 142 143 144 145 146

Pre

ssu

re, p

sig

Volume, mL

Pressure-Volume for CO2-Water Mixture

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Fig. 3—The bubblepoint for 38°API oil is 597.6 psi at 140.2 mL at 60°F temperature.

TABLE 1— BUBBLEPOINTS FOR THREE FLUIDS

Fluid Type 32°API Oil CO2-Water

Mixture 38°API Oil

Bubblepoint, psig 807.2 874.6 597.6

Fig. 4—The coefficient of isothermal compressibility of 32°API oil is relatively constant above the bubblepoint and increases significantly below the bubblepoint at constant temperature.

y = -386.58x + 54778

y = -90.975x + 13348

0

500

1,000

1,500

2,000

2,500

136 137 138 139 140 141 142

Pre

ssu

re, p

sig

Volume, mL

Pressure-Volume for 38°API Oil

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

700 900 1,100 1,300 1,500 1,700

c o, p

si-1

P, psig

Coefficient of Isothermal Compressibility of 32°API Oil

pb

of 16

Fig. 5—The coefficient of isothermal compressibility of water is relatively constant above the bubblepoint and increases significantly below the bubblepoint at constant temperature.

Fig. 6—The coefficient of isothermal compressibility of 38°API oil is relatively constant above the bubblepoint and increases significantly below the bubblepoint at constant temperature.

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

800 900 1,000 1,100 1,200 1,300 1,400 1,500

c w, p

si-1

P, psig

Coefficient of Isothermal Compressibility of CO2-Water Mixture

pb

0.00E+00

2.00E-04

4.00E-04

6.00E-04

8.00E-04

1.00E-03

1.20E-03

400 600 800 1,000 1,200 1,400 1,600 1,800

c o, p

si-1

P, psig

Coefficient of Isothermal Compressibility of 38°API Oil

pb

of 16

Fig. 7—The solution gas/oil ratio of 32°API oil is constant above the bubblepoint and decreases significantly below the bubblepoint at constant temperature.

Fig. 8—The solution gas/liquid ratio of water is constant above the bubblepoint and decreases significantly below the bubblepoint at constant temperature.

138

139

140

141

142

143

144

145

700 900 1,100 1,300 1,500 1,700 1,900 2,100

Rs,

scf

/STB

P, psig

Solution Gas/Oil Ratio for 32°API Oil

pb

198198.5

199199.5

200200.5

201201.5

202202.5

203203.5

800 1,000 1,200 1,400 1,600 1,800 2,000

Rs,

scf

/STB

P, psig

Solution Gas/Liquid Ratio for CO2-Water Mixture

pb

of 16

Fig. 9—The solution gas/oil ratio of 38°API oil is constant above the bubblepoint and decreases significantly below the bubblepoint at constant temperature.

Fig. 10—The total formation volume factor of 32°API oil increases significantly below the bubblepoint at constant temperature.

80

85

90

95

100

105

110

115

120

125

130

400 600 800 1,000 1,200 1,400 1,600 1,800 2,000

Rs,

scf

/STB

P, psig

Solution Gas/Oil Ratio for 38°API Oil

pb

1.02

1.025

1.03

1.035

1.04

1.045

1.05

1.055

1.06

700 900 1,100 1,300 1,500 1,700

Form

atio

n V

olu

me

Fac

tor,

re

s b

bl/

STB

P, psig

Formation Volume Factor for 32°API Oil

Bt

Bo

pb

of 16

Fig. 11—The total formation volume factor of water increases as pressure decreases at constant temperature.

Fig. 12—The total formation volume factor of 38°API oil increases significantly below the bubblepoint at constant temperature.

1.085

1.09

1.095

1.1

1.105

1.11

800 900 1,000 1,100 1,200 1,300 1,400 1,500

Form

atio

n V

olu

me

Fac

tor,

re

s b

bl/

STB

P, psig

Formation Volume Factor for CO2-Water Mixture

Bt

Bw

pb

1.00000

1.02000

1.04000

1.06000

1.08000

1.10000

1.12000

1.14000

1.16000

1.18000

1.20000

400 600 800 1,000 1,200 1,400 1,600 1,800

Form

atio

n V

olu

me

Fac

tor,

re

s b

bl/

STB

P, psig

Formation Volume Factor for 38°API Oil

Bt

Bo

pb

of 16


At 60°F temperature, the bubblepoint is the highest for CO2-water mixture followed by the 32°API oil

and 38°API oil. The 32°API oil has higher bubblepoint pressure compared to 38°API oil due to higher

amount of heavy hydrocarbon components within the oil. It is assumed that methane gas is evolved when

the oils reach the bubblepoint. It is also assumed that the pressure, temperature and z-factor at standard

conditions are 14.65 psia, 520°R and 1.0 respectively. It is assumed that the correlations used for

hydrocarbons can be applied to CO2-water mixture. However, the values should be used with caution

because CO2-water mixture has different properties than hydrocarbons. It is assumed that the fluids in the

PVT cells mimic the behavior of the reservoir fluids. The liquid is said to be undersaturated (single-

phase) at pressures above the bubblepoint and saturated (two-phase) when the pressure is at and below the

bubblepoint.

The evolution of gas from the oil has a significant impact on the FVF. This causes a large decrease in

volume of the oil when there is a lot of gas. As pressure decreases, the oil expands slightly at constant

temperature. When pressure decreases below the bubblepoint, gas evolve within the cell and the

remaining oil has less gas in solution, thus resulting in a lower FVF. The laboratory analysis indicates the

FVF of both oils are below 2.0 res bbl/STB, which is consistent with a typical black oil.

At pressures above the bubblepoint pressure, the solution GOR is constant due to no gas evolved inside

the cell. When pressure is reduced below the bubblepoint pressure, gas evolves in the cell making less gas

dissolve in the liquid thus decreasing the solution GOR (McCain 1990). Similar gas solubility behavior is

shown for CO2-water mixture.

The total FVF and the FVF of oil are identical at pressures above the bubblepoint because no gas evolves

from the solution inside the cell. At pressures below the bubblepoint, the total FVF is more than the FVF

of oil because of the evolution of gas. The evolved gas is called free gas. The difference between the total

FVF and the FVF of liquid at pressures below the bubblepoint represent the volume of gas released in the

cell.

The coefficient of isothermal compressibility of liquid at pressures above the bubblepoint is virtually

constant except at pressures near the bubblepoint. This finding is supported by McCain (1990). Below the

bubblepoint pressure, the volume of liquid decreases as pressure is reduced. There is a large shift in the

compressibility because of the evolution of gas.

It is important to determine the pressure-volume relationship of reservoir fluids because it helps to obtain

the bubblepoint pressure. Knowing the bubblepoint pressure is significant in understanding the phase

behavior of reservoir fluids by calculating integral parameters such as gas solubility, FVF, and coefficient

of isothermal compressibility. The bubblepoint and relative volumes can be used as inputs in tuning

equation of state which is useful in reservoir modeling or simulation. The team recommends performing

hydrocarbon analysis on both crude oils to have a better understanding of the compositional changes

during the phase transition at pressures below the bubblepoint.

of 16

Conclusion

The bubblepoint of a fluid can be determined by the significant change in slopes on a pressure vs. volume

plot.

The evolution of gas at bubblepoint has a significant impact on gas solubility, FVF, and coefficient of

isothermal compressibility values for liquid.

The team recommends performing hydrocarbon analysis on both crude oils to have a better understanding

of the compositional changes during the phase transition at pressures below the bubblepoint.

of 16

References

Ahmed, T. 2001. Reservoir Engineering Handbook, second edition. Houston, Texas: Gulf Professional

Publishing/Elsevier.

Devegowda, D. 2011. Phase behavior. Lecture notes on phase behavior. The University of Oklahoma,

Oklahoma, United States.

McCain, W.D. Jr. 1990. The Properties of Petroleum Fluids, second edition, Tulsa, Oklahoma: PennWell.


Whitson, C.H., and Brule, M.R. 2000. Phase Behavior, Vol. 20, 1–2. Richardson, Texas: Monograph

Series, SPE.

Appendices

Equations

𝛾𝑜 =141.5

°𝐴𝑃𝐼+131.5, ..............................(1)

𝑀𝑎 = ∑ 𝑦𝑗𝑀𝑗𝑗 , ..............................(2)

𝑦𝑔 =𝑀𝑔

𝑀𝑎𝑖𝑟, ..............................(3)

𝑐𝑜 = −1

𝑉(

𝜕𝑉

𝜕𝑝)

𝑇, ..............................(4)

𝑐𝑜 = −1

𝐵𝑜[(

𝜕𝐵𝑜

𝜕𝑝)

𝑇− 𝐵𝑔 (

𝜕𝑅𝑠

𝜕𝑝)

𝑇], ..............................(5)

(𝐶𝑁)𝑝𝑏 =𝑝𝑏

18.2+ 1.4, ..............................(6)

𝑅𝑠 = √(𝐶𝑁)𝑝𝑏

10(0.00091𝑇−0.0125𝐴𝑃𝐼)

0.83

𝛾𝑔 = √𝑝𝑏

18.2+1.4

10(0.00091𝑇−0.0125𝐴𝑃𝐼)

0.83

𝛾𝑔, ..............................(7)

𝐵𝑜 = 𝐵𝑜𝑏𝑒𝑐𝑜(𝑝𝑏−𝑝), ..............................(8)

(𝐶𝑁)𝐵𝑜𝑏 = 𝑅𝑠 (𝛾𝑔

𝛾𝑆𝑇𝑂)

0.5+ 1.25𝑇, ..............................(9)

𝐵𝑜𝑏 = 0.9759 + 12 × 10−5(𝐶𝑁)𝐵𝑜𝑏1.2 = 0.9759 + 12 × 10−5 [𝑅𝑠 (

𝛾𝑔

𝛾𝑆𝑇𝑂)

0.5

+ 1.25𝑇]1.2

, ..............................(10)

𝐵𝑔 =𝑧𝑇𝑝𝑠𝑐

𝑧𝑠𝑐𝑇𝑠𝑐𝑝=

𝑧𝑇∙14.65

1∙520𝑝= 0.0282

𝑧𝑇

𝑝 𝑓𝑡3/𝑠𝑐𝑓

𝑏𝑏𝑙

5.615 𝑓𝑡3, ..............................(11)

𝐵𝑡 = 𝐵𝑜 + 𝐵𝑔(𝑅𝑠𝑏 − 𝑅𝑠), ..............................(12)

Sample Calculations

32°API Oil

of 16

𝛾𝑜 =141.5

32 + 131.5= 0.865

𝑀𝑎 = 0.78 ∙ 28.01 + 0.21 ∙ 32 + 0.01 ∙ 39.94 = 29

𝛾𝑔 =16.04

29= 0.554

𝑦 = −284.96𝑥 + 43132

𝑦 = −4.6454𝑥 + 1497.2

Solve for 𝑦 and 𝑥,

𝑝𝑏 = 807.2 𝑝𝑠𝑖

𝑉𝑏 = 148.5 𝑚𝐿

𝑅𝑠 = √807.218.2 + 1.4

10(0.00091∙60−0.0125∙32)

0.83

∙ 0.554 = 144.5 𝑠𝑐𝑓/𝑆𝑇𝐵

𝐵𝑜𝑏 = 0.9759 + 12 × 10−5 [144.5 (0.554

0.865)

0.5

+ 1.25 ∙ 60]

1.2

= 1.0413 𝑟𝑒𝑠 𝑏𝑏𝑙/𝑆𝑇𝐵

Read 𝑧‐ 𝑓𝑎𝑐𝑡𝑜𝑟 from chart

𝑧 = 0.912

𝐵𝑔 =𝑧𝑇𝑝𝑠𝑐

𝑧𝑠𝑐𝑇𝑠𝑐𝑝=

0.912 ∙ (60 + 460) ∙ 14.65

1 ∙ 520 ∙ (807.2 + 14.7) ∙ 5.615= 0.0029 𝑟𝑒𝑠 𝑏𝑏𝑙/𝑠𝑐𝑓

𝐵𝑡 = 1.0413 + 0.0029(144.5 − 144.5) = 1.0413 𝑟𝑒𝑠 𝑏𝑏𝑙/𝑆𝑇𝐵

Above bubblepoint pressure

𝑑𝑝 = 924.4 − 1033.2 𝑝𝑠𝑖 = −108.8 𝑝𝑠𝑖

𝑑𝑉 = 148.2 − 147.7 𝑚𝐿 = 0.5 𝑚𝐿

𝑉 =148.2 + 147.7

2 𝑚𝐿 = 148.0 𝑚𝐿

𝑐𝑜 =−1

148.0

0.5

(−108.8)𝑝𝑠𝑖−1 = 29.7 × 10−6 𝑝𝑠𝑖−1

𝐵𝑜 = 1.0413𝑒29.7×10−6(807.2−924.4) = 1.038 𝑟𝑒𝑠 𝑏𝑏𝑙/𝑆𝑇𝐵

Below bubblepoint pressure

𝑐𝑜 = −1

1.039[(

1.039 − 1.040

779 − 789) − 0.003 (

138.6 − 140.7

779 − 789)] = 542 × 10−6 𝑝𝑠𝑖−1

Supplemental Tables

of 16

TABLE 2—DATA TO CALCULATE APPARENT MOLECULAR WEIGHT OF AIR

Component Composition mole fraction

Molecular weight

lb/lb mole

Mj × yj

lb/lb mole

Nitrogen 0.78 28.01 21.8478

Oxygen 0.21 32 6.72

Argon 0.01 39.94 0.3994

Ma

lb/lb mole

28.9672

TABLE 3—MOLECULAR WEIGHT OF METHANE AND CARBON DIOXIDE

Component Molecular weight

lb/lb mole

CH4 16.04

CO2 44.01

TABLE 4—PRESSURE-VOLUME RELATIONS AT 60°F

32°API Oil 38°API Oil CO2-Water Mixture

P Relative volume P Relative volume P Relative volume

psi

psi

psi

2,002.2 0.9726 1,928.4 0.9758 1,980.6 0.9733

1,623.8 0.9802 1,691.2 0.9797 1,457.2 0.9842

1,474.4 0.9836 1,410.0 0.9848 1,274.4 0.9888

1,212.6 0.9898 1,200.6 0.9887 1,117.6 0.9933

1,033.2 0.9947 998.8 0.9926 1,030.4 0.9964

924.4 0.9980 865.8 0.9953 955.6 0.9992

807.2 1.0000 794.6 0.9978 874.6 1.0000

800.6 1.0098 597.6 1.0000 870.6 1.0067

794.2 1.0174 590.8 1.0015 869.2 1.0137

789.0 1.0286 490.8 1.0064 858.2 1.0343

779.0 1.0399 466.0 1.0113 - -

of 16

TABLE 5—RELEVANT DATA FOR 32°API OIL

°API T γo γg Pb Vb

°F

psi mL

32 60 0.8654 0.5537 807.2 148.52883

P V dP dV Vave co Rs Bo z Bg Bt

psi mL psi mL mL psi-1 scf/STB res bbl/STB

res bbl/scf res bbl/STB

2,002.2 144.46614

144.53 0.0000 0.82 0.00106 0.00000

1,623.8 145.58734 -378.4 1.12120 145.027 2.04E-05 144.53 1.0240 0.819 0.00130 1.02404

1,474.4 146.0958 -149.4 0.50846 145.842 2.33E-05 144.53 1.0252 0.818 0.00143 1.02518

1,212.6 147.01853 -261.8 0.92273 146.557 2.40E-05 144.53 1.0312 0.819 0.00174 1.03116

1,033.2 147.74858 -179.4 0.73005 147.384 2.76E-05 144.53 1.0348 0.831 0.00207 1.03479

924.4 148.22719 -108.8 0.47861 147.988 2.97E-05 144.53 1.0376 0.891 0.00248 1.03764

807.2 148.52883 -117.2 0.30164 148.378 2.97E-05 144.53 1.0413 0.912 0.00290 1.04126

800.6 149.99046 -6.6 1.46163 149.260 5.21E-04 143.14 1.0408 0.914 0.00292 1.04486

794.2 151.11122 -6.4 1.12076 150.551 5.26E-04 141.81 1.0404 0.915 0.00295 1.04840

789.0 152.77672 -5.2 1.66550 151.944 5.33E-04 140.72 1.0400 0.921 0.00299 1.05138

779.0 154.45 -10.0 1.67328 153.613 5.42E-04 138.65 1.0393 0.924 0.00304 1.05720

TABLE 6—RELEVANT DATA FOR CO2-WATER MIXTURE


°F

psi mL

10 60 1 1.5193 874.6 140.3197

P V dP dV Vave cw Rs Bw z Bg Bt

psi mL psi mL mL psi-1 scf/ST

B res

bbl/STB res bbl/scf res bbl/STB

1,980.6 136.57417

203.08 0.0000 0.2811 0.00037 0.00000

1,457.2 138.10641 -523.4 1.53224 137.340 2.13E-05 203.08 1.0865 0.21763 0.00039 1.08647

1,274.4 138.75307 -182.8 0.64666 138.430 2.56E-05 203.08 1.0889 0.19589 0.00040 1.08887

1,117.6 139.38406 -156.8 0.63099 139.069 2.89E-05 203.08 1.0923 0.17704 0.00041 1.09234

1,030.4 139.81319 -87.2 0.42913 139.599 3.53E-05 203.08 1.0940 0.1676 0.00042 1.09402

955.6 140.21222 -74.8 0.39903 140.013 3.81E-05 203.08 1.0967 0.16024 0.00043 1.09666

874.6 140.31968 -81.0 0.10746 140.266 3.80E-05 203.08 1.1001 0.56094 0.00165 1.10005

870.6 141.26158 -4.0 0.94190 140.791 2.73E-04 202.00 1.0994 0.56605 0.00167 1.10124

869.2 142.24203 -1.4 0.98045 141.752 2.73E-04 201.62 1.0992 0.56605 0.00167 1.10167

858.2 145.1371 -11.0 2.89507 143.690 2.86E-04 198.64 1.0975 0.57589 0.00172 1.10520

of 16

TABLE 7—RELEVANT DATA FOR 38°API OIL


°F

psi mL

38 60 0.8348 0.5537 597.6 140.15325

P V dP dV Vave co Rs Bo z Bg Bt

psi mL psi mL mL psi-1 scf/STB res bbl/STB

res bbl/scf res bbl/STB

1,928.4 136.7551

125.47 0.0000 0.819 0.00110 0.00000

1,691.2 137.30453 -237.2 0.54943 137.030 1.69E-05 125.47 1.0168 0.817 0.00125 1.01681

1,410.0 138.01804 -281.2 0.71351 137.661 1.84E-05 125.47 1.0204 0.815 0.00149 1.02039

1,200.6 138.56381 -209.4 0.54577 138.291 1.88E-05 125.47 1.0241 0.814 0.00175 1.02408

998.8 139.11948 -201.8 0.55567 138.842 1.98E-05 125.47 1.0276 0.831 0.00214 1.02757

865.8 139.49596 -133.0 0.37648 139.308 2.03E-05 125.47 1.0302 0.895 0.00265 1.03015

794.6 139.84311 -71.2 0.34715 139.670 3.49E-05 125.47 1.0287 0.915 0.00295 1.02868

597.6 140.15325 -197.0 0.31014 139.998 1.16E-03 125.47 1.0358 0.957 0.00408 1.26446

590.8 140.36311 -6.8 0.20987 140.258 8.88E-04 123.83 1.0352 0.957 0.00412 1.27323

490.8 141.04649 -100.0 0.68338 140.705 1.07E-03 100.04 1.0275 0.958 0.00494 1.43047

466.0 141.73407 -24.8 0.68758 141.390 1.11E-03 94.28 1.0256 0.959 0.00521 1.47984

October 26, 2012

Experiment 6

Interfacial Tension, Contact Angle & Capillary Pressure Measurements


Team 002E


Manager Axel Hannenberg 1.0

Researcher Lemmy Oshenye 1.0

Technician Lucas Gurgel De Carvalho 1.0

Analyst Nor Ashraf Norazman 1.0



this exercise.

Name: _________________________________ Date: _____________________________

of 11

Abstract

It is important to have knowledge of the interfacial tension, contact angle & capillary pressure because

they help in understanding the nature of the reservoir and designing enhance oil recovery methods such as

water flooding.

Knowing capillary pressure curves of reservoir rocks helps to determine fluid saturations and connate

water saturation.

In this study, contact angles and interfacial tensions are measured and data from mercury injection are

used to plot intrusion pressure versus Hg saturation, calculate and plot pore throat size histogram, convert

and plot Hg-air data to air-brine capillary pressure, estimate R35 and calculate permeability using

Winland’s equation, and weighted geometric mean approach, and plot J-function versus wetting phase

saturation. The three samples, Cl, Red, and Tc are analyzed to determine which will be a better reservoir.

Data analysis shows that:

1. Permeability and capillary pressure are controlled by pore radii. Permeability affects the capillary

pressure curve. Low displacement pressure indicates good connectivity. Leverett J-function can

be used to group similar formations.

2. The air-brine contact angle is higher than air-oil contact angle for both glass and Teflon surfaces.

The contact angle of air-fluid is higher on Teflon surface compared to on glass surface.

3. Tc will be a better reservoir because it has the highest permeability and porosity, lowest

displacement pressure and is also well sorted.

The team recommends performing drainage and imbibition methods on the samples.

of 11

Introduction

The capillary pressure is the pressure difference between two immiscible fluids in contact with each other,

more specifically the pressure difference in the interface of these two fluids. The capillary pressure is

inversely proportional to the radius of curvature of this interface and to the radius of the pore. This

phenomenon occurs in oil reservoirs because of the presence of at least two immiscible fluids in

reservoirs. Molecules located in the interface between these fluids are surrounded by different types of

molecules. The molecules located in the fluids have a normal state of equal attraction in all directions but

when two immiscible fluids are in contact this equality no longer occurs.

The capillarity phenomenon occurs within the porous media of oil reservoirs. A reservoir rock is a porous

media which contain an infinite number of pores of different sizes. As the capillary pressure depends on

the radius of the pore, we can notice that it will vary for different zones in the same reservoir. For each

zone of the reservoir there will be a different capillary pressure curve. For a given capillary pressure the

lesser the permeability, the greater the water saturation. The Leverett J-function correlates these different

curves to combine them into one curve for the entire reservoir (Rosa, 2011).

Another important concept is the wettability. Wettability is the preference of a solid to contact one liquid

or gas, known as the wetting phase, rather than another. The wetting phase will tend to spread on the solid

surface (Schlumberger). The wettability can be determined by measuring the contact angle. When the

contact angle of the fluid is less than 90, the solid has a wetting preference for this fluid.

In this experiment, the contact angles of water and oil in different solids are measured using a contact

angle meter. Interfacial tension of a brine sample was taken using a DuNouy tensiometer. Finally data

from a high pressure mercury injection experiment in conjunction with a penetrometer was used to

calculate air-brine capillary pressure curve, pore throat size distribution, permeability, and J-function.


The interfacial tension of air-brine was measured using a CSC-DuNouy Tensiometer No. 70545 (Fig. 1).

First, the stand was filled with liquid. The ring on the tensiometer was calibrated and submerged into the

liquid. The adjustment of a combination of knobs gradually increases the tension in the liquid until the

ring finally brakes through the liquid. The interfacial tension recorded was the tension required to break

ring from contact with the fluid.

Fig. 1—CSC-DuNouy Tensiometer No. 70545 used for measuring interfacial tension in the lab. The unit of measurement is

dynes/cm.

of 11

The contact angles for water/glass, water/Teflon, mineral oil/glass, and mineral oil/Teflon were evaluated

using a CAM-PLUS MICRO contact angle meter (Fig. 2). The liquid samples (mineral oil or water) were

inserted onto the solid surfaces (glass or Teflon) using a micro syringe and a light was shined through the

sample. The radius for each sample (liquid on solid surface) was recorded. The contact angle was

observed by taking half of the radius and measuring the angle intersecting the surface of the liquid at the

intersection point.

Fig. 2—CAM-PLUS MICRO contact angle meter used for measuring contact angles in the lab.

The AutoPore IV Series mercury porosimeter as shown in Fig. 3 was used to compute the absolute

porosity of the porous medium. Rock samples were inserted into the porosimeter. The pressure was then

increased until the first injection of mercury occurred. Mercury is the ultimate non-wetting phase, when

pressure is applied it will go to the largest pores first. It must be forced into pores at a pressure equal to or

greater than its capillary pressure. Low pressures are needed for larger pore throats while small pores

need high pressure. The procedure was repeated until the pressure reaches 60,000 psi.

Fig. 3—AutoPore IV Series Mercury Porosimeter (left). Penetrometers used in the AutoPore IV Series Mercury Porosimeter

(right).

of 11

Results

Fig. 4—Intrusion pressure vs. Hg saturation plot. Displacement pressure is the highest for Red followed by Tc and Cl.

Fig. 5—Histogram for all three samples. According to the bin values used, all three samples show the same histogram.

1

10

100

1,000

10,000

100,000

0%20%40%60%80%100%

Intr

usi

on

Pre

ssu

re, p

sia

Hg Saturation

Cl

Red

Tc

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0

5

10

15

20

25

30

35

40

45

0.001 0.01 0.1 1 10

Fre

qu

en

cy

Pore Throat Radius, μm

Histogram for Cl, Red, and TcFrequency

Cumulative %

of 11

Fig. 6—Capillary pressure for air-Hg vs. capillary pressure for air-brine. The reciprocal of the slope represents a constant

value to convert Pc(air-Hg) into Pc(air-brine).

TABLE 1—R35, RWGM, AND PERMEABILITY VALUES FOR THREE SAMPLES

R35 Rwgm kR35 kRwgm kaverage

µm µm md md md

Cl 1.53952283 0.63749607 7.1 7.5 7.3

Red 0.56499651 0.23099749 1.3 1.4 1.4

Tc 5.87745512 2.32206718 74.3 71.6 73.0

Fig. 7—Leverett J-function vs. wetting phase saturation. J-function is used to categorize similar types of formations.

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000

Pc(

air-

Hg)

, psi

a

Pc(air-brine), psia

Cl

Red

Tc

𝑦 = 4.04𝑥

0

1

2

3

4

5

6

7

8

9

10

0.0 0.2 0.4 0.6 0.8 1.0

Leve

rett

J-f

un

ctio

n, d

ime

nsi

on

less

Water Saturation, fraction

Cl

Red

Tc

of 11

TABLE 2—CONTACT ANGLES FOR DIFFERENT COMBINATION OF PHASES

Brine/Glass Brine/Teflon Oil/Glass Oil/Teflon

° ° ° °

32 78 8 33

33 78 8 33

33 78 8 33

TABLE 3—INTERFACIAL TENSION OF AIR-BRINE USING TENSIOMETER

Reading Tensiometer

dynes/cm

1 76.7

2 77.8

3 77.2

Average 77.2


The mercury capillary pressure curves for three samples are compared with each other. The entry pressure

is the pressure where Hg first enters the pores and is determined by the largest pore aperture size. The

displacement pressure is the pressure where Hg becomes connected and is determined by the inflection

point from the capillary pressure curve. The mercury injection method is a drainage method. The

displacement pressure is lowest for Tc followed by Red and Cl. Low displacement pressure indicates

good connectivity. Fig. 11 shows that the critical pore throat aperture is the highest for Cl followed by Tc

and Red. The apexes represent the critical pore throat aperture for the samples. The histogram shows that

the samples are dominated by pore throat sizes within the range of 0.01 to 9.0 microns.

Permeability value affects the capillary pressure behavior. Higher permeability shifts the capillary

pressure curve downward while lower permeability shifts the capillary pressure curve upward. Tc has the

highest permeability followed by Red and Cl. Table 1 and Fig. 4 show this trend for the samples. Fig. 9

shows that Tc has more Hg saturation per incremental pressure, which supports the discussion about

permeability and displacement pressure above. The permeability values are calculated using Winland’s

equation and the weighted geometric mean approach. The R35 is estimated by using linear interpolation.

Hysteresis is the difference between the advancing and receding angles. Hysteresis makes the relationship

between capillary pressure and water saturation nonunique (Sondergeld 2011). Capillary pressure cannot

be determined from knowing water saturation alone without knowing the past wetting-drying history of

the reservoir. All of the samples show no hysteresis. Leverett J-function is used to group similar

formations together. Red and Tc samples show similar J-function curves and Cl has a different J-function

curve. This means that Red and Tc are from sandstone formation and Cl is from a limestone formation.

Fig. 6 shows the relationship between air-Hg and air-brine capillary pressures. The capillary pressure of

air-Hg can be converted into the capillary pressure of air-brine by multiplying it with a constant. The

of 11

constant is a function of contact angles and surface tensions of the phases. In this experiment, the contact

angles and surface tensions are constant. The contact angle of air-Hg, air-Hg surface tension, and air-brine

contact angle are given as 130°, 485 dynes/cm, and 0° respectively.

Contact angle is always measured through the denser fluid phase. The air-brine contact angle is higher

than air-oil contact angle for both glass and Teflon surfaces. Since the fluids are dropped onto the solid

surface, the contact angle measured is the advancing angle. The contact angle of air-fluid is higher on

Teflon surface compared to on glass surface because the coefficient of friction of Teflon is higher than

glass. Hence, both brine and oil molecules have a tendency to slip on a glass surface. Wettability is

related to the contact angle.

At the subsurface, oil-water contact depends on rock quality and is not uniform. Permeability and

capillary pressure are controlled by pore radii (Sondergeld 2011). In the industry, the capillary radius in

the lab and the field is assumed to be the same. Thus, the capillary pressure can be converted to

equivalent height or height above free water level at reservoir conditions. The normalized capillary

pressure curve (plot of Leverett J-function vs. water saturation) can also be used to determine the

transition zone in the reservoir. This is done by conducting drainage and imbibition methods on the

samples and plotting J-function vs. water saturation. Thus, the team recommends performing these

methods on the samples. The contact angle is one of the factors affecting the transition zone other than the

interfacial tension and density difference of multiple phases in the reservoir. The interfacial and surface

tension forces in porous medium, wettability and capillary pressure affect microscopic displacement

efficiency, which is important in water flooding (Akkutlu 2012).

Both Tc and Red are well sorted formations because the plateaus of the capillary pressure curves are

nearly horizontal. Compared to the other two samples based on the shape of the capillary pressure curve,

Cl is poorly sorted. This might indicate that that Cl formation is a shaly limestone formation.

Experimental results suggest Cl is the worst candidate for a reservoir.

From the analysis, the team concludes that Tc will be a better reservoir because it has the highest

permeability and porosity, lowest displacement pressure and is also well sorted.


Permeability and capillary pressure are controlled by pore radii. Permeability affects the capillary

pressure curve. Low displacement pressure indicates good connectivity. Leverett J-function can be used

to group similar formations.

The air-brine contact angle is higher than air-oil contact angle for both glass and Teflon surfaces. The

contact angle of air-fluid is higher on Teflon surface compared to on glass surface.

The team concludes that Tc will be a better reservoir because it has the highest permeability and porosity,

lowest displacement pressure and is also well sorted.

The team recommends performing drainage and imbibition methods on the samples.

of 11

References

Akkutlu, Y.I. 2012. Displacement of oil and gas. Lecture notes on displacement of oil and gas. The

University of Oklahoma, Oklahoma, United States.


Schlumberger Oilfield Glossary,

http://www.glossary.oilfield.slb.com/Display.cfm?Term=wettability (accessed 24 October 2012).

Sondergeld, C.H. 2011. Capillary pressure. Lecture notes on capillary pressure. The University of

Oklahoma, Oklahoma, United States.

Appendices

Equations

𝑃𝑐 =2𝐶𝛾 cos𝜃

𝑟, ..............................(1)

𝑃𝑐(𝑎𝑖𝑟‐𝑏𝑟𝑖𝑛𝑒) = 𝑃𝑐(𝑎𝑖𝑟‐𝐻𝑔)(𝛾 cos𝜃)(𝑎𝑖𝑟‐𝑏𝑟𝑖𝑛𝑒)

(𝛾 cos𝜃)(𝑎𝑖𝑟‐𝐻𝑔), ..............................(2)

𝐽(𝑆𝑤) =0.2166𝑃𝑐√𝑘 𝜙⁄

𝛾 cos𝜃, ..............................(3)

log𝑅35 = 0.732 + 0.588 log 𝑘 − 0.864 log𝜙, ..............................(4)

log 𝑘 = −1.245 + 1.469 log𝜙 + 1.701 log 𝑅35, ..............................(5)

log 𝑘 = −2.51 + 3.06 log𝜙 + 1.64 log𝑅𝑤𝑔𝑚, ..............................(6)

𝑅𝑤𝑔𝑚 = 𝑒[∑ 𝑤𝑖 ln(𝑅𝑖)𝑛𝑖=1∑ 𝑤𝑖𝑛𝑖=1

], ..............................(7)

𝑦 = 𝑦0 +(𝑥−𝑥0)(𝑦1−𝑦0)

𝑥1−𝑥0, ..............................(8)

of 11

Supplemental Figures

Fig. 8—Cumulative Hg saturation vs. pore radius on a semilog scale.

Fig. 9—Hg saturation/pressure vs. Hg saturation. The plot shows that Tc has more Hg saturation per incremental pressure.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.0010.010.1110100

Cu

mu

lati

ve H

g Sa

tura

tio

n

Pore Radius, μm

Cl

Red

Tc

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

0.022

0.024

0.026

0.028

0 0.2 0.4 0.6 0.8 1

Hg

Satu

rati

on

/Pre

ssu

re

SHg

Cl

Red

Tc

of 11

Fig. 10—Incremental pore volume vs. pore radius on a semilog scale.

Fig. 11—Incremental pore volume vs. pore throat diameter on a semilog scale.

0

10

20

30

40

50

60

70

80

90

100

0.0010.010.1110100

Incr

em

en

tal P

ore

Vo

lum

e, %

Pore Radius, μm

Cl

Red

Tc

0

0.001

0.002

0.003

0.004

0.005

0.006

0.0010.010.1110100

Incr

em

en

tal P

ore

Vo

lum

e, m

L/g

Pore Throat Diameter, μm

Cl

Red

Tc

December 07, 2012

Experiments 7, 8 and 9

Waterflooding and Enhanced Oil Recovery


Team 002E


Manager Lemmy Oshenye 1.0

Researcher Lucas Gurgel De Carvalho 1.0

Technician Nor Ashraf Norazman 1.0

Analyst Axel Hannenberg 1.0



this exercise.

Name: _________________________________ Date: _____________________________

of 12

Abstract

As production from oil reservoirs matures, improving the recovery factor will play a decisive role in

offsetting the decline in production. Many methods exist to improve the recovery factor. In this

experiment, waterflooding, surfactant flooding, and gas flooding were conducted. Significant findings

include:

1. The mobility ratios of waterflooding, surfactant flooding, and gas flooding are 1.79, 0.63, and 2.5

respectively. Oil recovery decreases as mobility ratio increases.

2. The microscopic displacement efficiency of waterflooding, surfactant flooding, and gas flooding

are 57.7, 49.2, and 33.9 respectively. High microscopic displacement efficiency results in low

residual oil saturation after flooding.

3. Surfactant flooding has the highest recovery factor followed by waterflooding and gas flooding.

of 12

Introduction

Recovering oil from a petroleum reservoir can be achieved by primary recovery, secondary recovery and

tertiary recovery. Primary oil recovery normally refers to the production of hydrocarbons using the

natural driving mechanisms in the reservoir. Secondary oil recovery describes the additional recovery that

results from water injection or immiscible gas injection. Waterflooding is the most common method of

secondary recovery. Tertiary (enhanced) oil recovery refers to the additional recovery that is beyond what

could be recovered by primary and secondary recovery methods (Ahmed 2001). Tertiary recovery

includes chemical, thermal and miscible processes. In this experiment, waterflooding, surfactant flooding

and gas flooding are conducted.

Waterflooding

Waterflooding is the use of water injection to increase the production from oil reservoirs. This is

accomplished by the injection of water to increase the reservoir pressure to its initial pressure and

maintain it near that pressure (Warner Jr. 2007). The water displaces oil from pore spaces but the

microscopic displacement efficiency is affected by the interfacial tension in porous medium, rock

wettability, water-/oil-relative permeability, and capillary pressure, which in turn affect waterflood

recovery factor. Waterflood recovery factor is also influenced by intrinsic factors such as mobility ratio,

reservoir heterogeneity, pore geometry, and initial water-/oil-saturation distribution. The grain shape, size,

and sorting determine the pore-geometry heterogeneity. The wettability affects the capillary pressure and

relative permeability. The viscosity and relative permeability of the fluids contribute to the mobility ratio.

The initial water-oil-saturation distribution is important because it controls the efficiency of the

waterflood in portions of the reservoir and also relates directly to the residual oil saturation that can be

achieved at the end of a waterflood (Warner Jr. 2007). Higher oil saturation at the beginning of flood

operations increases the oil mobility and hence gives higher recovery factor (Ahmed 2001). Connate-

water saturation and residual oil saturation after waterflood are the most important numbers in

waterflooding because they are used to determine the displacement efficiency.

Surfactant Flooding

Surfactant flooding is a method where surfactant is injected into the reservoir either for wettability

alteration or to reduce the water-/oil-interfacial tension (Zitha et al. 2011). When a surfactant is added to

the sand pack that consists of oil and brine, the surfactant molecules adsorb at the interface, displacing

some of the water and oil molecules. Accumulation of surfactant at the interfacial zone disrupts the fluid

structure and decreases interfacial tension (Akkutlu 2012). Surfactant flooding recovery factor is affected

by the same factors that affect waterflooding recovery factor. The front-end cost of surfactant is very

high. To overcome this, the surfactant should be injected in a small volume for mobility control.

Retention of surfactants, which involves adsorption, precipitation, and phase trapping, is one of the main

factors for the unfavorable economics in chemical flooding (Austad & Milter 2000). A proper amount of

electrolyte is essential to maintain low interfacial tension with the oil globules trapped in the sand pack. In

the industry, the surfactant flooding process requires a pre-flush to condition reservoir, followed by

surfactant solution for releasing oil, followed by polymer solution for mobility control, and water to drive

the chemicals and oil bank towards the production well.

Gas Flooding

There are two different types of gas flooding: miscible gas injection and immiscible gas injection. In the

miscible gas injection, the injected gas mixes with oil, makes the oil lighter and reduces the oil viscosity

and surface tension of oil and rock. Consequently it becomes easier to produce the oil. In the immiscible

of 12

gas injection the injected gas does not mix with oil. It only provides formation energy via incremental

pressure. Typically it yields only about half the recovery of miscible floods. Each technique has

advantages and disadvantages and is applicable to different types of reservoirs and conditions. CO2

miscible gas flooding is a major source of oil production in the U.S., particularly in West Texas,

Wyoming and Mississippi where natural sources of CO2 can be obtained at reasonable cost. CO2

applications are increasingly popular due to the increasing desire to sequestrate manufactured CO2.

Besides the miscible CO2 injection, there is also the enriched gas injection and the high pressure dry gas

injection (Rosa 2011).


Initial Preparation

Before conducting the experiment, special safety requirements should be met. The use of safety goggles

and gloves is required. A sand pack is built using a pre-weighed 300 ml Lucite tube and various sized

(coarse, medium, and fine) sand grains. The relationship of coarse to medium to fine grains in the tube

was approximately 1:1:2. In an attempt to obtain 27% or less porosity, the sand grains are packed tightly

by pounding and continuously shaking the Lucite tube as it is being filled with the sand mixture. For

additional packing, the container is connected to a vacuum to pack the sand as tightly as possible. The

container is weighed again to calculate the pore volume and dry porosity. Next, the sand pack is

completely saturated with brine at a constant flow rate and then weighed. The wet porosity and absolute

permeability were computed.

Fig. 1—Weighing tubing assembly.

Waterflooding

The sand pack is flooded with mineral oil at a constant flow rate to determine the irreducible water

saturation and relative permeability of the fluids. A waterflood is conducted by injecting water at a

constant flow rate to displace the mineral oil. The volume of mineral oil displaced is collected to

determine the residual oil saturation and the effective permeability. The sand pack is weighed again after

waterflooding.

Surfactant Flooding

The sand pack is flooded with mineral oil until no water (or only fine oil bubbles) is produced to prepare

it for surfactant flooding. The displaced water is measured to determine the irreducible water saturation,

Swir, initial oil saturation, and relative permeabilities. The sand pack is weighed again. Surfactant is

injected into the sand pack at a constant rate to displace the mineral oil. The effective permeability to the

surfactant solution was determined during the last 1-2 pore volumes. The cylinders are allowed to set so

that the oil and water will separate so that the oil and water recovered can be measured. All equipment

and work area is cleaned as a safety precaution.

of 12

Figure 2—Injection of surfactant and volume of mineral oil and surfactant.

Gas Flooding

A second sand pack is prepared with the same process as the initial preparation. The sand pack is flooded

with oil so as to reach original hydrocarbon saturation. This is checked by weight measurements. Oil is

then displaced from the sand pack with compressed air at constant pressure. Oil production is measured as

a function of time and gas injection is recorded at the same times. Flooding is continued until oil

production is zero.

of 12

Results

Fig. 3—The cumulative oil production vs. amount of water injected for waterflooding.

Fig. 4—The cumulative fluids produced vs. time.

15

20

25

30

35

40

0 20 40 60 80 100 120 140

Np, c

m3

Wi, cm3

Np vs. Wi for Waterflooding

20

40

60

80

100

120

140

160

180

0 20 40 60 80 100 120 140 160 180

Np

+ W

i, cm

3

t, s

Np + Wi vs. t for Waterflooding

of 12

Fig. 5—The cumulative oil production vs. amount of surfactant injected for surfactant flooding.

Fig. 6—Comparison of the performance plots for waterflooding and surfactant flooding.

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 160 180

Np, c

m3

Wi, cm3

Np vs. Wi for Surfactant Flooding

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 160 180

Np, c

m3

Wi, cm3

Np vs. Wi for Waterflooding and Surfactant Flooding

Waterflooding

Surfactant flooding

of 12

Fig. 7—The cumulative oil production vs. amount of gas injected for gas flooding.

Fig. 8—Comparison of RF, Ed, and M. Surfactant flooding has the highest RF and Ed, followed by waterflooding and gas flooding. The figure also shows a reverse trend for mobility ratio.

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400 450

Np, c

m3

Gi, cm3

Np vs. Gi for Gas Flooding

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

10

20

30

40

50

60

70

Surfactant Flooding Waterflooding Gas Flooding

Mo

bili

ty R

atio

Re

cove

ry F

acto

r, %

Dis

pla

cem

en

t Ef

fici

en

cy,

%

Recovery Factor

Displacement Efficiency

Mobility Ratio

of 12

TABLE 1—COMPARISON OF SAND PACKS 1 AND 2

Sand pack Pore volume φdry φsaturated kabs Soi Swi kro

cm3 % % darcy % % fraction

1 73.09 26.91 25.24 3.84 97.14 2.86 0.24

2 75.29 27.34 26.00 3.74 92.97 7.03 0.23

TABLE 2—COMPARISON OF THREE ENHANCED RECOVERY METHODS

RF M Ed

% fraction %

Surfactant flooding 57.7 0.63 57.7

Waterflooding 52.1 1.79 49.2

Gas flooding 38.6 2.50 33.9

TABLE 3—WATERFLOODING AT RESIDUAL OIL

kw at Sor krw at Sor Sor Sw

darcy fraction fraction fraction

3.4330 0.8935 0.4938 0.5062

TABLE 4—SURFACTANT FLOODING AT RESIDUAL OIL

ksurfactant at

Sor krsurfactant at

Sor Sor Sw Ssurfactant

darcy fraction fraction fraction fraction

3.4482 0.8975 0.4104 0.0286 0.5609

The efficiency of the surfactant flood in terms of the oil in the sand pack at the beginning of the surfactant flood is 0.2033.

of 12


The mobility ratio is lowest for surfactant flooding, and increasing from waterflooding to gas flooding. A

low mobility ratio is favorable for flooding operations because it will be easier for the injected fluid to

displace the recoverable oil. The recorded relative permeability after surfactant flooding is higher than

that of waterflooding. The microscopic displacement efficiency is highest for surfactant flooding followed

by waterflooding and gas flooding. High relative permeability and high displacement efficiency are

favorable for flooding operations because they result in low residual oil saturation after flooding.

The surfactant flooding method is the most efficient with the highest recovery factor, microscopic

displacement efficiency, and lowest mobility ratio. The waterflooding method also seems efficient and

can be a viable alternative if surfactant flooding is unavailable or too costly. The gas flooding process is

least efficient with the lowest recovery factor because it has poor sweep efficiency. Also, the mobility

ratio is highest for gas flooding and there is tendency for viscous fingering to occur. The oil recovery after

breakthrough is lower than other processes. However, it must be acknowledged that gas flooding is more

efficient in volatile oil reservoirs.

Conclusion

It can be concluded that the mobility ratio, relative permeability after flooding, microscopic displacement

efficiency, and the initial water-/oil-saturation distributions for flooding operations have significant effect

on the recovery factor.

Based on the analysis of the three methods, without the consideration of cost of operation and type of

reservoir, surfactant flooding is most favorable for oil recovery.

of 12

References

Ahmed, T. 2001. Reservoir Engineering Handbook, second edition. Houston, Texas: Gulf Professional

Publishing/Elsevier.

Austad, T. and Milter, J. 2000. Surfactants: Fundamentals and Applications in the Petroleum Industry.

United Kingdom: Cambridge University Press.

Evolution Petroleum Corporation. 2012.

http://www.evolutionpetroleum.com/solutions_flooding.html.


Warner Jr., H.R. 2007. Petroleum Engineering Handbook, Vol. 5, V-1037–V-1096. Richardson, Texas,

SPE.

Zitha, P., Felder, R., Zornes, D., et al. 2011. Increasing Hydrocarbon Recovery Factors.

www.spe.org/industry/docs/recoveryfactors.pdf.

Appendices

Equations

𝑊𝑖 = 𝑊1 − 𝑊2, ..............................(1)

𝑉 =𝑚

𝜌= 𝜋 (

𝐷𝑖

2)

2𝐿 = 𝑉1 − 𝑉2, ..............................(2)

𝜙 =𝑉𝑝𝑜𝑟𝑒

𝑉𝑏𝑢𝑙𝑘, ..............................(3)

𝑞 =𝑉

𝑡, ..............................(4)

𝑘 =𝑞𝜇𝐿

𝐴∆𝑃, ..............................(5)

𝑘𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 =𝑘𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒

𝑘𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒, ..............................(6)

𝑀 =𝑘𝑟𝑒(𝑖𝑛𝑗 𝑓𝑙𝑢𝑖𝑑)

𝑘𝑟𝑜𝑒

𝜇𝑜

𝜇(𝑖𝑛𝑗 𝑓𝑙𝑢𝑖𝑑), ..............................(7)

𝑆𝑝ℎ𝑎𝑠𝑒 =𝑉𝑝ℎ𝑎𝑠𝑒

𝑉𝑝𝑜𝑟𝑒, ..............................(8)

1 = 𝑆𝑓𝑙𝑢𝑖𝑑 1 + 𝑆𝑓𝑙𝑢𝑖𝑑 2 + 𝑆𝑓𝑙𝑢𝑖𝑑 3, ..............................(9)

𝐸𝑑 =𝑆𝑜𝑖−𝑆𝑜𝑟

𝑆𝑜𝑖, ..............................(10)

𝑅𝐹 =𝑉𝑜𝑖𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑

𝑉𝑡𝑜𝑡𝑎𝑙, ..............................(11)

Supplemental Tables

Waterflooding

Δp Δp Vtotal Voil Vbrine t q Sw So kw krw Np+Wi

of 12

psig atm cm3 cm3 cm3 s cm3/s fraction fraction darcy fraction cm3

5.59 1.3816 20 20 0 22.1 0.9050 0.2736 0.7264 1.6053 0.4178 40

5.62 1.3836 40 28 12 54.4 0.6192 0.3831 0.6169 1.0967 0.2854 68

5.59 1.3816 60 33 27 80.6 0.7634 0.4515 0.5485 1.3541 0.3524 93

5.31 1.3625 80 34 46 102.64 0.9074 0.4652 0.5348 1.6322 0.4248 114

5.31 1.3625 104 36 68 121.23 1.2910 0.4925 0.5075 2.3222 0.6044 140

5.31 1.3625 117 37 80 139.94 0.6948 0.5062 0.4938 1.2498 0.3253 154

5.27 1.3597 125 37 88 158.23 0.4374 0.5062 0.4938 0.7883 0.2052 162

At residual oil

RF Vbrine t q kw at Sor krw at Sor Sor Sw Weight Relative error M Ed fraction cm3 s cm3/s darcy fraction fraction fraction g fraction fraction fraction

0.5211 40 21 1.9048 3.4330 0.8935 0.4938 0.5062 1,311.6 0.9894 1.7853 0.4917

Surfactant flooding

Δp Δp t Voil Vsurfactant

injected Vsurfactant q Sw Ssurfactant So ko kro ksurfactant krsurfactant WOR

psig atm s cm3 cm3 cm3 cm3/s fraction fraction fraction darcy fraction darcy fraction fractio

n

5.53 1.3775 18.21 20 20 0 1.0983 0.0286 0.2736 0.6978 4.1119 1.0702 1.7053 0.4438 0.0

5.46 1.3727 37.29 31 31 0 0.5765 0.0286 0.4241 0.5473 2.1659 0.5637 0.8983 0.2338 0.0

5.28 1.3604 54.19 36 53 17 1.3018 0.0286 0.4925 0.4789 4.9348 1.2844 2.0466 0.5327 0.5

5.01 1.3420 94.66 38 112 74 1.4579 0.0286 0.5199 0.4515 5.6024 1.4582 2.3235 0.6047 1.9

4.48 1.3058 110.92 40 128 88 0.9840 0.0286 0.5473 0.4241 3.8862 1.0115 1.6117 0.4195 2.2

4.39 1.2997 128.06 41 149 108 1.2252 0.0286 0.5609 0.4104 4.8616 1.2654 2.0162 0.5248 2.6

4.38 1.2990 146.35 41 164 123 0.8201 0.0286 0.5609 0.4104 3.2560 0.8474 1.3503 0.3515 3.0

At the beginning of the surfactant flood

y x

Ed 0 0.6978 18.2100

fraction

0.77393 1

0.2033

1 0.5473 54.19

At residual oil

RF Vbrine t q

ksurfactant

at Sor krsurfactant

at Sor Sor Sw Ssurfactant Weight

Relative error

M Ed fraction cm3 s cm3/s darcy fraction fraction fraction fraction g fraction fraction fraction

0.5775 40 19.1 2.0942 3.4482 0.8975 0.4104 0.0286 0.5609 1,306.9 0.9894 0.6276 0.5775

Gas flooding

Δp t Vgas injected Voil produced qg So Sw Sg kg krg psig s cm3 cm3 cm3/s fraction fraction fraction darcy fraction

5.08 30 50 10 2.1 0.8571 0.0703 0.0725 0.8841 0.2363

60 128 15

0.7857 0.0703 0.1440

90 184 21

0.7000 0.0703 0.2297

120 256 24

0.6571 0.0703 0.2725

150 291 26

0.6286 0.0703 0.3011

180 357 27

0.6143 0.0703 0.3154

210 381 27

0.6143 0.0703 0.3154

At residual oil

RF M Ed

fraction fraction fraction

0.3857 2.4962 0.3393

reservoir fluid mechanics lab

Documents

oil droplets

crude oil emulsions

water emulsions

oil phase

wateroil interface

oil type

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