development of a correlation for the estimation of condensate to gas ratio and other key gas...

8/18/2019 Development of a Correlation for the Estimation of Condensate to Gas Ratio and Other Key Gas Properties From …

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SPE 160170

Development of a Correlation for the Estimation of Condensate to GasRatio (CGR) and Other Key Gas Properties From Density/Molecular WeightBirol Dindoruk, Shell International E&P Inc.

Copyright 2012, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 8-10 October 2012.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not beenreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, itsofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohi bited. Permission toreproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Condensate to Gas Ratio (CGR) is a measure of liquid content of a naturally occurring hydrocarbon mixture that is classified

as gas condensate at reservoir conditions. It is also one of the most important parameters that impacts the economics of gas

projects. In many cases, especially in the case of stranded gas, significant project value will be drawn from the liquid content

of the gas. There are number of difficulties in measuring the CGR of a gas stream in the laboratory, or sometimes simply the

value may not be known. Some of the difficulties in lab processes (but not limited to) originate from:

1. Non-equilibrium flash and carry-over2. Amount of the fluid used (volume constraints and errors)

In this paper, we have developed a simple easy to use semi-empirical correlation that accurately estimates the CGR of a gas

condensate system using fluid densities (or molecular weights). Fluid densities can be obtained either from gradient

measurements or directly from the laboratory measurements. To our knowledge, there is no equivalent correlation published

in literature. The proposed correlation can be used for:

a) Exploration support to estimate the CGR ranges (valid up to CGR = 350 STB/MMSCF). b) Form a yard-stick to quality-check laboratory experiments.c) Generate necessary input parameters for other key gas properties: such as Z-factor, gas formation volume factor,

Molecular weight, gas viscosity and even compositions.

d) Reconciliation of contaminated samples against the measured or estimated fluid densities.

Introduction

Condensate to Gas Ratio (CGR) is a measure of liquid content of a naturally occurring hydrocarbon mixture that is classified

as a “generic gas” at reservoir conditions. Here the “generic gas” is used in the context of thermodynamic definition of

hydrocarbon fluid typing. According to this definition, any fluid that is on the right of the (or east of the) critical point is

classified as gas at reservoir conditions (Figure 1). The sub-classes of the gases include:

Dry gases

Wet gases

Condensates (or retrograde condensates)Condensates can also be divided into sub categories based on the observed CGR’s that usually reflect the surface separation

conditions. A sketch of a systems like that is shown in Figure 2 where CGR is defined by the ratio of the residual liquid at

standard conditions to the volume of the total gas evolved during the process at standard conditions. Most of the times the

units are in terms of barrels at standard conditions (STB) per million SCF of the fluid produced (STB/MMSCF). Usually the

condensates are classified based on their liquid content:

Lean if CGR < 50 STB/MMSCF

Medium if 50 < CGR < 125 STB/MMSCF

Rich if 125 < CGR < 250 STB/MMSCF

Very rich or near critical if CGR > 250 STB/MMSCF


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Depending on the inherent compositions,if the CGR > 300 – 350 STB/MMSCF, often phase inversion occurs and

volatile/near-critical oil regime starts. Note that in this manuscript, unless otherwise stated, all CGR values are assumed to be

reflect direct flash process to standard conditions (60 F and 14.696 psia)

Figure 1: Computed phase envelope for a condensate.

Figure 2: A simple two-stage separation process for a condensate. CGR is defined as the ratio of volumes at standard

conditions (CGR = VOIL/(VGAS1 + VGASStockTank )).

Figure 3: Sensitivity of CGR and API to separator conditions for various Single Stage CGR’s. The differences are calculated

based on the two flash conditions: a) The wellstream fluid is assumed to be flashed to directly standard conditions and b) The

wellstream fluid is assumed to go through four stage separation (including the last step to standard conditions).

Tres


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SPE 160170 3

The CGR/richness boundaries cited above make more sense if we were to define a set of reference processing conditions,

otherwise the boundaries have to be changed according to the processing conditions. The processing/separator conditions

often vary from one fluid sample to another (from one PVT report to another one), therefore the CGR as an outcome for the

subject processing conditions will vary. Thus when all the CGR data available in the reports reflect wide spectrum of

separator trains and separator conditions, it becomes a difficult task to come up with screening criteria for the condensate

yield of a given fluid. The more volatile and leaner the fluid, the more the spread of the magnitude of the CGR, reflecting the

conditions of separation (Figure 3). Therefore it is difficult to correlate the readily available CGR data reflecting varyingseparator conditions. In addition, such data will also contain systematic and/or non-systematic experimental errors further

complicating such efforts. However, in many of the PVT reports compositional analysis sheets include CGR or its equivalent

(as GLR) where direct flash process to ambient conditions are the most common. Therefore, among all the data that can be

used to correlate the CGR’s across the board for all the condensates, the CGR values reported along with the compositional

analysis will be the most practical set to utilize for this work. However, there are number of issues that may be intrinsically

associated with such CGR’s. They are namely:

1) Non-equilibrium nature of the flash: for many cases, the flash is performed in one step without an opportunity forthe gas to equilibriate with the associated dropped out liquid. In such cases, the two fluids may not be in true,

mechanical and/or chemical equilibrium. Most of the times, mechanical dis-equilibrium is related to suspended

liquid droplets in the gas phase (mist/fog form of the liquid). Such inefficient separation process will lead to liquid

carryover in the gas phase and has an adverse effect on the condensate volumes recovered (i.e., lower CGRs). In

essence, this phenomenon is equivalent of separator carryover.

2) Flash to ambinent conditions or to a predefined set of pressure and temperatures: Many times, the flash operation todetermine the compositions is performed at ambient laboratory conditions. Basically this translates into ambient

pressure and ambient laboratory conditions. Ambient pressure variations tend to be rather small as compared to the

temperature variations that one may observe at the laboratory. In some of the cases, the flash operation is performed

to ambient pressure and to a predefined temperature. Predefined temperature is often selected to be 60 F (Standard

temperature) or room temperature. Sometimes, that temperature condition may be as high as 120 F.

3) Undefined liquid volume errors: when very volatile and/or lean fluids are flashed due to (1) and (2) and volumetricmeasurement errors, it will be extremely difficult to quantify errors made in terms of CGRs. In many of these cases,

the dead liquid volumes acquired tend to be insufficient to accurately determine the associated density. Therefore, it

will be difficult to quantify the errors (mass balance) due to lack of critical data components.

Although the CGR’s measured in the PVT reports show variability in terms of the items highlighted above, normally they are

only considered as part of compositional measurements rather than a hard statement in terms of the CGRs of the fluid. In

other words, those CGRs mainly serve to determine the overall wellstream compositions. As highlighted in this manuscript,they can also be used as an estimate against the wellstream properties.

Statement of the Problem

The problem that we are trying to solve here is the following: for a given intact overall fluid sample what would be the CGR

for an assumed reference flash condition? For a given fluid, somewhat easily accessible instrinsic fluid property is the fluid

density itself (or the MW if known). Fluid density can be obtained from two separate and yet independent sources: from

gradient measurements, where density is extracted from the Pressure-Depth relationship, or using the fluid samples acquired

from the field (both surface and subsurface samples). Fluid density is defined with the following thermodynamic

relationship:

T R Z

MW P

…………………………………………………………………………………………………….…….(1) Where:

= the fluid density (lb/ft3), 62.42796 g/cc = 1 lb/ft3

P = pressure (psia)

MW= Molecular Weight

Z= Compressibility factor

R= Gas Constant (ft3-psi/lb-mol-oR)T= Temperature (oR)

Equation (1) states that the density is function of pressure, temperature and the overall fluid composition (MW). For a given

depth (or in the laboratory) we always know or have an idea of the pressure and the temperature. Therefore, using Equation

(1), it is possible to decouple MW from the rest of the variables since Z=Z(P pc(MW), T pc(MW)). Then, the next step is to be


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able to figure out the volumetric product ratio out of the calculated MW. However, for the stated problem the solution of

Equation (1) is not unique. Such non-unique behavior is more related to the internal composition of the fluid that is reduced

to an averaged parameter, MW. In other words, it is possible to come up with the same MW using (theoretically) infinite set

of compositions. These compositions in principle will translate into different sets of CGR’s and API’s. However, natural

variations of these compositions are limited to the liquid extraction conditions in the reservoir if we were to consider the gas

as being the solvent and the condensate as being the solute.

For a given set of T and P the only unknown in Equation 1 is MW since Z=Z(T pc(MW), P pc(MW)). Therefore, for a given Pand T set, the MW can be solved by iterative methods. We use Standing (1981) correlation to calculate T pc and P pc values

from the MW (where g = MW/28.97).

Table 1: Pseudocritical property correlations as a function of gas specific gravity.

Z-Factor can be calculated using Hall and Yarborough correlation.

y

t t P Z

pr ))1(2.1exp(06125.0 2

……………………………………………………………..…………….(2)

Where,

t=T pc/T and P pr =P/P pc

y is the root of the nonlinear equation below:

04.422.2427.90

58.476.976.14)1(

06125.0)(

)82.218.2(32

232

3

432)1(2.1 2

t

t

pr

yt t t

yt t t y

y y y yte P y F

………………..(3)

The equation above can be solved for y using Newton-Raphson technique

dy

ydF

y F y y

k

k k k

)(

)(1 …………………………………………………………………………………………...(4)

where

t yt t t t

yt t t y

y y y y

dy

ydF

82.218.132

232

4

432

)4.422.2427.90)(82.218.2(

16.952.1952.29)1(

4441)(

…………………………..………..(5)

Using the relationships in Table 1 in Equation 5, Equation 1 can be solved for MW. The outcome, MW is expected to be the

function of the CGR, the higher the MW, the higher the CGR as is shown in Figure 4. The relevant correlations obtained are

given by Equations 6 and 7.

Fluid Type T pc or P pc Validity Condensate wellfluids (wet gas)

T pc =187+330 w - 71.5 w 2

P pc =706 - 51.7 w - 11.1 w 2

w >=0.75 w >=0.75

Miscellaneousgases (dry gas)

T pc =168+325 w - 12.5 w 2

P pc =677+15 w - 37.5 w 2

w


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SPE 160170 5

Figure 4: Measured single-stage flash CGRs versus measured molecular weights, MW


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the excess, 6-2 = 4 mole % of the non-Hydrocarbons should be taken away from the calculated MW’s. In addition, naturally

occurring intermediate gas components will also give boost to the molecular weight while they have no or small contributions

to the liquid content (they increase the MW but not the CGR) along with the natural deviations of the calculated molecular

weight values from Equation 1 against the measured molecular weight values. Therefore, we propose the following

correction for the calculated MW from Equation 1:

MWcorr = 1.425027 310 MW3-0.1222435 MW2 +4.447774 MW-31.60120 ……………………………..(8)

Now the next step is how to split the corrected MW in Equation 8 to a relevant reference (direct flash to standard conditions)

CGR’s. CGR is a natural outcome of a separation process that intrinsically satisfies a mass balance equation and this is well

covered in the petroleum engineering literature. The most well-known (or classical approach taught in reservoir engineering

classes) overall balance equation is covered by Craft and Hawkins (1959).

o

o s

o g sw

M R

R

132800

4584

………………………………………………………………………………….. (9)

or

owo

g w

M

CGR132800

4584

106

………………………………………………………….………………. (10)

Where the molecular weigh of oil Mo can be calculated using Cragoe correlation

o

oo M

03.1

29.44 ………………………………………………………………..………………………(11)

Substitution of Equation 11 into Equation 10 yields

owo

g wCGR

03.142.29984584

106

…………………………………………………………………(12)

Where

R s= Initial surface GOR, SCF/STB

CGR= Initial surface CGR, STB/MMSCF

o =specific gravity of oil (specific gravity of water = O H 2 = 1)

w =specific gravity of the overall well-stream (specific gravity of air a =1), calculated from MWcorr

g =specific gravity of (separator) gas (specific gravity of air a =1)

o M =Molecular weight of the tank oil (condensate at Standard Conditions)

Strictly speaking the Equations 9 or 10 subject to Equation 11 (Equation 12) do not have a unique solution for R s (or CGR) as

highlighted by Standing (1977 - unless the separator products are defined). Unique solution will require a consistent set of

API and separator gas gravity (how the total wellstream is split into two product streams). However, for correlative purposes

or quick calculations it is possible to come up with sensible solutions as long as MW of the well stream is known, where wealready outlined how it can be obtained using Equation 1.

Based on a data set (included quality checked 185 data points), we obtained an average representative API of 43.18 ( o

=0.81) and the average apparent separator gas gravity of 0.6454 (MW=18.696). Using the default API (43.18) and gas gravity

(0.6454), Equation 12 should be used with the following correction: CGR=(CGR+13.45)/1.2854 leading to

46.10

03.142.29984584

777968

owo

g wCGR

to offset the deviations at high CGR values. Using these values two sets of

CGR equations were obtained from Equation 9, 10 or 12 with correlated adjustments (where the wellstream is split into a

condensate with API=43.18 and gas with a specific gravity of 0.6454):


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SPE 160170 7

2995.196169.305 wCGR ……………………………………………………….…… (13)

Based on the assumed representative averages of the condensates with API=43.18 and gas with a specific gravity of 0.6454,

Equation 9 (10 or 12) forms a good representation of CGR (provided that Crague correlation gives sensible condensate

molecular weights). As may be clear from the average gas gravity, the equation above should not be used for overall well

stream gravities less than 0.6454 (or MW < 18.696). It is also interesting to observe that the CGR can be represented as

simple as a linear function of the wellstream gravity.

A quadratic version of a CGR correlation is also developed:

3052.856806.10177885.82 2 wwCGR …………………………………………. (14).

The outcome of Equation 13 (linear) and Equation 14 (quadratic) is shown in Figure 6.

Figure 6: Cross comparison of calculated versus measured single-stage (to Standard Conditions) flash CGR’s using linear and

quadratic equations.

As can be seen in Figure 6, the differences between the values obtained from Equation 13 and Equation 14 are quite small.

As long as the overall well stream gravity (or MW) is known, Equation 9 (or alternative forms: Equation 10 or 12) can also

be used to split the wellstream into different products besides what was assumed in this manuscript (condensate with

API=43.18 and gas with a specific gravity of 0.6454). Solution of Equation 1 will yield calculated (with corrections using

Equation 8) molecular weights. Those molecular weights can be used to compute the CGR’s using Equations 13 or 14

leading to more scattering in the predicted CGR’s (Figure 7) as compared to using composition based molecular weights

(Figure 6).


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Figure 7: Cross comparison of calculated versus measured single-stage (to Standard Conditions) flash CGR’s using linear and

quadratic equations. MW’s are calculated using Equations 1 and 8.

Solution Procedure

In the following, we will go through a simple algorithm for the solution of the system of equations (Equations 1-14). The

algorithm in brief is as follows:

1) Guess g=0.7, and calculate MWgue= g * 28.97. Calculation of Z-factor requires T pc and P pc of the fluid. UseStanding (1981) correlation to estimate the T pc and P pc given in Table 1.

2) Calculate Z-factor using Equation 2.

3) Recalculate MW using the calculated Z-factor P

T R Z MW calc

. If the initial guess is right, MWgue should be

equal to (or very close) to MWcalc IF |MWgue – MWcalc| > 1E-4, updating g= MWcalc / 28.97, GOTO Step 1. IF

|MWgue – MWcalc| < 1E-4 GOTO the next Step.

4) Calculate the corrected MW (MWcorr ) using Equation 8 and the Z-factor using the corrected MW( RT

MW Z corr

p )

5) Calculate CGR to flash to standard conditions using Equations 13 or 14. If different values of API and product(flash) gas gravity values are assumed, then they need to be plugged into Equation 9. The solution of Equation 9 (or

other forms of it: Equations 10 and 12) for R s or CGR (CGR = 106/R s) will yield a CGR value specific to the

assumed separation conditions that are intrinsic to the assumed set of API and product gas gravity.

Following the steps 1 to 5 above, once the corrected MW (MW corr ), and Z-factor, and CGR known, it is possible to calculatemost of the key gas condensate properties. If the Molecular weight is known (i.e., when the compositional analysis is known,

for example from the laboratory) then the CGR can be calculated directly from Equation 13 and 14.

Sample Calculations

Condensate A:

Limited compositional analysis of a condensate system (Condensate A) performed at a mobile analysis unit is given in Table

2. During the sampling process gradient based density (later confirmed at the laboratory) is determined to be 0.327 g/cc at

reservoir conditions (Z=1.2945).


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SPE 160170 9

Table 2: Compositional Analysis of Condensate System A (Pres = 8000 psia and Tres = 196 F).

In order to calculate the CGR of this system all we need to know is the density of the fluid at some reference Pressure and

Temperature (it does not have to be reservoir pressure and temperature). Based on the algorithm defined earlier, solution ofEquation 1 subject to the correlation set in Table 1 and Equation 8, will yield MW corr =23.276 & Z = 1.2914, being the

molecular weight of wellstream (or w= 0.8035) . This value, w= 0.8035 and as well as the Z-factor, are very close to the

reported values in Table 2 (w= 0.8022, Z=1.2945). Now the second step is to figure out what the CGR would be for that

MW. Using Equation 13 and 14 will yield 48.89 and 49.83 STB/MMSCF, respectively, which is somewhat different than

what is reported in Table 2. One of the reasons behind that departure is that Equations 13 and 14 assume a fixed set of

API=43.18 and g=0.6454 wheres as the split shown in Table 2 indicates different end products with API=44.34 and

g=0.6492. Using calculated w= 0.8035 in combination with the observed product API=44.34 and g=0.6492 in Equation 12,

we will get a CGR of 49.04 STB/MMSCF which is even closer to the measured value. It is clear that as long as we have a

sensible molecular weight, we will be able to get a CGR for a defined gas ( g) and oil properties (API).

Condensate B:

Next system that we consider is a relatively high in CO2 (> 10 mol %) described in Table 3. This time to test ourmethodology, we used the density data (0.2785 g/cc) obtained at the laboratory at P=6550 psia and T=275 F. Again MW and

Z-factor values using Equation 1 and Equation 8 determined to be 24.15 and 1.1543, respectively. The measured values for

those variables were: MW=23.759 and Z= 1.1353, which are remarkably similar to the computed values. Using the calculated

MW, CGR values are determined to be 58.13 and 57.02 STB/MMSCF (using both methods in Equations 13 and 14). Both of

those values are far from the reported value of 19.58 STB/MMSCF. There are two reasons for such differences: 1) calculated

Z-factor values that are intermediary to get the MW’s are not generated using pseudocritical property corrections for non -

hydrocarbons, and 2) The products that are coming out of the flash operation are quite different than the hard-wired values

integrated in Equations 13 and 14. Basically, for all practical purposes, all the CO2 that is leading to higher MW (and thus

excessive CGR) will end up being in the flash gas, not benefiting the CGR, as opposed to most intermediate and heavy

hydrocarbons (C5+) will end up being in the liquid condensate phase. In other words, the elevation of the MW due to non-

hydrocarbons will have to be discounted. This can be achieved using the Equation 12 where larger flash gas gravity, g , will

remediate the issue observed. Therefore, the recalculated CGR using the flash gas gravity and API will be much lower:

CGR= 24.48 STB/MMSCF, which is a lot closer to the observed CGR = 19.58 STB/MMSCF. Bulk of the difference is basically is remediated by using the right product properties. However, many times we may not have such information,

especially if we are limited to gradient based densities. Even in such cases that we have very limited data, we can still use

Equation 12 to explore such elevated non-hydrocarbon concentrations or heavier hydrocarbon gases. Such information,

perhaps notionally, may also be available from Geochemistry and basin modeling and as well as mud gas analysis.


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Table 3: Compositional Analysis of Condensate System B (Pres = 6550 psia and Tres = 275 F).

Condensate C:

The third system that we consider (Condensate C) is a medium rich condensate with significant amount of CO2 and N2 (5.3

%). The compositional information along with the relevant flash data is given in Table 4.

Table 4: Compositional Analysis of Condensate System C (P res = 7500 psia and Tres = 230 F).

For this system, using the reservoir fluid density of 0.4292 g/cc (7500 psia & 230 F), MW and Z-factor values using Equation

1 and Equation 8 are determined to be 34.16 and 1.2921, respectively. The measured values for those variables were:

MW=34.63and Z=1.3093, which are remarkably similar to the computed values. Using the calculated MW, CGR values are

determined to be 163.53 and 149.68 STB/MMSCF (using both methods in Equations 13 and 14). Both of those values are

considerably different from the reported value of 132.29 STB/MMSCF. Similar to the case of condensate B, we have applied

Equation 12 using the measured gas gravity and API. This calculation resulted in CGR of 122.11 STB/MMSCF (again using

the calculated MW of 34.16) which is quite close to the observed value of 132.29 STB/MMSCF.

Condensate D:

The fourth system that we consider (Condensate D) is a very rich/near critical condensate. Compositional information along

with the relevant flash data are given in Table 5.


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SPE 160170 11

Table 5: Compositional Analysis of Condensate System D (Pres = 10000 psia and Tres = 166 F).

For this system, using the reservoir fluid density of 0.5841 g/cc (10000 psia & 166 F), MW and Z-factor values using

Equation 1 and Equation 8 are determined to be 48.75 and 1.9915, respectively. The measured values for those variables

were: MW=50.16 and Z= 2.0485 which are very similar to the computed values. Using the calculated MW, CGR values aredetermined to be 317.3 and 320.2 STB/MMSCF (using both methods in Equations 13 and 14). Both of those values are not

too far from the reported value of 340.7 STB/MMSCF. Similar to the cases of condensates B&C, we have applied Equation

12 using the measured gas gravity and API. This calculation resulted in CGR of 318 STB/MMSCF (again using the

calculated MW of 48.75) which is within 6.5 % of the observed value of 340.72 STB/MMSCF.

Condensate E:

The last system that we consider (Condensate E) is a rich condensate. Compositional information along with the relevant

flash data are given in Table 6.

Table 6: Compositional Analysis of Condensate System E (Pres = 15000 psia and Tres = 200 F).

For this system, using the reservoir fluid density of 0.5473 g/cc (15000 psia & 200 F), MW and Z-factor values using

Equation 1 and Equation 8 are determined to be 37.7 and 2.3395, respectively. The measured values for those variables were:

MW=40.3 and Z= 2.4823 which are close to the computed values. Using the calculated MW, CGR values are determined to

be 201 and 187.4 STB/MMSCF (using both methods in Equations 13 and 14). Both of those values are close to the reported

value of 207.9 STB/MMSCF. Similar to the case of condensates B&C, we have applied Equation 12 using the measured gas

gravity and API. This calculation resulted in CGR of 181 STB/MMSCF (again using the calculated MW of 37.7) which is

still close to the observed value of 207.9 STB/MMSCF.


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From Density to MW, Key Gas Properties, Compositions and Depletion Performance

Once the molecular weight of the fluid is known (or gas gravity), it is possible to calculate the Z-factor (which comes out of

Equation 1 as a by product). Then the gas volume factors will be known from the Z- factor and the CGR’s:

Calculation of Gas Formation Volume Factor

Once the Z-factor is calculated, wet gas Bg is simply:

P

ZT0.02827B wetg, (in ft

3/SCF) …………………………………………………………………………..…….….(14)

The dry gas Bg is related to the wet gas Bg with the following relationship (Whitson, 2000):

CGR BGR wet g eq,eqdryg, V1CV1P

ZT0.02827B

…………………………………………………..…..……(15)

Vapor equivalent of a condensate (Veq), in MMSCF/STB, is defined by Cragoe correlation:

o

oeq

M V

133.0

…………………………………………………………………………………….……………..…(16)

Using the condensate E, Bg,wet=0.002909 ft3/SCF and Bg,dry=0.003295 ft

3/SCF using the CGR obtained from Equation 13 and

Bg,dry =0.003269 ft3/SCF using the CGR obtained from Equation 14.

Gas Viscosity

Gas viscosity can be calculated by various methods. Perhaps the most common one is the one by Lee and Gonzalez (1966),

where all we need is to provide the Z-factor and pressure and temperature of the system:

Y g X K exp101 4 …………………………………………………………………….……………...……..(17)

ZT

pMW 3104935.1 …………………………………………………………………………..……….………(18)

Where the gas density is defined in g/cc

)67.45926.192.209(

)67.459)(01607.0379.9( 5.1

T MW

T MW K

…………………………………….…………………………………..(19)

MW T

X 01009.067.459

4.986448.3

………………………………….…………………………………………(20)

X Y 2224.0447.2 ………………………………………………………………………………………….……(21)

Lee and Gonzalez (1966) correlation is valid for 100< P (psia) < 8000, 100 < T (F) < 340 and 0.90 < CO 2 (mol %) < 3.20. It

performs relatively poorer when the gas gravities are greater than one (heavier than air) with lower gravity condensates.

Dempsey (1965) correlation can also be used for viscosity correlations and valid only in the range 1.2 T pr 3 and 1 P pr

20.

pr pr pr P T f T

pr

w g e

T

T g ,ln,

……………………………………………………………………………..(22)


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SPE 160170 13

31521413123311210982

3

7

2

654

3

3

2

210,ln

pr pr pr pr pr pr pr pr

pr pr pr pr pr pr pr pr pr pr

P a P a P aaT P a P a P aaT

P a P a P aaT P a P a P aa P T f T

……………(23)

and

2282

72

6

2543

2210

67.45967.459

67.45967.45967.459)67.459(,

MW T b MW T b MW b

MW T b MW T b MW bT bT bbT g w

..….(24)

Reduced properties can be obtained using Standing’s correlation presented in Table 1, and the correlation coefficients in

tabular form are given in Table 7.

Table 7: Coefficients for Dempsey’s viscosity correlation.

Coefficient Value Coefficient Value

a0 -2.46211820 b0 1.11231913e-2

a1 2.97054714 b1 1.67726604e-5

a2 -2.86264054e-1 b2 2.11360496e-9

a3 8.05420533e-3 b3 -1.09485050e-4a4 2.80860949 b4 -6.40316395e-8

a5 -3.49803305 b5 -8.99374533e-11

a6 3.60373020e-1 b6 4.57735189e-7

a7 -1.04432413e-2 b7 2.12903390e-10

a8 -7.93385684e-1 b8 3.97732249e-13

a9 1.39643306

a10 -1.49144925e-1

a11 4.41015512e-3

a12 8.39387178e-2

a13 -1.86408848e-1

a14 2.03367881e-2

a15 -6.09579263e-4

Note: the correlation is valid only in the range 1.2 T pr 3 and 1 P pr 20

When extrapolated for dense region (high pressure and/or high very high condensates), Dempsey’s correlation will

underpredict the viscosities. For very rich condensates, gas correlations should be used with care, and perhaps light oil

correlations may be more appropriate.

Dew Point Pressure

Using the estimated CGR, it is possible to compute an effective compositional split that defines the insitu compositions for

various classes of condensates using a set of benchmark gas and condensate compositions.That process is defined in detail in

Appendix A. Using the generated compositions (see Appendix A) and by utilizing any appropriate combinations of the gas

and oil compositions given here (selecting an appropriate set of oil and gas pair, considering the mass recombination rather

than the equilibrium aspects), an EOS model can be generated subject to further calibrations for expected. Dew point pressureis one of the key variables that may be needed to calibrate/constrain the EOS model for the model compositions. Dew point

pressure can be estimated using Nemeth and Kennedy (1967) Correlation, where the dew point pressure is defined by:

113

10

2

98

3

77

2

7675432

1

0001.00001.00001.0

002.0

2.04.02

7

7

7

7

7

7

7

77

7

1

7

215436222

A MW

A MW

A MW

A MW z A

MW z A MW z AT A z

z A A

z z z z z z z z z A LnP

C C C

C

C C

C

C

C

C

C

C

C

C C

C C C C

C

C

C

N C C C C C S H COcdp

…………………... (25)


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14 SPE 160170

Where

zi= mole fraction of component in the wellstream

C7+ = specific gravity of C7+ (to H 2O),

MWC7+ = molecular weight of C7+,

T = Temperature (R )

Pdp = Dew point pressure, psia

Table 8: Coefficients for Nemeth-Kennedy (1967) Correlation.

Coefficient Value

A1 -2.0623054

A2 6.6259728

A3 -4.4670559E-3

A4 1.0448346E-4

A5 0.032673714

A6 -3.6453277E-3

A7 7.4299951E-5

A8 -0.11381195

A9 6.2476497E-4

A10 -1.0716866E-6

A11 10.746622

Another alternative Pdp correlation is developed by ElSharkawy (2002), which is an improved version of Nemeth and

Kennedy (1967) correlation and introduces additional correlation coefficients:

6543

7

21

7

7

7

7

7

777

654321222

1817

716157141371211

10987654321 67.459

C C C C

C

cC

C

C

C C

C

C

C C C C C

C C C C cC N COS H odp

z z z z

z A

z z

z A

MW z A

MW A MW z A A MW A z A

z A z A z A z A z A z A z A z A z AT A A P

C C

……. (26)

Table 9: Coefficients for Elhsharkawy (2002) Correlation.

Coefficient Value Coefficient Value

A1 4268.85 A10 691.5298A2 0.094056 A11 40660.36A3 -7157.87 A12 205.26A4 -4540.58 A13 -7260.32A5 -4663.55 A14 -352.413A6 -1357.56 A15 -114.519

A7 -7776.1 A16 8.133A8 -9967.99 A17 94.916

A9 -4257.1 A18 238.252

Both Nemeth and Kennedy (1967) and Elsharkawy (2002) correlations underpredict dew point pressure of the fluids when

the dew point pressures are higher than 7000-8000 psia range. The underprediction is more severe with Nemeth and Kennedy

correlation. As an example, we have calculated the Pdp of Condensate C. T=230 F was calculated to be 3314 and 3521 psia

using Nemeth and Kennedy and Elsharkawy correlations, respectively (Measured Pdp = 3960 psia).

Once the dew point pressure is known, it is also possible to calculate CGR versus scaled pressure (ratio of current pressure to

dew point pressure, P/Pdp). A special correlation is developed for relative gas gravity (ratio of current gas gravity to initial gas

gravity). This correlation can be used to estimate the changes in initial CGR with respect to pressure. Development of this

correlation assumes constant volume depletion process with invariant API, and given by:


15/18

SPE 160170 15

1097

54

2

167.45967.459

tanh1

67.4591

1

1

86

3

1

1 A

dp

A p

p A

A A

A p

p

wi

w

p

p

API

T CGR A

CGR

T A

CGR API A

API

T CGR A

dp

dp

(27)

Table 10: Correlation coefficients for gas gravity relative to initial gas gravity (P> Pdp).

Coefficient Value

A1 0.000571790

A2 0.280799940

A3 0.001972785

A4 1.817659459

A5 -0.290397062

A6 -1.076899721

A7 -0.848554813

A8 0.001507504

A9 -15.041672464A10 0.498022637

Figure 8: Comparison of calculated versus observed gas gravity ratios,wi

w

, for constant volume depletion process for

two condensate systems (lean and very rich), and calculated wellstream CGR’s as a function of P/Pdp.

Once we know the initial wellstream gravity from the solution of Equation 1 and the gas gravity ratio from Equation 27, it is

possible to calculate the CGR’s using Equation 13 or 14 by varying the w according to the Equation 27. It is possible to

modify this correlation further if the pressure where the maximum liquid dropout occurs is known (a correlation similar to

Cho et al, 1985, correlation) or the minimum value ofwi

w

can be used to estimate the P/Pdp ratio at which the maximum


16/18

16 SPE 160170

liquid drop out occurs (where the derivative ofwi

w

with respect to the P/Pdp is zero). However, for depletion process (i.e.,

constant volume depletion, CVD) where the process is stepsize dependent, estimation of the exact pressure at which the

maximum liquid dropout occurs will be difficult to estimate. In general, it is possible to estimate such a value for a constant

composition expansion process.

Summary and Conclusions

We have developed a simple correlation to calculate CGR values for condensates. The proposed method can be used in

various ways.

1) Using the density measurements (from lab or from the gradient measurements) it is possible to calculate the initialCGR and relative CGR variations during depletion process.

2) During the process of estimating CGR, Z-factor and MW will be the natural outcome of the computations leading toestimation of other key properties, such as gas viscosity, formation volume factor, and even estimated compositions

and then the dew point pressures.

3) If the MW is known (from compositional measurements), it is possible to estimate the CGR quite accurately.4) The non hydrocarbon impurities should be decoupled from the computed MW to be able to estimate the CGR’s

accurately using Equation 12.

5) Using the estimated CGR’s it is possible to do scenario analysis by perturbing the densities or vice versa.

Acknowledgements

The author would like to thank Shell International Exploration and Production Inc. for granting permission to present this

manuscript.

Nomenclature

Bg = Gas Formation Volume Factor (ft3/SCF)

Bg,dry = Dry Gas Formation Volume Factor (ft3/SCF)

Bg,wet = Wet Gas Formation Volume Factor (ft3/SCF)

C7+=Plus fraction

CGR = Condensate to gas ratio (STB/MMSCF)

o M =Molecular weight of the tank oil (condensate at Standard Conditions)

MW = molecular weightMWcorr = corrected molecular weight

MWliq = Molecular weight of liquid

MWC7+ = molecular weight of C7+fraction

P= Pressure (psia)

Pdp= Dew point pressure (psia)

P pc=pseudo-critical pressure (psia)

P pr =pseudo-reduced pressure, P/P pc

R= gas constant

R s= Solution Gas Oil Ratio (SCF/STB)

T= Temperature ( R)

T pc=Pseudo-critical Temperature (R )

T pr =pseudo-reduced temperature, T/T pc

Veq = Vapor equivalent of the condensate (MMSCF/STB)V= Mole fraction of vapor (gas) phase

xi = Mole fraction of component i in liquid (oil) phase

yi = Mole fraction of component i in vapor (gas) phase

zi = Wellstream (feed) composition, overall more fraction of component i (i=1,…, nc )

Z = Z-factor

g = Gas viscosity (cp)

=Density (g/cc)

liq = Liquid density (g/cc)

w =Specific gravity of the overall well-stream (specific gravity of air a =1), calculated from Equation 27 or MW corr

wi =Initial specific gravity of the overall well-stream (specific gravity of air a =1), calculated from MWcorr


17/18


18/18

18 SPE 160170

b) If we have liquid and vapor (oil and gas) compositions (estimates) at standard conditions, we can use the CGR

estimate directly along with the API of the fluid (which can be converted to liq at standard conditions: o=

141.5/(API+131.5)) . If the liquid molecular weight is not known (i.e., C7+ molecular weight), for example, Cragoe

(1929) correlation

o

oo M

03.1

29.44can be used to estimate the MW of the liquid.

An example case using the methodology above is shown in Table A-1. For this system, CGR=123.37 STB/MMSCF,

MWliq=143.6 and liquid density at standard conditions=0.7818 g/cc (API=49.49), mole fraction of vapor is calculated to be

V=0.918, using Equation A-1.

Table A-1: Recombination of flash gas and flash fiquid at CGR=123.37 STB/MMSCF where MW liq=143.6 and liquid density

at standard conditions=0.7818 g/cc (API=49.49).

development of a correlation for the estimation of condensate to gas ratio and other key gas...

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