SPE 124264

Investigation of Formation Connectivity Using Asphaltene Gradient Log Predictions Coupled with Downhole Fluid Analysis Julian Y. Zuo, SPE, Oliver C. Mullins, SPE, Chengli Dong, SPE, Soraya S. Betancourt, SPE, Francois X. Dubost, SPE, Michael O’Keefe, SPE, and Dan Zhang, SPE, Schlumberger

Copyright 2009, Society of Petroleum Engineers This paper was prepared for presentation at the 2009 SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 4–7 October 2009. 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 been reviewed 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, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce 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 Reservoir fluids often demonstrate complicated phase behaviors in a single column as a result of the impacts of gravity,

thermal gradients, biodegradation, active charging, water washing, leaky seals, and so on. Moreover, reservoir

compartmentalization can cause discontinuous distributions of fluid compositions and properties, making the proper

characterization of fluids and reservoirs even more challenging yet compelling. The recognition of flow barriers or

compartmentalization is key to effective and efficient reservoir characterization, production, and management. Downhole

fluid analysis (DFA) is an essential tool for determination of the compositional gradients in real time at reservoir conditions.

However, analysis of flow connectivity in the reservoir by DFA can be complex, especially when the reservoir fluid

compositional gradients are small with depth. In this case, the analyses of bulk fluid properties may not be sufficiently

sensitive. However, DFA of asphaltene gradients provides an excellent method to delineate the complexity of black oil

columns. Moreover, DFA measurements are very sensitive to and often linear in the asphaltene content.

A methodology has been developed to estimate downhole fluid coloration variations with depths using an equation-of-state

(EOS) approach coupled with the DFA tools. The DFA tools are used to determine downhole fluid compositions of CO2, C1,

C2, C3–C5, C6+, and the coloration associated with asphaltene contents. Recent additions to DFA measurements include fluid

density and viscosity. The delumping and characterization procedures proposed by Zuo et al. (2008) are applied to obtain the

detailed compositions including asphaltenes and the parameters of the EOS model. Fluid profile and coloration logs are

computed by “tuning” the molar mass of asphaltene nanoaggregates against the DFA coloration logs. The methodology has

been successfully applied to investigate reservoir connectivity for offshore and laboratory centrifugation cases. The adjusted

molar mass of asphaltene nanoaggregates is determined to be in a range of 3,000–8,000 g/mol for the cases studied, yielding

molecular aggregation numbers of roughly 7 in reservoir fluids, which is in agreement with laboratory studies. The results

obtained in this work demonstrate that the proposed method provides a useful tool to reduce the uncertainties related to

reservoir compartmentalization and to optimize DFA during the logging run. In addition, the results indicate that treating part

of the Cn+ (e.g., C36+) fraction as an asphaltene component (monomer) in the traditional cubic EOS approach is contradicted

by the recent observations that asphaltenes are nanoaggregates in crude oils.

Introduction In the past few decades, fluid homogeneity in a reservoir has often been assumed. There is an increasing awareness that fluids

are really often heterogeneous in the reservoir. Reservoir fluids frequently demonstrate complicated fluid compositions,

properties, and phase behaviors in single oil columns because of a variety of factors including gravity, thermal gradients,

biodegradation, active charging, water washing, leaky seals, and so on. Most of these mechanisms result in nonequilibrium or

nonstationary-state conditions in the reservoir and hence become very difficult to model. There has been a tendency to

believe simple models; however, the reservoirs are unconstrained by these simplistic models. Knowing actual fluid

distributions allows determination of compromises that occur when applying simple models. In addition, reservoir

compartmentalization often leads to discontinuous compositional distributions, at least of one fluid analyte. A density

inversion (higher-density fluids are in the shallower oil column) usually implies a likely sealing barrier. The knowledge of

actual fluid profiles in the reservoir enables identification of corresponding compartments. Consequently, the family of DFA

measurements is expanding in part to enable greater efficacy in reservoir characterization. In addition, identifying continuous

2 SPE 124264

fluid gradients in the reservoir provides a method to suggest connectivity of the reservoir. In particular, since continuous

gradients are generally produced by time-dependent mechanisms, the existence of fluid gradients implies connectivity albeit

with an unknown time scale. Nevertheless, if considerable fluid flow is required to yield such a gradient, this suggestion of

connectivity is much more powerful than that of pressure communication where little fluid flow is required. In particular, if

the asphaltenes are observed to have equilibrated across a reservoir, laterally and vertically, this is a strong connectivity

because 1) asphaltenes necessarily charge into the reservoir in a nonequilibrated state and 2) to equilibrate the component of

crude oil with by far the least mobility necessitates substantial permeability. We note that measurements of fluid gradients are

a far better way to detect connectivity than measurement of homogeneous properties of a fluid. One could easily imagine a

single reservoir charged with a homogeneous fluid where the reservoir subsequently develops a sealing barrier either from

compaction or faulting. Maintaining continuous gradients in evolving separate compartments is much harder to justify. DFA

has been used to measure continuous fluid profiles and stair-step discontinuous fluid properties addressing connectivity and

compartmentalization. Fluid compositional variations are very useful to identify sealing barriers or compartments in

hydrocarbon columns (Fujisawa et al. 2004; Mullins et al. 2005; Dong et al. 2007; Mullins 2008).

DFA measurements provide a useful tool to determine the compositional gradients at downhole conditions in real time.

Recently, Zuo et al. (2009) integrated the EOS-based DFA log predictions with DFA measurements to delineate the

complexity of reservoir fluids and reservoir architecture. This methodology is most suitable for the reservoirs that exhibit

significant compositional grading of at least one chemical analyte. As mentioned by Hoier and Whitson (2001) and Mullins

(2008), for equilibrium fluid distributions, the variations of fluid compositions and properties are usually small with depth if

the reservoir conditions are far away from the critical point and the saturation point (e.g., highly undersaturated black oil).

This especially applies to the alkane distributions (Mullins 2008). For example, a case study showed that in an undersaturated

black oil, the gas/oil ratio (GOR) and compositional gradient were small for large sand bodies in the Gulf of Mexico

(Betancourt 2007; Mullins et al. 2007). Nevertheless, the asphaltene gradient was rather substantial considering the 1,000-m

vertical offset of the tilted sheet reservoir. The flow connectivity in the reservoir might not be identified by the information

on bulk fluids such as compositions, GOR, and density provided by the DFA tools. Fortunately, the DFA tools not only

measure bulk fluid properties such as compositions of C1, C2, C3–C5, C6+, and CO2; GOR; and density; but also coloration,

which is directly associated with asphaltene contents. The asphaltenes are the densest components of crude oils and have the

greatest grading with depth owing to a gravitational force. In the cases shown by Betancourt et al. (2007), Mullins et al.

(2007), and Indo et al. (2009), the detailed DFA and laboratory analyses of asphaltene contents indicated evident asphaltene

grading with depth whereas resin gradients were much smaller than asphaltenes. The asphaltenes are dispersed in crude oils

as nanoaggregates. This information provides us with a new method of determining flow connectivity (or barriers) in the

reservoir by measuring asphaltene contents with depth at downhole conditions, especially when bulk fluid properties and

compositional gradients are not observable.

Continuous and equilibrium asphaltene gradients have been observed in deepwater oil fields (Betancourt et al. 2007; Mullins

et al. 2007; Betancourt et al. 2009). To confirm that the asphaltene gradient is in equilibrium, the colloidal nature of

asphaltenes in crude oil must be established (Mullins et al. 2007). It has been proved that asphaltenes are nanocolloidally

dispersed in a laboratory setting as well as in a field setting. We note that higher aggregation (clusters of nanoaggregates)

might exist in the reservoir for large asphaltene mass fractions or unstable crude oils, or both, but there is a class of black oils

with asphaltenes dispersed as ~2-nm nanoaggregates. This is currently under investigation. With this knowledge, equilibrium

distributions of asphaltenes across a field can be established. Asphaltenes in reservoir crude oils, dispersed as asphaltene

nanoaggregates, have by far the lowest rate of diffusion compared with any crude oil components. Consequently, when they

are in equilibrium throughout a column, considerable fluid flow is indicated, thereby positively constraining connectivity.

Nevertheless, the time frame is still unknown in these novel analyses. Still, the constraint indicates greater connectivity than

simply pressure communication, which requires almost no fluid flow.

DFA tools cannot directly measure asphaltene contents other than the coloration of reservoir fluids, which is directly

associated with the asphaltene contents. Mullins et al. (2007) developed a method to calculate asphaltene gravitation gradient

by combining DFA data with the Boltzmann equation. However, as mentioned by Hirschberg (1988), the Boltzmann

equation is valid only for ideal solutions. The nonideality should be taken into account by either the activity coefficient model

(e.g. a Flory-Huggins type solubility model) or by the EOS.

To our knowledge, until now no one has applied an EOS approach to describe asphaltene gradient in reservoirs, although

there have been many publications in the open literature on modeling asphaltene precipitation using the approach. Following

the traditional cubic EOS approach, which has been widely used for modeling reservoir fluids, Nghiem et al. (1993, 1996)

arbitrarily split the heaviest component (C31+ fraction) in the crude oil into two parts: nonprecipitating and precipitating

components. The precipitating component was considered an asphaltene component. Qin et al. (2000) integrated the model of

Nghiem into their compositional model. They treated asphaltenes as a pure component with the same critical properties as

heavy hydrocarbons, except for the binary interaction parameters. Pedersen and Christensen (2007) treated the aromatic

fraction of C50+ as asphaltene. All these quoted authors assumed that asphaltenes are monomers and are part of the Cn+

SPE 124264 3

fraction (e.g, C31+, C36+) in crude oils, which is contradicted by the recent observations that asphaltenes are nanoaggregates in

crude oils (Betancourt et al. 2007; Mullins et al. 2007; Indo et al. 2009). DFA provides a measure of the relative asphaltene

content, which is excellent for establishing gradients (Mullins 2008). In this work, the EOS approach was employed to

account for the nonideality of oils. A methodology for interpreting DFA results was adapted for estimating downhole

asphaltene variations with depth. The methodology can be integrated into the new workflow (Gisolf et al. 2009; Zuo et al.

2009) as one useful means in analyzing asphaltene coloration gradients.

EOS and Characterization of Asphaltene Component

For simplicity, the Peng-Robinson EOS (Peng and Robinson 1976, 1978) is used to describe phase behavior of reservoir

fluids with the Peneloux et al. (1982) volume shift. The three-parameter EOS is expressed as

bvcbbcvcv

Ta

bv

RTP

2, (1)

where P, T, v, and R are the pressure, the temperature, the molar volume, and the universal gas constant, respectively. The a,

b, and c parameters are the energy, covolume and volume shift of the EOS. The classical van der Waals mixing rules are used

to calculate parameters a, b, and c for a mixture of reservoir fluids.

The EOS calculations require the physical properties (e.g., Tc, Pc, and ) of all the components. The method proposed by Zuo

et al. (2008) is used to delump the group C3–C5 (or C2–C5) and characterize the C6+ fraction. These lumped hydrocarbon

groups are measured by the latest generation of DFA tools and thus represent our starting point for analysis. If the

compositions analyzed by gas chromatography (GC) are available, the characterization procedures of Zuo and Zhang (2000)

are used. The characterization procedure is then extended to characterize asphaltene component in this work.

For simplicity, a new component referred to as asphaltene (the heaviest fraction of crude oils) is added based on the

coloration measured by the DFA tools and the other components that are characterized by the method of Zuo et al. (2000,

2008) are kept unchanged. The asphaltene content of the dead oil is calculated by means of the correlation. To obtain

asphaltene content of the live fluid, the recombination is conducted by the EOS flash approach. Because the asphaltene

component is added, the mass fraction(s) of the heaviest pseudocomponent(s) characterized by the method of Zuo et al.

(2000, 2008) must be subtracted from the mass fraction of the asphaltene component. The molar mass, specific gravity,

critical properties, and acentric factor of the asphaltene component must be specified.

As documented by Indo et al. (2009) and Mullins et al. (2007), asphaltenes are dispersed in crude oils as nanoaggregates ( ~ 4

to 8 monomer-asphaltene molecules). With asphaltene molar mass being ~750 daltons (Groenzin and Mullins 1999), the

corresponding aggregate molar masses are in the range of 3,000 to 6,000 daltons. For example, Akbarzadeh et al. (2005)

studied heavy oils and Alberta bitumen and found the average molar masses of asphaltene aggregates are 4,635 to 10,000

daltons, which from our perspective would correspond to 6 to 13 monomers in a nanoaggregate. The extent of asphaltene

aggregation can be dependent on temperature and concentration as well as on pressure. Nevertheless, there is some

suggestion that the asphaltene nanoaggregates are rather invariant but that the clustering of nanoaggregates is very sensitive

to conditions (Mullins et al. 2007). To preclude improper assumptions, we treat the molar mass of asphaltene aggregates as

an adjustable parameter in this work. The specific gravity of asphaltene is set at 1.2 g/cm3. The critical properties of the

asphaltene aggregate component are discussed later in the article.

Mathematical Formulation of Compositional Gradients

To calculate compositional gradients with depth in a hydrocarbon reservoir, it is usually assumed that all components have

zero mass flux; i.e., a stationary state in the absence of convection (Hoier and Whitson 2001; Zuo et al. 2009). To satisfy the

assumption a balance of driving forces or flux equations is applied. If the chemical potential, gravity, and thermal diffusion

are taken into account, the set of stationary-state equations for a mixture with N components are expressed as

NiTT

FgvMn

n

N

j

Tiiij

nPTj

i

ij

,...,2,1,1

,,

, (2)

where i, ni, vi, Mi, g, , and T are the chemical potential, the mole number, the partial molar volume, the molar mass (or

4 SPE 124264

molar aggregate mass for asphaltenes) of component i, the gravitational acceleration, the density, and the temperature,

respectively. FTi is the thermal diffusion flux of component i.

Because the chemical potential is a function of pressure, temperature, and mole number, it can be expressed as at constant

temperature

N

j

j

nPTj

i

nT

i

Ti nn

PP

ij1

,,,

. (3)

The hydrostatic equilibrium is given by

gP . (4)

According to thermodynamic relations, partial molar volume can be expressed as

nT

ii

Pv

,

. (5)

Therefore, the chemical potential change can be rewritten as

N

j

j

nPTj

iiTi n

ngv

ij1

,,

. (6)

Substituting Eq. 6 into Eq. 2, we finally obtain

NiTT

FgM Ti

iTi ,...,2,1 . (7)

The thermal diffusion flux of component i (FTi) can be calculated by different thermal diffusion models (Haase et al. 1971;

Pedersen and Lindeloff 2003). The chemical potential is calculated by fugacity. The resulting vertical one-dimension

equations are given by

NiT

T

M

H

M

HM

RT

hgMf

i

i

m

mi

ii ,...,2,1,0ln

, (8)

where fi is the fugacity of component i and h is the vertical depth. The compositional grading is then obtained by solving a set

of the nonlinear equations numerically.

Results and Discussions

Case 1—Tahiti Field

The Tahiti field was studied by Betancourt et al. (2007) and Mullins et al. (2007) using the Boltzmann distribution equation.

The reservoir has a 3,000-ft vertical column of undersaturated black oil with GOR in the range of 500 to 650 scf/STB, which

slightly decreases with depth. The formation pressure and temperature at 27,000 ft are 20,000 psia and 200ºF, respectively.

The formation has two main sands: M21A and M21B. The case was used to test the methodology proposed in this work.

The composition (analyzed to C30+) as well as saturate, aromatics, resin, and asphaltene (SARA) analysis data were measured

at different depths in the laboratory. The laboratory-measured compositions were then lumped into the DFA-type five

SPE 124264 5

components/groups (CO2, C1, C2, C3–C5 and C6+, referred to as pseudo-DFA data). The weight percentages of the five

lumped components/groups were the inputs of the EOS model. The SARA analysis and the DFA coloration (optical density,

OD) data were applied to determine the relationship between asphaltene contents in stock-tank oil (STO) and DFA coloration

measured at downhole conditions. The linear relation was obtained by Betancourt et al. (2007): OD = 0.38 wt% + 0.0059.

Based on the compositions of the five lumped components/groups and asphaltene content at a relative depth of 5,100 ft in the

M21B sand (reference DFA station), as well as the delumping and characterization method of Zuo et al. (2008), the pseudo-

DFA data were delumped and characterized to full C30+ compositions. The agreement is good between the deplumed and GC

data. The physical properties and binary interaction parameters were generated; they are required in the EOS calculation.

The predicted phase envelop of this fluid indicates the formation condition is far away from its critical and bubblepoints.

According to the observation of Hoier and Whitson (2001), it is expected that the fluids have slight compositional and

property grading with depth because the fluids are hardly compressible and highly undersaturated. Compositional gradients

with depth were estimated by solving Eq. 8 in terms of the pseudo-DFA data at a relative depth of 5,100 ft. The predicted

formation and bubblepoint pressures are compared with the pretest and laboratory data. The results show that the predicted

formation and bubblepoint pressures agree very well with the measurements.

The predicted compositions are compared with the measurements as shown in Fig. 1. Good agreement is obtained between

the measurements and the predictions.

4,000

5,000

6,000

7,000

0 20 40 60 80 100Composition, wt%

Rela

tive d

epth

, ft

Lab C1

Lab C2-C5

Lab C6+

Cal. C1

Cal. C2-C5

Cal. C6+

Fig. 1—Compositional variation with depth for Tahiti fluids.

The compositional gradients of the reservoir fluids with depth are not obvious. It is difficult to determine whether the fluid is

in equilibrium or in different compartments using the traditional compositional grading method (Zuo et al. 2009) because the

variation of bulk fluid properties (except asphaltenes) is not evident. However, the asphaltene gradient in the column can be

used for determining whether the reservoir is in equilibrium or is disconnected because asphaltenes are the heaviest

components in crude oil and appear in nanoaggregates (<10 monomers). In the equilibrium model, asphaltenes have the

greatest grading in crude oil owing to a gravitational segregation, although other components do not have significant gradient

with depth. Furthermore, asphaltene contents are usually low in crude oil and have little impact on the bulk fluid properties of

GOR, light-end composition, or density. As viscosity soon joins the pantheon of DFA measurements, asphaltene content can

be crosscorrelated to viscosity.

As already mentioned, the EOS calculations require the critical and physical properties of the asphaltene nanoaggregate

component. For simplicity, asphaltenes were treated as others have done, as one pseudocomponent (Nghiem et al. 1993;

Nghiem and Coombe 1996; Pedersen and Christensen 2007), but as nanoaggregates instead of monomers. The critical

temperature, pressure, and acentric factor of the characterized asphaltene component were taken from the properties of an

asphaltene monomer proposed by Sabbagh et al. (2006): Tc = 1,474 K, Pc = 472 kPa, and = 2. A factor f was applied to the

properties of the asphaltene nanoaggregates:

mcmccmc ffPPfTT ;/; . (9)

The f value was arbitrarily set as 1.1 because asphaltenes are nanoaggregates and should be heavier than their monomers. On

the other hand, according to the asphaltene properties and the Peng-Robinson EOS, parameter b in Eq. 1 can be estimated

(covolume b = 0.0778 RTc/Pc). Furthermore, the diameter of the asphaltene aggregates is estimated to be 2 nm for f = 1.1 if it

6 SPE 124264

is presumed that asphaltene aggregates are spherical. This value is in accord with the asphaltene sizes measured by different

techniques (Groenzin and Mullins 1999; Wargadalam et al. 2002; Andrews et al. 2006; Groenzin and Mullins 2007; Freed et

al. 2007).

Based on these asphaltene properties, the molar mass of the asphaltene aggregate component was adjusted to match the

coloration data measured by DFA. The adjusted molar mass of the asphaltene aggregate component is 5,423 daltons

corresponding to ~seven monomers in an asphaltene nanoaggregate. This is in good agreement with the experimental

observations (Freed et al. 2007).

Fig. 2 shows the predicted OD variations and DFA measurements with depth. The results are similar to those obtained by

Betancourt et al. (2007) using the Boltzmann distribution equation. The coloration analyses also indicate that the sands of

M21A (center), M21A North, and M21B are in different compartments. In the paper of Betancourt et al. (2007), detailed

discussions were given with regard to reservoir connectivity and coloration log predictions. The ideas are employed in this

work as well.

3,000

4,000

5,000

6,000

7,000

8,000

0 1 2 3

OD at 1070 nm

Rela

tive d

epth

, ft

EoS (M21A)

EoS (M21A North)

EoS (M21B)

M21A

M21A South

M21A North

M21B

Fig. 2—Optical density variations with depth.

The same fitted molar mass of the asphaltene aggregate component is suitable for the entire reservoir. This means that

asphaltenes have the same average size in nanoaggregates in the oil column. Therefore, the entire field has the same

asphaltene gradient, but the north part of M21A has a much lower asphaltene concentration than the south and centric parts of

M21A. As mentioned by Betancourt et al. (2007), after a careful review of the seismic data, it is plausible that the north part

of M21A is disconnected from the M21A sand (center). The M21B sand is in a different compartment than the M21A sands

as determined by the formation pressure gradient and geochemistry fingerprinting of the crude oil samples; the coloration

analysis is consistent but not conclusive in this assessment, as seen in Fig. 2.

The value that should be applied to f for the calculation was not clear, so a sensitivity analysis was conducted. The

relationship between the fitted molar masses of the asphaltene nanoaggregate component and f values (blue curve) is

illustrated in Fig. 3. If it is assumed that density of the asphaltene nanoaggregates is 1.2 g/cm3 and the asphaltene

nanoaggregates are spherical, the molar volumes and diameters of the asphaltene nanoaggregates can be calculated in terms

of their fitted molar masses. The calculated diameters of the asphaltene component as a function of f values are also shown in

Fig. 3 (pink curve). The greater f value, the higher molar mass, and the bigger diameter of the asphaltene nanoaggregates. If f

= 0.7–1.1, the asphaltene nanoaggregates are 2 to 2.4 nm in diameter. These values are in good agreement with the

asphaltene aggregate sizes measured by different techniques (Groenzin and Mullins 1999; Wargadalam et al. 2002; Andrews

et al. 2006; Freed et al. 2007; Groenzin and Mullins 2007) and by the covolume of the Peng-Robinson EOS (~2 nm). With

the most likely molar mass of the asphaltene monomer being ~750 daltons, the fitted molar masses of 3,000 to 6,000 daltons

means that four to eight monomers form an asphaltene nanoaggregate for f = 0.7–1.1. One can also use more advanced EOS

(such as SAFT EOS) for analysis of this oil column; however, the result is the same: There is little variation in the liquid

phase of the black oil in this oil column, and to match the observed asphaltene gradient, asphaltene nanoaggregates with four

to eight monomer molecules in the nanoaggregate must be presumed.

SPE 124264 7

0

2,000

4,000

6,000

0.6 0.8 1.0 1.2Factor f

Mola

r m

ass,

dalton

1.5

2.0

2.5

3.0

Dia

mete

r, n

m

M ~ f

Diameter ~ f

Fig. 3—Molar mass and diameter of asphaltene versus factor f.

Case 2—Pioneer Field

Recently, Betancourt et al. (2009) reported that black oil in a 658-ft vertical column was analyzed by DFA and advanced

laboratory analytical chemistry methods. The oil samples were taken from two wells with low and similar GORs of ~700

scf/STB; the shallower sample PER-1 is from a depth of xx335 ft, the deeper sample PER-2 is from xx993 ft. The asphaltene

content in STO was analyzed by a standard n-heptane precipitation method. This case was also used to test the methodology

proposed in this work. Similar to the Tahiti field, the compositional and property grading is small according to both the

laboratory measurements and the EOS model. The fluids are highly undersaturated and rather imcompressible; therefore, the

hydrostatic head pressure in the reservoir does little to impact a compositional variation. Instead of the absolute pressure, it is

the relative pressure difference in the 658-ft vertical column of oil that plays an important role in generating gradients. It is

impossible to conclude whether or not the oil column is connected in terms of the traditional compositional grading method.

Again, coupling the asphaltene grading analysis with the other advanced chemical analyses could give a conclusion.

If it is assumed that the reservoir is isothermal, almost the same parameters (molar mass and diameter) of the asphaltene

aggregate component used in the Tahiti case can be applied for this case as well. The EOS coloration analysis shows the

sands in the oil column are connected and the black oils are in equilibrium. The two sands were shown to be in pressure

communication, a necessary but insufficient condition to establish flow communication on production time scales. The two

black oils have similar low GORs, which is consistent with their being in equilibrium. Furthermore, the reservoir sand

properties are consistent with the contained fluids being in equilibrium. The primary reservoir sand has permeability of ~ 1

darcy, which favors convective mixing (much faster than diffusive mixing). These conditions are very similar to those in the

Tahiti reservoir, which also appeared to be in equilibrium. The other advanced chemical analyses gave the same conclusion

as described by Betancourt et al. (2009).

During the work, it was noted that increases in the temperature gradient with depth significantly increased the fitted molar

mass of the asphaltene nanoaggregates. For example, when the temperature gradient is 0.008ºF/ft and f = 1.1, the fitted molar

mass of asphaltene nanoaggregates increases to 7,233 daltons from the 5,423 daltons at isothermal conditions. With a

temperature gradient, variations of oil properties often change with depth. In this case study, for instance, increase of

temperature gradients causes increases of the oil (maltenes) density, molar mass and molar volume and a decrease of the oil

solubility parameters with depth. As a result, the temperature gradients weaken the asphaltene grading. Hence, a bigger molar

mass of asphaltene aggregates is required to compensate the asphaltene distribution in the oil column. On the other hand,

until now it has been very difficult to accurately model the impact of temperature gradients on compositional grading with

depth. Therefore, isothermal conditions are recommended for coloration analysis by the EOS model.

Case 3—Laboratory Centrifugation Data

Centrifugation equipment has successfully generated gradients in light crude oils, resulting in gradients similar to those

observed in reservoirs (Ratulowski et al. 2003). Most recently, Indo et al. (2009) published the experimental data of

8 SPE 124264

gravitationally induced asphaltene grading for a live crude oil by centrifugation under conditions of reservoir temperature

(~100oC) and elevated pressure. This live crude oil has the asphaltene content of ~ 2 wt% and GOR of ~ 900 scf/STB.

Compared to those in the Tahiti and Pioneer reservoirs, this fluid has a higher GOR and API gravity and is, to a certain

extent, compressible (more gas dissolved in oil). The reservoir pressure is not far away from the bubblepoint. Therefore, the

fluids demonstrated a greater GOR and compositional gradients than those in the Tahiti and Pioneer reservoirs because

hydrostatic pressure squeezes the bottom of the fluid column to a higher density. The density gradient creates the

thermodynamic driving force for creating compositional gradients. With finite compressibility yield, a density gradient in a g-

field, the system reacts (per Le Chatelier’s principle) to move low-density (molar mass) components out of the bottom of the

column and into the top.

After successful spin, 13 alliquots were removed (effectively denoting sequentially different heights) for laboratory property

analyses. Asphaltene content was also analyzed along with the resin, aromatic, and saturate fractions. The equivalent depth is

about 850 ft. Strong asphaltene gradients were obtained using the centrifugation experiment. The bulk resin gradient is very

slight, although a tiny fraction of heavy resins shows relatively high gradients (but not as high as asphaltene gradients). This

centrifugation case was applied to test the model proposed in this work as well.

This is an isothermal equilibrium case. The fitted molecular weight of the asphaltene component is 6,500 g/mol with f = 1.1,

which is in the reasonable range that shows asphaltenes are nanoaggregates. The fitted results are illustrated in Fig. 4. The

EOS calculations are in accord with the OD measurements directly related to the asphaltene contents. The results indicate the

proposed model is able to calculate the equilibrium distribution of asphaltenes with depth.

0

200

400

600

800

1,000

0.000 0.002 0.004 0.006 0.008 0.010

Derivative of OD at 1100 nm

Eq

uiv

ale

nt

dep

th,

ft

Lab OD

EoS

Fig. 4—Derivative of OD versus equivalent depth.

To simulate variations of SARA components with depth using the EOS model, the pseudocomponents are grouped in

different molar masses that represent the SARA components in the characterization procedure. The comparisons of the

simulated SARA analysis with the laboratory measurements are shown in Figs. 5 and 6. The corresponding molar masses of

saturate, aromatic, resin, and asphaltene components are 361, 506, 655, and 6,500 g/mol, respectively. It can be seen that with

depth asphaltenes increase significantly, resins increase slightly, saturates decrease slightly, and aromatics almost do not

change. The simulations are in good agreement with the measurements.

SPE 124264 9

0

200

400

600

800

1,000

0 5 10 15 20 25 30

wt% of asphaltene and aromatics

Eq

uiv

ale

nt

dep

th, ft Lab asphaltene

Cal. asphaltene

Lab aromatics

Cal. aromatics

Fig. 5—wt% of asphaltene and aromatics versus equivalent depth.

0

200

400

600

800

1,000

15 25 35 45 55

wt% of resins and saturates

Eq

uiv

ale

nt d

ep

th, ft

Lab resins

Cal. resins

Lab saturates

Cal. saturates

Fig. 6—wt% of resins and saturates versus equivalent depth.

From the case studies presented, one can see that the model proposed in this work describes the equilibrium distributions of

asphaltenes in the reservoir columns. The model can be applied to delineate the complexity of the reservoirs if the

equilibrium distribution of asphaltenes with depth is not followed by comparing the real-time DFA measurements with the

equilibrium asphaltene log predictions (coloration analysis). If a discrepancy occurs, some unknown factors may exist and

more DFA stations are required to uncover the source. This requires the attention of senior technologists, preferably from

both the operating company and the service company, who must be on the job during the crucial time when the DFA tool is

in the well. Thus, the operating company can make a decision in real time to reduce the uncertainties during acquisition.

Conclusions This paper presented a methodology to analyze asphaltene grading with depth using the EOS approach and the DFA tools.

The inputs are the DFA measurements such as CO2, C1, C2, C3–C5, C6+, and the coloration associated with asphaltene

contents. The delumping and characterization procedures proposed by Zuo et al. (2008) were applied to obtain the detailed

compositions including asphaltenes and the parameters of the EOS model. Fluid-profile and coloration logs were computed

10 SPE 124264

by tuning the molar mass of asphaltenes against the DFA coloration logs. The methodology has been successfully applied to

three cases. The results obtained in this work demonstrate that the proposed method provides a useful tool to reduce the

uncertainties related to reservoir compartmentalization and to optimize the DFA logging during acquisition.

In addition, the results show that the treatment of part of the Cn+ fraction as an asphaltene component (monomer) in the

traditional cubic EOS approach is contradicted by the recent observations that asphaltenes are nanoaggregates in crude oils.

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