Modeling Asphaltene Precipitation in Reservoir Simulation - Industrial

2644

Ind. Eng. Chem. Res. 2000, 39, 2644-2654

Modeling Asphaltene Precipitation in Reservoir Simulation Xiangjun Qin, Peng Wang, Kamy Sepehrnoori,* and Gary A. Pope Department of Petroleum Engineering, The University of Texas at Austin, Austin, Texas 78712

Asphaltene precipitation is a serious problem during oil recovery processes. Many models have been developed to predict the precipitation. This paper summarizes these precipitation models and implements the model of Nghiem et al. in The University of Texas Compositional simulator to predict the effects of asphaltene precipitation on fluid flow through porous media. An algorithm is proposed to efficiently couple the precipitation calculation with the fluid-flow computation. A rock-fabric model is introduced to relate the asphaltene precipitation to the changes of permeability and relative permeability. Reservoir simulation results show that consideration of the asphaltene precipitation leads to a different prediction of oil recovery. Introduction and Research Background Asphaltene precipitation is a serious and complex problem in oil recovery and affects all aspects of oil production, processing, and transportation.1 It is very important to predict asphaltene precipitation during the oil production process. Asphaltenes are complex molecules, which are defined as the nonhydrocarbon molecules that are soluble in benzene but insoluble in low-molecular-weight n-alkanes, and can be derived from petroleum oil or shale oil.2 Asphaltenes dissolved in the crude oil are regarded as colloidal by many researchers. They are dispersed in the crude oil because of the resins. Both asphaltenes and resins have a tendency to aggregate with each other to form colloids. When the flocculation of asphaltene colloids reaches the onset point, a deposition of asphaltene occurs in the crude oil. Asphaltene precipitation can have profound effects on oil production during miscible flooding, heavy oil recovery, or even primary depletion. Several studies have shown that asphaltene precipitation in a porous medium leads to changes in some of its properties such as wettability and permeability.3,4 Most of these effects have been recognized as a result of asphaltene adsorption and precipitation on the rock surface. Ali and Islam5 performed a set of experiments of chemical flooding through a limestone core to study the effect of asphaltene adsorption and precipitation in low-permeability carbonate rocks. They found that most asphaltene deposition takes place near the wellbore, for which the continuous plugging process is likely to prevail. Kamath et al.6 conducted a series of dynamic displacement tests in order to evaluate the effect of asphaltene precipitation on waterflooding in both consolidated and unconsolidated sandpacks. They reached the conclusion that asphaltene precipitation has an impact on reservoir rock permeability and end-point saturation. de Pedroza et al.4 studied the presence of asphaltenes in Venezuelan crude oil and verified that the precipitation altered the wetting state of the rock in the direction of an oil-wet state and that the permeability decrease caused by the precipitation is more severe than the porosity decrease. * To whom correspondence should be addressed. Telephone: 512-471-3161. E-mail: [email protected].

They also found that the relative permeability of the oil phase decreases because the rock becomes more oilwet. Because asphaltene precipitation severely reduces both absolute permeability and relative permeability, it is important to simulate the asphaltene precipitation behavior during oil production processes. Many models have been developed to predict the onset point and the amount of asphaltene precipitation. However, they are seldom used in reservoir simulation. In this study, a survey of these models was first conducted; then one of the models was selected and implemented into the UTCOMP (The University of Texas Compositional) simulator to calculate the amount of precipitation during the oil production. Physical models were also implemented to estimate the effect of asphaltene precipitation on porosity and permeability. The primary goal of this study was to simulate the effects of asphaltene precipitation on miscible-gas flooding. Overview of Asphaltene Precipitation Models It has been observed that, in a certain range of pressure and temperature, asphaltene precipitates in a reservoir. As shown in Figure 1, in an isothermal reservoir, when pressure drops and reaches point A, asphaltene begins to precipitate. The amount of precipitation may change with pressure until it reaches point B, where asphaltene disappears. Many thermodynamic and kinetic models have been developed to predict this onset point A and the amount of precipitation. These predicting models can be divided into four groups: solubility, solid, colloidal, and micellization models. Solubility Models. These models are based on the simplified Flory-Huggins theory7 and describe asphaltene stability in terms of reversible solution equilibrium. First, the vapor-liquid equilibrium (VLE) is solved to determine liquid-phase properties; then the liquidpseudoliquid equilibrium (LLE) computation is performed, assuming no influence of the precipitated asphaltene phase on the previously calculated VLE.8 Sometimes a three-phase equilibrium calculation is needed.9 Hirschberg et al.8 proposed a solubility precipitation model based on the Soave equation of state (EOS).10 This is a fully thermodynamic model and is easily

10.1021/ie990781g CCC: $19.00 © 2000 American Chemical Society Published on Web 06/28/2000

Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000 2645

Figure 1. Asphaltene precipitation envelope.

implemented, but the ability of this theoretical approach to reproduce the observed behavior is poor.8 Kawanaka et al.11 and Cimino et al.12 developed a precipitation model on the basis of polymer-solution thermodynamics. It is assumed that, on phase separation, the asphaltene phase nucleates and contains both asphaltene components and solvent. This model is believed to be a good application of polymer-solution theory, so it leads to a good representation of asphaltene phase behavior. However, it needs several groups of experimental data to determine its parameters, and inconsistency among those data would lead to a deviation in the estimation of the parameter. Park and Mansoori13 and later Nor-Azlan and Adewumi14 proposed another model based on the statistical thermodynamics of polymer solutions. The concept of material balance combined with the Flory-Huggins theory of polymer solution was used. First a VLE flash calculation is performed using an EOS to obtain the vapor and liquid fractions and compositions. Then an LLE calculation is conducted using the Flory-Huggins theory to obtain the fraction of asphaltene component by assuming no effect on the previous VLE. The model is simple, but the performance of the model is not very good. It is unable to match experimental precipitation data quantitatively but predicts only the correct trend of the precipitation behavior. Solid Models. These models treat the precipitating asphaltene as a single component residing in the solid phase, while oil and gas phases are modeled with a cubic EOS. Solid models may require many empirical parameters and excessive tuning to match experimental data.15 Nghiem et al.16 proposed their model by considering the precipitated asphaltene as a pure dense phase, while the heaviest component in the oil can be split into two parts: nonprecipitating and precipitating components. The precipitating component is considered to be asphaltene. The amount of asphaltene precipitation can be obtained by equating the fugacities of asphaltene components in the liquid and solid phases. The model is easy to implement, but it needs experimental data to determine one of its parameter, and a three-phase flash calculation may also be necessary.

Chung17 developed his precipitation model by treating asphaltene as a lumped pseudocomponent and the other components as solvents. The asphaltene content of a crude oil is determined by nC5 titration, and then experiments are conducted to measure the solubility parameter of the asphaltene. This is also a simple model because the solubility of asphaltene in crude oil can be computed directly. However, this model does not include the effect of pressure, which is necessary in reservoir simulation. Thermodynamic Colloidal Model. Leontaritis and Mansoori18 proposed a model based on statistical thermodynamics and colloidal science. This model was later completed by Park and Mansoori.19 The assumption is that asphaltenes exist in the oil as solid particles in colloidal suspension, stabilized by resins adsorbed on their surface. The model is based on the following methods: 1. Resin chemical potential and statistical thermodynamics theory of polymer solutions. 2. Resin adsorption and Langmuir isotherm. 3. Electrokinetic phenomena during asphaltene deposition. In this model, a VLE calculation is first performed using an EOS to establish the composition of the liquid phase from which asphaltenes may flocculate. Based on experimental measurements of the onset of precipitation, a critical chemical potential for resins is estimated using the Flory-Huggins polymer-solution theory.7 This critical chemical potential is subsequently used to predict the onset of precipitation at other conditions. The approach is more applicable to situations where there is a dissociation of the asphaltene.16 Thermodynamic Micellization Model.20,21 In this model, the asphaltene molecules are assumed to form a micelle core and the resin molecules adsorb onto the core surface to stabilize the micelle. The principle of the minimization of the Gibbs free energy is used to determine the micelle structure and concentration. This method can be used to compute the size of asphaltene micelles in a crude oil and agrees well with experimental data. Calculated results of the amount of asphaltene precipitation have not been presented. Precipitation Model for UTCOMP Description of UTCOMP. UTCOMP is a threedimensional, compositional simulator used for reservoir simulation.22 An EOS is used to describe the phase behavior of the hydrocarbon mixtures. A third-order method is used for its effectiveness in reducing numerical dispersion and the grid-orientation effect. The simulator can be used to study the effects of physical dispersion, gravity, and reservoir heterogeneity for reservoir simulation. A typical reservoir simulation in UTCOMP takes the following steps:22 (1) Initialize the reservoir condition. (2) Compute the required derivatives and coefficients for the pressure equation using information from the previous time step. (3) Solve for the gridblock pressure implicitly. (4) Update the block porosity at the new pressure. (5) Solve the mass-balance equation to obtain the number of moles in each gridblock for each component using the new pressure. (6) Perform the flash calculation in each gridblock to obtain the equilibrium phase compositions.

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Ind. Eng. Chem. Res., Vol. 39, No. 8, 2000

(7) Compute the aqueous and hydrocarbon phase saturations. (8) Calculate the required physical properties. (9) Go to step 1 for the next time step. To implement an asphaltene precipitation model into UTCOMP, a new flash algorithm is needed to determine the amount of asphaltene precipitation. In addition, a relative permeability model is used to represent the effect of asphaltene precipitation on oil production. Selection of a Precipitation Model. Because the primary goal of this study is to simulate the effect of precipitation on reservoir flow behavior and also because it is desirable to minimize the computational effort for the calculation of the amount of precipitation when using the UTCOMP simulator, a simple predictive method was preferred. Among the introduced models, we selected the precipitation model of Nghiem et al.16 for the UTCOMP simulator. This model treats the precipitated asphaltene as a pure dense phase and assumes that the heaviest component in oil can be split into two parts: nonprecipitating and precipitating components. The precipitating component is considered to be asphaltene. The fugacity of asphaltene in the solid phase is given by

ln fa ) ln f*a +

va(P - P*) RT

(1)

where va is the mole volume of asphaltene. In a mixture of nc components, when the vapor, liquid, and asphaltene phases coexist, the following thermodynamic equilibrium equations are satisfied:

ln fiv ) ln fil

for i ) 1, ..., nc - 1

ln fncv ) ln fnc1 ) ln fa

(2)

(6)

ln fnc1 ) ln fa

(7)

and

(4)

Whenever a solid phase exists, the amount of asphaltene precipitation can be obtained by the following equilibrium condition:

fnc1 ) fa

ln fncv ) ln fnc1

(3)

In this calculation, the asphaltene component in the liquid phase is considered to be the ncth component. A three-phase flash algorithm is used to solve eqs 2 and 3, and the fugacities for components in oil and gas are computed using an EOS. The existence of a solid phase satisfies the following criterion:

ln fnc1 g ln fa

many equations had to be reformulated in the simulator, including the mass-conservation equations and the pressure equation. Also implemented in the simulator were some physical-property models to compute the changes in porosity and permeability because of the deposition. This section is a summary of how these models were selected and implemented for UTCOMP. Basic Assumptions. Because the precipitation model of Nghiem et al.16 is adopted for the simulator, the basic assumptions proposed in the model are followed. To simulate its effects on oil production, other assumptions are made. These include the following: (1) Asphaltene can be treated as a pure component. (2) Asphaltene is a part of the heaviest component in the oil. It has physical properties identical with those of the heaviest hydrocarbon component except for the binary interaction coefficients used in the EOS. (3) The precipitated asphaltene solid is immobile unless it is redissolved in the oil. (4) Asphaltene is considered as part of the rock. (5) The precipitated solid affects both the permeability and the relative permeability, and its effects on wettability account for the change in the relative permeability. Asphaltene Precipitation Model. Originally, Nghiem et al. introduced a multiphase flash algorithm to obtain the amount of precipitated solid and the fluidphase compositions at equilibrium. To simplify this algorithm and save computational time, a pseudomultiphase calculation is performed instead of an actual multiphase algorithm. The equilibrium condition as shown in eq 3 is decoupled into two equations:

Equations 2 and 5 are satisfied using a phaseequilibrium algorithm with an equation of state. Equation 6 is satisfied by tuning the amount of asphaltene precipitation. The flowchart for the algorithm is shown in Figure 2. The most important step in the algorithm is to make a guess for the amount of precipitation. If asphaltene exists at the previous time step, then the previous value is used as the initial guess. However, if asphaltene begins to precipitate in the current time step, then the following equation is used to make the guess:

χa )

(5)

Compared to other models we have studied, this model is implemented into UTCOMP more simply. The only parameter that should be obtained from the experiment is P* in eq 1, which can be estimated by extrapolating the experimental data, because it is just the onset pressure of asphaltene precipitation. Moreover, the prediction results of this model are quite reasonable compared to experimental data. Implementation of Models After the precipitation model had been selected, the next step was to implement the model into the simulator. With the introduction of asphaltene precipitation,

fnc1 - fa fnc1

(8)

where χa is the mole fraction of the heaviest component that would precipitate from the crude oil. The secant method is applied to determine a new value of χa from the previous information:

) χka χk+1 a

(fka - fnk c1)(χka - χk-1 a ) (fka - fnk c1) - (fk-1 - fnk-1 ) a c1

(9)

where the superscript k is the iteration index. With the introduction of asphaltene precipitation, the mass-conservation equation for the heaviest component in UTCOMP becomes


Porosity and Permeability. The effect of asphaltene precipitation on rock properties is represented by the porosity and permeability changes. Because asphaltenes precipitate as solid grains and are adsorbed to the rock surface, they plug the formation pores and become immobile in the reservoir. In this respect, they are considered as “newly created rock” in the reservoir, and the change in porosity from asphaltene precipitation can be expressed as

(

φa ) φ* 1 -

Va

)

φ *V b

(13)

where φ* is the porosity without asphaltene precipitation. The precipitated asphaltene can decrease rock permeability, but it is difficult to theoretically derive the relationship between the change in permeability and the precipitation. However, with the assumptions that asphaltene can be treated as part of the rock and that only the change in permeability introduced by the change in porosity is considered, a power-law model can then be applied to compute the effect of asphaltene precipitation on permeability. The power-law model can be expressed as Figure 2. Flowchart for the asphaltene precipitation calculation.

∂Wnc

∂Wa +∇ B ‚F Bnc - Rnc )0 ∂t ∂t

(10)

where Wa is the amount of asphaltene precipitation in moles. The mass-conservation equations for all other components remains unchanged. Besides the flash calculation, another key step in the simulator is to establish and solve the pressure equation. With the introduction of asphaltene precipitation, a new premise should be made to derive the pressure equation: the pore volume is filled with the total fluid volume in addition to a precipitated asphaltene solid volume, which can be described as

B ) + Va(P,N B) Vp(P) ) Vt(P,N

(11)

where Va is the precipitated asphaltene volume, which is affected by both the pressure and the number of moles of each component. Differentiating both sides with respect to time and using the chain rule gives the following pressure equation:

{ ( ) [ ( ( ))]( )}( ) ∑( ∑ ( )) V0pcf -

∂Vt ∂P

- 1 + ξa V h ti +

nc+1

V h ti +

i)1

∂Va ∂P

∂Va

∂Va

∂P

∂P

∂P

∂t

)

np

{qi - Vb∇ B ‚(

(ξjxijb uj -

j)1

B φξjSjK B ij∇xij))} (12)

This pressure equation introduces two important partial derivatives related to asphaltene precipitation: the derivative of precipitated asphaltene volume with respect to the total moles of component i and the derivative of precipitated asphaltene volume with respect to reservoir pressure. These two derivatives can be obtained from the equilibrium conditions listed in eqs 2 and 3. Other derivatives in eq 12 can be computed using an EOS.

k ) aφb

(14)

where a and b are constants. Thus, the change in permeability can be computed by

∆k ∆φ b )1- 1k φ

(

)

(15)

where ∆φ is the porosity change from asphaltene precipitation and is equal to φ* - φ. The best-fit value of the exponent b for sandstone is around 5.23 Many researchers concluded from their experiments that rock permeability is more significantly affected by the precipitation process than is rock porosity;4,24 nevertheless, no relationship between precipitation and permeability was developed from these experiments. Hence, it would be desirable to develop new permeability models in order to obtain a better prediction of the effect of asphaltene precipitation on permeability. Relative Permeability Model. To simulate the effect of precipitation on fluid flow in the reservoir, it is also necessary to compute the phase-relative-permeability change. The first reason is that, with the plug of asphaltene in the pore space, the pore flow channels become smaller and more difficult for fluid to flow through. The second reason is that the precipitated solid adsorbed on the rock surface changes the wettability of the rock from a water-wet state to an oil-wet state,4 which results in a decrease in the oil relative permeability. However, no report was found to mathematically relate the asphaltene precipitation to wettability and relative permeability. In this study, the idea of a resistance factor is introduced and a relative permeability model proposed by Ngheim et al.23 is used to compute the change in relative permeability resulting from asphaltene precipitation. Relative permeability with asphaltene precipitation is given by

kr )

kr0 kr0 ) Rf0 1 + RWa

(16)

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Table 1. Constants a and b in a Power-Law Model for Different Rock-Fabric Classifications25 classification

constant a

constant b

1 2 3

45.35 × 1.595 × 105 2.884 × 103

8.537 5.184 4.275

108

where kr0 is the original relative permeability without considering asphaltene precipitation, Rf0 is the resistance factor, and R is an adjustable parameter. The key point here is to estimate R from the given information. Rock-Fabric Classification for Permeability. In the previous section, both permeability and relative permeability models were introduced. In this section, we will introduce a method to estimate the parameters b in eq 15 and R in eq 16 using the rock-fabric classification model.25,26 Rock-fabric classification is a model that relates grain size, pore space, and pore structure to its permeability field. In this model, the permeability fields are divided into three classes, which are referred to as rock-fabric petrophysical classes 1-3. Class 1 fields have large pore size and are well-sorted in grain size, and therefore their permeabilities increase sharply with an increase of porosity. Class 2 fields have medium pore size and are fairly grain-sorted with medium grains. Class 3 permeability fields have small pore size and poor sorting. The permeabilities of these rocks increase slowly with an increase of porosity. In a carbonate reservoir, the relationship between permeability and porosity can also be described with a power-law model as shown in eq 14. However, the constants a and b are different for different permeability fields, as shown in Table 1. Most likely, there is a continuum of rock-fabric classification rather than the three integer rock-fabric fields described above. This means that a rock fabric with a given permeability and porosity can be classified as any continuous value of class, and different values of constants a and b are assigned to all of those continuous classifications. The rock-fabric classification can be determined from the permeability and porosity data required for a reservoir simulation. A continuous rock-fabric designation is used, and the classification number for a rock with given permeability and porosity is obtained by

Crf ) 2 +

ln(k0/a1φ0b1) b2

b1

ln(a2φ0 /a1φ0 )

when k0 e a2φ0b2 (17)

or

Crf ) 1 +

ln(k0/a2φ0b2) ln(a3φ0b3/a2φ0b2)

when k0 > a2φ0b2 (18)

where k0 and φ0 are the original permeability and porosity for a given reservoir, and subscripts 1-3 for constants a and b refer to classifications 1-3, respectively. By assuming that pressure change and asphaltene precipitation have no impact on rock-fabric classification, the permeability under asphaltene precipitation is given by

ln ka ) ln(a1φab1) + (Crf - 1) ln(a2φab2/a1φab1) when Crf e 2 (19)

or

ln ka ) ln(a2φab2) + (Crf - 2) ln(a3φab3/a2φab2) when Crf > 2 (20) where φa is the porosity with the effect of asphaltene precipitation, which can be computed from eq 13. Smaller pore structure has a higher comparative surface area, which leads to a much stronger adsorption of asphaltene on the rock surface. Because the wettability is greatly affected by the adsorbed asphaltene, it is reasonable to conclude that the relative permeability in such rocks is more sensitive to asphaltene precipitation. From this point, a rock with a higher classification number and a smaller pore space is more likely to be plugged by the precipitated solid. Therefore, the mobility of each phase in such rocks is more sensitive to the asphaltene precipitation, and their relative permeability changes more markedly compared to rocks with lower classification number and larger pores. Equation 16 is still used to calculate the relative permeability change, and the resistance factor Rf0 is estimated by

Rf0 ) 1 + 10Crf

( ) Wa

W*a

(21)

where W/a is the amount of asphaltene in moles per unit pore volume when all of the asphaltene component precipitates as a solid. However, the effect of asphaltene precipitation on each phase may be different. More likely, the relative permeability of the oil phase is much more sensitive to the asphaltene precipitation than those of the water and gas phases. Thus, a different resistance factor may be given to each phase. Efficient Algorithm To Improve the Calculation Performance As discussed before, a pseudo-multiphase calculation algorithm is used for the phase-equilibrium calculation to obtain the amount of asphaltene precipitation. It is reasonable to make such a simplification, because the solid phase contains only one component and its fugacity can be simply computed with eq 1. Compared to the multiphase algorithm, this algorithm saves much computational time, but the results are still accurate because eq 3 is also satisfied. However, when compared with the process without asphaltene precipitation, much more time is needed. This approach might repeat the flash calculation several times in each time step to obtain the amount of asphaltene precipitation, while a simulation without the asphaltene precipitation model calls the phase flash algorithm only once in each time step. Phase flash calculation consumes the majority of the computational time for most compositional reservoir simulations. Thus, the computational time for the algorithm with asphaltene precipitation could be several times more than that without asphaltene precipitation. This is a serious problem in reservoir simulation when a large number of gridblocks and/or components are necessary. To save computational time, we have derived a more efficient algorithm to explicitly obtain the amount of asphaltene precipitation with a single flash calculation in each time step. The equilibrium condition for asphaltene precipitation is decoupled from the flash


calculation; that is, eq 3 is satisfied explicitly with the results from the previous time step. Suppose at time step k that the phase-equilibrium conditions are satisfied, which gives

fnk c1 ) fka

(22)

Applying a first-order finite-difference method in time step k + 1 gives

fnk+1 ) fnk c1 + ∆fnk c1 ) fk+1 ) fka + ∆fka a c1

(23)

∆fnk c1 ) ∆fka

(24)

Hence,

Assuming that the molar volume of asphaltene remains constant, the differential term for the asphaltene fugacity can be derived from eq 1 as

( )

va dfka ∆Pk ∆Pk ) dP RT

∆fka )

(25)

The left side of eq 25 is given by

∆fnk c1 ) nc

∑ m)1

( ) ∂ ln fnc1 ∂nml

k k ∆nml

P,nil(i*m)

+

( ) ∂ ln fnc1 ∂P

k

∆Pk (26)

nil

Substituting eqs 25 and 26 into eq 24 and reformulating give an expression for the difference in moles of component nc in the oil within time step k:

∆nnk*c1

)

{[ ( ) ] va

-

∂ ln fnc1

k

∂P

nil

RT

nc-1

∑

m)1

( ) ∂ ln fnc1 ∂nml

component

mol %

nitrogen CO2 methane ethane propane isobutane n-butane isopentane n-pentane hexanes heptanes plus total C7+ molecular weight C7+ specific gravity live-oil molecular weight API gravity, stock-tank oil reservoir temperature saturation pressure (psia)

0.57 2.46 36.37 3.47 4.05 0.59 1.34 0.74 0.83 1.62 47.96 100 329 0.9594 171.4 19 212 2950

Table 3. Static Precipitation Results27 test pressure (psia)

precipitates from live oil (wt %)

precipitates remaining in residual stock-tank oil (wt %)

1014.7 2014.7 3034.7 4014.7

0.403 1.037 0.742 0.402

15.73 14.98 15.06 14.86

Table 4. Oil Composition Used in Simulations component

mol %

mol wt

CO2 C1-C2 C3-C5 C6-C19 C20-C30 C31+ asphaltene

2.46 40.41 7.55 27.19 10.64 11.75 4.01

44.01 17.42 53.52 164.22 340.93 665.62 665.62

∆Pk -

k

k ∆nml

P,nil(i*m)

}/( ) ∂ ln fnc1 ∂nml

k

(27)

P,nil(i*m)

∆nnk*c1 are the moles of the ncth component that tend to flow away from the liquid within the gridblock, including that “flowing into” precipitated asphaltene. Equating the fugacity of the precipitated asphaltene to the fugacity of the ncth component in the vapor phase gives a similar expression for ∆nnk*cv, the change of the mole number of component nc in time step k for the vapor phase. In the simulation step 5 introduced before, we also obtain two mole changes, ∆nnk c1 and ∆nnk cv, for both liquid and vapor phases. They are computed from the flow equations in the simulator without considering the equilibrium condition for asphaltene. The difference between these two sets of values represents the number of moles of the ncth component flowing into precipitated asphaltene. Therefore, the change in asphaltene precipitation in moles within time step k can be expressed as np

∆nka )

Table 2. Oil Sample Data27

(∆nnk*j - ∆nnk j) ∑ j)1 c

c

(28)

where j is the phase index in which the water phase is not counted. In eq 27, the partial derivatives of fugacity with respect to pressure and moles for a component are

computed in the solution of the pressure equation. The change in the phase mole number of a component in time step k is calculated from the flow equation, and the change in pressure is given by the pressure equation in time step k. All of these terms are used directly in eq 27 without recalculating. Hence, eq 28 gives a direct way to compute asphaltene precipitation without coupling it with the phase-equilibrium calculation. Reservoir Simulation with Asphaltene Precipitation This section is a summary of the simulations that have been made to test the asphaltene precipitation model in UTCOMP. Simulation Input. The oil sample was from Burke et al.,27 as shown in Table 2. They performed a set of experiments to measure asphaltene precipitation both in live oil and at stock-tank conditions. The experimental results are shown in Table 3. The sum of the parts of precipitation is considered as the total asphaltene in the oil. In this work, the C7+ fraction of the oil is first split into six pseudocomponents from C7 to C31+, and then C31+ is further split into a nonprecipitating component, C31A+, and a precipitating component, C31B+, which is considered to be asphaltene and has the same physical properties as C31A+, except for binary interaction coefficients. Then the 13 components are lumped into seven, as shown in Table 4, which lists the compositions used in the simulations. The two heaviest components have

2650


Table 5. Binary Interaction Coefficients Used in PR EOS CO2 CO2 C1-2 C3-5 C6-19 C20-30 C31+ asph.

0.000 0.000 0.007 0.038 0.065 0.095 0.220

C1-2 C3-5 C6-19 C20-30 C31+ asph.

Table 6. Simulation Input and Results for Different Reservoir Conditions oil recovery (%)

0.000 0.006 0.035 0.062 0.091 0.220

0.000 0.013 0.032 0.055 0.220

0.000 0.005 0.016 0.000

0.000 0.004 0.000

0.000 0.000 0.000

Figure 3. Comparison of simulation results and experimental data for precipitation.

identical physical properties but different binary interaction coefficients with other components. The binary interaction coefficients used in the simulations are listed in Table 5. The binary interaction coefficients between any two components up to C31A+ are computed by

dik ) 1 -

(

2vci1/6vck1/6

vci1/6 + vck1/6

)

e

(29)

where vci is the molar volume of component i and the exponent e can be obtained by matching the saturation pressure.28 The binary interaction coefficients between asphaltene and the three light components are set at 0.22 and at zero for the heavier components.16 Another key input for the simulations is the reference pressure, P*, used in eq 1 for asphaltene precipitation. This is the onset point of asphaltene precipitation and can be obtained from experimental data. From the experimental data shown in Table 3, P* is obtained by extrapolating the experimental pressure to where the precipitation amount in live oil is zero. For the given oil sample, P* is 5173 psia. The reference fugacity of asphaltene, fa*, is determined by equating the fugacity of precipitated asphaltene to the fugacity of the asphaltene component in the crude oil at the reference pressure. Figure 3 shows the comparison of the computational results of the asphaltene precipitation model implemented in UTCOMP with experimental data. Compared to most of the prediction models, this model predicts the precipitation more reasonably. Results. We simulated three different cases to investigate the effect of asphaltene precipitation on oil production for different rock fabrics. The size of the reservoir is 560 × 560 × 100 ft3, which is divided into a 7 × 7 × 3 grid system for simulation. The dimensions for grids are 80 ft constant in the x and y directions and

case

k (md)

φ

class

proc. 1

proc. 2

1

800

0.25

1.69

24.9

27

2

200

0.25

1.94

28.6

25.8

3

300 50 200

0.25 0.25 0.25

1.84 2.36 1.94

27.1

23.3

prod. diff. (%) oil

gas

8.4

-6.7

-9.8

-3.9

-14

-9.8

Figure 4. Comparison of cumulative oil production for case 1.

20, 30, and 50 ft from the top in the z direction. There are two wells existing in the opposite corners of the reservoir, one for production and one for injection. The production process is 1-year primary depletion followed by 3-year waterflooding. Water injection is used instead of gas injection to simplify the calculation and comparisons. To investigate the effects of asphaltene precipitation on oil production, the production well is set to constant bottomhole pressure at 1500 psia. Water was injected from the beginning of the second year at a constant rate of 300 STB/day. The reservoir pressure is initially at 5200 psia, where no asphaltene precipitates. Porosity and permeability vary with different cases, as is shown in Table 6. Results are plotted to compare the cumulative oil production, gas production, and average pressure for each case. In the following, we call the production process without the precipitation model “process 1” and that with the precipitation model “process 2”. Test Case 1. The permeability is 800 millidarcies (md) and the porosity is 0.25. The classification of this rock is class 1.69. The results are shown in Figures 4-6. Figure 4 shows the comparison of the cumulative oil production for both processes. Process 1 produces more oil in the first 1.5 years, but thereafter its production increases much more slowly, and at the end of the simulation, it has produced less oil than did process 2. Figure 6 shows that the average pressure drops faster in process 1. Because the saturation pressure for the sample oil is around 2800 psia, in process 1, more gas evolves from the crude oil and is produced at the surface, as shown in Figure 5, which decreases the oil production. Moreover, a lower average reservoir pressure decreases the driving force for the oil mobility, which also leads to a lower oil production. As a result, asphaltene precipitation in such a high-permeability reservoir prevents the pressure from dropping too fast


Figure 5. Comparison of cumulative gas production for case 1.

Figure 6. Comparison of average reservoir pressure for case 1.


and therefore helps oil production. The oil recovery in process 1 is 24.9%, and it is 27.0% in process 2. Test Case 2. Next consider a lower permeability (200 md) reservoir while keeping other parameters the same as in case 1. The reservoir rock has a classification number of 1.94, higher than that in case 1. Figures 7-10 are the results for this case. As shown in Figures 7 and


Figure 9. Comparison of average reservoir pressure for case 2.

Figure 10. Comparison of asphaltene precipitation in an injection grid for case 2.

8, the cumulative oil production in process 2 is less than that in process 1 during the whole production period, while the cumulative gas production in process 1 is also less than that in process 2, although they get closer in the end. The oil productions for both processes 1 and 2 are close to that in case 1, while the gas productions

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Figure 13. Comparison of average reservoir pressure for case 3. Table 7. Simulation Performance for a Precipitation Model in UTCOMP case 2


are much lower, because the average pressure is much higher in case 2, as shown in Figure 9. The average pressure in process 2 increases markedly after water injection begins. In this low-permeability reservoir, the pore size is small and the pore space is easily plugged by precipitated solid, so water is difficult to move along and the residence of the water in the reservoir increases the pressure. In this case, oil recovery in process 1 is 9.8% less than that in process 2, while gas production is only 3.92% lower. Test Case 3. In this case, we investigate the effect of asphaltene precipitation on the reservoir with layered permeability. The reservoir has three layers, with thicknesses of 20, 30, and 50 ft, and permeabilities of 300, 50, and 200 md, respectively. The porosity of the reservoir remains at 0.25; then the classifications of the three layers are 1.86, 2.36, and 1.94, respectively. The volume-average permeability in this reservoir is a little lower than that in case 2, while the average classification is a little higher. Asphaltene precipitation has similar effects on cumulative oil production, cumulative gas production, and average pressure as in case 2 but is more pronounced, as shown in Figures 11-13. The oil production in process 2 is 14.0% lower than that in process 1, together with a 9.8% lower gas production. These results imply that layered permeability zones may be more easily affected by asphaltene precipitation.

precip. model

Ttotal (s)

Tphase (s)

Tave (s)

total time steps

no old new

291 709 361

209 630 284

0.374 1.394 0.639

559 452 445

They also imply that a higher degree of rock-fabric classification is more sensitive to asphaltene precipitation. Table 6 gives a summary of the permeability field, oil recovery difference, and gas production difference between processes 1 and 2 for these three cases. Simulator Performance. As discussed before, an efficient algorithm was implemented to compute the equilibrium phase behavior of asphaltene precipitation. Test results of the efficient algorithm compared with the old pseudo-multiphase flash algorithm are presented in this section. Case 2 is executed again under the same conditions, using the efficient precipitation algorithm to compute asphaltene precipitation. Figures 7, 9, and 10 also contain the results for the efficient algorithm. As for the oil production and average reservoir pressure, the efficient algorithm well reproduces the predictions using the old algorithm. Figure 10 also indicates that the new algorithm predicts asphaltene precipitation very well compared to the multiphase flash algorithm. Table 7 gives a summary of the CPU time for the simulations without precipitation, with precipitation using the old algorithm, and with precipitation using the efficient algorithm. The three CPU times are the total CPU time, Ttotal, the CPU time for phase flash, Tphase, and the average CPU time in each time step, Tave. Ttotal is the standard for our comparison. In this case, compared to the 291 s total CPU time for the simulation without a precipitation model, the old pseudo-multiphase algorithm consumes 140% more time, while the new efficient algorithm costs only 24% more. In summary, simulations using the new efficient algorithm give excellent agreement with those using the old algorithm, while saving a lot of computational time. Summary and Conclusions The following conclusions can be obtained from this study:


(1) The asphaltene precipitation model of Ngheim et al. is easy to implement and gives reasonable results in matching the experimental data. (2) Dynamic asphaltene precipitation introduced into oil recovery prediction leads to results different from simulation results without the precipitation. (3) The combined permeability model with rock-fabric classification can be used to simultaneously predict the effect of asphaltene precipitation on both absolute and relative permeability. (4) A high degree of rock-fabric classification, which corresponds to small pore size and poor sorting, implies that the rock is more easily plugged by the precipitated solid. The oil production processes in such rocks are more sensitive to asphaltene precipitation. (5) Asphaltene precipitation may help a production process when a high-permeability zone is encountered, because it prevents the pressure from dropping too fast. (6) Asphaltene precipitation shows much stronger effects in a layered permeability reservoir than in a homogeneous reservoir with the same average permeability. (7) The simplified algorithm for asphaltene precipitation gives simulation results in agreement with simulations using the pseudo-multiphase algorithm and saves significant computational time. (8) Waterflooding is used in the simulation to simplify the calculation and comparisons. Because UTCOMP is a compositional simulator, the implemented model is also applicable to miscible-gas flooding processes. Nomenclature a ) constant in permeability model b ) constant in permeability model Crf ) rock-fabric classification number F Bi ) flux term of component i in conservation equation fa ) fugacity of asphaltene in the solid phase k ) permeability kr ) relative permeability P ) pressure P* ) reference pressure R ) gas constant Rf ) resistance factor Ri ) source term of component i in conservation equation T ) temperature Va ) mole volume of asphaltene V h ti ) partial derivative of total fluid volume with respect to the total moles of component i V0p ) initial pore volume Wi ) accumulation term of component i in conservation equation Subscripts 0 ) original condition 1 ) rock-fabric classification 1 2 ) rock-fabric classification 2 3 ) rock-fabric classification 3 a ) asphaltene phase l ) liquid phase v ) vapor phase nc ) ncth component Greek Symbols R ) adjustable parameter φ ) porosity

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Received for review October 18, 1999 Revised manuscript received May 11, 2000 Accepted May 12, 2000 IE990781G

Modeling Asphaltene Precipitation in Reservoir Simulation - Industrial

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