Modeling asphaltene precipitation and flow behaviorin the processes of CO2 flood for enhanced oil recovery

Binshan Ju n, Tailiang Fan, Zaixing JiangSchool of Energy Resources, China University of Geosciences (Beijing), Key Laboratory of Marine Reservoir Evolution and Hydrocarbon AccumulationMechanism, Ministry of Education, Xueyuan Road No. 29, Haidian District, Beijing 100083, China

a r t i c l e i n f o

Article history:Received 11 June 2012Accepted 1 August 2013Available online 13 August 2013

Keywords:CO2 floodingenhanced oil recoveryasphaltene precipitationmathematical modelnumerical simulator

a b s t r a c t

This paper focuses on the idea for enhancing oil recovery by CO2 injection into oil formation as well asreducing CO2 emission into the atmosphere. The mechanism of asphaltene flocculation during CO2

flooding in oil formations is analyzed and the regressive correlation between CO2 concentration and theamount of flocculated asphaltene for an oil sample is set up for coupling with the flow governingequations for the flocculated asphaltene transport in porous media. A three-dimensional multiphasemathematical model describing CO2 transport in oil reservoirs and asphaltene precipitation is presentedfor predicting CO2 flooding performances for enhanced oil recovery. The finite difference method andpreconditioned conjugate gradient algorithm are used to solve the discrete nonlinear equation systems. Anumerical simulation software is developed to study CO2 flooding performances and the effects ofasphaltene precipitation on production behaviors. The numerical result indicates that water-cutdecreases from initial 92.5% down to 40.3% after continuous CO2 injection for 10 years. It is also shownthat 0.130 million tons of crude oil is displaced by CO2 injection in the 1 km2 of the reservoir within 10years. Asphaltene precipitation leads to the decrease in permeability, and the decline in production rates.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Worldwide CO2 emission is vast, and is regarded as a majorfactor leading to global warming (Akimoto et al., 2005; Radhi,2009). Annual CO2 emission in the 11 southeastern states (Ala-bama, Arkansas, Florida, Georgia, Louisiana, Mississippi, NorthCarolina, South Carolina, Tennessee, Virginia and East Texas), ofU.S.A. is up to about 1045 million metric tons. Coal-fired electricpower generation and other fossil-fueled plants account for 860million tons (Petrusak et al., 2009). Depleted or mature oil and gasfields provide excellent sites for enhanced oil recovery (EOR) aswell as CO2 geological storage in known porous and permeablereservoirs (Li et al., 2006; Gaspar Ravagnani et al., 2009). Many oilfields in main oil production countries offer good opportunities forCO2 injection into oil formations for EOR.

Previous experimental work on CO2 displacement in long core(Moreno et al., 2011) and the field-trial history of CO2 flooding forEOR purpose have verified that it can improve oil recovery to alarger extent. However, one adverse factor of CO2 flooding for EOR isthe asphaltene precipitation and deposition. This may not only leadto the formation damages (Monteagudo et al., 2001; Zekri andShedid, 2004) for reducing porosity and permeability, but also have

some adverse influences on production facilities such as well bore,tubing and pumps (Ruksana and David, 1990; Rashid et al., 2003).

The kinetic theory of aggregation of asphaltene is reported byBranco et al. (2001). It is critical to understand the asphaltenebehaviors in petroleum production from oil reservoirs. Idem andIbrahim (2002) studied experimentally the kinetics of CO2-induced asphaltene precipitation. Their results show that the rateof asphaltene precipitation depends on the concentrations ofasphaltene and CO2 in petroleum. It provides a clue to set up acorrelation between the amount of asphaltene precipitation andthe concentrations of asphaltene and CO2.

Nghiem et al. (2004) presented an asphaltene deposition modelfor CO2 flooding for EOR. It includes reversible and irreversibleasphaltene precipitation followed by surface deposition and pore-throat plugging. In the model, the authors gave two types ofasphaltene solids to describe the transfer between small and large-size solids. The transferring rate depends on the concentrations ofthe two particles in the oil and two reaction coefficients. It seemsfeasible to describe asphaltene precipitation phenomenon causedby CO2 injection. However, the methods to obtain the twoconcentrations of two types of solids are not reported in previousreferences. The objective of this work is to develop a numericalsimulator to predict CO2 injection performances, formationdamage and their effects on the performances of oil production.In this work, a new mathematical model considering asphalteneprecipitation is proposed, and a three dimensional numerical

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0920-4105/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.petrol.2013.08.029

n Corresponding author. Tel.: þ86 10 82320972.E-mail address: jubs2936@163.com (B. Ju).

Journal of Petroleum Science and Engineering 109 (2013) 144–154

simulator is developed to predict CO2 flooding for enhanced oilrecovery.

2. The mechanism and description of asphaltene flocculation

Asphaltene is defined as the fraction of the crude oil that issoluble in benzene or toluene but insoluble in liquid normal alkanes(Mitchell and Speight, 1973; Papadimitriou et al., 2007). It isgenerally in the soluble or suspended state under original condi-tions of oil reservoirs. The factors such as pressure, temperature andcomponents of oil determine the flocculation onset of asphaltene.The change in any of the factors may lead to unbalance ofasphaltene solubility and asphaltene precipitation, which is adverseto production and may lead to formation damage. Several models(Almehaideb, 2004; Huang et al., 2009; Jamialahmadi et al., 2009;Nghiem et al., 2004; Thanyamanta et al., 2009; Zahedi et al., 2009)have been developed to predict asphaltene precipitation. However,most of them (Almehaideb, 2004; Jamialahmadi et al., 2009; Zahedi

et al., 2009) focused on the asphaltene precipitation problems in theprimary recovery or deposition on the production facilities such astubes and well bores.

Srivastava and Huang (1997) studied the deposition behaviorsof asphaltene during CO2 flooding by an experimental approach. Inthe operating conditions of 16 MPa and 59–61 1C, they gave therelations between the CO2 concentration and flocculated asphal-tene for Weyburn oil samples. More recently, an experimentalapproach and calculation method were given by Huang et al.(2009) to predict asphaltene precipitation induced by CO2 injec-tion. One of their important conclusions is that asphalteneprecipitation starts to flocculate when CO2 concentration reachesan onset value. Then asphaltene precipitation quantity sharplyincreases as injected CO2 increases before a maximum precipita-tion reaches. Then, a further increase in CO2 concentration leads tothe decrease in asphaltene precipitation. Some of their experi-mental data are shown in Fig. 1.

The asphaltene precipitation onsets may be different from oneoil sample to another for the different oil components. For an

Nomenclature

a1–a4 correlation coefficients for asphaltene flocculated(dimensionless)

B volume factor of fluid (dimensionless)Cao volume concentration of asphaltene in oil phase

(dimensionless)CCO2 CO2 the mole fractions in the oil phase

(dimensionless)Conset asphaltene flocculation onset of CO2 concentration

(dimensionless)Cs volume concentration of asphaltene dissolved in oil

phase (dimensionless)D diffusivity of asphaltene in oil phase (m2/s)f flow efficiency factor (dimensionless)f vif mole fraction of component i (dimensionless)f vCO2f mole fraction of CO2 (dimensionless)f vgasf mole fraction of natural gas (dimensionless)f vof mole fraction of dead oil (dimensionless)h distance from reference level (m)k transient absolute permeability of a porous media

(m2)k0 initial permeability of a porous media (m2)kr relative permeability of a porous media

(dimensionless)n index for modifying permeability(dimensionless)pc capillary pressure (Pa)PWF bottom-hole flowing pressure (Pa)q production/injection rate (STM/D)qs the rate of change of soluble asphaltene caused by a

source/sink term (1/s)Qao the rate of change of flocculated asphaltene caused by

a source/sink term (1/s)Raf the ratio of flocculated asphaltene to total asphaltene

in oil (dimensionless)Rao net asphaltene change rate on the pore surfaces and at

pore throats (1/s)RLoss flocculated rate of asphaltene (1/s)Rsio solution gas–oil ratio (dimensionless)Rsiw solution gas-water ratio (dimensionless)S saturation (dimensionless)t time (s)u Darcy velocity of flow in porous media (m/s)

v real flow velocity in porous media (m/s)voc critical velocity (m/s)x distance in x direction (m)y distance in y direction (m)z distance in z direction (m)αdao rate constant for asphaltene deposition on pore sur-

faces (m-1)αf eao coefficient of flow efficiency (dimensionless)αhao release rate of asphaltene by hydrodynamic forces

(m-1)αpao capture rate constant of asphaltene at pore throats

(m-1)βk12 forward rate coefficient of formation of asphaltene

aggregates (s-1)βk21 reverse rate coefficient of formation of solid asphal-

tene aggregates (m3/s)δao volume of asphaltene deposited on the pore surfaces

per unit bulk volume (dimensionless)δnao volume of asphaltene trapped at throats per unit bulk

volume (dimensionless)ϕ porosity of the porous media (dimensionless)ϕ0 initial porosity of the porous media (dimensionless)γ specific gravity of fluids (N/m3)λf constant for fluid seepage allowed by the plugged

pores (dimensionless)μ viscosity of fluid (Pa s)ρ density (kg/m3)

Subscripts

0 Initial valueao asphaltene in oil phasec critical value or capillary pressured depositione entrainmentfe flow efficiencyg gash hydrodynamicso oilomix mixture of oil and gas and CO2

w water

B. Ju et al. / Journal of Petroleum Science and Engineering 109 (2013) 144–154 145

isobaric and isothermal system, there is an asphaltene flocculationonset of CO2 concentration,Conset according to Fig. 1,. If CO2

concentration is high enough, the asphaltene in oil begins toflocculate. Asphaltene flocculated from oil can be expressed in thefollowing form:

Cao ¼�a1C3CO2

þa2C2CO2

�a3CCO2 þa4 ðC4ConsetÞ ð1Þ

Cao ¼ 0 ðCrConsetÞ ; ð2Þ

where a1, a2, a3 and a4 are the correlation coefficients. Asphalteneflocculated from oil may be suspended in oil and may be adsorbedon pore surfaces or captured by pore throats. Asphaltene in asuspension state will flow with oil flow in the porous media.

For a non-isobaric and isothermal system, Takahashi et al.(2003) gave an asphaltene precipitation envelope (APE) with iso-asphaltene content map. According to their experimental data, wecan draw a chart of the pressure versus CO2 concentration todescribe the ratio of flocculated asphaltene to total asphaltene inoil (Figs. 2 and 3). Supposing the solubility of asphaltene in oil is Cs,and the ratio of flocculated asphaltene to total asphaltene inoil is Raf, then, the percentage of asphaltene flocculated in the oilphase is

Cao ¼ CsRaf ðp;CCO2 Þ; ð3Þ

where p is the pressure and CCO2 is the mole concentration of CO2

in the oil phase.

3. Mathematical model

3.1. Assumptions of the flow model

The mathematical model is based on the followingassumptions:

(1) The model is three-dimensional.(2) The fluids in porous consist of four components (oil, water,

hydrocarbon gas and CO2).(3) Considering three phases: oil, water and gas.(4) CO2 can be dissolved in oil and water.(5) There is no water component in oil and no hydrocarbon

component in water.(6) Considering the compressibility of reservoir rock and fluids.(7) The flow in porous media follows Darcy's law.(8) Asphaltene precipitation and its effects on porosity and

permeability are considered.(9) Both capillarity and gravity are considered.

(10) The temperature of injection fluids is closed to the reservoir'stemperature, and the flow is isothermal.

3.2. The governing equations for multiphase flows in porous media

The governing equations for multiphase flow in porous mediashould include mass and energy conservation. For most scenarios,the temperature would change in the vicinity of the injection wellbore. However, the temperature in most parts of a reservoir has alittle change when the injection rate is relatively low or thetemperature of injection fluids is closed to the reservoir's tem-perature. Therefore, the process is proximately regarded as iso-thermal flow, and only mass conservation is considered in the flowprocess. When the flow of oil, water and gas in porous mediafollows Darcy's law, the governing equations (Peaceman, 1977) fordescribing multiphase Newtonian flows can be written by thefollowing expressions:

For water:

divkkrwBwμw

ρwgradΦw

� �þqw ¼ ∂

∂tðϕρwSw=BwÞ: ð4Þ

For oil:

divkkro

BoμomixρogradΦo

� �þqo ¼

∂∂tðϕρoSo=BoÞ; ð5Þ

For gas:

div f vifkkrgBgμg

ρggradΦgþkkroRsio

BoμomixρogradΦoþkkrwRsiw

BwμwρwgradΦw

!

þqgi ¼ ∂∂t f vifϕ ρg

SgBgþρo

RsioSoBo

þρwRsiwSwBw

� �h ii¼ natural gas; CO2 :

ð6Þ

Fig. 2. Pressure vs. CO2 concentration used for predicting asphaltene flocculation inoil (modification based on Takahashi et al. (2003)).

Fig. 3. CO2 equilibrium solubility in crude oil (experimental data).Fig. 1. The relations between CO2 concentration and asphaltene flocculated for W3oil sample (experimental data from Srivastava and Huang (1997)).

B. Ju et al. / Journal of Petroleum Science and Engineering 109 (2013) 144–154146

For saturated porous media, the sum of the saturations of oil,water and gas is equal to 1, i.e.:

SoþSwþSg ¼ 1: ð7ÞThe sum of the fractions of all components in gas phase is equal

to 1:

∑f vif ¼ 1: ð8Þ

Three parameters regarding the potentials in Eqs. (4)–(6) aredefined as follows:

Φo ¼ poþγoh; ð9Þ

Φw ¼ pwþγwh¼ poþpcwoþγwh; ð10Þ

Φg ¼ pgþγgh¼ poþpcgoþγgh; ð11Þ

where f vif is a mass fraction of component i; t is time; ϕ is theporosity of porous media; S, μ, and p are the saturation, viscosityand pressure, respectively; k is the absolute permeability; kr is therelative permeability; B is the volume factor of fluid; q is theproduction or injection rate of a component; Rs is the solution gas–oil ratio; γ is the specific gravity of fluids; h is the distance from areference level, and pc is the capillary pressure. The viscosity of themixture of oil, gas and CO2 can be approximately expressed as thefollowing function:

μomix ¼ f ðμo; μnatural gas; μCO2; f vif Þ ð12Þ

Eq. (12) is an implicit function to calculate the viscosity; however,it is very difficult to find an explicit function to accurately predictthe viscosity of CO2–hydrocarbon mixture. Centeno et al. (2011)have tested 17 mixing rules reported in the literature used forpredicting the kinematic viscosity of petroleum and its fractionsare examined for accuracy by comparing the estimated values withthe experimental data. The result indicates a general trend to failas the API gravity of crude oil decreases. No accurate rule iscapable of estimating the viscosities for all the crude oils. There-fore, predicting viscosity is a challenging task. Considering theavailability of the parameters for calculating the viscosity, linearmixture rule reported by Centeno et al. (2011) is used to estimatethe viscosity. For black oil system, only three components (oil, gasand CO2) co-exist in the mixture. The mixing rule for the viscositycan be rewritten as

μomix ¼ f vof μoþ f vgasf μnatural gasþ f vCO2 f μCO2; ð13Þ

where f vof , f vgasf and f vCO2 f are the mole fractions of dead oil,dissolved natural gas and CO2 respectively.

3.3. Governing equation for the transport of asphaltene in solublestate

Transport of asphaltene in the soluble state in porousmedia can be described mathematically by a convection-diffusionequation.

∂∂xðuxomixCs�ϕSoDxs

∂Cs

∂xÞþ ∂

∂yuyomixCs�ϕSoDys

∂Cs

∂y

� �

þ ∂∂z

uzomixCs�ϕSoDzso∂Cs

∂z

� �þϕSo

∂Cs

∂tþRLossþqs ¼ 0 ð14Þ

where Cs is the solubility of asphaltene in oil; D is the diffusivity ofasphaltene; RLoss is the flocculated rate of asphaltene from solublestate in oil; x, y and z are three space dimensions; qs is the changingrate of asphaltene caused by a source/sink term.

In Eq. (14), RLoss can be treated as a reaction item. Nghiem et al.(2004) regarded it as a transform item between smaller asphalteneparticles and larger aggregates. It is a feasible treatment fordescribing the dynamic balance of asphaltene transfer. Therefore,

flocculation rate of asphaltene can be expressed as

RLoss ¼ βk12Cs�βk21Cao; ð15Þwhere βk12 is the forward rate of formation of asphaltene; βk21 isthe reverse rate of formation of solid asphaltene aggregates. If βk21is zero, the reaction is irreversible, and the aggregates will notcome back to solution.

3.4. The governing equations for the transport of flocculatedasphaltene

The description of the transport of flocculated asphaltene isbased on the following assumptions:

(1) The flocculated asphaltene aggregate is treated as particlematerial.

(2) Flocculated asphaltene either suspends in the oil phase orcoats on pore walls.

(3) The retention of flocculated asphaltene has two types (adsorp-tion on pore walls and capture at small pore throats).

Inasmuch as the asphaltene particles are small enough in size,diffusion should be considered. Thus, considering Brownian diffu-sion effects in the process of asphaltene migration in porousmedia, the continuum equation for asphaltene in the oil phasecan be expressed as following by modifying the equation proposedJu et al. (2007):

∂∂x

uxomixCao�ϕSoDxao∂Cao

∂x

� �þ ∂∂y

uyomixCao�ϕSoDyao∂Cao

∂y

� �

þ ∂∂z

uzomixCao�ϕSoDzao∂Cao

∂z

� �þϕSo

∂Cao

∂tþRaoþQao ¼ 0; ð16Þ

where Cao is the volume concentration of flocculated asphaltene inoil phase; D is the diffusivity of asphaltene; Rao is the net retentionrate of asphaltene on the surfaces of pore bodies and pore throats;x, y and z are three space dimensions; Qao is the injection orproduction rate of asphaltene described by a source/sink term.

In Eq. (16), the mathematical description of the net retentionrate of particle materials on pore surfaces was discussed by Ju et al.(2003, 2007), Nghiem et al. (2004) presented a discretized form ofthe deposition rate equation of asphaltene. These references treatthe particle transfer rate between pore surfaces and crude oil asthree scenarios: deposition, entrainment and pore-throat plug.The following section shows how the net retention rate couples inEq. (16).

Hydrodynamic forces can release the asphaltene coating onpore walls. Asphaltene deposition on pore surfaces will occurwhen the onset of asphaltene precipitation reaches. And porethroats may also capture asphaltene particles when the size of theparticles is large enough comparing to the diameters of porethroats of porous media. According to the mechanisms of asphal-tene transformation from the oil phase and onto pore surfaces orat pore throats, the Rao in Eq. (16) can be further written as

Rao ¼ RhaoþRdaoþRpao; ð17Þwhere the asphaltene release rate from the pore wall by hydro-dynamic forces ðRhaoÞ, the deposition rate on pore surfaces ðRdaoÞ,and the capture rate at pore throats ðRpaoÞ can be respectivelydefined as follows:

Rhao ¼�αhaoδaoðvo�vocÞ; ð18Þwhere voc is the critical flow velocity of the oil phase forasphaltene release from pore surfaces by hydrodynamic forces.The equation indicates that the forces acting on the asphalteneattaching on pore walls must be high enough to trigger asphaltenerelease from pore walls. The minimum flow velocity needed to

B. Ju et al. / Journal of Petroleum Science and Engineering 109 (2013) 144–154 147

trigger asphaltene release is the critical flow velocity. αhao is acoefficient for the release of asphaltene by hydrodynamic forces.When flow velocity of oil phase satisfies voovoc, no asphaltene isreleased by hydrodynamic forces (i.e. αhao ¼ 0). δao is the volume ofasphaltene deposited on the pore surfaces per unit bulk volume.

Rdao ¼ αdaovoCao; ð19Þwhere αdao is a coefficient for asphaltene deposition on the poresurfaces. During the transportation of asphaltene carried byflowing fluids, some asphaltene may be adsorbed again on thepore walls.

Rpao ¼ αpaovoCao; ð20Þwhere αpao is a capture coefficient of asphaltene at the porethroats. During asphaltene transportation in porous media, itmay be captured by bridging and blocking. In this case, acoefficient, αpao, is used to describe the capture rate.

Considering the asphaltene dynamic in porous media, we canfurther define

∂δao∂t

¼ RdaoþRhao; ð21Þ

∂δnao∂t

¼ Rpao; ð22Þ

where δao is the volume of the asphaltene deposited on the poresurfaces per unit bulk volume, and δao is equal to δ0ao at the initialtime; δnao is the volume of the asphaltene trapped at the porethroats per unit bulk volume, and δnao is equal to δn0ao at theinitial time.

3.5. The equations for the changes in porosity and absolutepermeability

Generally, the pore bulk volume is regarded as being slightlycompressible and permeability is regarded as a constant (Cathrine,2001; Mauran and Coudevylle, 2001). However, the asphaltenerelease from pore surfaces, the adsorption on pore surfaces, andblocking at pore throats in the process of asphaltene migrationmay lead to the changes in local porosity and permeability. Theinstantaneous porosity is expressed by

ϕ¼ ðϕ0�∑ΔϕÞ; ð23Þwhere ∑Δϕ denotes the variation of porosity by release andretention of asphaltene in porous media, and it is expressed by

∑Δϕ¼ ðδaoþδnaoÞ�ðδ0aoþδn0aoÞ: ð24ÞIf ∑Δϕ is greater than 0, the retention of asphaltene is dominant,and the porosity will decrease, (i.e. ϕoϕ0). If ∑Δϕ is less than 0,the release of asphaltene is dominant, and the porosity willincrease.

The change in permeability in this study is caused by asphal-tene release and retention. Modifying Kozeny Equation, by takinginto account the asphaltene plugging effect and according to Juet al. (2007), the expression for instantaneous permeabilitychanged by release and retention of asphaltene is given by

k¼ k0½ð1�f Þλf þ fϕ=ϕ0�n; ð25Þwhere k0 and ϕ0 are the initial permeability and porosity; k and ϕare the instantaneous local permeability and porosity of porousmedia; and λf is a constant for fluid seepage allowed by theplugged pores; n is the range of index and ranges from 2.5 to 3.5.Pore throats may be plugged by blocking or bridging, which causessome pore throats being too small for fluid flow. A flow efficiencyfactor, f, is defined as the fraction of the original cross-sectionalarea opened for flow. According to Ju et al.(2007), f can be treatedas a linear function of the volume of asphaltene entrapped at pore

throats and be given empirically by

f ¼ 1�αf eaoδn

ao ð26Þ

where αf eao is a coefficient of flow efficiency. It is used fordescribing the reduction in flowability. When pore throats pluggedby solid asphaltene completely, αf eao arrives to zero and f reaches 1.

4. Solution procedure for model

The mathematical model developed above consists of a set ofnonlinear equations, which mainly include the continuum equa-tions (Eqs. (4)–(6)) of water (w), oil (o), gas (g) and CO2, theconvection-diffusion equations (Eqs. (14) and (16)), and a series ofauxiliary equations (Eqs. (7)–(11) and Eqs. (13), (23) and (25)). Thefinite-difference method is used to discretize the nonlinear equa-tion to linear ones. An iterative preconditioned conjugate gradientalgorithm is used to solve the pressure-saturation equations, andan explicit method is used to solve the continuum equations of thetransport of asphaltene in porous media. Automatic Time-StepControl technology is used to improve computing efficiency duringan iteration process.

5. Numerical results and discussions

To demonstrate the functions of the developed simulator andanalyze the effects of asphaltene precipitation on CO2 floodingperformances, the following numerical simulations are based onthe common input data such as CO2 solubility (Fig. 3) in oil andrelative permeability curves shown in Figs. 4 and 5. The otherparameters and initialization are given in the following eachsimulation samples.

Fig. 4. Relative permeability curve of oil and water.

Fig. 5. Relative permeability curve of oil and gas.

B. Ju et al. / Journal of Petroleum Science and Engineering 109 (2013) 144–154148

5.1. Validation of the model and simulator

In this section we validate the mathematical model thatpredicts the formation damage caused by asphaltene precipitationduring CO2 immiscible flooding. The simulation result of one-dimensional immiscible flooding is compared to the sandstonecore flooding experimental data. The main parameters used in thenumerical simulation are shown in Table 1. The MMP of the CO2–

Oil system is 26.9 MPa which was obtained by slim tube experi-ments. The crude oil for MMP and CO2 flooding experiments wassampled from an oil well, CH. L. oil field, eastern China. Theviscosity and density at the reservoir condition are 5.21 mPa s and0.8015 g/cm3. All conditions such as pressure and temperature innumerical run are kept the same as experiments. It is very difficultto measure the reduction in permeability of each site along a coreby an experimental approach; however, the average permeabilitycan be calculated by Darcy's law when having experimental data.

Fig. 6 shows that the permeability ratio (K/K0) decreases drama-tically with continual injection of CO2 before 1.0 PV of CO2 is injected.Then the ratio decreases slowly after injection of 1.00 PV becausemost oil is displaced out of the core and small amount residual oil istrapped in the core. Therefore, only small amount of asphaltenedeposits on the pore surface after 1.0 PV of CO2 injection, which leadsto the slow reduction in permeability ratio. It also shows that thepermeability ratio predicted by the numerical simulation matcheswell to the experimental data. There is only a small deviationbetween the numerical and experimental results; therefore, themathematical model and simulator is valid and reliable.

5.2. Simulation example to demonstrate CO2 flooding performances

This section gives the numerical simulation results of a 5-spotwell pattern example. The size of the geological model is 1000 m

in length, 1000 m in width and 30 m in thickness and the gridnumber of the model are 51�51�3 (three layers in the verticaldirection). The main parameters are given in Table 2. The outerboundary condition of the geological model is sealed, and no fluxoccurs at the boundary. For inner boundary conditions, productionand injection rates for wells are specified. Fluid production ratesfor all production wells are shown in Table 3. CO2 injection rate foreach well is 12,742.65 STM3/D. The production rates of all oil wellsand CO2 injection rates keep constants during the whole produc-tion history.

The locations of 16 production wells and 9 CO2 injection wellsare shown in Fig. 7 All perforated intervals of the production wellsare located in bottom layer and perforated intervals of CO2

injection wells are located the top layer, which provide sufficientCO2 flooding because CO2 has a lower density than that of crudeoil. Figs. 8–10 plot the formation pressure distribution along thediagonal line of the reservoir. They show that the pressure at thevicinities of CO2 injection well is higher than that in other regions,and the pressure distribution in the vicinities of production wellslooks a funnel in the view of cross section. The pressure depletesin each layer with elapsed production time. The modeling resultindicates that the production fluid is more than injected CO2 involume at conditions of oil reservoir pressure and temperature.

Fig. 11 shows the water-cut change with elapsed times. Beforethe 2500th day, the water-cut in the production fluid is more than92%. The water-cut dramatically reduces after the 2500th day.Fig. 12 shows that the accumulated water production is muchmore than the oil production during the production history. At the3650th day (10th year), the accumulated produced water and oilare 0.921 million m3 and 0.163 million m3 respectively.

Fig. 13 demonstrates the changes in gas saturation distributionof three layers at the 5th year and the 10th year. The gassaturations in the top layer (Fig. 13(A) and (B)) are the highestamong the three layers for the perforated intervals for CO2

injection located in this layer, and its density is lighter than thedensities of oil and water phases. No gas breakthrough occurs atproduction wells after five-year injection of CO2 according toFig. 13(A), (C) and (E). Fig. 13(F) implies that gas breakthrough atthe following four production wells (P6, P7, P10 and P11).

5.3. Simulation example for asphaltene precipitation and its effectson permeability and production performances

This section gives the numerical simulation results of fourproducers and one CO2 injector. The size of the geological modelis 320 m in length, 320 m in width and 45 m in thickness. The gridnumber of the model are 21�21�3. The main parameters are

Table 1Main Parameters of the experiment and simulation.

Parameter name Value

The length of the core, cm 8.40The node numbers 21The size of grid of x, cm 0.4Temperature, 1C 85. 0Initial pressure, MPa 16.50Initial oil saturation 0.55Initial water saturation 0.45Initial gas saturation 0.00Porosity 0.29Permeability, mm2 0.10

Fig. 6. The comparison between numerical results and experimental data (PV: porevolume number at experimental condition).

Table 2Parameters of the field example.

Parameters of the geological model Value

The node numbers 51�51�3The size of grid of x and y, m 19.61The size of grid of z, m 10.00Initial reservoir pressure, MPa 28.20Viscosity of water, mPa s 0.501Viscosity of crude oil in reservoir, mPa s 5.161Viscosity of CO2, mPa s 0.0651Initial oil saturation 0.525Initial water saturation 0.475Initial gas saturation 0.000Initial horizontal permeability for all grids at x direction, 10�3 mm2 80.00Initial horizontal permeability for all grids at y direction, 10�3 mm2 80.00Initial vertical permeability for all grids at z direction, 10�3 mm2 40.00

B. Ju et al. / Journal of Petroleum Science and Engineering 109 (2013) 144–154 149

Table 3Production rates and well names.

Production well name P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16

Production rate STM3/D 8.67 17.34 17.34 8.67 17.34 34.69 34.69 17.34 17.34 34.69 34.69 17.34 8.67 17.34 17.34 8.67

Fig. 7. Well locations in x–y plain (five-spot well pattern. In: CO2 injection well; Pn: production well).

Fig. 8. Formation pressure distributions along the diagonal line of the top layer ofthe reservoir.

Fig. 9. Formation pressure distributions along the diagonal line of the mid layer ofthe reservoir.

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given in Table 4. In the simulations, the outer boundary conditionof example is sealed and no flux occurs at the boundary. Forinner boundary conditions, bottom-hole flowing pressures forproduction and injection wells are specified. The production andinjection rates are calculated based on individual fluid mobilitiesof each layer and productivity index (PI) and bottom-hole flowingpressure (PWF). For the four production wells, they will be shut in ifthe block pressureoPWF (PWF¼17.23 MPa). For the CO2 injectionwell, it will be shut in if block pressure 4PWF (PWF¼20.67 MPa).

Fig. 14 shows the permeability ratio distribution in the top layeron the 2200th day since CO2 injection starts. The permeabilityratio is defined as the ratio of transient permeability to initialpermeability. It indicates that permeabilities decline in the CO2

swept region, which is caused by asphaltene deposition on poresurfaces and capture at pore throats. However, the permeability ofthe oil formation near the injector location is not minimum. Thismay result from the following facts: (1) The flow velocity in thepores of the region near the injector is very high. When thevelocity is greater than the critical flow velocity for the release ofthe asphaltene coating on pore walls, a fraction of the asphaltenecan be entrained by the flow stream. (2) The local flow volume ofcrude oil in the region is less than that the region far from the

injector, which leads to capture relatively small amount of solidasphaltene particles. Fig. 15 demonstrates asphaltene precipitationin the oil formations on the 350th, 1100th and 2200th dayrespectively. The formation damage region expands with contin-uous injection of CO2. The damage region covers over 90% of thewell pattern on the 2200th day.

To obtain insight into the effects of asphaltene deposition onthe simulations, two scenarios with and without asphaltenedeposition are studied by numerical simulation. Fig. 16 showsthe differences in the oil recoveries of original oil in place (OOIP) ofthe two scenarios. It indicates that the recoveries are almost thesame before the 1000th day. The reason is that the permeabilitiesin the vicinities of production well bore do not decline before CO2

breakthroughs. After the 1000th day, CO2 breakthroughs in pro-duction well bore and leads to permeability reduction (Fig. 17).Thus, the productivity index of oil reduces, which leads to thereduction in the oil production rate. That is the reason why the oilrecovery with asphaltene deposition is lower than that of noasphaltene deposition. At the 5000th day, the difference in oilrecovery reaches 4.1%.

5.4. The effect of asphaltene precipitation on the simulation solver

Consideration of asphaltene precipitation during CO2 injectionmay not only cause formation damage, but also leads to strongernonlinear impacts on computational aspects such as convergencerate and CPU time. To validate the effect of asphaltene precipita-tion on CPU time consuming, a switch of the simulator is set forconsidering asphaltene precipitation modeling. If the switch is“on”, asphaltene precipitation in the simulation is considered,otherwise, the simulation runs without asphaltene precipitation.Fig. 18 gives the differences in relations between iterative stepsand elapsed time of two scenarios. It implies that consideration ofasphaltene precipitation and transport in oil formation slowsdown the convergence rate. The average time steps with andwithout asphaltene deposition are 1.72 and 3.75 days respectivelywithin 5000 days. The CPU time is 102 s without consideration ofasphaltene deposition, and 572 s with asphaltene deposition. Itindicates that the simulation with asphaltene deposition costsmore 461% CPU time than that without asphaltene deposition.

6. Conclusions

(1) A 3-D comprehensive mathematical model consideringasphaltene precipitation caused by CO2 flooding in oil reser-voirs for EOR is developed. And an oil field scaled numericalsimulator is developed to predict for CO2 flooding forenhanced oil recovery purpose.

(2) The permeability reduction predicted by a 1D numericalsimulation of CO2 immiscible flooding matches well withexperimental data obtained by CO2 immiscible core floodingin Lab, which validates the proposed mathematical model inthis paper.

(3) The numerical simulation result of a 3D oil formation with 16producers and 9 CO2 injectors indicates that the water-cutdecrease from initial 92.5% down to 40.3% after 10 yearinjection of CO2. Accumulated 0.406 million tons of CO2 aretrapped in the 1 km2 reservoir within 10 years. And 0.130million tons of crude oil are displaced by injected CO2.

(4) Accumulated 0.406 million tons of CO2 are trapped in a 1 km2

of the reservoir and 0.130 million tons of crude oil aredisplaced by 10-year CO2 injection.

(5) Asphaltene precipitations leads to the reduction in perme-ability within the CO2 swept region. The permeability of theblock with a sink reduces to about 70% of its initial value.

Fig. 10. Formation pressure distributions along the diagonal line of the bottomlayer of the reservoir.

Fig. 11. Water-cut of all production wells.

Fig. 12. Accumulated production water and oil of all production wells.

B. Ju et al. / Journal of Petroleum Science and Engineering 109 (2013) 144–154 151

Fig. 13. Gas saturation distributions of three layers at different time. (A) Gas saturation distribution in the 1st (top) layer at the 5th year; (B) Gas saturation distribution in the1st (top) layer at the 10th year; (C) Gas saturation distribution in the 2nd layer at the 5th year; (D) Gas saturation distribution in the 2nd layer at the 10th year; (E) Gassaturation distribution in the 3rd (bottom) layer at the 5th year; (F) Gas saturation distribution in the 3rd (bottom) layer at the 10th year.

B. Ju et al. / Journal of Petroleum Science and Engineering 109 (2013) 144–154152

(6) The numerical simulation for asphaltene precipitation in oilformation predicts the reductions in permeability as well asthe productivity index. Asphaltene precipitation results in

4.1% OOIP (original oil in place) production reduction com-pared to that of no asphaltene precipitation.

(7) Asphaltene precipitation increases the difficulty in numericalconvergence as well as the CPU time.

(8) This work provides a practical approach to get insight ofasphaltene precipitation and its effects on production perfor-mance for CO2 flooding for EOR.

Table 4Parameters of the simulation example.

Parameters of the geological model Value

The node numbers 21�21�3The size of grid of x, y and z, m 15.24Initial reservoir pressure, MPa 28.20Viscosity of water, mPa s 0.501Viscosity of crude oil in reservoir, mPa s 5.161Viscosity of CO2, mPa s 0.0651Volume concentration of asphaltene in oil phase 0.05Rate constant for asphaltene deposition on pore surfaces (m�1) 0.00895Critical velocity (m/s) 0.0001

Initial oil saturation 0.600Initial water saturation 0.400Initial gas saturation 0.000Initial horizontal permeability for all grids at x direction, 10�3 mm2 100.00Initial horizontal permeability for all grids at y direction, 10�3 mm2 100.00Initial horizontal permeability for all grids at Z direction, 10�3 mm2 100.00Release rate of asphaltene by hydrodynamic forces (m�1) 0.00001Capture rate constant of asphaltene at pore throats (m�1) 0.00851

Fig. 15. Asphaltene precipitation volume per unit volume of the rock distributions in the top layer at various times.

Fig. 14. Permeability ratio distributions in the top layer of the model at elapsed2200 days.

Fig. 16. The oil recovery differences between considerations of asphaltene and noasphaltene deposition.

Fig. 17. The permeability ratio changes with elapsed time at the block of produc-tion well location.

Fig. 18. The comparison of the relations between iterative steps and elapsed time.

B. Ju et al. / Journal of Petroleum Science and Engineering 109 (2013) 144–154 153

Acknowledgments

Parts of this work were supported by the National Science andTechnology Major Projects (2011ZX05009-002, 2011ZX05009-006),the Fundamental Research Funds for the Central Universities(2652012091), the Project-sponsored by SRF for ROCS, SEM, whichsupports are appreciated. We thank Dr. Jincai Zhang at HessCorporation for his review and edition.

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