Article pubs.acs.org/EF
Investigation on Asphaltene Deposition Mechanisms during CO2 Flooding Processes in Porous Media: A Novel Experimental Study and a Modified Model Based on Multilayer Theory for Asphaltene Adsorption Taraneh Jafari Behbahani,† Cyrus Ghotbi,*,† Vahid Taghikhani,† and Abbas Shahrabadi‡ †
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran Exploration and Production Division, Research Institute of Petroleum Industry (RIPI), Tehran, Iran
‡
ABSTRACT: In this paper, oil recovery and permeability reduction of a tight sandstone core sample in miscible CO2 flooding processes due to asphaltene deposition were studied using an Iranian bottom hole live oil sample in order to distinguish between the mechanical plugging and adsorption mechanisms of asphaltene involved in the interfacial interaction of the asphaltene/ mineral rock system. A novel experimental method was designed and proposed to measure the amount of deposited asphaltene due to different mechanisms using the cyclohexane or toluene reverse flooding and spectrophotometer. In this work, the bottom hole live oil sample was injected first to a long core and then CO2 injection was performed which is close to reservoir conditions, whereas in the majority of previous works, the mixture of recombined oil (mixture dead oil and associated gas) and CO2 was injected in a short core sample which is far from reservoir conditions. Then, the cyclohexane and toluene reverse flooding was performed, and the amount of deposited asphaltene was measured by spectrophotometer. It was found that by increasing the flow rate of injected CO2, pressure drop across the core increased significantly and then decreased. These significant increases in pressure drops indicate more asphaltene deposition and consequently more permeability reduction. Also, it has been found that 20−40% permeability reduction by asphaltene deposition was caused by adsorption mechanism in the CO2 flooding process during a slow process, whereas 60−80% of formation damage is due to a mechanical plugging mechanism and takes place in a short time. Also, a modified model based on multilayer adsorption theory and four material balance equations (oil, asphaltene, light components, and water phase) was developed to account asphaltene adsorption in core sample during CO2 flooding and the model was verified using experimental data obtained in this work. The results show that the developed model based on multilayer adsorption theory and four material balance equations is more accurate than those obtained from the monolayer adsorption theory and two material balance equations (the existing models) and is in good agreement with the experimental data reported in this work.
1. INTRODUCTION CO2 flooding is one of successful EOR (enhanced oil recovery) method applied in oil fields. CO2 can improve oil production by reducing the interfacial tension and viscosity or increasing mobility. One common problem during CO2 injection is asphaltene instability, which induces deposition and adsorption of asphaltene and may cause pore-throat-plugging or wettability alteration.1 Field and laboratory data confirm that the asphaltene solubility is lower in the light oil. Asphaltenes tend to precipitate more easily in light oils rather than in heavy oils. For instance, the Venezuelan Boscan crude with 17.2 wt % asphaltene was produced with very few issues whereas HassiMessaoud in Algeria has numerous production problems with only 0.15 wt % asphaltene. The Hassi-Messaud reservoir is a tight reservoir with small pore throats. In addition in the HassiMessaud reservoir, the resin-to-asphaltene ratio is very low which results in high asphaltene precipitation and deposition. Contrary to the Hassi-Messaud reservoir, the Boscan reservoir has high asphaltene content, but its resin-to-asphaltene ratio is also high which results in considerably lower asphaltene precipitation and deposition.2 Since light-oil reservoirs are more often candidates to gas injection processes, the danger is even bigger. Due to the complexity of asphaltene deposition © 2012 American Chemical Society
phenomena during CO2 injection, very little experimental results currently exist on asphaltene deposition under dynamic conditions using bottom hole live oil in porous media. The majority of existing works study the asphaltene deposition during CO2 flooding using the injection of mixture of recombined oil (mixture dead oil and associated gas) and CO2 to the core and or with static systems and in the absence of a reservoir rocks.3−6 Zanganeh et al.7 studied asphaltene deposition during CO2 injection by a novel experimental set up to employ a high pressure visual cell using synthetic oil. Also, Okwen et al.8 studied the chemical influence of formation water in decreasing the rate or amount of asphaltene deposition during CO2 injection and suggested the relevant parameters necessary to determine the formation type that is appropriate for CO2 injection. Nobakht et al.9 investigated mutual interactions between crude oil and CO2 under different pressures and found that the measured crude oil CO2 equilibrium interfacial tension (IFT) is reduced almost linearly with the equilibrium pressure, as long as it is lower than a Received: April 17, 2012 Revised: July 15, 2012 Published: July 20, 2012 5080
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
adsorption behavior of asphaltenes on mineral surfaces that is studied by surface excess or Langmuir theory.26−29 In this work, the bottom hole live oil sample was injected first to a long core sample and then CO2 injection was performed which is close to reservoir conditions. Second, a novel set of experiments was designed and proposed with the purpose to distinguish between the asphaltene mechanical plugging and adsorption mechanisms involved in the interfacial interaction of the asphaltene/mineral rock system using the cyclohexane or toluene reverse flooding. Also, a new model based on multilayer adsorption theory and four material balance equations (oil, asphaltene, gas, and water phase) was developed to account asphaltene multilayer adsorption on core sample during CO2 flooding and the model was verified using experimental data obtained in this work.
threshold pressure. It is observed that if the equilibrium pressure is high enough, the light components in the original crude oil are quickly extracted from the oil drop to CO2 phase at the beginning. Hamouda10 studied miscible and immiscible flooding and proposed a model based on the solubility theory to account for the effect of CO2 flooding. The asphaltene deposition is governed by four mechanisms; surface deposition, entrainment, plugging, and adsorption. Ali and Islam11 investigated the effect of asphaltene deposition on carbonate rock permeability in single-phase flow. A model was coupled to deposition and adsorption mechanisms, and the results were compared to experimental data of carbonate rocks. Gruesbeck and Collins12 proposed a model that has been used for mechanical entrapment of solids and developed the equation for the deposition of fines in porous media. Minssieux et al.13 investigated the flow properties of crude oils at reservoir temperature in different rocks. Leontaritis14 developed a simplified model for prediction of formation damage and productivity decline by asphaltene deposition under saturated conditions in radial flow. The hydraulic diameter was estimated by the ratio of the total pore volume to the total pore surface area of the flow channels. Civan15 developed a two-phase model to predict paraffin and asphaltene deposition. The permeability of plugging and nonplugging pathways was given by the empirical relationships. Wang and Civan16 proposed a deposition model including the static and dynamic pore surface deposition and pore throat plugging. The model incorporates the features of Civan’s dual-porosity model for a single-porosity treatment in the laboratory core flow tests. The oil, gas, and solid phases were assumed to be at thermal equilibrium. Nghiem et al.17 proposed a model to study compositional simulation of asphaltene precipitation. They used the developed equation of Kumar and Todd18 based on the Kozeny−Carman equation. Kocabas et al.19 developed a wellbore model coupled to asphaltene adsorption model based on Langmuir equation for linear and radial systems. The coupled model predicts permeability damage owing to mechanical trapping and adsorption. The model proposed by Ali and Islam, was used and the equation was solved analytically through Laplace transform. Wang and Civan20 proposed a model into which the asphaltene mass balance equation is incorporated into a three-dimensional, three-phase black oil simulator. The deposition rate for asphaltene includes three terms: the surface deposition, the entrainment, and the pore throat plugging rate. It can be concluded that the surface deposition is a predominant mechanism of asphaltene deposition. Almehaideb21 developed a model to simulate asphaltene precipitation, deposition, and plugging of oil wells during primary production. A four-component, four-phase limited compositional formulation was described. The model was implemented in cylindrical coordination to match the flow direction around the well. Monteagudo et al.22 used network modeling to simulate one-phase flow in porous media in order to predict the change in petroleum flow by asphaltene deposition. The network model is used to predict formation damage caused by asphaltene deposition. The adsorption of asphaltenes on solids is the result of favorable interactions of the asphaltene species or its aggregates with chemical species on or near the mineral. The major forces that can contribute to the adsorption process include electrostatic (Coulombic) interactions, charge transfer interactions, Van der waals interactions, repulsion interactions, and hydrogen bonding.23−25The majority of existing models proposed monolayer
2. EXPERIMENTAL SECTION 2.1. Materials. A bottom hole live oil sample from an Iranian reservoir on the Southeast region of Iran was used in this study. The density and viscosity of the reservoir fluid sample were measured to be ρoil = 767.4 kg/m3 and μoil = 4.35 cP at the reservoir pressure, respectively. The compositional analysis result of this crude oil, given in Table 1, was obtained using the gas chromatography method.30
Table 1. Studied Bottom Hole Live Oil Compositions components
bottom hole live oil (mol %)
components
bottom hole live oil (mol %)
H2S N2 CO2 C1 C2 C3 i-C4 n-C4 i-C5
0 0.3 1.83 22.7 8.24 6.14 1.19 3.61 1.38
n-C5 C6 C7 C8 C9 C10 C11 C12+ total
1.59 6.95 4.1 3.88 2.49 4.03 2.85 28.74 100
A formation water sample was collected from the same oilfield, cleaned, and analyzed. Its detailed physical and chemical properties are listed in Table 2. One sandstone core having cylindrical shape with length of 30 cm, constant diameter equal to 4 cm, weight of 543 g, and pore volume of 28.7 was characterized and tested in the EOR Research Center laboratory, Research Institute Petroleum of Industry (RIPI). The investigated core was cleaned prior its uses, by using various solvents (Soxhlet extraction with xylene, methanol, and chloroform) according to ASTM D2172 procedure.31 The asphaltene content of the bottom hole live oil was measured to be wasp = 16.3 wt % using the SARA analyses. The constituents of crude oils are typically classified by solubility: saturates aromatics, resins, and asphaltenes (SARA). For SARA fraction analysis, asphaltene fraction was extracted from crude oil by precipitation with n-heptane as described by the ASTM D327997 procedure.32 Subsequent elution with a series of increasingly polar solvents as the mobile phase yields saturates (eluted with a nonpolar solvent such as hexane), followed by the elution of aromatics with toluene, and finally by the elution of resins with a more polar solvent. The SARA analyses results of bottom hole live oil are shown in Table 3. To determine the PVT and phase behavior of the bottom hole live oil, various experiments were conducted (DBR, VINCI PVT Cell). In Tables 4 and 5, the PVT characteristics and phase behavior of the studied bottom hole live oil are shown. Also, solution gas−oil ratio, liberated gas−oil ratio, oil formation volume factor, and oil density versus pressure are shown in Figures 1 and 2. GOR is a measure of how much gas is evolved from oil as it goes from reservoir pressure and temperature to separator conditions. 5081
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
Table 2. Physical and Chemical Properties of Formation Water Sample property
value
viscosity (CST @40 °C) pH at 20 °C oil (mg/L) chemical oxygen demand (mg/L) biological oxygen demand (mg/L) total suspended solids (mg/L) chloride (mg/L) CaCO3 (mg/L) sulfate (mg/L) total dissolved solids (mg/L) potassium (g/L) sodium (g/L) calcium (mg/L) magnesium (mg/L) iron (mg/L) strontium (g/L) lithium (mg/L) sulfide (mg/L) barium (mg/L)
0.9166 6.5 4 1216 530 352 123100 177 291 202050 1.1 60 13280 1262 42 0.58 13 7.2 1.2
Figure 1. GOR results for the studied bottom hole live oil.
Table 3. SARA Test Results of the Studied Bottom Hole Live Oil type of group
bottom hole live oil
saturate (wt %) aromatic (wt %) resin (wt %) asphaltene (wt %)
32.61 43.48 7.61 16.3
Table 4. PVT Characteristics and Phase Behavior of the Studied Bottom Hole Live Oil reservoir pressure, Pres (bar) reservoir temperature, Tres (°C) molar weight of the bottom hole live oil (g/mol) saturation pressure, Psat (bar) specific gravity of bottom hole live oil (g/cm3) molar weight of the heavy group (bottom hole live oil), C12+ (g/mol) specific gravity of the heavy group (bottom hole live oil), C12+ (g/cm3) molar weight of the heavy group (dead residual oil), C12+(g/mol) specific gravity of the heavy group (dead residual oil), C12+(g/cm3) GOR (SCF/STB)
326 96 182 97 0.9322 491
Figure 2. Differential liberation results versus pressure for the studied bottom hole live oil. Also, variation of oil formation volume and liquid phase density were from 1.05 to 1.3 and 0.76 to 0.88, respectively, as shown in Figure 2. 2.2. Experimental Apparatus. Figure 3 shows the schematic of the experimental setup used in this work in order to determine the effect of asphaltene deposition on the properties of a reservoir rock. This setup consists mainly of the following devices: - An automatic displacement pump (Vinci, p = 10 000 psi, accuracy = 0.1 psi). The pump was used to displace the crude oil, formation water, and CO2 through the composite reservoir core plug inside a core holder (Temco). - Five high pressure stainless steel cylinders (500-10-P-316-2, DBR, Canada). The cylinders were used to store and to deliver the bottom hole live oil sample, CO2, and reservoir brine, cyclohexane, and toluene (DBR, capacity of 500 mL). - Core holder (Temco, p = 10 000 psi, T = 150 °C). The core holder, horizontally placed, held a core through a sleeve. A constant overburden pressure was applied around this sleeve, which was always kept 5 MPa higher than the inlet pressure of the core holder. The inlet and outlet ports of the core holder were connected to the pressure transducer. The inlets ports of the core holder were also connected to the positive displacement pump. Five cylinders containing reservoir brine, bottom hole live oil sample, CO2, cyclohexane, and toluene allowed injection of sample inside the core holder. The positive displacement pump was operated at constant rate or in pressure
0.9853 395 0.9203 305
Table 5. Summary of Constant Mass Expansion Data for the Studied Bottom Hole Live Oil test temperature saturation pressure solution GOR formation volume factor @ sat. pressure density of total gas evolved API gravity of residual oil specific gravity of residual oil
°C bar SCF/STB Rbbl/STB g/cm3 °API 60/60 °F
96 110.5 341.63 1.3073 1.3839 20.29 0.9322
Solution GOR is cubic feet of solution gas per barrel of residual oil and cumulative liberation GOR is cubic feet of librated gas per barrel of residual oil at 15 °C and 1 bar. The results of Figure 1 show that variation of the solution GOR and liberation GOR were from 360 to 0. 5082
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
core plug. The spectrophotometer used in this study was slightly modified to accommodate a quartz flow cell (Starna Cells, Inc.) with a 4 cc nominal volume and 10 mm path length in the sample compartment. 2.3. Experimental Procedure. Three sets of experiments were conducted with different objectives regarding inducement and/or removal of damage due to asphaltene deposition. In each experiment, first the sandstone core plug was dried and vacuumed at 0.7 bar for 1 h. Then, the formation water was imbibed to measure the pore volume of the reservoir core plug. Afterward, the formation water was injected at different rates (10−60 cm3/h) to determine water permeability of the core plug. The measured porosity was Ø = 12.6%, and the measured water permeability was k = 1.4 mD. Then formation water was displaced by the bottom hole live oil until irreducible water saturation at a flow rate of 10 cm3/h. The initial connate water saturation was found to be Swc = 37%, and the initial oil saturation was Soi = 63% for sandstone core. 1. CO2 Flooding Experiments: Tests 1, 2, and 3. The conditions of the experiments given in Table 6, were conducted to determine the additional amount of asphaltene deposition induced by CO2 injection in a core plug. After the core plug was fully saturated with the bottom hole live oil sample, two pore volumes of bottom hole live oil were injected to the core plug. Then CO2 injection was performed at different flow rates and a constant temperature of T = 70 °C. The differential pressure between the inlet and outlet of the core holder was measured by digital pressure indicator and was indicated by data acquisition system at the preset time interval. To study the effect of flow rate of CO2 injection on oil recovery and asphaltene deposition, CO2 was injected at different rate from 6 to 18 cm3/h. In each test, the CO2 injection was continued to reach a stable differential pressure and no more oil was produced. The volume of produced gas and oil were measured and recorded using the gas flow meter and oil collector, respectively. Also in each experiment, the gas−oil ratio and oil recovery factor were determined. In each test of CO2 flooding, the bottom hole live oil was injected to core sample before and after CO2 flooding for calculated of oil effective permeabilities. 2. Experimental Method for Investigation of Formation Damage Due to Mechanical Plugging Mechanism: Tests 1, 3, and 5. The conditions of the experiments, given in Table 7, were designed to measure the permeability reduction and the amount of deposited asphaltene during CO2 flooding and recovery of formation damage due to mechanical plugging mechanism. These experiments consisted of CO2 flooding to deposit asphaltene and then a reverse flooding with cyclohexane to measure and to restore formation damage due to mechanical plugging mechanism. In each test, the cyclohexane injection was continued until a stable differential pressure reaches and the permeability recovery factors were determined. Then, the oil flooding was performed to measure the oil effective permeability reduction due to mechanical plugging mechanism. Finally, a doublebeam UV−vis spectrophotometer to measure amount of deposited asphaltene in core plug due to mechanical plugging during CO2 flooding was used. To calibrate the spectrophotometer for each sample, a cyclohexane solution including asphaltene with concentration of 500 mg/L was prepared and diluted for making lower concentration solutions. Then, absorbance of each solution was
Figure 3. Schematic of experimental setup.
-
mode. The outlet port of the core holder was connected to the liquid collector and gas flow meter through a back pressure regulator for collection of produced fluids from the core sample. The pressure drop during the core flood tests was measured with a digital pressure indicator. The core flooding system was thermo regulated by means of an air bath oven. An important feature was the possibility for continuous measurement of the pressure drop along a section of the porous medium. The annular space between the sleeve and the body was filled with paraffin oil which the confining pressure was applied on the external surface of the sleeve. The advantage of this setup is the uniform pressure in both axial and radial direction. A pressure transducer (Jumo, accuracy = 0.05). A back-pressure regulator (Jeafer DBR, p = 10 000 psi, T = 250 °C). The regulator was used to maintain the specified injection pressure inside the core holder during each flooding test. An overburden pump (Enerpac, p = 10 000 psi). An air-bath oven (Vinci, T = 200 °C). Rigid valves. Data acquisition system (Logger screen 500 Jumo: pressure, temperature, volume). A double-beam UV−vis spectrophotometer (Cary 4000, Varian, Inc.) to measure amount of deposited asphaltene in
Table 6. Experimental Conditions, Oil Recovery Factors, and Oil Effective Permeability Reduction Data for CO2 Flooding Testsa oil effective permeability reduction (%) test no.
Q (cm /h)
ΔP1 (kPa)
ΔP2
total RF (%)
ΔKo/Ko (%)
mechanical plugging mechanism
adsorption mechanism
WA (%)
1 2 3
6 12 18
120 450 1320
160 535 1512
15 50 80
9.25 10.5 12.8
5.55 7.14 10.24
3.7 3.36 2.56
0.098 0.084 0.076
3
a Notes. ΔP1: stable differential pressure between the inlet and outlet of the core holder during bottom hole live oil injection before CO2 flooding. ΔP2: stable differential pressure between the inlet and outlet of the core holder during bottom hole live oil reinjection after CO2 flooding. ΔKo/Ko: oil effective permeability reduction in percentage after CO2 flooding. WA: asphaltene content of produced oil.
5083
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
(μ p − μ0p)
Table 7. Experimental Results of Formation Damage by Mechanical Plugging and Adsorption Mechanismsa
RT
deposited asphaltene (mg/m2) test no.
ΔP3 (kPa)
mechanical plugging mechanism
1 2 3 4 5 6
70 40 62 42 183 204
4.5
⎛ Vp ⎞ Vp = ln Φp + ⎜1 − [(δp − δs)Φs]2 ⎟Φs + Vs ⎠ RT ⎝ (1)
adsorption mechanism
The solubility parameter in eq 1 is written as below: δp =
4.1 5.5
⎛ Δu ⎞0.5 ⎜ ⎟ ⎝ v ⎠
(2)
The values of Δu and v are calculated by the SRK equation of state (EOS). In this study, it is assumed that the asphaltene phase is as a pure liquid pseudocomponent in which asphaltene precipitation has no effect on liquid−vapor equilibrium. Also, crude oil is considered as a binary homogeneous mixture of asphaltene and solvent. By equating the fugacity of asphaltene in liquid and solid phase, we have:
3.5 7.25 2.97
Note. ΔP3: stable differential pressure between the inlet and outlet of the core holder during the cyclohexane/toluene injection after CO2 flooding. a
⎛ VL ⎞ VpL p ΦLp = exp⎜⎜ L − 1⎟⎟Φs − (δp − δs)2 Φs 2 RT V ⎝ ⎠
measured in the 100−700 nm range. Finally, asphaltene content of cyclohexane solution obtained from cyclohexane reverse flooding process was measured using UV−vis spectrophotometer. 3. Experimental Method for Investigation of Formation Damage Due to Adsorption Mechanism: Tests 2, 4, and 6. The conditions of the experiments given in Table 7 were proposed to measure the permeability reduction and the amount of deposited asphaltene during CO2 flooding and recovery of formation damage due to adsorption mechanism of asphaltenes. For this purpose, first, the steps of mechanical damage removal experiment were done. Second, the reverse flooding of the core with toluene was followed .Toluene is the dissolving agent of asphaltenes that cannot be removed with the cyclohexane reverse flooding in previous test. In each experiment, permeability recovery factors were determined. Then, the oil flooding was performed to measure the oil effective permeability reduction due to asphaltene adsorption mechanism. Also, the double-beam UV−vis spectrophotometer was used to measure the amount of deposited asphaltene in a core sample due to the adsorption mechanism. In this section, to calibrate the spectrophotometer, a toluene solution including asphaltene with concentration of 500 mg/L was prepared and diluted for making lower concentration solutions. Finally, the asphaltene content of the toluene solution obtained from the toluene reverse flooding process was measured using a UV−vis spectrophotometer. Formation damage in petroleum reservoirs occurs as a consequence of the combined effects of many complex phenomena. First, the asphaltene deposits in the core sample by adsorption mechanism and then mechanical plugging mechanism occurs in the core sample. The above-mentioned mechanisms occur at different times, that is, first a gradual reduction of the average porous size due to asphaltene adsorption happens and then trapping due to the comparable size between the asphaltene particles and the average radii of pore throats occurs. Before developing the asphaltene plugging mechanism, a fast adsorption of asphaltenes onto active sites of rock surface occurs; subsequent thicker molecular structures (i.e., multilayer) seem to form on various dry mineral surfaces. It then follows by a slower reversible hydrodynamic aggregation of asphaltene molecules suspended in the crude oil, possibly forming large enough aggregates so as to be retained at pore throats (asphaltene plugging mechanism). Due to neutrality of cyclohexane on asphaltene precipitation/ dissolving, the only effect of reversal of the flow direction with cyclohexane is removal of deposited asphaltene due to mechanical plugging mechanism. But while toluene reacts with remaining asphaltene from the previous step, the effect of reversal of the flow direction with toluene is removal of the trapped asphaltene by adsorption mechanism onto active sites of rock surface.
(3)
The weight fraction of asphaltene precipitation is calculated as below: WSAL =
L (1 − ΦLp )(M w/ ) VL L (1 − ΦLp )(M w/ ) + (ΦLp )(M wp/Vp) VL
(4)
3.2. Asphaltene Deposition Modeling. There are the two asphaltene deposition mechanisms on porous media: adsorption and mechanical plugging. Modeling of Asphaltene Adsorption Mechanism. The asphaltenes adsorption mechanism, which is related to the interactions between the asphaltenes functional groups and the rock surface, involves surface polarity, affinity, or other attractive forces. Asphaltene is a polar component therefore formations have ability to adsorb asphaltene. The asphaltene adsorption was modeled using the Zhu and Gu (ZG) model35 based on multilayer theory of asphaltene adsorption. Although the model proposed by Zhu and Gu was used for hemimicelles of amphiphiles, it will be shown here that the model is justified for the asphaltene molecule as well, due to its amphiphilic character to aggregate and adsorb to rock interfaces.36 The ZG model is as follows: Γ=
Γ∞k1C(n−1 + k 2C n − 1) 1 + k1C(1 + k 2C n − 1)
(5)
Also, the asphaltene adsorption was modeled using a Langmuir isotherm equation that shows monolayer type of asphaltene adsorption:21 Wsa =
Wsa,maxK aCsf K aCsf + 1
(6)
Modeling of the Mechanical Plugging Mechanism. The asphaltene deposition problems are represented by mass balance models for the liquid and asphaltene, the momentum balance equation, the asphaltene precipitation and deposition models, and the porosity and permeability reduction models. The majority existing works use two material balance based on oil and asphaltene phase for core samples. The proposed model in this work is an extension of the traditional black oil equations described by Wang and Civan.20 The material balance equations are included for the water and gas component
3. THEORETICAL BASIS 3.1. Thermodynamic Modeling. According to FloryHuggins theory,33,34 the chemical potential of asphaltene component is calculated as follows: 5084
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
during CO2 flooding processes. The model equations are as follows:
⌀ = ⌀0 − EA − Ead The instantaneous, local permeability, k, is calculated by20
Oil phase ∂ ∂ (φSLρL wOL) + (ρ uLwOL) = 0 ∂t ∂x L
⎛ ⌀ ⎞m k = k 0⎜ ⎟ ⎝ ⌀0 ⎠
(7)
∂ ∂ (φSLρA CA + φSLρL wAL) + (ρ uLwSAL + ρL uLwAL) ∂t ∂x L (8)
Light components phase: The light component S is present in vapor and liquid phases. ∂ ∂ (φS VρG + φSLρL wG) + (ρ uLwG + ρL uG) = 0 ∂t ∂x L
(9)
(10)
(11)
The momentum balance equation is given by Darcy’s law:
uL = −
k ∂P μL ∂x
0≤x≤L
t=0
(18)
EA = 0
0≤x≤L
t=0
(19)
Ø = ⌀0
0≤x≤L
t=0
k = k0
0≤x≤L
t=0
(12)
)The deposition rate for asphaltene is given: ∂EA /∂t = αSLCAφ − βEA (υL − υc) + γSLuLCA
(21)
t>0
(22)
⎛⎛ ⎞ ⎞2 ⎛k⎞ k ⎟ −⎜ ⎟ ∑ ⎜⎜⎜ ⎟ k ⎝ k 0 ⎠calculated ⎟⎠ i = 1 ⎝⎝ 0 ⎠measured n
objective function =
(13)
where the first term represents the surface deposition rate. The second term represents the entrainment of asphaltene deposits by the flowing phase when the interstitial velocity is larger than a critical interstitial velocity. This term shows that the entrainment rate of the asphaltene deposition is directly proportional to the amount of asphaltene deposits present in porous media, and also, the difference between the actual interstitial velocity and the critical interstitial velocity necessary for asphaltene deposit mobilization. The last term indicates the pore throat plugging rate, which is directly proportional to the product of the superficial velocity and the asphaltene precipitate concentration in the liquid phase. The value of β is described as follows:
(23)
As a result, the model parameters obtained by optimization procedure are Γ∞, k1, k2, m, n, α, β, vc, γ, Ka, σ.
4. RESULTS AND DISCUSSION 4.1. Effect of CO2 Injection Flow Rate on Permeability Reduction Due to Asphaltene Deposition. After injection of CO2 into the core sample, conditions and properties of the bottom hole live oil changes; this may lead to the precipitation and deposition of asphaltenes. In this study, the oil effective permeabilities were calculated from the measured differential pressures between the inlet and outlet of the core holder during the bottom hole live oil injection before CO2 flooding and during its final reinjection after CO2 flooding. The calculated oil effective permeability reduction data in percentages for all CO2 oil recovery tests (Tests 1, 2, and 3) are listed in Table 6. Figures 4 and 5 show the plot of the pressure drop versus the injected pore volume of CO2 at different injection flow rate of 6−18 cm3/h and effective permeability retention versus pore volume of oil injected respectively for sandstone core sample. These plots show that an increase in CO2 injection flow rate is followed by an increase in pressure drop and permeability retention. Test 3 was conducted with a CO2 injection flow rate of 18 cm3/h, and in test 1, CO2 was injected into the core at a rate of 6 cm3/h. During test 3, a greater increase in pressure drop across the core sample was observed than that obtained in test 1. It can be found from these results that the highest permeability reduction is obtained during the highest CO2 injection flow rate at 18 cm3/h. Thus, the damage of the core
β = βi , when vL > vc
β = 0, otherwise
uL ⌀ The value of γ is set as follows:
x=L
(20)
The above-mentioned models were coupled and discretized using the finite-difference method, backward both in time and space and solved using Newton’s method in MATLAB software version 2008. A fully implicit numerical model was performed and solved by iteration. Numerical simulation runs were conducted to obtain the best match between experimental and numerical results. For optimization and determination of the model parameters, history matching was used. In this study, the square root of the summation of the differences between measured and calculated porosity data were defined as the objective function:
The saturations of phases are given: SL + S V + S W = 1
CA = 0
P = back pressure
Water phase ∂ ∂ (φS W ρW WWL) + (ρ uW wWL) = 0 ∂t ∂x W
(17)
The boundary and initial conditions can be considered as follows:
Asphaltene phase
= −ρA ∂EA /∂t
(16)
vL =
(14)
γ = γi(1 + σEA ), when Dpt < Dptcr
(15)
γ = 0, otherwise
Thus, the pore throat plugging deposition rate increases proportionally with the total deposits. When Dpt is less than Dptcr, pore throat plugging deposition will occur. The instantaneous local porosity during asphaltene deposition is equal to the difference between the initial porosity and the fractional pore volume occupied by the deposited asphaltene and adsorbed asphaltene:11 5085
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
were conducted and the oil recovery process was studied. The detailed experimental data of Tests 1, 2, and 3 are listed in Table 6. Moreover, it is worthwhile to mention that, after reaching the initial connate water saturation through the initial live crude oil injection, no more water was produced during the CO2 oil recovery. The oil recovery factor (RF) at any pore volume of the injected fluid under the core flood test conditions is defined as the ratio of the volume of the produced oil at any time to that of the initial live crude oil in the core sample. Figure 6 shows the measured oil RF versus the injected pore
Figure 4. Differential pressure between the inlet and outlet of the core holder versus the injected pore volume of CO2 during the CO2 flooding.
Figure 5. Oil effective permeability retention.
sample was found to be increased when the CO2 injection flow rate was increased. Greater asphaltene deposition caused severe blockage of pore throats and thus greater reduction in permeability of the core sample induced. In the miscible CO2 flooding process, the amount of precipitated asphaltenes left in the reservoir core plugs reaches its largest value, which results in the largest oil effective permeability reduction. An explanation for this phenomenon is that the solubility parameter of CO2 is lower than the solubility parameter of the oil, and therefore, the solubility parameter of the mixture decreases with an increasing CO2 injection rate. Hence, the oil becomes unstable and the asphaltenes readily precipitate. Also, Table 6 shows that, in the miscible CO2 flooding process, oil effective permeability reduction reaches to its largest value, whereas the asphaltene content of the produced oil reaches its lowest value. On the other hand, higher asphaltene precipitation and deposition leads to the larger oil effective permeability reduction. 4.2. Effect of CO2 Injection Flow Rate on Oil Recovery Factor, Gas−Oil Ratio, and Producing Water−Oil Ratio. In this work, different miscible CO2 flooding tests (P > MMP)
Figure 6. Measured oil RF versus the injected pore volume of CO2 at three different injection rates.
volume of CO2 at three different injection rates. The pore volume of injected CO2 at different rate is 2.5. As expected, oil RF is increased with the injected pore volume of CO2. The oil recovery at each injection rate reaches its maximum value after injecting 1.5 pore volumes of CO2 at the most. The increased oil recovery with the injection rate is attributed to the increased solubility of CO2 in oil, increased mobility and reduced viscosity and equilibrium IFT of the crude oil and CO2. Also, the measured accumulative producing water−oil ratio (WOR) versus the injected pore volume of CO2 is plotted in Figure 7. It can be seen from this figure that, prior to water breakthrough at 0.8 pore volume, the producing WOR is extremely low, whereas it increases dramatically after water breakthrough. As oil production begins, the WOR is initially 0 5086
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
Figure 7. Producing variation of WOR versus injection rate of CO2.
Figure 9. Variation of pressure drop for removal of damage due to mechanical plugging mechanism after CO2 flooding versus pore volume of injected cyclohexane.
and more oil is produced before breakthrough as shown in Figure 7. The height of oil column below the perforation decreases as production proceeds. At breakthrough point and after that, WOR increases and oil production decreases. The CO2 injection reduces the interfacial tension between oil and water and also the mobility ratio bur increases capillary number. The gas−oil ratio (GOR) variation versus the injected pore volume of CO2 is shown in Figure 8. It can be concluded that
of asphaltene in cyclohexane solution (measured by spectrophotometer), after reaching a stable differential pressure in cyclohexane reverse flooding, introduces the amount of deposited asphaltene by mechanical plugging mechanism as shown in Table 7. Also, Table 7 indicates that an increase in CO2 injection flow rate is followed by an increase in amount of deposited asphaltene due to mechanical plugging mechanism which is more than those obtained by the adsorption mechanism. Figure 9 shows the variation of pressure due to reversal flow of cyclohexane. It can be found that deposited asphaltene by mechanical plugging mechanism can be removed by cyclohexane reverse flooding. The removal of damge by mechanical plugging mechanism using the reverse cyclohexane flooding takes in a very short time about two pore volume places. This typical experimental study can be proposed to measure deposited asphaltene due to mechanical plugging mechanism and also to remove this formation damage. There are some kinds of uncertainties in asphaltene deposition measurement due to shearing and gravity effects. But the likelihood of these uncertainties is negligible for following reasons: - The cyclohexane reversal flooding is in the laminar flow region which is in the Darcy region and the effect of shear in this region is negligible. - It should be noted that the cyclohexane is a neutral agent which has no effect in adsorbing asphaltenes. - The asphaltene desorption in the core surface takes place over a long time, whereas cyclohexane flooding is a fast process. 4.4. Permeability Reduction Measurement Due to Adsorption Mechanism and Removal by Toluene Flooding. The results of formation damage due to asphaltene deposition by the mechanism of adsorption and recovery of damage are shown in Tables 6 and 7 and Figure 10. As shown in Table 7, the contribution of this mechanism is about 20− 40% of the total percent permeability reduction. It can be found that deposited asphaltene by adsorption mechanism can be removed by toluene reverse flooding. Due to reaction of toluene with adsorbed asphaltene on active sites of the core sample, toluene reverse flooding removes the deposited asphaltene by adsorption mechanisms. Thus, the amount of
Figure 8. Gas−oil ratio (GOR) variation versus the injected pore volume of CO2.
the producing GOR was extremely low before CO2 breakthrough but increased drastically after CO2 breakthrough. Moreover, a higher injection rate generally resulted in a maximum GOR value at 2.0 pore volume of injected CO2. 4.3. Permeability Reduction Measurement Due to Mechanical Plugging Mechanism and Removal by Cyclohexane Flooding. The results of formation damage due to asphaltene deposition by the mechanism of mechanical plugging and recovery of damage are shown in Tables 6 and 7 and Figure 9. Table 6 indicates that 60−80% of the total damage is due to mechanical plugging and can be recovered by simple reverse flow of cyclohexane. So, the mechanical plugging is the dominant mechanism of permeability damage during CO2 flooding. Due to neutrality of cyclohexane on asphaltene precipitation/dissolving, cyclohexane reversal flooding removes the deposited asphaltene on the surface. Therefore, the amount 5087
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
Langmuir isotherm or surface excess equation based on monolayer theory and two material balance equations. In this work, a new model based on multilayer adsorption theory and four material balance equations (oil, asphaltene, light components, and water phase) was developed to account for asphaltene adsorption on core sample during CO2 flooding processes, and the model was verified using experimental data obtained in this work. Figure 11 shows the results of modeling
Figure 10. Variation of pressure drop for removal of damage due to adsorption mechanism after CO2 flooding versus pore volume of injected toluene.
asphaltene in toluene solution (measured by spectrophotometer), after reaching a stable differential pressure in toluene reverse flooding; introduces the amount of deposited asphaltene by adsorption mechanism. The results of experiments on core sample during toluene flooding showed that toluene injection is able to increase the permeability recovery approximately by 80%, after 1.5 pore volume injection of toluene. In fact, the removal of damage caused by the asphaltene adsorption mechanism by the toluene reverse flooding takes a long time, about 3.7 pore volume places. Also, Table 7 shows a decrease in the adsorbed amount of asphaltene with an increase in flow rate. Different explanations have been reported for the effect of flow rate on asphaltene adsorption mechanism as the shear effects, residence time, and zone isolation in the pore space at higher flow rates. Mass transfer is the movement of solute between mobile and immobile zones that states by physical or chemical processes. Physically immobile zones have low hydraulic conductivity and may be of any size including individual mineral grains. Movement between these low-K and high-K zones is by advection and diffusion and occurs over multiple time scales within a porous medium. Sorption and desorption transfer of solute between mobile and immobile states in both the lowand high-K zones increase the capacity for the low-K zones to take up mass and decrease the rate of exchange between zones. Variability in sorption strength and kinetics also adds to the variability in mass-transfer time scales. Mass transfer is considered rate-limited when an exchange time scale is of the same magnitude or longer than the characteristic time scale of advection through the porous medium that may be controlled by advection or diffusion within low-K immobile regions (fast processes) or rate-limited sorption (slow kinetics). Key consequences of mass transfer on solute transport include (1) increased sequestration time within geologic formations; (2) reduction in average solute velocity relative to a conservative solute by up to several orders of magnitude; (3) long tails in concentration histories during movement of solute from a porous media with high permeability; and (4) increased solute mixing and access to rock surface for reactions.25,37,38 4.5. Modified Modeling Approach. In the majority of previous models, the permeability reduction by asphaltene adsorption and deposition during CO2 flooding is modeled by
Figure 11. Comparison of the performance of the multilayer model and model based on in correlating the permeability reduction.
based on the modified model. As shown in Figure 11, the modified model can predict better the experimental adsorption asphaltene data on core sample during CO2 flooding in comparison to those obtained using Langmuir model. Table 8 shows average absolute deviation of the predicted permeability reduction from the experimental data due to asphaltene deposition based on developed and Langmuir model. These results show that the modified model is capable of predicting the permeability reduction experimental data with AADs of 5088
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
Table 8. Absolute Deviation of the Correlated Permeability Reduction from the Experimental Results by the Modified Model and the Studied Model Based on Langmuir Theory absolute deviation of asphaltene deposition modeling (%) CO2 injection flow rate (cm3/h)
modified model
Langmuir model
6 12 18
4.7 5.3 6.8 5.6
6.5 8.4 10.2 8.3
AAD
4.7−6.8%, whereas modeling based on the Langmuir model is less accurate with regard to CO2 flooding processes with AADs 6.5−10.2%. As shown in Table 8 and Figure 11, the asphaltene adsorption behavior is far from Langmuir model and is closer to modified model which is based on multilayer behavior. The asphaltenes adsorption mechanism, which is related to the interactions between the asphaltenes functional groups and the core surface, involves surface polarity, affinity, or other attractive forces. It is known that asphaltene surface groups may be acidic (carboxylic, benzoic, phenolic) and/or basic (pyridine, pyrazine, dimethylsulfoxide).39 Table 9 shows the adjusted parameter values of modeling based on multilayer and monolayer theory for the CO2 flooding process.
Figure 12. Effect of surface deposition rate coefficient on permeability reduction.
Table 9. Adjusted Parameters of the Proposed Model CO2 injection rate (cm3/h) adjusted parameter
6
12
18
wsa,max Ka α β vc γ Γ∞ k1 k2 n m
0.2 2500 0.0094 0.005 0.0015 0.015 166.2 1.49 × 10−4 9.2 × 10−29 11 38
0.2 2500 0.0085 0.0055 0.0021 0.0019 166.2 1.49 × 10−4 9.2 × 10−29 11 49
0.2 2500 0.0051 0.0062 0.0027 0.0012 166.2 1.49 × 10−4 9.2 × 10−29 11 64
Figure 13. Effect of entrainment rate coefficient on permeability reduction.
two mechanisms is dominant, and the other one might be ignored. The effects of pore throat plugging coefficient on asphaltene deposition is shown in Figure 14. The results show that when pore throat plugging coefficient increases deposition of asphaltene at the pore throat increases. Due to this mechanism, partial or total pore plugging is expected. Figure 15 represents the effect of critical velocity on permeability reduction When vc increases, deposited asphaltene increases. Asphaltene deposition continues when the interstitial velocity is less than vc. At critical velocity, the entrainment mechanism is dominant, so the deposited asphaltene decreases.
4.6. Sensitivity Analysis. The asphaltene deposition model comprises some parameters that control the deposition of asphaltene. Sensitivity analysis was done to investigate the effect of each parameter on asphaltene deposition. These parameters are the surface deposition rate coefficient (α), the entrainment rate coefficient (β), the pore throat plugging rate coefficient (γ), and the critical interstitial velocity (vc). Figure 12 shows the effect of surface deposition rate coefficient on permeability reduction. It can be concluded that permeability reduction increases as the value of surface deposition rate coefficient increases. Once the solid phase has adsorbed on the reservoir rock, plugging of the formation is expected. Figure 13 indicates the effect of entrainment rate coefficient on permeability reduction. It can be seen that the permeability reduction decreases with increasing entrainment rate coefficient. The entrainment and surface deposition mechanisms proceed against each other. So, in most situations one of these
5. CONCLUSIONS In this work, a set of experiments was proposed and conducted using bottom hole live oil sample under dynamic conditions in porous media during CO2 flooding with the purpose of studying the CO2 flow rate effect on oil recovery and permeability reduction. Also, a novel experimental procedure was proposed with the purpose of studying the mechanical plugging and adsorption mechanisms involved in the interfacial 5089
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
■
- The experimental results show the contribution of adsorption mechanism in permeability reduction is about 20−40% of the total percent permeability reduction and deposited asphaltene by adsorption mechanism can be removed by toluene reverse flooding that takes place in a long time. - The proposed model based on multilayer theory and four material balance equations is found to be more accurate than the model based on the Langmuir equation. - It can be concluded from sensitivity analysis that permeability reduction increases as the value of surface deposition rate coefficient and pore throat plugging coefficient increases. Also, the permeability reduction decreases with increasing entrainment rate coefficient.
AUTHOR INFORMATION
Corresponding Author
Figure 14. Effects of pore throat plugging coefficient on permeability reduction.
*Tel.:+98 21 66165424. Fax: +98 21 66022853. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The sponsorship of this research by the Research Institute of the Petroleum Industry (RIPI) is gratefully acknowledged.
■
Figure 15. Effect of critical velocity on permeability reduction.
interaction of the asphaltene/mineral rock system using the cyclohexane or toluene reverse flooding. Also, a new model based on multilayer adsorption theory and four material balance equations (oil, asphaltene, light components, and water phase) was developed to account for asphaltene adsorption on the core sample during CO2 injection flooding. The proposed model was verified using experimental data obtained in this work. The sensitivity analysis was also done to investigate the effect of each parameter on the asphaltene deposition. The experimental and modeling results of asphaltene deposition and adsorption during CO2 flooding resulted in several conclusions, as follows. - The experimental results show that an increase in CO2 injection flow rate is followed by an increase in pressure drop and permeability reduction of core sample. - The experimental results indicate that oil RF and GOR is increased with the injected pore volume of CO2 and a higher injection rate of CO2 generally resulted in a maximum GOR value. - The experimental data indicates that 60−80% of the total damage is due to mechanical plugging and can be recovered by cyclohexane reverse flooding rapidly. 5090
NOMENCLATURE Csf = the mass of suspended asphaltenes per mass of the oil phase C = the experimental concentration (mol/L) CA = the volume fraction of the suspended asphaltene precipitates in the liquid phase Dpt = the average pore throat diameter Dptcr = the critical pore throat diameter, assumed constant EA = the volume fraction of the deposited asphaltene in the bulk volume of the porous media Ead = Fractional pore volume of asphaltene adsorbed f = Fugacity Ka = the ratio of adsorption/desorption rate constants k = permeability k1 = First adsorption step parameter (in our case, this step is taken to be adsorption of asphaltenes in solution to the surface of the rock) k2 = the second adsorption step parameter (in our case, this step is taken to be the adsorption of asphaltenes in solution to those asphaltenes already adsorbed to the rock) R = gas constant Soi = initial oil saturation Swc = initial connate water saturation n = the mean aggregation number of the adsorbed asphaltenes (in modified model) u = internal energy uL = the flux of the liquid phase v = molar volume vL = the interstitial velocity of liquid phase vc = the critical interstitial velocity of liquid phase (cm/s) wAL = the dissolved asphaltene in the liquid phase Wasp = asphaltene content of the bottom hole live oil wG = the mass fraction of gas wOL = the mass fraction of the oil in the liquid phase Wsa = the mass of adsorbed asphaltene per mass of rock dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
Energy & Fuels
Article
(15) Civan, F. Modeling and simulation of formation damage by organic deposition, First International Symposium on Colloid Chemistry in Oil Production: Asphaltene and Wax Deposition, Rio de Janeiro, Brazil, November 26−29, 1995. (16) Wang, S.; Civan, F.; Strycker, A. R. Simulation of paraffin and asphaltene deposition in porous media, SPE 50746. SPE International Symposium on Oilfield Chemistry, Houston, Texas, February 16−19, 1999. (17) Nghiem, L.; Kohse, B. F.; Ali, S. M. F.; Doan, Q. Asphaltene precipitation: phase behavior modeling and compositional simulation, SPE 59432. Asia Pacific Conference on Integrated Modeling for Asset Management, Yokohama, Japan, April 25−26, 2000. (18) Kumar, T.; Todd, A. C. A new approach for mathematical modeling of formation damage due to invasion of solid suspensions, SPE 18203. SPE Annual Technical Conference and Exhibition, Houston, Texas, October 2−5, 1988. (19) Kocabas, I.; Islam, M. R.; Modarress, H. J. Pet. Sci. Eng. 2000, 26, 19−30. (20) Wang, S.; Civan, F. Productivity decline of vertical and horizontal wells by asphaltene deposition in petroleum reservoirs, SPE 64991. SPE International Symposium on Oilfield Chemistry, Houston, Texas, February 13−16, 2001. (21) Almehaideb, R. A. J. Pet. Sci. Eng. 2004, 42, 157−170. (22) Monteagudo, J. E. P.; Rajagopal, K.; Lage, P. L. C. Chem. Eng. Sci. 2002, 57, 323−337. (23) Dubey, S. T.; Waxman, M. H. SPE Reservoir Eng. 1989, 6, 389− 395. (24) Murgich, J. Pet. Sci. Technol. 2002, 20, 983−997. (25) Moschopedis, S. E.; Fryer, J. F.; Speight, J. G. Fuel 1976, 55, 227−232. (26) Acevedo, S.; Ranaudo, M. A.; García, C.; Castillo, J.; Fernández, A. Energy Fuels 2003, 17, 257−261. (27) Collins, S. H.; Melrose, J. C. Adsorption of asphaltenes and water on reservoir rock minerals, SPE 11800. SPE Oilfield and Geothermal Chemistry Symposium, Denver, Colorado, June 1−3, 1983. (28) Kokal, S.; Tang, T.; Schramm, L.; Sayegh, S. Colloids Surf. 1995, 94, 253−265. (29) Kariznovi, M.; Nourozieh, H.; Jamialahmadi, M. A.; Shahrabadi,A. Optimization of Asphaltene Deposition and Adsorption Parameter in Porous Media by Using Genetic Algorithm and Direct Search, SPE 114037. SPE Western Regional and Pacific Section AAPG Joint Meeting, Bakersfield, California, March 29−April 2, 2008. (30) Annual Book of ASTM Standards; American Society for Testing and Materials: Philadelphia, PA, 2005; Vol.05.01, Standard No. D2007-03. (31) Annual Book of ASTM Standards; American Society for Testing and Materials: Philadelphia, PA, 2007; Vol.05.01, Standard No. D2172. (32) Annual Book of ASTM Standards; American Society for Testing and Materials: Philadelphia, PA, 2007; Vol.05.01, Standard No. D3279. (33) Flory, P. J. J. Chem. Phys. 1941, 9, 660. (34) Huggins, M. J. J. Chem. Phys. 1941, 9, 440. (35) Zhu, B.-Y.; Gu, T. Colloids Surf. 1990, 46, 339−345. (36) González, G.; Travalloni-Louvisse, A. M. SPE Prod. Facil. 1993, 91−96. (37) Dutta, P. K.; Holland, R. J. Fuel 1983, 62, 732. (38) Jada, A; Salou, M. J. Pet. Sci. Eng. 2002, 33, 185−93. (39) Coats, K. H.; Smith, B. D. SPE J. 1964, 4, 73−84.
wSAL = the mass fractions of the suspended asphaltene precipitates Wsa, max = the maximum adsorbed mass fraction, mg/g wWL = the mass fraction of water in liquid phase Greek Symbols
⌀ = porosity μ = viscosity ρ = density Γ = the amount of adsorbed substance (mol/L) Γ∞ = the maximum possible adsorption for the whole isotherm α = the surface deposition rate coefficient, (1/s) β = the entrainment rate coefficient, (1/cm) γ = the plugging deposition rate coefficient, (1/cm) σ = the snowball-effect deposition constant μp = chemical potential δp = solubility parameter of a liquid Φs = the volume fraction of solvent (liquid oil)
Subscripts
AAD = average absolute deviation cal = calculated exp = exponential function MMP = minimum miscible pressure O = the oil phase pres = reservoir pressure Q = flow rate RF = oil recovery factor Tres = reservoir temperature
■
REFERENCES
(1) Leontaritis, K.; Mansoori, G. J. Petr. Sci. Eng. 1988, 1, 229−239. (2) Sarma, H. K. Can We Ignore Asphaltene in a Gas Injection Project for Light-Oils? SPE 84877. SPE International Improved Oil Recovery Conference, Kuala Lumpur, Malaysia, October 20−21, 2003. (3) Sim, S. S. K.; Takabayashi, K.; Okatsu, K.; Fisher, D. AsphalteneInduced Formation Damage: effect of Asphaltene Particle size and core permeability, SPE 95515. SPE Annual Technical Conference, Dallas, Texas, USA, October 9−12, 2005. (4) Srivastava, R. K.; Huang, S. S.; Mingzhe, D. SPE Prod. Facil. 1999, 14, 235−245. (5) Bagheri, M. B.; Kharrat, R.; Ghotbi, C. Rev. Inst. Fr. Pet. 2011, 66 (3), 1−13. (6) Moghadasi, J.; Kalantari-Dehghani, A. M.; Gholami, V.; Abdi ; R. Formation Damage Due to Asphaltene Precipitation Resulting From CO2 Gas Injection In Iranian Carbonate Reservoirs SPE 99631. SPE Europe/EAGE Annual Conference and Exhibition, Austria, June 12−15, 2006. (7) Zanganeh, P.; Ayatollahi, S.; Alamdari, A.; Zolghadr, A.; Dashti; Kord. Energy Fuels 2012, 26, 1412−1419. (8) Okwen, R. T. Formation damage by CO2 induced Asphaltene Precipitation, SPE 98180. SPE International Symposium and Exhibition on Formation damage control, Lafayet, LA, February 15−17, 2006. (9) Nobakht, M.; Moghadam, S.; Gu, Y. Fluid Phase Equilib. 2008, 265, 94−103. (10) Hamouda, A. A.; Chukwudeme, E. A.; Mirza, D. Energy Fuels 2009, 23, 1118−1127. (11) Ali, M. A.; Islam, M. R. The effect of asphaltene precipitation on carbonate rock permeability: An experimental and numerical approach, SPE 38856. SPE Annual Technical Conference and Exhibition, San Antonio, October 5−6, 1997. (12) Gruesbeck, C.; Collins, R. E. Soc. Pet. Eng. J. 1982, 22, 847−856. (13) Minssieux, L.; Nabzar, L.; Chauveteau, G.; Longeron; Bensalem, R. Rev. Inst. Fr. Pet. 1998, 53 (3), 313−327. (14) Leontaritis, K. J. Asphaltene near-wellbore formation damage modeling. SPE 39446. Formation Damage Control Conference, Lafayette, Louisiana, February 18−19, 1998. 5091
dx.doi.org/10.1021/ef300647f | Energy Fuels 2012, 26, 5080−5091
