Abstract

Asphaltene deposition is a common phenomenon during CO2 flooding in ultralow permeability reservoirs. The deposited asphaltene occupies the pore volume and decreases permeability, resulting in serious formation damage and pore well productivity. It is urgent to investigate the asphaltene deposition mechanisms, adverse effects, and preventive measures. However, few asphaltene deposition investigations have been systematically conducted by now. In this research, the asphaltene precipitation mechanisms and adverse effects were comprehensively investigated by using experimental and numerical methods. To study the effects of pressure, asphaltene content, and temperature on asphaltene precipitation qualitatively and quantitatively, the microscope visible detection experiment and the PVT cell static experiment were firstly conducted. The adverse effects on porosity and permeability resulted from asphaltene deposition were also studied by the core flooding experiment. Secondly, simulation models of asphaltene precipitation and deposition were developed and validated by experimental data. Finally, a case study from Changqing oil field was presented to analyze the asphaltene deposition characteristic and preventive measures. The experimental results showed that the asphaltene precipitation increases with the increased pressure before reaching the minimum miscible pressure (MMP) and gets the peak value around the MMP, while decreases slowly. The asphaltene precipitation increases with the increased temperature and asphaltene content. The variation trend of adverse effects on porosity and permeability resulted from asphaltene deposition is similar to that of asphaltene precipitation under the influence of pressure, asphaltene content, and temperature. The case study shows that the water-altering-gas (WAG) with high injection rate suffers more serious asphaltene deposition compared with the WAG with low injection rate, for the asphaltene precipitation increases as the increased pressure before reaching the MMP. The CO2 continuous injection with high injection rate is the worst choice, for low sweep efficiency and the most severe formation damage. Thus, the WAG with optimal injection rate was proposed to maintain well productivity and to reduce formation damage resulted from asphaltene deposition during developing ultralow permeability reservoirs.

1. Introduction

CO2 flooding is a favorable enhanced oil recovery and carbon geosequestration method particularly for reservoirs with ultralow permeability [15]. Due to the low viscosity of CO2, the CO2 injectivity is better than that of water [6]. And the CO2 addition can change the oil composition and fluid property [7, 8]. As the CO2 added in oil increases, the oil swells and the volume increases, which results in the decreased oil viscosity and the increased mobility [9]. What is more, the increasing CO2 addition also leads to an considerable decrease in interfacial tension between CO2 solvent and oil, which results in the residual oil saturation decreases greatly and the displacement efficiency increases significantly [10, 11]. Due to the advantages of CO2 flooding, it has been widely applied in oil reservoirs particularly with ultralow permeability and received a remarkable development effect on site [12, 13]. However, adverse effects of CO2 flooding also come; the oil composition change caused by CO2 addition results in asphaltene precipitation [1417]. Part of precipitated asphaltene suspends in the fluid and flows away. The remained asphaltene precipitation deposits on the porous medium [18, 19] and narrows the pore space and throat, which leads to formation damage and brings negative influence on well productivity [2022]. The formation damage resulted from asphaltene deposition is difficult to remedy and results in economic losses [23], so predicting the asphaltene deposition and avoiding the formation damage have attracted much attention and are very important to improve oil recovery particularly for ultralow permeability reservoirs.

The asphaltene precipitates from the crude oil and then deposits on the porous medium. The mechanisms of asphaltene precipitation and deposition have been widely studied in literature. It is recognized that resins stabilize the asphaltene and act as oil stabilize agent [18, 19]. The ratio of asphaltene content to resin content is taken as the stability index to evaluate asphaltene precipitation possibility and oil stabilization [24]. Investigations on asphaltene precipitation were conducted using the static PVT cell. It has been found that the influences of pressure on asphaltene precipitation during CO2 flooding and water flooding are different. The precipitated asphaltene reaches the maximum value around the saturation pressure for water flooding [25, 26]. However, the asphaltene precipitation reaches the maximum value near the minimum miscible pressure (MMP) for CO2 flooding [27, 28]. The influence of pressure on asphaltene precipitation is more severe than that of temperature. The asphaltene precipitation increases slightly with the increased temperature [29]. [30, 31] studied the impact of asphaltene content of crude oil on asphaltene precipitation and concluded that the possibility of asphaltene precipitation is also great for light oil with small asphaltene content. The process of asphaltene deposition is more complex than asphaltene precipitation, for the porous medium property has an obvious influence on asphaltene deposition. The core flooding dynamic experiment is always conducted to study the asphaltene deposition. It has been found that the ratio of asphaltene particle to pore throat diameter affects the asphaltene deposition significantly [20, 32]. The experiments discussed above rarely investigate the asphaltene precipitation and deposition systematically. In this research, three kinds of experiment were conducted to study the asphaltene precipitation and deposition from different aspects considering the effects of pressure, temperature, and asphaltene content during CO2 flooding.

Many models predicting the asphaltene precipitation and deposition were proposed. The asphaltene precipitation models with different bases were mainly classified into two categories. Most researchers hold the point that the precipitated asphaltene is reversible, and lots of models proposed are based on that [3339], such as Flory-Huggins solubility model, solid model, and dense-liquid model. However, few researchers think the precipitated asphaltene is irreversible, and models proposed by [40, 41] are based on that. They considered that resins can hardly recovery once destroyed, so the stability of oil can never recovery once decreased. Among the developed models describing the asphaltene deposition, the simulation model proposed by [42] is widely applied in many researches, considering the effects of asphaltene absorption on the pore surface, asphaltene entrainment by high velocity, and asphaltene precipitation plugging throat. The asphaltene precipitation and deposition reduce pore spaces and narrow seepage throats, which lead to the decreased porosity and permeability, and many models were also proposed to describe this phenomenon [4345]. In this research, we choose models developed by Wang and Civan [42] and Kohse and Nghiem [38] to describe the asphaltene deposition and precipitation, respectively.

Based on the stated above, we systematically investigated the asphaltene precipitation and deposition by using experimental and numerical methods. Firstly, three kinds of experiments from different aspects were conducted: the asphaltene precipitation microscopic detection experiment, the PVT cell static asphaltene precipitation experiment, and the core flooding dynamic asphaltene deposition experiment. These experiments were designed to study the influence of pressure, asphaltene content, and temperature on asphaltene precipitation and deposition from different aspects. Then, the simulation models of the asphaltene precipitation and deposition were built. The good match between the results calculated by models, and the experimental data validates the simulation models. Finally, the asphaltene deposition characteristic was investigated through a case study based on X block from Changqing oil field under different injection patterns and injection rates. Suggestions on how to reduce formation damage caused by asphaltene damage were proposed, which are very useful for engineers to enhance oil recovery.

2. Experiment Study

Three different kinds of experiments were designed to study the asphaltene precipitation and deposition from different aspects considering the influences of pressure, asphaltene content, and temperature. The microscopic detection experiment studied the asphaltene precipitation qualitatively at the microscale. The PVT cell static experiment further evaluated the asphaltene precipitation quantitatively. The core flooding dynamic experiment was more close to realistic condition considering the effects of porous medium structure and multiple contact processes between injected CO2 and oil on asphaltene precipitation and deposition.

Three Changqing oil samples with different asphaltene content were investigated in this study. The four-component analysis and the oil composition of the three samples were shown in Tables 1 and 2, respectively. Yen et al. [24] proposed the asphaltene stability index CII to describe the possibility of asphaltene precipitation. The Changqing oil samples are very unstable and the possibility of asphaltene precipitation is very high, for the asphaltene precipitation index CII is much higher than the critical value 0.9.

2.1. Asphaltene Precipitation Microscopic Detection Experiment

The microscopic solid detection experiment qualitatively evaluated the asphaltene precipitation under experimental pressures and temperatures. Figure 1 shows the microscopic solid detection experimental apparatus. It mainly consists of a pressure control device, a temperature control device, two piston cylinders, a reaction vessel, and an imaging system.

The microscopic solid detection experimental procedures are as follows: (1) The CO2 was injected in the reaction vessel, and the vessel was maintained at desired temperatures and pressures. Firstly, the reaction vessel was maintained at 8.0 MPa, which is 0.2 MPa above the saturation pressure to avoid the release of dissolved gas. (2) Then, 2.5 ml oil sample was injected in the reaction vessel with low flow rate so as to form an oil film with a thickness of 0.032 cm. (3) The imaging system was employed to capture the microscope property of CO2-oil mixture online. The precipitated asphaltene amount was qualitatively evaluated by comparing the difference of captured images. (4) Repeat the above procedures, asphaltene precipitation under different pressures and temperatures were captured and analyzed. The oil samples, experimental pressures, and experimental temperatures in the microscopic detection experiment were shown in Table 3.

Figure 2 shows the asphaltene precipitation microscope images under different pressures at the same temperature 50°C. The precipitated asphaltene particles present as black dots marked on the images. There is no precipitated asphaltene present at 8 MPa for no black dots marked on the image. With the increase of pressure, the black dots marked on the picture increase, which indicates the increased pressure results in the increased asphaltene precipitation.

Figure 3 shows the asphaltene precipitation microscope images under different temperatures at the same pressure 15 MPa. The amount of precipitated asphaltene qualitatively evaluated by comparing the black dots number. The pictures show that with the increase of temperature, the number of black dots increase, indicating that the precipitated asphaltene increases with the increased temperature.

2.2. Asphaltene Precipitation Static Experiment

The microscopic solid detection experiment can only evaluate the asphaltene precipitation qualitatively, while the static PVT experiment can evaluate asphaltene precipitation quantitatively. Figure 4 shows the static PVT apparatus for asphaltene precipitation studies. It mainly consists of a PVT piston cylinder, a syringe pump, and few pressure regulators. The PVT piston cylinder was acted as reaction vessel for CO2 and crude oil mixture. The PVT cylinder was maintained at the desired pressures and temperatures by using the syringe pump and the thermostat, respectively. The CO2 and crude oil mixture reached an equilibrium state after a long reaction time at a certain pressure and temperature. The precipitated asphaltene amount was measured quantitatively by comparing the difference of asphaltene content between flashed crude oil and original crude oil.

The detailed static PVT experimental procedures of asphaltene precipitation are as follows: (1) The PVT piston vessel was first charged with enough pure CO2 and then was maintained at the desired pressure and temperature for 2 hours. To avoid the release of solution gas in crude oil, the maintained pressure is higher than the saturation pressure. (2) The PVT piston vessel then was charged with certain crude oil. To let the mixture of CO2 and crude oil have enough time to reach equilibrium state, more than 4 hours reaction time was needed. (3) After the asphaltene was fully precipitated, the reaction oil was flashed out the PVT cell and measured the amount of remained asphaltene. (4) The amount of precipitated asphaltene was calculated on the base of material’s balance. The asphaltene precipitation amount is equal to the change of asphaltene content between the flashed oil and the original crude oil.

Figure 5 shows the amount of precipitated asphaltene with pressure change when temperature at 50°C and asphaltene content is 0.93%. The asphaltene precipitation amount increases with the increased pressure below the MMP and significantly increases and gets the maximum value around the MMP at 14.8 MPa. After the pressure exceeds the MMP, the asphaltene precipitation decreases with the increased pressure. The main reason behind the phenomenon is that the dissolved CO2 in oil increases with the increased pressure below the MMP, which results in the oil composition changes and the equilibrium state breaks, so the precipitated asphaltene increases. With the increase of pressure after reaching the MMP, the oil becomes denser and asphaltene solubility increases, which lead to the decrease of asphaltene precipitation.

Figure 6 shows the asphaltene precipitation amount with temperature change when pressure at 15 MPa and asphaltene content is 0.93%. Increasing temperature results in an obvious increase in asphaltene precipitation when the temperature is at the range of 30°C to 40°C. After that, the asphaltene precipitation increases slightly with the increased temperature. This is because the increased temperature results in the instability of resins, which act as the oil-stabilizing agent. With the increase of temperature, the instability of resins increases resulting in the slightly increase of asphaltene precipitation.

Figure 7 shows the asphaltene precipitation amount with asphaltene content change when pressure is at 15 MPa and temperature at 50°C. Figure 7 shows the increased asphaltene content results in a significant increase in asphaltene precipitation. The asphaltene content of three oil samples are 0.43%, 0.93%, and 1.32%, respectively. The asphaltene precipitation amount of three oil samples is 0.33%, 0.45%, and 0.74%, respectively. The ratio of asphaltene precipitation amount to asphaltene content of the three oil samples are 76.7%, 48.4%, and 56.1%, respectively. Further analysis indicates that the increased asphaltene content always results in the increased asphaltene precipitation, but the ratio of asphaltene precipitation amount to asphaltene content does not follow this rule. The crude oil with the least asphaltene content has the biggest ratio of asphaltene precipitation amount to asphaltene content, which accounts for the light oil with low asphaltene content suffering from severe asphaltene precipitation.

2.3. Asphaltene Deposition Dynamic Experiment

The asphaltene firstly precipitates from the crude oil and then deposits on the pore surface. Asphaltene precipitation process was studied using microscopic detection experiment and PVT cell static experiment. Asphaltene deposition process is not only influenced by pressure and temperature but also porous medium structure, so core flooding dynamic experiments were conducted. Compared with the PVT cell static experiment, the core flooding asphaltene deposition dynamic experiment is closer to realistic condition considering the influence of porous media structure and the multiple contact process between CO2 and oil. The adverse influences of asphaltene deposition on core porosity and permeability under different pressures, temperatures, and asphaltene contents were studied. Figure 8 shows the asphaltene deposition dynamic experimental apparatus. It mainly consists of the ISCO pump, back pressure value, core holder, thermostat, and metering device. The thermostat and pump were used to maintain the required temperature and pressure, respectively.

The dynamic experimental procedures of asphaltene deposition are as follows: (1) The core original porosity was measured using the weight method. The core original absolute permeability was also measured by core flooding experiment based on Darcy’s law. (2) We injected the crude oil sample into the core already saturated with formation water until the oil was fully saturated the core at the studied pressure and temperature. (3) We continuously injected the pure CO2 into the core at a slow rate 0.01 ml/min until almost no oil flows out. (4) The flashed core porosity and permeability were measured using weight method and core flooding experiment, respectively. (5) The variations of porosity and permeability between the original core and the flashed core were calculated, and they were used to evaluate the effects of asphaltene deposition on the core. Table 4 shows the core parameters and studied pressures and temperatures in these experiments.

The deposited asphaltene occupies the pore space and narrows the pore throat resulting in the decreased porosity and permeability, respectively. We used the reduction rates of porosity and permeability to characterize the influences of asphaltene deposition on porous media porosity and permeability, respectively. The porosity reduction rate iscalculated by

The permeability reduction rate is calculated by

Figure 9 shows the porosity and permeability reduction rates with pressure change. The change trends of porosity and permeability reduction rates with pressure change are the same, for porosity and permeability have strong positive correlation. The porosity and permeability reduction rates increase with the increase of pressure before reaching the MMP and get the maximum value around the MMP, which indicates the formation damage is the worst around the MMP. However, the porosity and permeability reduction rates decrease with the increased pressure after exceeding the MMP. The reason lies in that the CO2 dissolved in the oil increases with the increase of pressure below the MMP and gets the maximum value around the MMP. Due to the increase of asphaltene precipitation and deposition resulted from the increased CO2 solubility in oil, the porosity and permeability reduction rates increase. However, the oil density increases with the increased pressure after exceeding the MMP, leading to the increase of asphaltene solubility, so the deposited asphaltene decreases and the porosity and permeability reduction rates decrease.

Figure 10 shows the porosity and permeability reduction rates change along with temperature. The porosity and permeability reduction rates increase with the increase of temperature. This is because the increased temperature destroys the structure of resins, which have the function of stabilizing the asphaltene. The instability of resins leads to the increased asphaltene precipitation and deposition and the increased occupied pore spaces and throats, so the porosity and permeability reduction rates increase.

Figure 11 shows the porosity and permeability reduction rate change along with asphaltene content. The porosity and permeability reduction rates increase with the increase of asphaltene content. This is because the increased asphaltene content increases the possibility of asphaltene precipitation and deposition. For the increased asphaltene deposition attributes to the decrease of porosity and permeability, the porosity and permeability reduction rate increases.

3. Simulation Method

The static and the dynamic experiments have provided amount of data for characterizing the realistic phenomena. To further analyze main factors influencing asphaltene precipitation and deposition, the numerical simulation method is needed.

3.1. Asphaltene Precipitation Static Simulation

The asphaltene precipitation model developed by Kohse and Nghiem [38] was used in this research. The model assumes that the precipitated asphaltene is reversible, that is, the asphaltene precipitation increase process and decrease process happen at the same time. Considering the difference of the two adverse process rates, the amount of asphaltene precipitation is calculated. where Ra is the asphaltene precipitation rate, and are the asphaltene precipitation and the precipitated asphaltene dissolution rate coefficient, and and are the volumetric concentration of precipitated asphaltene dissolution and asphaltene precipitation, respectively.

The rate coefficients of asphaltene precipitation and precipitated asphaltene dissolution need to be determined. They are influenced by many related factors, for example pressure, temperature, oil composition change, and porous medium structure. The two coefficients mimicking the asphaltene precipitation at studied pressure and temperature were tuned and achieved by matching the experimental data. The comparison of asphaltene precipitation simulation predicted and experimental data was shown in Figure 12. The good match between experimental data and simulation predicted data validates the asphaltene precipitation model and provides the basis for further simulation studies.

3.2. Asphaltene Deposition Dynamic Simulation

The model accounting for asphaltene deposition proposed by Wang and Civan [42] is widely used and generally accepted. The model precisely describes the asphaltene deposition phenomenon with the consideration of pore throat plugging, surface deposition and deposited particle entrainment. The asphaltene firstly precipitates from the crude oil and then deposits on the surface of porous medium because of the variation of pressure, oil composition and temperature. The asphaltene surface deposition results in the decreased porosity and permeability, so the flow rate decreases for the increased flow resistance. To keep the original flow rate, the increased displacement pressure gradient is needed, which results in the increase of interstitial oil velocity. Once the increased interstitial oil velocity exceeds the critical value, the surface deposited asphaltene is entrained, otherwise no deposited asphaltene is entrained. The precipitated asphaltene may directly plugs the small throat and no asphaltene is entrained away, which is called the pore throat plugging. The asphaltene deposition model developed by Wang and Civan [42] considers these phenomena, and the asphaltene deposition rate is calculated where is the asphaltene deposition volume each grid block. is the rate coefficient of surface deposition, and is the volumetric concentration of asphaltene precipitation. is the pore throat plugging coefficient, and is the Darcy velocity of oil phase. is the entrainment coefficient of deposited asphaltene, is the velocity of interstitial oil, and is the critical velocity of interstitial oil.

The deposited asphaltene occupies the pore space of porous media, which results in the decrease of porosity. The instantaneous porosity is calculated by

The permeability also decreases due to the decrease of porosity. The power law function [43] was used to calculate the instantaneous permeability

The coefficients used in the asphaltene deposition model were tuned by matching the experimental values. Table 5 shows the detailed parameters turned and obtained by matching experimental data. The comparison of asphaltene deposition experimental data and simulator predicted data is shown in Figure 13. The asphaltene deposition model was validated by the good match between the experimental data and the simulator predicted data.

4. Case Study

Due to the good match of the simulation predicted data and the experimental data, the simulation models of asphaltene precipitation and deposition were validated, which is important for further simulation investigation. We assumed that the reservoir is isothermal, and only investigated the influence of pressure on asphaltene deposition during CO2 flooding, and different pressure cases were set through controlling different gas injection rates. A simulation model based on X block of Changqing oil field was built to investigate asphaltene deposition characteristics under different production patterns and injection rates, and the guidance on reducing formation damage and maintain well productivity was provided.

The X block of Changqing oil field with average permeability 0.39 mD and porosity 7.1% is an ultralow permeability reservoir. The W2 oil sample with asphaltene content 0.93% is taken from that. The X block bury depth is 1780 m, the reservoir pressure is 16.3 MPa, and the temperature is 48.8°C. The oil viscosity and gravity are 2.07 mPa·s and 0.78 g/cm3, respectively, when pressure at 8.96 MPa and temperature at 48.8°C. The MMP was measured at 14.8 MPa at reservoir condition by slim tube experiment. Figure 14 shows the rhombic inverted nine-spot pattern of X block, and X60-22, X60-24, X62-22, and X62-24 wells acted as injection well, other wells acted as production well. The well array and well space are 150 m and 500 m, respectively. In 2004, X block began to conduct water flooding development, and the water cut reached 48.5% by 2013, while the oil recovery factor is 3.79% far below the expected value. The high reservoir heterogeneity results in the increased invalid water injection that is more injected water flows along high permeability layers or dominant channels and early breakthroughs, thus some production wells produce more water and less oil as Figure 15 shows.

We first investigated the influence of injection pattern on asphaltene deposition, and the water-altering-CO2 (WAG) injection pattern and continuous CO2 injection with same injection rate 8000 sm3/day were simulated. For WAG, the water and CO2 injection slug keeps 1 : 1, and each of water and CO2 slug injection period keeps 3 months. As Figure 16 shows, the asphaltene deposited around the gas injection well, and the continuous CO2 injection suffers more serious asphaltene deposition than the WAG. The reason behind this phenomenon is that the CO2 continuous injection provides more CO2 than the WAG, and the increased CO2 dissolved in reservoir oil results in the increase of asphaltene deposition. The calculation results shown in Figures 17 and 18 further illustrate that quantitatively. The decreased oil recovery caused by asphaltene deposition of CO2 continuous injection and WAG are 2.7% and 0.9%, respectively. What is more, the oil recovery of WAG is superior to the CO2 continuous injection, for the WAG improves sweep efficiency by controlling mobility particularly for high permeability heterogeneity reservoirs. Therefore, the WAG was suggested to reduce formation damage and achieve favorable oil recovery compared with the CO2 continuous injection.

Then, we further investigated the influence of the WAG injection rate on asphaltene deposition. Two different CO2 injection rates 8000 sm3/day and 6000 sm3/day were set, representing high- and low-pressure cases, respectively. Figures 19 and 20 show the pressure and asphaltene deposition distributions at high and low injection rates, respectively. The pressure around the gas injection well is higher than that around the production well. The asphaltene deposition around the gas injection well is very rich and decreases along the mainstream line between the injection well and the production well. This is because the asphaltene deposition increases with pressure below the MMP and gets the maximum value around the MMP, so asphaltene deposition decreases along the mainstream line. However, there is few asphaltene depositions near the gas injection well, for many of them were carried away with high flow rate. The high injection rate leads to more serious asphaltene deposition than the low injection rate as Figures 19(b) and 20(b) show, resulting in more serious formation damage and lower oil productivity. This is because the increased pressure before the MMP leads to the increase of asphaltene precipitation and the pressure increases with the injection rate. However, further investigations are needed to determine the optimal injection rate changed with production time for reducing formation damage resulted from asphaltene deposition. Thus, the WAG with optimal injection rate was proposed to reduce formation damage and to maintain well productivity.

5. Summary and Conclusions

In this study, the asphaltene deposition during developing ultralow permeability reservoirs by CO2 flooding was systematically investigated by using experimental and numerical methods, and many conclusions have been drawn. (1)The experiment results show that the precipitated asphaltene increases with the increased pressure before reaching the MMP and gets the maximum value around the MMP, while decreases with the increased pressure after exceeding the MMP. This is because the increased pressure before reaching the MMP increases the CO2 solubility in oil, which leads to the increased instability of resins acted as oil stability agent. The increased asphaltene solubility increases with pressure above the MMP, leading to the decrease of asphaltene precipitation. The precipitated asphaltene increases with the increased temperature, for increased temperature leads to the increased instability of resins. The increased asphaltene increases with the increased asphaltene content; this is because the increased asphaltene content increases the asphaltene precipitation possibility(2)The variation trend of adverse effects on porosity and permeability resulted from asphaltene deposition is similar to that of asphaltene precipitation considering the influences of pressure, asphaltene content, and temperature(3)The asphaltene deposition were further investigated based on the asphaltene precipitation and deposition models through a case study based on X block of Changqing oil field. The simulation results show that the decreased oil recovery resulted from asphaltene deposition of the CO2 continuous injection is higher than that of the WAG injection; this is because more CO2 is injected and mixtures with reservoir oil resulting in an increase in asphaltene deposition. The WAG with high injection rate has higher asphaltene deposition than that of the WAG with low injection rate, for the asphaltene deposition increases with the increased pressure proportional to injection rate before reach the MMP. Therefore, the WAG with optimal injection rate is suggested to reduce formation damage and maintain high productivity(4)The asphaltene deposition characteristics of CO2 flooding were also studied. Asphaltene depositions decrease along the mainstream line, because asphaltene depositions increase with an increased pressure and get the maximum value around the MMP. There are few asphaltene depositions near the gas injection well, for many of them were carried away with high flow rate

Nomenclature

:Asphaltene precipitation rate, fraction
:Asphaltene precipitation rate coefficient,/day
:Precipitated asphaltene dissolution rate coefficient, /day
:Volumetric concentration of precipitated asphaltene dissolution, fraction
:Volumetric concentration of asphaltene precipitation, fraction
PorR:Porosity reduction rate, fraction
:Original core porosity, fraction
:Flashed core porosity, fraction
PermR:Permeability reduction rate
:Original core permeability, mD
:Flashed core permeability, mD
:Asphaltene deposition volume each grid block
:Rate coefficient of surface deposition, /sec
:Pore throat plugging coefficient, /cm
:Oil phase Darcy velocity, m/day
:Entrainment coefficient of deposited asphaltene,/cm
:Interstitial oil velocity, m/day
:Critical interstitial oil velocity, m/day
:Power law exponent, fraction.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The National Natural Science Foundation of China (U1762210), “Key scientific problems of seepage law and efficient development of ultra-low permeability reservoirs”, and the National Natural Science Foundation of China (51604243, 52004247) supported this work. Also, thanks for the Opening Fund of the Key Laboratory of Unconventional Oil & Gas Development (China University of Petroleum (East China)), Ministry of Education and the Fundamental Research Funds for the Central Universities.