Copyright © the author(s). This work is licensed under a Creative Commons Attribution 4.0 International License. DOI:10.14800/IOGR.1187 Received March 23, 2021; revised May 15, 2021; accepted June 18, 2021. *Corresponding author: dongzz@xsyu.edu.cn 1 Research on Oil-CO2-Water Relative Permeability of the Low Permeability Reservoir Based on History Matching Fengli Zhang, Tianjin Branch of CNOOC, Tianjin, China; Wenfeng Lv, Research Institute of Petroleum Exploration and Development (RIPED), PetroChina, Beijing, China; Yongyi Zhou, North China Petroleum Bureau, Sinopec, Zhengzhou, China; Bochao Qu,Yawen He, Xinle Ma, Weidong Tian, and Zhenzhen Dong*, Xi’an Shiyou University, Xi’an, China Abstract Accurate prediction of the relative permeability curve provides the basis for study of the CO2 flooding effects (such as swept volume and oil displacement efficiency) and optimization of the CO2 flooding plan. Considering that laboratory experiments are time-consuming and effort-consuming, and experimental results are easily affected by external factors, a method was proposed to calculate the relative permeability curve of the oil-CO2-water multiphase fluid based on particle swarm optimization (PSO). The typical CO2 flooding experiments in the low-permeability cores were performed, a multiphase flow numerical model was established in CMG-GEM, and 26 parameters of the model were optimized using the PSO method. The results of the model fitting are consistent with the results of the experiment, and the relative permeability of oil-CO2 water, the capillary pressure of oil-water and the capillary pressure of gas-liquid of the low-permeability core were obtained. The validity of the model was verified in the research that the prediction from the numerical model is consistent with the laboratory experiment results. This study provides guidance for determining the oil-CO2-water relative permeability of the low-permeability core. Introduction The relative permeability curve, a parameter reflecting the seepage law of multi-phase fluids in the porous media, is used to describe the movement of each fluid phase in the reservoir and predict the basic production index such as oil recovery rate, ultimate recovery factor, and water cut, and it is an important indicator in reservoir evaluation(Zhang et al. 2010). The relative permeability curve is of great significance to the study of fluid distribution in the process of CO2 flooding, and it is used to understand the characteristics of both miscible and immiscible CO2 flooding(Zhang et al. 2019). Therefore, accurate prediction of the relative permeability curve in CO2 flooding provides the basis for the study of the swept volume, the oil displacement effect, fine reservoir description, and plan optimization in CO2 flooding(Zhang et al. 2016). Currently, the oil-water relative permeability curve is obtained through the steady-state method, the transient method, and the history matching method(Toth et al. 2002; Li et al. 2018; Li 1989; Eydinov et al. 2009). mailto:dongzz@xsyu.edu.cn 2 Typical CO2 Flooding Experiment of Low-Permeability Cores Experimental Materials and Fluids. The CO2 flooding device in the low-permeability core is shown in Figure 1. Figure 1—Device of displacement in the low-permeability core: 1.Displacement pump; 2.Oil vessel; 3.CO2 gas vessel; 4.Brine vessel; 5.Long core clamp; 6.Thermostat; 7.Pressure sensor; 8.Inspection window; 9.Pressure relief valve; 10.Separation bottle; 11.Sample tap; 12.Gasometer. Constant composition expansion experiments of the oil from low- permeability reservoirs were carried out to obtain the in-place oil and its volume factor. The fluid model was established by dividing the pseudo- components through PVT fitting. The compositions of original components and pseudo-components are listed in Table 1. Table 1—Pseudo-components of fluids in low-permeability reservoirs. Original components Mole compositions, mol% Post-division components Mole compositions, mol% CO2 0.113 CO2 0.11 N2 1.39 N2 -CH4 22.90 CH4 21.533 C2H-C3H 5.26 C2H6 3.148 IC4-C6 1.76 C3H8 2.119 C7-C11 23.31 i-C4H10 0.348 C11-C20 23.31 n-C4H10 0.658 C21+ 23.31 i-C5H12 0.167 n-C5H12 0.216 C6H14 0.367 C7+ 69.941 Total 100 100 The fitting error of fluid viscosity and density with the pressure of the experiment is less than 5% (Figures 2 and 3). 3 Figure 2—Fitting result of the oil viscosity at the formation temperature. Figure 3—Fitting result of the oil density at the formation temperature. Experimental Method. The experiments of water flooding in the cores under the formation state were performed. Water flooding continued until the water cut is above 98% and is stabilized for a period of time. Then, CO2 flooding started and continued until the core is at the residual oil state. In the experiments, the displacement pressure and the oil, water and gas production were recorded at the designed time interval. The basic parameters of the displacement experiment of the cores from the low permeability reservoirs are listed in Table 2. Table 2—Basic parameters and conditions of the displacement experiment of the cores from the low permeability reservoirs. Parameters Values Experimental temperature (oC) 75.0 Experimental pressure (MPa) 17 Water injection rate (cm3/min) 0.1 CO2 injection rate (cm3/min) 0.1 Air permeability (mD) 1.2 Porosity (%) 13.2 Irreducible water saturation (%) 35 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 O il V is co si ty ( c p ) Pressure(kPa) Oil Visc. Exp. Oil Visc. Legend 640 660 680 700 720 740 760 780 800 0 5000 10000 15000 20000 25000 30000 35000 O il d e n si ty ( k g /m 3 ) Pressure(kPa) Oil density Exp Oil density(kg/m3) Legend 4 Results. The experimental results are shown in Figure 4, which include gas-oil ratio, water cut, injection well bottom-hole pressure, and oil recover. In the water flooding period, the water cut increases to 98%, the gas-oil ratio is zero, and the recovery factor increases to 41%. During CO2 flooding period, gas-oil ratio rises up quickly in the beginning and stabilizes around 14900 m3/m3, water cut drops dramatically and then increases to 80%, and the oil recovery increases from 41% to 89%. (a)Gas-oil Ratio, m3/m3 (b)Water Cut, % (c) Injection Well Bottom-hole Pressure, kPa (d)Oil Recovery, % Figure 4—Results of displacement experiment of the low-permeability cores. Theoretical Model Relative Permeability Curve Model of CO2 Flooding. The compositional model in the commercial software CMG was used to simulate CO2 flooding, and the Corey model of the relative permeability model in CMG was first proposed and has been widely adopted(CMG Manual 2015). The Corey model is expressed as follows. Oil and water relative permeability 𝑘𝑟𝑤 = 𝑘𝑟𝑤𝑖𝑟𝑜 × ( 𝑆𝑤−𝑆𝑤𝑐𝑟𝑖𝑡 1−𝑆𝑤𝑐𝑟𝑖𝑡−𝑆𝑜𝑖𝑟𝑤 ) 𝑛𝑤 ,…………………………………………………………....………(1) 𝑘𝑟𝑜𝑤 = 𝑘𝑟𝑜𝑐𝑤 × ( 𝑆𝑜−𝑆𝑜𝑟𝑤 1−𝑆𝑤𝑐𝑜𝑛−𝑆𝑜𝑟𝑤 ) 𝑛𝑜𝑤 .…………………………………………………..………….........(2) Gas and liquid relative permeability 5 𝑘𝑟𝑜𝑔 = 𝑘𝑟𝑜𝑔𝑐𝑔 × ( 𝑆𝑙−𝑆𝑜𝑟𝑔−𝑆𝑤𝑐𝑜𝑛 1−𝑆𝑔𝑐𝑜𝑛−𝑆𝑜𝑟𝑔−𝑆𝑤𝑐𝑜𝑛 ) 𝑛𝑜𝑔 ,……………………….…………………………......……...(3) 𝑘𝑟𝑔 = 𝑘𝑟𝑔𝑐𝑙 × ( 𝑆𝑔−𝑆𝑔𝑐𝑟𝑖𝑡 1−𝑆𝑔𝑐𝑟𝑖𝑡−𝑆𝑜𝑖𝑟𝑔−𝑆𝑤𝑐𝑜𝑛 ) 𝑛𝑔 ..…………………………..…………………..………......……(4) The relationship between the capillary pressure and the saturation of core is expressed as follows. Oil and water 𝑝𝑐𝑜𝑤 = [𝑝𝑐𝑜𝑤(𝑆𝑤 = 𝑆𝑤𝑐on ) − 𝑝𝑐𝑜𝑤(𝑆𝑤 = 1 − 𝑆𝑜𝑟𝑤)] × [ (1−𝑆𝑜𝑟𝑤−𝑆𝑤) (1−𝑆𝑤𝑐𝑜𝑛−𝑆𝑜𝑟𝑤) ] 𝑛𝑜𝑤 + 𝒑𝒄𝒐𝒘(𝑆𝑤 = 1 − 𝑆𝑜𝑟𝑤).………………….……………………(5) Gas and liquid 𝑝𝑐𝑜𝑔 = [𝑝𝑐𝑜𝑔(𝑆𝑙 = 𝑆𝑙𝑐𝑜𝑛) − 𝑝𝑐𝑜𝑔(𝑆𝑙 = 1 − 𝑆𝑔𝑐𝑜𝑛)] × [ (1−𝑆𝑜𝑟𝑔−𝑆𝑔) (1−𝑆𝑔𝑐𝑜𝑛−𝑆𝑜𝑟𝑔) ] 𝒏𝒐𝒈 + 𝑝𝑐𝑜𝑔(𝑆𝑤 = 1 − 𝑆𝑜𝑟𝑔).…………………….……………….(6) In the CMG-GEM module, the relative permeability curve is interpolated with the interfacial tension method. Fluids are considered immiscible when the interfacial tension is relatively large. The relative permeability curve and the capillary curve are assigned to both oil and gas. When the interfacial tension drops to the critical value, interpolation is performed with the formulas method to obtain the relative permeability curve and the capillary curve of oil and gas. The fluids are miscible when the interfacial tension is lower than the critical value. The relative permeability curves are selected according to the miscible modes. The effect of interfacial tension on relative permeability is considered to obtain the linear functions of gas and oil saturation from gas and oil relative permeability curves when the fluid phases are miscible (the dual phase interfacial tension approaches 0). The corrected kro and krg are expressed with krot and krgt as follows. 𝑘𝑟𝑜𝑡 = 𝑓 ∗ 𝑘𝑟𝑜 − (1 − 𝑓) ∗ 𝑘𝑟𝑜 𝑆𝑜 (1−𝑆𝑤) ,……………………………………………….….……….……..(7) 𝑘𝑟𝑔𝑡 = 𝑓 ∗ 𝑘𝑟𝑔 − (1 − 𝑓) ∗ 𝑘𝑟ℎ 𝑆𝑔 1−𝑆𝑤 ,………..……………………...………………..………….……..(8) where, 𝑘𝑟ℎ = 0.5 ∗ (𝑘𝑟𝑜𝑤(𝑆𝑤)) + 𝑘𝑟𝑔(𝑆𝑔 = 1 − 𝑆𝑤) ,…………………………………..…….…………….…(9) 𝑓 = { 1, 𝑖𝑓(𝜎 > 𝜎0) ( 𝜎 𝜎0 ) ^𝑒𝑘𝑠𝑖𝑔, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 ,……………..…………...……………...………………….……..…...(10) 𝜎 1 4 = [𝑃](𝜌𝐿 − 𝜌𝑔) .……………………….………………………………………….………………..(11) where [P] is a temperature-independent parameter, which is estimated by molecular structure. When the interfacial tension is determined using this method, the unit of interfacial tension is dyn/cm and the unit of density is mol/cm3. When eksig>1 and 𝜎 < 𝜎0 , the function is transformed into the linear function. When eksig<1, the transformation is delayed. When 𝜎 drops to a small part of 𝜎0, the function is transformed into the linear function. When eksig=1, the function is in a transition to an asymptotic linear function. The effect of interfacial tension on the gas-oil capillary pressure causes the dual-phase pressure difference approach zero. The modified pcog is expressed with pcogt as, 6 𝑝𝑐𝑜𝑔𝑡 = { 𝑝𝑐𝑜𝑔, 𝑖𝑓 𝜎 > 𝜎0 𝑝𝑐𝑜𝑔 ∗ ( 𝜎 𝜎0 ) 𝑒𝑝𝑠𝑖𝑔 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 .…………….……..…………………..(12) Parameter Selection. In this paper, based on the known core data and by integrating Eqs. 1 through 12, the parameters listed in Table 3 are selected to fit the data from the CO2 flooding experiments. Table 3—Model parameters and their value. Model parameters parameters range CO2 Miscible interpolation parameters eksig 0.01~1 epsig 0.01-1 𝜎0 0.01~20 sigms 0.0005-0.0015 Oil and water permeability parameters SWCON(%) 0.46 SWCRIT(%) >0.46 1-SORW(%) 0.5-0.9 1-SOIRW(%) >1-SORW KROWMAX 0.1-1 KRWMAX 0.1-1 NO 0.5-5 NW 0.5-5 Gas and liquid permeability parameters SOIRG(%) 0.05-0.3 SORG(%) >SOIRG SGCON(%) 0-0.1 SGCRIT(%) >SGCON KRGMAX 0.1-1 KROGMAX =KROWMAX NL 0.5-5 NG 0.5-5 Capillary pressure parameters PCOWMAX(kPa) 120-300 PCOGMAX(kPa) 30-100 PCOWMIN(kPa) 0-400 PCOGMIN(kPa) 0-100 NPOW 1-10 NPGL 1-10 Particle Swarm Optimization (PSO) Algorithm. The parameters are optimized with the PSO method, where each particle has a memory to track the optimum iteration positions of the previous generation of particles. One position is found by the particle itself and is called the best position of the individual particle, and the other position is found by the entire particle group currently and is called the global best particle position. It is assumed that there are N particles in the D-dimensional search space, i.e., the population size of the particle swarm is N, where the position parameter of the ith particle in the D-dimensional position is expressed as 𝑥𝑖(𝑘) = (𝑥𝑖1(𝑘), 𝑥𝑖2(𝑘),⋅⋅⋅, 𝑥𝑖𝐷(𝑘)) …………..…………………….…...……………………..…..….(13) The cost function of the optimization problem is used to judge whether the current position of the particle is superior to its history positions (Zhang 2017).The individual optimum position parameter (pbest) searched by the ith particle is expressed as 7 𝑝𝑏𝑒𝑠𝑡 = (𝑝𝑖1, 𝑝𝑖2,⋅⋅⋅, 𝑝𝑖𝐷) .………………………………………………………….....………..….……(14) The optimal position parameter (gbest) of the population searched by all particles is expressed as 𝑔 best = (𝑝𝑔1, 𝑝𝑔2,⋅⋅⋅, 𝑝𝑔𝐷) .……………………………………..…………………………….……...…(15) The velocity is expressed as 𝑣𝑖(𝑘) = (𝑣𝑖1(𝑘), 𝑣𝑖2(𝑘),⋅⋅⋅, 𝑣𝑖𝐷(𝑘)) .…………..…………………………………………...….….…...(16) The velocity and position of the ith particle are updated in kth iteration as follows 𝑣𝑖(𝑘 + 1) = 𝜔𝑣𝑖(𝑘) + 𝑐1𝑟1(𝑝𝑖(𝑘) − 𝑥𝑖(𝑘)) + 𝑐2𝑟2(𝑝𝑘(𝑘) − 𝑥𝑖(𝑘))𝑥𝑖(𝑘 + 1) = 𝑥𝑖(𝑘) ,………...…(17) where k is the iteration times, ω is the weight of inertia, and c1 and c2 are acceleration factors, which control individual information feedback and group information communication of the particles, and causes the particles approach the potential optimal position through judgments based on the information from individual and group optimization and adjustment of the position. r1 and r2 are random numbers between 0 and 1, which improves the fault tolerance and optimization ability of the particles. Analysis of PSO-based Automatic History Matching Results Numerical Fitting of Experimental Data. The relative permeability curve and capillary curve were calculated by controlling points of the relative permeability curve. The value of parameters is listed in Table 3. The PSO algorithm was used to perform history matching for 3,000 times to obtain the recovery degree, injection pressure, water cut and gas-oil ratio of cores from the low-permeability reservoir. The results are shown in Figure 5, and the error is less than 2%. (a)Gas-oil ratio,m3/m3 (b)Water cut,% (c)Injection well bottom-hole pressure, kPa (d)Oil recovery,% Figure 5—Fitting of data from the flooding experiment of the low-permeability cores. 8 The variation of the global error of historical matching with the test trial is shown in Figure 6. It shows that the model error is less than 3% after 500 trials, but more trials are required to reduce the error. The distribution of model parameters optimized with the PSO algorithm in 3000 times is shown in Figure 7. Figure 6—Global error of historical matching vs the trial number. (a)eksig (b)epsig (c) 𝝈𝟎 (d)sigms (e)KROWMAX (f)NO 9 (g)PCOWMAX (h)1-SORW (i)KRWMAX (j)NW (k)PCOWMIN (l)NPOW (m)SOIRG (n)KRGMAX (o)NG (p)PCOGMAX 10 (q)SGCON (r)NL (s)PCOGMIN (t)NPG Figure 7—Distribution of parameters 3000 times during optimization. A total of 51 cases of historical matching with an error of less than 2% were selected, and the distribution of the model parameter in the optimization of PSO is shown in Figure 8. It can be seen that the parameter uncertainty has been searched to a range small enough with the PSO optimization. (a)eksig (b)epsig 11 (c) 𝝈𝟎 (d)sigms (e)KROWMAX (f)NO (g)PCOWMAX (h)1-SORW 12 (i)KRWMAX (j)NW (k)PCOWMIN (l)NPOW (m)SOIRG (n)KRGMAX 13 (o)NG (p)PCOGMAX (q)SGCON (r)NL (s)PCOGMIN (t)NPG Figure 8—Distribution of 51 groups of model parameters with an error of less than 2%. Analysis of Relative Permeability Curve Characteristics. The capillary curves (Figure 9) and the relative permeability curves (Figure 10) of the low permeability reservoir cores were obtained by normalization of the capillary curves and the relative permeability curves from 51 cases of history matching with an error of less than 2%, and the characteristics of the curve endpoints are illustrated in Table 4. As shown in Figure 9a, the oil-water capillary pressure of low-permeability reservoirs is low, ranging from 0 to 3 MPa, and the gas-liquid capillary pressure is even lower, ranging from 0 to 0.2 MPa (Figure 9b). 14 (a)Oil-water (b)Gas-liquid Figure 9—Capillary curve of low-permeability cores. The characteristics of the relative permeability curves are summarized as follows. Oil-water relative permeability curve: (1) The water saturation at the same permeability point of the oil-water relative permeability curve is 56.2%, which is greater than 50%, indicating that the reservoirs in the study area are hydrophilic. (2) The oil-water relative permeability curve shows obvious characteristics of the displacement of water by oil in low-permeability reservoirs. The irreducible water saturation of the cores exceeds 30%, while the residual oil saturation exceeds 20%, and the range of common permeability is 33%. (3) As water saturation increases, the relative permeability of the oil decreases rapidly and the relative permeability of the water increases. Gas-liquid relative permeability curve: (1) The irreducible liquid saturation exceeds 30%, and the residual gas saturation is 11%. (2) As the gas saturation increases, the relative permeability of the liquid decreases significantly, and the relative permeability of the gas increases significantly, indicating that the oil flow is affected both by gas and liquid. (3) The gas-liquid common permeability range is 54%. The common permeability range of oil and gas is larger than that of oil and water, which is conducive to more oil displacement. This indicates that compared to the development of water flooding, CO2 injection is more conducive to improving oil recovery of this type of reservoir and increases oil recovery by more than 10%. Table 4—Relative permeability of low permeability reservoirs. Oil-water Permeability (mD) Porosity (%) Swcon (%) Sorw (%) krwiro (%) Sw @ isosmotic point (%) Two-phase flow region (%) 1.2 13.2 35 32 18 56.2 33.0 Gas-liquid Permeability (mD) Porosity (%) Slcon (%) Sgcrit (%) krgcl (%) Sl @ isosmotic point (%) Two-phase flow region(%) 1.2 13.2 35 11 42.4 60.1 54.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.4 0.5 0.6 0.7 0.8 O il -W at er c ap il la ry p re ss u re , M P a Sw,% 0.00 0.05 0.10 0.15 0.20 0.4 0.5 0.6 0.7 0.8 G as -l iq u id c ap il la ry p re ss u re , M P a SL,% 15 (a)Oil-water (b)Gas-liquid Figure 10—Relative permeability curve of low permeability cores. Conclusions In this paper, a PSO-based method of fitting the relative permeability was proposed. The CO2 flooding experiments in long cores from low-permeability reservoirs were performed to obtain flow and pressure data. The Corey model was used to characterize the permeability curve, where the permeability and capillary pressure models include 26 parameters. The core experimental data were fitted by adjusting the Corey model and the capillary curve with the PSO method, and the fitting error is less than 2%. The relative permeability curve and the capillary curve of the experimental core were obtained. The curve characteristics are as follows. 1. The water saturation at the same permeability point of the oil-water relative permeability curve is 56.2%, which is higher than 50%, indicating that the reservoirs in the study area are hydrophilic. The oil-water relative permeability curve shows obvious characteristics of the displacement of water by oil in low-permeability reservoirs. 2. The common permeability range of oil and gas is larger than that of oil and water, which is conducive to more oil displacement. This indicates that compared to the development of water flooding, CO2 injection is more conducive to improving the oil recovery of this type of reservoir. 3. The oil-water capillary pressure of low-permeability reservoirs is low, ranging from 0 to 3 MPa, and the gas-liquid capillary pressure is even lower, ranging from 0 to 0.2 MPa. Nomenclature krg = relative permeability of gas krgcl = krg at connate liquid saturation krw = relative permeability of water krwiro = krw at irreducible oil saturation krow = krw in the presence of the given water saturation krocw = krw at connate water saturation krog = krw in the presence of the given water saturation krogcg = krog at connate gas saturation ng = exponent for calculating krg nw = exponent for calculating krw 0.0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1 K rw ， kr o Sw Krw_DST1(1.2mD) Kro_DST1(1.2mD) 0.0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1 K rl ， kr g Sl Krl_DST1(1.2mD) Krg_DST1(1.2mD) 16 now = exponent for calculating krow nog = exponent for calculating krog Sgcon = connate gas saturation Sgcrit = critical gas saturation Sl = liquid saturation Slcon = irreducible liquid saturation, Swcon+Soirg So = oil saturation Sorg = residual oil saturation for gas-liquid table Sorig = non-reducible oil saturation for oil-gas table Soirw = non-reducible oil saturation for oil-water table Sorw = residual oil saturation for oil-water table Sw = water saturation Swcrit = critical water saturation Swcon = connate water saturation pcow = oil-water capillary pressure pcog = gas-liquid capillary pressure SWCON = connate water saturation SWCRIT = critical water saturation SORW = residual oil saturation SOIRW = irreducible oil saturation for oil-water table KROWMAX = maximum krow KRWMAX = maximum krw NO = exponent for calculating krow from krocw NW = exponent for calculating krw from krwiro SOIRG = irreducible oil saturation for gas-liquid table SORG = residual oil saturation for gas-liquid table SGCON = connate gas saturation SGCRIT = critical gas saturation KRGMAX = maximum krg KROGMAX = maximum krog NG = exponent for calculating krog from krogcg NL = exponent for calculating krg from krgcl PCOWMAX = maximum oil-water capillary pressure PCOGMAX = maximum oil-gas capillary pressure PCOWMIN = minimum oil-water capillary pressure PCOGMIN = minimum oil-gas capillary pressure NPOW = exponent for calculating oil-water capillary pressure NPGL = exponent for calculating gas-liquid capillary pressure Greek letters σ = oil-gas interfacial tension calculated through the MacLeod-Sugden correlation 𝜎0 = referenced interfacial tension when calculating the relative permeability eksig = gas-oil relative permeability index (dimensionless) epsig = gas capillary pressure index (dimensionless) 17 Acknowledgements The authors are grateful for financial support from the National Science and Technology Major Project (Grant No. 2016ZX05016-005 and 2016ZX05016-001), the Major Project of China National Petroleum Corporation (Grant No. RIPED-2020-JS-50214) and (Grant No. RIPED-2020-JS-50215), the project of Sinopec North China Petroleum Bureau (Grant No. 290018276) and project of Petroleum Engineering Technology Institute of SINOPEC Shengli Oilfield (Grant No. 290018276). Conflicts of Interest The author(s) declare that they have no conflicting interests. References CMG Manual 2015. Computer Modeling Group. Eydinov, D., Gao, G., Li, G., et al. 2009. Simultaneous Estimation of Relative Permeability and Porosity/Permeability Fields by History Matching Production Data. Journal of Canadian Petroleum Technology 48(12):13-25. Li, K.1989. An Optimization Method for Calculating the Relative Permeability Curve of Oil And Water Based on the Experimental Data of Dynamic Displacement. Journal of Oil and Gas Technology 11(3) :45-54. Li, Y., Li, Y., Yu, L., et al. 2018. Review of History Matching Method for Calculating Oil-Water Relative Permeability Curves. Journal of Longdong University 29(3):55-58. Toth, J., Tibor, B., Peter, S., et al. 2002. Convenient Formulae for Determination of Relative Permeability from Unsteady-State Fluid Displacements in Core Plugs. Journal of Petroleum Science and Engineering 36(1):33-44. Zhang, F., Wang, Z., Cheng, Y., et al. 2010. Processing Methods for Relative-permeability Curves in Reservoir Numerical Simulation. Natural Gas Geoscience 21(5):859-862. Zhang, Q. 2017. Research on the Particle Swarm Optimization and Differential Evolution Algorithms. PhD dissertation, Shandong University, Jinan, China. Zhang, X., Du, J., Bai, L., et al. 2016. New Calibration Method for Oil-Water Relative Permeability Curves Based on Unsteady State Method. Fault-Block Oil & Gas Field 23(2):185-188. Zhang, Z., Tong, Y., and Wu, Y. 2019. Effects of Diffusion on Relative Permeability Curves of CO2 Flooding in Low Permeability Reservoirs. Journal of Xi'an Shiyou University (Natural Science Edition) 34(2):73-77. Weiling Zhang is a engineer in Tianjin Branch of CNOOC. His research interests include numerical simulation and field development of offshore reservoirs. Wenfeng Lv is a senior engineer at the Research Institute of Petroleum Exploration and Development (RIPED), PetroChina. He holds a PhD degree from China University of Petroleum. His research interest includes numerical simulation and gas flooding. Yongyi Zhou, North China Petroleum Bureau, Sinopec. His research interest includes numerical simulation and field development for unconventional reservoirs. Bochao Qu is a master candidate in Petroleum Engineering Department at Xi’an Shiyou University. His research interests include reservoir simulation and production analysis. 18 Yawen He is a master candidate in Petroleum Engineering Department at Xi’an Shiyou University. Her research interests include reservoir simulation and hydraulic fracturing design. Xinle Ma is a master candidate in Petroleum Engineering Department at Xi’an Shiyou University. Her research interests include big data, reservoir simulation, and production analysis. Weidong Tian is a master candidate in the Department of Petroleum Engineering at Xi’an Shiyou University. He has focused his research in areas involving reservoir simulation, well testing and production analysis. Zhenzhen Dong is a Professor in the Department of Petroleum Engineering at Xi’an Shiyou University. She worked as a reservoir engineer at Schlumberger from 2012 to 2016. Her research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. Dr. Dong holds a bachelor’s degree in Mathematics from Northeast Petroleum University, China; a master’s degree in Petroleum Engineering from Research Institute of Petroleum Exploration and Development (RIPED), China; and a PhD degree in Petroleum Engineering from Texas A&M University.