Relative Permeability Characteristics During Carbon Capture and Sequestration Process in Low-Permeable Reservoirs

The injection of carbon dioxide (CO2) in low-permeable reservoirs can not only mitigate the greenhouse effect on the environment, but also enhance oil and gas recovery (EOR). For numerical simulation work of this process, relative permeability can help predict the capacity for the flow of CO2 throughout the life of the reservoir, and reflect the changes induced by the injected CO2. In this paper, the experimental methods and empirical correlations to determine relative permeability are reviewed and discussed. Specifically, for a low-permeable reservoir in China, a core displacement experiment is performed for both natural and artificial low-permeable cores to study the relative permeability characteristics. The results show that for immiscible CO2 flooding, when considering the threshold pressure and gas slippage, the relative permeability decreases to some extent, and the relative permeability of oil/water does not reduce as much as that of CO2. In miscible flooding, the curves have different shapes for cores with a different permeability. By comparing the relative permeability curves under immiscible and miscible CO2 flooding, it is found that the two-phase span of miscible flooding is wider, and the relative permeability at the gas endpoint becomes larger.


Introduction
The injection of carbon dioxide (CO 2 ) in depleted oil and gas reservoirs, saline aquifers, or coal seams, is an important means of reducing air pollution and mitigating the greenhouse effect on the environment, and it has been extensively discussed in previous studies [1][2][3][4][5][6][7]. Figure 1 shows some typical Carbon Capture and Sequestration (CCS) projects around the globe. For developing countries such as China, it can serve as an important measure to enhance oil and gas recovery, especially in lowor ultralow-permeable reservoirs, since the oil in low-permeable reservoirs accounts for approximately 60% of the proven reserve which has not been developed [8]. For example, the injected CO 2 in the ultralow-permeable reservoir in the Jilin oilfield, whose permeability is less than 0.01 × 10 −3 µm 2 , can not only fracture the near the wellbore region and also improve the oil recovery in the reservoir.
Water flooding in low-permeable reservoirs results in a very unsatisfactory recovery, due to serious heterogeneity, tight lithology, high filtration resistance, poor pressure transmissibility and water sensitive minerals, and so on. With this regard, CO 2 flooding is superior to water flooding, because it can not only maintain the reservoir pressure, but also improve the displacement efficiency [9][10][11]. There are several known reasons for that. For example, CO 2 can easily dissolve into crude oil, so as to reduce the interfacial tension, the viscosity of crude oil and the residual oil saturation. In order to increase oil production and CO 2 injection efficiency, a number of methods are used, and among them, horizontal Water flooding in low-permeable reservoirs results in a very unsatisfactory recovery, due to serious heterogeneity, tight lithology, high filtration resistance, poor pressure transmissibility and water sensitive minerals, and so on. With this regard, CO2 flooding is superior to water flooding, because it can not only maintain the reservoir pressure, but also improve the displacement efficiency [9][10][11]. There are several known reasons for that. For example, CO2 can easily dissolve into crude oil, so as to reduce the interfacial tension, the viscosity of crude oil and the residual oil saturation. In order to increase oil production and CO2 injection efficiency, a number of methods are used, and among them, horizontal wells play a vital role due to their large flow areas [12]. The CO2 flooding process in the subsurface takes place either in aquifers or sandstone reservoirs with a certain amount of oil. An important parameter for estimating the amount of oil and gas in a reservoir, and for predicting the capacity for fluid flow throughout the life of the reservoir, is the relative permeability, an indication of fluid distribution and movement, pore structure variation, and the chemistry of the solids and fluids. Moreover, all of the changes induced by the injected CO2 can also be observed in the relative permeability curves [13,14]. For the determination of relative permeability in lowpermeable reservoirs, several concepts have to be explained. A Minimum Miscibility Pressure or MMP, the boundary of miscible flooding and immiscible flooding, shall be determined when measuring the CO2/oil relative permeability curve. There are several commonly-used experimental methods for the MMP determination, such as the slim-tube test, core flooding, rising-bubble apparatus, and so on [15]. In this experiment, the slim tube method is adopted. A threshold pressure, the pressure that the injected gas has to overcome to displace the fluid, has to be measured prior to the relative permeability measurement, because the complex pore structures, narrow pore throat and large tortuosity in low permeable reservoirs lead to complex physical and chemical reactions between In this paper, the typical experimental methods and empirical correlations are reviewed and discussed with regards to the determination of relative permeability. With special focus on CO 2 flooding, the CO 2 /water and CO 2 /oil relative permeability measurement is performed using core displacement experiment for immiscible CO 2 flooding scenarios. Since there is little study on relative permeability in miscible flooding, the experimental method for miscible CO 2 flooding will also be introduced.

Experimental Methods for Relative Permeability Determination
A variety of methods to measure relative permeability in porous media are basically categorized as steady-state and unsteady-state methods

Steady-state Methods
In steady-state methods, both phases are injected simultaneously at constant rates. Injection continues until a steady-state is reached, as indicated by a constant pressure drop and constant saturations. The subcategories of the steady-state methods include the multiple-core method, high-rate method, stationary-liquid method and uniform-capillary-pressure method, and so on. It was used to measure the relative permeability relations of supercritical CO 2 and brine, both in imbibition and drainage processes [16,17]. However, capillary entry and end effects during two-phase flow are not considered in their work. In Chen and Amir (2014), the capillary end effect was detected during the measurement of CO 2 -brine relative permeability in a sandstone core [18]. Robin G. and Daniel R.M. (2016) introduced a novel modified steady-state approach in which corrections for end-effect artifacts are applied as data are measured [19]. However, the method process is too complex. In many studies the influence of surface tension and viscosity on the behavior of fluids is considered, but the influence of the physical state is always ignored. Florian et al. (2015) conducted the measurement of relative permeability under High Temperature and Pressure conditions with gaseous CO 2 /water and supercritical CO 2 /water with a steady-state method, and the results show that the physical state does not influence very much [20].

Unsteady-state Methods
In unsteady-state methods, which is also known as external-drive methods or displacement methods, only one phase is injected at either a constant flow rate or a constant pressure drop. Its subcategories include the high-rate method, low-rate method, and centrifuge methods. Unsteady-state methods are much faster than steady-state methods, but many operational difficulties are involved in unsteady-state methods, such as capillary end effects. Therefore, some modifications have been developed to improve unsteady-state methods. The Johnson-Bossier-Naumann (JBN) method, or some modification of it, interprets that high-flow-rate displacements can eliminate the capillary pressure end effects [21,22]. It consists of injecting a displacing phase into a core fully saturated with a displaced phase; during the unsteady-state portion of the displacement, both the overall pressure drop and the effluent phase ratio are measured versus time. By using fractional flow theory and a mathematical inversion, relative permeability data to both phases are obtained at the outlet as the displaced phase saturate decreases. A unique and practical method, including the capillary end effects, has been presented using sufficiently high flow rates to minimize the rate of the capillary end effects in Janos et al. (2002) [23]. However, the high-flow-rate is usually difficult to accomplish, especially in tight cores, so the end effects are often neglected in some development of simplified interpretation methods [24]. For example, a new unsteady-state model for calculating the oil-water relative permeability of low-permeability has been established, which considers the effects of threshold pressure gradient and capillary pressure [25]. In addition, a method using genetic algorithms to estimate relative permeability and minimize adjustable parameters is suggested when the capillary end-effect is high [26].

Empirical Correlations for Relative Permeability Determination
Relationships for the relative permeability as a function of saturation are usually based on experimental data. However, in the absence of data, empirical correlations are often used. The empirical correlations use the effective wetting phase saturation as the correlating parameter. In 1949, Purcell proposed an equation to compute permeability by using capillary pressure measurement. Burdine (1953) introduced a tortuosity factor into the Purcell equation, and obtained the Burdine equation (Equations (1) and (2)) [27]. Mualem (1976) modified the Burdine model, and the modification is known as the Mualem model (Equations (3) and (4)) [28]. This section is an excerpt from Bai et al. (2014) [29].
Burdine Model (Burdine, 1953) Mualem Model (Mualem, 1976) Van Genuchten (1980) has proposed the classical capillary pressures, that is, saturation relations to describe the behavior of soils. By introducing them into the Burdine model and the Mualem model, there was obtained the famous van Genuchten/Burdine model and van Genuchten/Mualem model [30,31]. In 1966 Brooks and Corey proposed the second classical capillary pressure, namely, saturation relations to describe the behavior of petroleum reservoir rock [32]. By substituting it into the Burdine model and the Mualem model with S nwr = 0, one obtains the Brooks-Corey/Burdine and the Brooks-Corey/Burdine model. In earlier experiments, Corey (1954) had obtained a linear relationship between the reciprocal of the capillary pressure squared and the effective water saturation, which is known as Corey's correlation [33]. Corey's correlation has been widely used, and works well, not only in the lab, but also in field applications. It is a special Brooks and Corey equation. The limitations are, for instance, that the porous media must be well-sorted, and that it is only derived for drainage process.

Relative Permeability for CO 2 Flooding in a Low-permeable Reservoir
For a CCS project in the Jilin oilfield, a typical low-permeable reservoir, both retrieved natural cores from the reservoir and artificial cores are used to determine relative permeability in the experiment, where the unsteady-state method was adopted during immiscible CO 2 flooding, while the steady-state method was applied during miscible CO 2 flooding, where the evenly mixed oil and CO 2 was injected into the cores for the relative permeability measurement. Since the miscible CO 2 flooding is actually achieved after multi-contact and gradual extraction, even if the pressure is higher than MMP, direct gas displacement cannot ensure a completely miscible state in the cores. Thus, live oil with dissolved gas in it is used for the experiment.

CO 2 /Oil Relative Permeability Curve in Immiscible CO 2 Flooding
The unsteady-state method was adopted to conduct an immiscible CO 2 flooding experiment based on the Buckley-Leverett theory. The immiscible flooding implies that the CO 2 injection pressure is less than MMP of CO 2 and oil, and CO 2 and oil in the cores fail to reach the miscible state and are still two-phase fluid. The oil and gas flow rate versus time at the outlet of rock samples were recorded during the displacement process. Under the premise of considering the threshold pressure and gas slippage in low-permeable cores, the "JBN" method was used to calculate the oil and gas relative permeability.
The main experimental steps include the determination of the geometric data of the core samples and the air permeability, vacuumization of the core samples and saturation with formation water, the calculation of the porosity of the rock samples, determination of the oil saturation and irreducible water saturation by displacing water with oil until no water comes out, and the measurement of oil permeability corresponding to irreducible water saturation. After this, a proper displacement pressure is applied to displace the oil by CO 2 to ensure that the flooding velocity is between 7-30 mL/min, and the pressure is smaller than MMP. The oil and gas rate versus time is recorded during the displacement process until the residual oil saturation is reached, and then the effective permeability to gas is measured. The oil and gas flow rate measured at the outlet under atmospheric pressure is modified to the one under the average pressure in the samples, according to Equation (5). The relative permeability curves can be obtained by performing calculations according to Equation (6).
where, l denotes liquid (oil or water); V i-1 and V l i denote cumulative oil and gas rate at time i-1 and i, respectively, mL; ∆V l i denotes incremental liquid rate, mL; p a denotes atmospheric pressure, MPa; ∆p denotes differential pressure, MPa; α l denotes solubility of CO 2 in liquid, mL/mL; E l denotes the volume expansion coefficient of liquid, dimensionless.
where, G denotes threshold pressure, MPa; ∆P 0 denotes the initial pressure differential, MPa; P ave denotes the average pressure differential, MPa; b denotes gas slippage factor, dimensionless; I denotes relative injectivity, dimensionless; f denotes oil or water fractional content, dimensionless; Q 0 denotes initial liquid rate at the outlet, cm 3 /s; Qi denotes liquid rate at the outlet at time I, cm 3 /s. For the CO 2 /oil relative permeability measurement under an immiscible state, the oil is a mixture of dead oil and kerosene, and the formation water has a Total Dissolved Solid (TDS) of 5500 mg/L. Experimental temperature is 74.9 • C and 45 • C for natural and artificial cores, respectively. The basic geometric and physical properties of the cores are listed in Table 1. The experimental scenarios are listed in Table 2. In the tables hereunder, K permeability, L length of the core, D cross-sectional area, ϕ porosity, P in injection pressure and T temperature, respectively. Similar to the CO 2 /oil relative permeability, the CO 2 /water relative permeability characteristics can also be obtained by injecting CO 2 into the water-saturating cores and recording the oil and gas rate, etc., versus time at the outlet. The "JBN" method was used to calculate the oil and gas relative permeability and corresponding saturation. For the experiment, the first step is the measurement of air permeability, saturating the rocks with water and determination of the porosity. The next step is to adjust the injection pressure by regulating the pressure valve, and to inject CO 2 into the cores under constant pressure. The differential pressure must overcome the end effect, without leading to turbulent flow. After that, the data, such as gas breakthrough time, cumulative water and gas flow rate versus time, are all recorded. When the water saturation reaches the irreducible value, the gas permeability is measured under the displacement pressure and 1/2 displacement pressure, respectively.
The total oil and gas flow rate measured under atmospheric pressure at the outlet is modified to the one under the average pressure of the rock sample, according to Equation (5). The relative permeability curves can be obtained by performing calculations according to Equation (6).
For CO 2 /water relative permeability measurement under an immiscible state, the formation water has a TDS of 5500 mg/L. Experimental temperature is 45 • C for artificial cubic cores. The basic geometric and physical properties of the cores are listed in Table 3. The experimental scenarios are listed in Table 4. The steady-state method for CO 2 miscible flooding is based on Darcy's law without consideration of capillary pressure and gravity effect. CO 2 and live oil are fully mixed in a certain proportion under a pressure greater than MMP to reach the miscible state. The mixture is injected into the samples under a constant pressure, while keeping the inlet and outlet pressure constant and above the MMP as well.
When the oil and gas flow at the outlet is stable, it is deemed that the distribution of oil and CO 2 in the sample is uniform and stable. At this time the effective permeability to oil and CO 2 is constant, and the effective permeability and relative permeability value of oil and gas can be directly calculated with Darcy's law by using the recorded data. A series of CO 2 /oil relative permeabilities under different oil saturations can be obtained by calculating the average oil saturation with the material balance method and by changing the mixing ratio of oil and CO 2 .
The first step is to put the core samples saturated with formation water into the core holders where the water is injected through the cores with a certain flow rate via a pump. The water permeability is measured for three times after the differential pressure and flow rate at the outlet are stable. The second step is to displace the water in the samples with live oil, and to measure the effective permeability of this oil at the irreducible water saturation. The third step is to inject the CO 2 /oil mixture into the cores and record the oil and gas volume at the outlet under ambient pressure, as well as the cumulative injection volume, until the oil and gas flow is stable. In order to keep the mixture miscible, the pressure at the outlet is set to be 30 MPa. The proportion of live oil and CO 2 in the mixture is changed, and step 3 is repeated. The effective and relative permeability of CO 2 and oil can be calculated based on Darcy's law.
For the CO 2 /oil miscible phase, the live oil with dissolved GOR of 30 Sm 3 /m 3 is used. The TDS of the formation water is 5500 mg/l, and the temperature is 45 • C. The basic core data is listed in Table 5. According to the indoor experiments, the bubble point pressure is 7 MPa, the MMP of CO 2 and live oil is 24.5 MPa, so for the four cores, the injection pressure and discharge pressure are 35 MPa and 30 MPa, respectively. The scenarios are designed in Table 6.

Relative Permeability Curves for Immiscible CO 2 /Oil Displacement
The main experimental steps are described in Section 4.1. It includes mainly the determination of the oil saturation and irreducible water saturation by displacing water with oil until no water comes out, and then measurement of oil permeability corresponding to an irreducible water saturation.
After this, a proper displacement pressure is applied to displace the oil by CO 2 to ensure that the flooding velocity is between 7-30 mL/min and the pressure is smaller than MMP. The relative permeability curves are obtained by performing calculations for CO 2 /oil immiscible displacement. The results are shown in Figures 2-5 for natural cores and Figures 6-9 for artificial cores, respectively. In the figures, K ro-b,G and K rg-b,G represent the relative permeability considering gas slippage and threshold pressure, while K ro and K rg represent relative permeability without considering them. and gas slippage. But the relative permeability of oil does not reduce as much as that of CO2. When considering gas slippage, only the relative permeability of CO2 is modified, which has no influence on oil relative permeability. The decrease of the relative permeability of oil is because the energy exerted to displace oil is lowered when considering the threshold pressure in low permeable rocks, given that the total differential pressure is constant. When both the gas slippage and threshold pressure are considered, the relative permeability of CO2 decreases a little more than that to oil.   considering gas slippage, only the relative permeability of CO2 is modified, which has no influence on oil relative permeability. The decrease of the relative permeability of oil is because the energy exerted to displace oil is lowered when considering the threshold pressure in low permeable rocks, given that the total differential pressure is constant. When both the gas slippage and threshold pressure are considered, the relative permeability of CO2 decreases a little more than that to oil.                  The situation of artificial cores is similar to that of natural cores. A typical feature is that the CO2 critical flow saturation of artificial cores is larger than that of natural cores as a whole. There are two reasons. Firstly, the natural rock sample is characterized by a wider distribution of pore size, complex    The situation of artificial cores is similar to that of natural cores. A typical feature is that the CO2 critical flow saturation of artificial cores is larger than that of natural cores as a whole. There are two reasons. Firstly, the natural rock sample is characterized by a wider distribution of pore size, complex It can be observed from the Figures that both K ro and K rg are greater than K ro-b, G and K rg-b, G , indicating that the relative permeability of both phases reduces when considering threshold pressure and gas slippage. But the relative permeability of oil does not reduce as much as that of CO 2 . When considering gas slippage, only the relative permeability of CO 2 is modified, which has no influence on oil relative permeability. The decrease of the relative permeability of oil is because the energy exerted to displace oil is lowered when considering the threshold pressure in low permeable rocks, given that the total differential pressure is constant. When both the gas slippage and threshold pressure are considered, the relative permeability of CO 2 decreases a little more than that to oil.
The situation of artificial cores is similar to that of natural cores. A typical feature is that the CO 2 critical flow saturation of artificial cores is larger than that of natural cores as a whole. There are two reasons. Firstly, the natural rock sample is characterized by a wider distribution of pore size, complex pore structure and relatively strong heterogeneity, while the artificial cores have a uniform pore structure. Secondly, the porosity and size of artificial cubic cores are larger than that of natural cores, and the saturated oil quantity in it is relatively more, so the amount of the dissolved gas of CO 2 in immiscible flooding is relatively greater.
The experimental data of natural and artificial cores are listed in Tables 5 and 6. It can be observed from the table that no matter for natural core or artificial core, with decreasing permeability, the irreducible water saturation increases. Given that the injection pressure is the same (natural core), when the permeability decreases, the residual oil saturation will increase, and the range of the two-phase region will be narrower consequently.
The relative permeability of gas at the endpoint under immiscible flooding is relatively low due to the fact that irreducible water and residual oil in rock sample account for 61.81%-87.65% of pore space at the end of the experiment, thus the flowing space of gas is relatively small, which means the relative permeability value at the gas endpoint is relatively low.

CO 2 /Water Relative Permeability Curve Under Immiscible Phase
The relative permeability curves are obtained by performing calculations for the CO 2 /water immiscible situation. The results are shown in Figures 10-13. In the figure, K ro-b,G and K rg-b,G represent the relative permeability considering the solubility of CO 2 , oil viscosity change, gas slippage and threshold pressure, while K ro and K rg represent relative permeability without considering the gas slippage or threshold pressure. phase region will be narrower consequently.
The relative permeability of gas at the endpoint under immiscible flooding is relatively low due to the fact that irreducible water and residual oil in rock sample account for 61.81%-87.65% of pore space at the end of the experiment, thus the flowing space of gas is relatively small, which means the relative permeability value at the gas endpoint is relatively low.

CO2/Water Relative Permeability Curve Under Immiscible Phase
The relative permeability curves are obtained by performing calculations for the CO2/water immiscible situation. The results are shown in Figures 10-13. In the figure, Kro-b,G and Krg-b,G represent the relative permeability considering the solubility of CO2, oil viscosity change, gas slippage and threshold pressure, while Kro and Krg represent relative permeability without considering the gas slippage or threshold pressure.
There is critical gas saturation when considering the CO2 solubility. A critical saturation of gas refers to the minimum saturation at which a phase becomes mobile. In the figure, the initial section value of gas relative permeability is zero. Meanwhile, it is observed that as to the cores with similar permeability, the larger the injection pressure is, the faster the gas will breakthrough, and consequently the narrower the two-phase region will be. In the figure, both Kro and Krg are greater than Kro-b, G and Krg-b, G, and it indicates that the water and gas relative permeability reduces when considering gas slippage and threshold pressure. In addition, the influence of gas slippage effect becomes smaller with the decrease of displacement pressure.

CO2/Live Oil Relative Permeability Curve under Miscible Phase
The relative permeability curves are obtained by performing calculations for CO2/oil miscible situation. The results are shown in Figure 14. It can be observed from the figures that as the

CO2/Live Oil Relative Permeability Curve under Miscible Phase
The relative permeability curves are obtained by performing calculations for CO2/oil miscible situation. The results are shown in Figure 14. It can be observed from the figures that as the There is critical gas saturation when considering the CO 2 solubility. A critical saturation of gas refers to the minimum saturation at which a phase becomes mobile. In the figure, the initial section value of gas relative permeability is zero. Meanwhile, it is observed that as to the cores with similar permeability, the larger the injection pressure is, the faster the gas will breakthrough, and consequently the narrower the two-phase region will be. In the figure, both K ro and K rg are greater than K ro-b, G and K rg-b, G , and it indicates that the water and gas relative permeability reduces when considering gas slippage and threshold pressure. In addition, the influence of gas slippage effect becomes smaller with the decrease of displacement pressure.

CO 2 /Live Oil Relative Permeability Curve under Miscible Phase
The relative permeability curves are obtained by performing calculations for CO 2 /oil miscible situation. The results are shown in Figure 14. It can be observed from the figures that as the permeability reduces, the pore throat becomes smaller. The outcome is the decrease of the mobility of CO 2 and oil in the cores, and the oil relative permeability decreases fast. one can find that the two-phase span of miscible flooding is wider, and the relative permeability at the gas endpoint becomes larger. In miscible flooding, the kr curves have different shapes for cores with different permeability, even under the same pressure difference. As the permeability of rock sample decreases, the gas endpoint permeability decreases, the two-phase flow region becomes narrower, and the gas saturation at the isotonic point decreases.

Conclusions and Discussions
For immiscible flooding, the relative permeability of both phases decreases when considering threshold pressure and gas slippage, and the relative permeability of oil does not reduce as much as that of CO2. The relative permeability of gas phase at the endpoint is relatively low. The larger the injection pressure is, the faster the gas will breakthrough, and consequently the narrower the twophase region will be.
In miscible CO2 flooding, the relative permeability curves have different shapes for cores with different permeability, even under the same pressure difference. As the permeability of the rock sample decreases, the gas endpoint permeability decreases, the two-phase flow region becomes narrower, and the gas saturation at the isotonic point decreases.
By comparing the kr curves under immiscible and miscible flooding situations, one can find that the two-phase span of miscible flooding is wider, and the relative permeability at the gas endpoint becomes larger.   By comparing the kr curves under immiscible and miscible flooding situations for core samples with similar permeability, which are shown in Figure 6 through Figure 9, and Figure 14, respectively, one can find that the two-phase span of miscible flooding is wider, and the relative permeability at the gas endpoint becomes larger. In miscible flooding, the kr curves have different shapes for cores with different permeability, even under the same pressure difference. As the permeability of rock sample decreases, the gas endpoint permeability decreases, the two-phase flow region becomes narrower, and the gas saturation at the isotonic point decreases.

Conclusions and Discussions
For immiscible flooding, the relative permeability of both phases decreases when considering threshold pressure and gas slippage, and the relative permeability of oil does not reduce as much as that of CO 2 . The relative permeability of gas phase at the endpoint is relatively low. The larger the injection pressure is, the faster the gas will breakthrough, and consequently the narrower the two-phase region will be.
In miscible CO 2 flooding, the relative permeability curves have different shapes for cores with different permeability, even under the same pressure difference. As the permeability of the rock sample decreases, the gas endpoint permeability decreases, the two-phase flow region becomes narrower, and the gas saturation at the isotonic point decreases.
By comparing the kr curves under immiscible and miscible flooding situations, one can find that the two-phase span of miscible flooding is wider, and the relative permeability at the gas endpoint becomes larger.