New Insights into Spontaneous Imbibition Processes in Unfractured and Fractured Carbonate Cores with Stress-Induced Apertures Odilla Vilhena, Amir Farzaneh, Jackson Pola, Rafael March, Adam Sisson, and Mehran Sohrabi, Heriot-Watt University Summary Spontaneous imbibition (SI) experiments in fractured and unfractured Indiana limestone cores were performed to evaluate the impact of fractures in oil recovery. Numerical simulations were performed to reproduce the experimental setting and to history match fracture and matrix properties. Tracer tests were carried out to investigate the effect of changing stresses in hydraulic fracture conductivity. The pore space and connected pores in the fractured plug were analyzed via microscopic computed tomography (micro-CT) scan, and a thin petrography analysis was carried out to observe the matrix heterogeneity of the samples. Relative permeability, capillary pressure, and fracture properties were estimated numerically to match the SI curves measured at a temperature of 58.7 C. The investigation shows that the fractured core has suffered deformation under higher stress conditions, impacting the fracture aperture and the initial values of total permeability measured in the laboratory at a constant net stress. This deformation has led to decreased flow rates in the fracture and oil trapping in the fracture channel. At the field scale, this phenomenon could lead to decreased oil recovery rates in the initial stages of production. Introduction The study of multiphase flow in fractured rocks subject to in-situ stresses is relevant to numerous energy-related applications, such as enhanced geothermal systems (Olasolo et al. 2016), CO2 storage in naturally fractured reservoirs (March et al. 2018), CO2 leakage through fractured cap-rocks (Vialle et al. 2016), and enhanced oil recovery (EOR) techniques (Moortgat and Firoozabadi 2017). While there has been a series of theoretical (Berard et al. 2007; Teklu et al. 2012), numerical (Jiang et al. 2014; Kumar et al. 2015), and experimental (Ng et al. 2017; Zhou et al. 2018) studies on the topic, there are still open research questions in the field. In particular, while it has been acknowledged that stress-induced fracture apertures are important to predict fluid flow in fractures, there is still a lack of experimental data quantifying its impact on oil recovery for carbonate rocks. An experimental evaluation was carried out by Jones (1975) to study the effects of confining pressure on fracture flow and storage capacity in carbonate rocks. In the study, the author has used fabricated cores with ideal planar fractures. The two main observations were related to the fracture permeability, which was greatly reduced by increasing confining pressure, and to the large reduction in fracture capacity. In Gale (1982), the author has compared the flow rates and fracture apertures of induced and natural fractures tested in the uniaxial compression mode over a range of 0 to 30 MPa. The author has shown that both types of fractures exhibited permanent deformation, but the closure of a natural fracture is lower due to its higher stiffness. Consequently, the flow in natural fractures will decrease at given normal stress but will be comparatively higher than the flow through induced fractures under the same stress conditions. Hydraulic conductivity of fractures subject to single-phase flow is discussed in Zimmerman and Bodvarsson (1996), where the effective hydraulic aperture is related with the statistics of the aperture distribution and tortuosity effect caused by regions where the rock walls are in contact. The study suggests a correction factor that depends on the area occupied by the contact regions. Chen and Bai (1998) considered variations in the geometric property of fractures in the modeling of stress-dependent permeability assuming the flow direction is aligned with the direction of the principal stresses. They considered a three-dimensional (3D) fracture network and showed that there is a strong impact of the mechanically responsive fracture apertures in the upscaled permeability of the fracture system. Numerical tools have been used in past studies to understand the impact of mechanics in the permeability of fractured rocks. In Latham et al. (2013), the authors have modeled stress-dependent permeability in a fractured rock in response to uniaxial and biaxial stress states including realistic intersections, bends, and segmented features. The authors have considered single-phase flow and have used the finite-discrete element method to couple mechanics with fluid flow. The authors showed that changes in stress state also causes reactivation of preexisting fractures and the creation of new fractures. Moreover, they showed that a highly heterogeneous stress distribution induces a localized deformation along certain zones and nonuniform fracture aperture, which changes the fluid flow behavior. More recently, Obeysekara et al. (2018) have combined the capability of the finite-discrete element method and the control-volume finite-element method to simulate multiphase flow capturing the geomechanical behavior of the rock matrix and natural fractures under isotropic and anisotropic stress conditions. In the past few years, several scientific publications have addressed the issue of estimating stress-dependent fracture aperture, permeability, capillary pressure, and relative permeability in multiphase flow. Experimental results from Huo et al. (2014) using a saw-cut fractured sandstone core have shown permeability drops of 73% when increasing effective stress from 0.34 to 22.06 MPa and a change in the capillary behavior from “fracture-like” to “matrix-like.” Ali and Sheng (2015) have evaluated stress-dependent properties on production performance in shale gas reservoirs assuming uniaxial stress and isotropic permeability and have shown that hydraulic fractures lose over 90% of its permeability at the late time of production when the bottomhole pressure declines. Meshcheryakova et al. (2015) observed a reduction of 20% in the cumulative oil production when permeability is moderately reduced in core experiments with C 2020 Society of Petroleum Engineers Copyright V This paper (SPE 195452) was accepted for presentation at the SPE Europec featured at 81st EAGE Conference and Exhibition, London, England, UK, 3–6 June 2019, and revised for publication. Original manuscript received for review 4 March 2019. Revised manuscript received for review 19 November 2019. Paper peer approved 22 November 2019. 2020 SPE Reservoir Evaluation & Engineering 1 fractured dolomites. Rozhko et al. (2017b) developed a two-phase flow model in fractured carbonate rock replacing the aperture distribution by a network of elliptical cavities forming connected pathways from the inlet to the outlet of the reservoir. The estimation of fracture relative permeability revealed a nonlinear function of water saturation depending on the initial aperture distribution and on the effective stress, also impacting the capillary pressure-saturation curves. In a subsequent study, Rozhko et al. (2017a) have used these predicted properties to analyze the effect of net stresses in oil recovery, and later Rozhko et al. (2018) used fracture aperture distributions on the basis of micro-CT scan and aspect ratio distribution of fracture voids from stress-displacement laboratory measurements to simulate the stress effect on two-phase flow of naturally fractured chalk samples. SI was addressed by Haghi et al. (2018) where they developed relationships for geo-dynamic rock properties, such as relative permeability and capillary pressure, and analyzed how it influences the oil recovery in naturally fractured carbonate reservoirs. They have used a semianalytical model reproducing a cubic block of fractured carbonate rock with three orthogonal fractures. The results for the case of a mix-wet reservoir reveal a reduction of approximately 50% in the oil recovery factor when the effective stress increases from 10 to 30 MPa. Endpoints and wettability of the relative permeability curves were also shown to be impacted by confining stress. In this paper, SI experiments using carbonate cores extracted from outcrops were conducted to understand oil displacement processes and estimate the effects of fractures in oil recovery. Tracer tests, micro-CT, and thin petrography analyses helped the interpretation of the results obtained by the SI tests, providing insights into the heterogeneity of the cores and supporting the assumption that the stress applied during the preparation of the imbibition experiments may have led to permanent deformation of the fracture, affecting the early time oil recovery. Experimental Evaluation As a common practice in a routine core analysis, some procedures were followed before the start of the SI experiments. The dimensions and weight of the dry cores were measured before wrapping the samples to load them in the core holder. The porosity was calculated from the helium pore volume (PV) experiments described in Fig. 1. To confirm the measured values, the liquid PV was measured by injecting synthetic brine through the pre-evacuated core until it reaches the total saturation. The PV and the bulk volume were used to determine the porosity. The steady-state method was applied to calculate brine permeability using Darcy’s law. At this stage, the net confining pressure applied to the core holder was kept constant at 500 psi. Px Vr Pressure indicator Pr Vs in Vs out Helium regulator Helium out Helium in V1 V2 V3 Coreholder Vp Fig. 1—Schematic of the helium PV porosimeter. V1 and V2 represent valves used to isolate the reference volume Vr. V2 and V3 isolate the expansion volume Vs in the inlet and outlet of the core holder. Extracted from McPhee et al. (2015). A fractured and an unfractured Indiana limestone carbonate plugs with length of 13 cm and diameter of 3.8 cm2 were used in the experiments. The outcrop cores came from the same formation and are assumed to be water-wet, since they were not kept in preserved conditions. In order to create the induced fracture in the core, a rectangular block was broken in two parts and a plug was extracted around the fracture. To maintain the external faces of the fracture open, the core was kept together with two thin strips of aluminum tape holding it at both ends, as shown in Fig. 2. Table 1 lists the measured core properties used in the SI experiments: length, diameter, dry weight, PV, permeability, and porosity. Fig. 2—Indiana limestone cores and the aluminum tape fixing the fractured core at both ends. 2 2020 SPE Reservoir Evaluation & Engineering Core Type Carbonate Fractured Carbonate Length (cm) 12 . 7 13 D i a m e t e r ( c m) 3 .7 9 2 3.81 Dry weight (g) 325.57 329.371 2 5.785 24. 172 Pore volume (cm3) Total permeability (md) 7 75 Total porosity (%) 17.98 16 . 3 1 Table 1—Properties of the fractured and unfractured carbonate cores measured in the laboratory. SI Experiments In Si, the wetting fluid invades a porous medium by capillary forces. The capillary pressure is a function of interfacial tension and surface forces in combination with the pore geometry (Morrow and Mason 2001). SI is generally described as being cocurrent and/or counter-current. In cocurrent imbibition, the wetting and nonwetting phases (water and oil in the present context) flow in the same direction and in counter-current imbibition the fluids flow in opposite directions (Behbahani et al. 2006). SI is considered one of the key production mechanisms in fractured reservoirs that host the majority of the world’s remaining conventional oil (Morrow and Mason 2001; Schmid et al. 2016). The displacement mechanism observed in the experiments reported in this paper is considered to be countercurrent imbibition since all the external faces of the core are open and the matrix is surrounded by water in the fractures. Moreover, the capillary driving force is strong and effective when the rock is water-wet (Delshad et al. 2006), as the samples used in the experiments reported here. In preparation for the SI experiments, the cores were fully saturated with synthetic brine (total salinity 10,000 ppm). Then, four types of mineral oils were injected in the plugs under different net stresses to establish connate water saturation (Swc ) by displacement method; namely N4000 (mineral oil with very high viscosity), heavy mineral oil (HMO), light mineral oil, and kerosene. Because of the higher viscosity of the first two, the overburden pressure applied in the core holder needed to be increased, reaching a value 2,000 psi higher than the core pressure. In the first step, N4000 was injected with the pumps of the overburden and core pressure set to be working at constant pressure delivery. A higher initial injection rate was observed, followed by a gradual decrease as the oil front advances through the core’s pore space. In the second stage, HMO was injected also with the pumps at constant pressure delivery until the system stabilized, when the injection pump was set to work with constant rate delivery. As the HMO started to dissolve in N4000, the core pressure decreased due to reduction of the oil viscosity, increasing the net confining pressure. Then, the overburden pressure was decreased to keep the system working within the safety pressure, and the following fluids, light mineral oil, and kerosene were also injected at a constant rate. Flooding was carried until no brine was produced. The system was heated to a temperature of 58.7 C, and the pressure drop was measured across the core through a pressure transducer installed in the inlet and outlet. The produced fluid was collected in a glass test tube and then put into a centrifuge to separate the oil and brine content, allowing the quantification of the amount of immobile water in the cores. The measured values of Swc for the fractured and unfractured core were 0.2 and 0.21, respectively. Although the same procedure was carried out in both cores, the production of rock material was noticed when injecting the last mineral oil in the fractured core, and an additional 2 PV of fluid was injected at a higher rate to flush the heaviest particles. Fig. 3 shows a schematic of the rig used to establish Swc in the samples. Temperature-controlled area Pressure transducer Overburden Injection cell BPR N2 Pump 2 (overburden pump) Pump 1 (injection pump) Coreholder Fig. 3—Schematic of the rig used to establish Swc in the samples. After the water saturation in the cores has reached its irreducible value, the cores were removed from the core holder, placed inside an Amott cell, and immersed in the synthetic brine. The imbibition cells were kept inside an oven at 58.7 C (at atmospheric pressure), and oil recovery was monitored during 49 days. The oil displaced by the imbibing brine flows to the top of the cell, as shown in Fig. 4. The accumulated volume of oil was measured as a function of time. The results of the experiments comparing the fractured core with the unfractured core are presented in Fig. 5. The points of the curve were reported initially with short time intervals, each half an hour or 1 hour until the oil produced started to stabilize. Then, they were collected every 1 or 2 days. The volume of oil produced in the Amott cell is measured in cubic centimeters (cm3), and the oil recovery factor is shown in the figure as a percentage of original oil in place (OOIP %). 2020 SPE Reservoir Evaluation & Engineering 3 Fig. 4—Amott cells used during the brine imbibition experiments. The left picture shows the unfractured core highlighting the oil accumulated at the top of the cell. The central picture shows the fractured core, and in the right-hand side, a zoom of the image around the core sample is shown. Oil Recovery (OOIP %) 35 30 25 20 15 10 Unfractured carbonate core Fractured carbonate core 5 0 0 10 20 30 40 50 60 Time (days) Fig. 5—Oil recovery (%) 3 time (days) comparing the SI results from the fractured carbonate core (green) and the unfractured core (purple). Fig. 5 shows that the recovery factor of the fractured core was 11.6% higher than the value reached by the unfractured core. This behavior is often seen during imbibition experiments in the fractured cores. Fractures often induce higher recovery due to the increase in surface area (Cheng et al. 2015). However, the “flat” early time recovery for the experiment with the fractured core does not conform pffi with the typical t behavior seen in the imbibition processes. Tracer Tests Tracer tests are typically conducted to study flow path and quantify fluid flow in hydrological systems (Axelsson et al. 2005). Radioactive and chemical tracers have been used for many years in groundwater hydrology. In petroleum engineering, tracer tests are important to aid the characterization of complex heterogeneous reservoirs including naturally fractured reservoirs (Ramirez-S et al. 1995). Concentration data from these analyses are normally plotted as breakthrough/elution curves, and the shapes of these curves depend on the diffusion, dispersion, and adsorption-desorption effects (Greenkorn 1962). The dispersion may cause the breakthrough curves to have an S shape due to heterogeneous fingering and variations in velocity due to anisotropic pore sizes and dead-end pore spaces (Greenkorn 1962). The objective of the tracer test presented here is to investigate the hydraulic behavior of the fractured and unfractured cores under different net stresses. Synthetic brine containing the tracer was injected at a constant rate of 50 cm3/h in all the experiments. Sodium iodide (NaI) was used as a reference tracer, increasing the density of the brine. Measurements were taken each 3 cm3 produced for the first 10 samples and each 5 cm3 until the tracer has reached the maximum concentration, after around 4 PV tracer-brine injected. 4 2020 SPE Reservoir Evaluation & Engineering Fig. 6 shows the results obtained with the fractured and unfractured cores for a net stress of 500 psi. Fig. 7 depicts the tracer concentration in the fractured core under different net stresses, 500, 1,000, 2,000, and then returning to 500 psi. It is evident from Fig. 7 that under 2,000 psi, the breakthrough/elution curve of the fractured core becomes very similar to the unfractured core. This suggests that the fracture closed, and it did not return to the original condition after decreasing the net stress to 500 psi. 1.2 1.0 C/C0 0.8 0.6 0.4 Unfractured core, net stress = 500 psi 0.2 Fractured core, net stress = 500 psi 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4 PV Fig. 6—Breakthrough/elution curves comparing the NaI concentration in the fractured core (green) and unfractured core (dark blue) under net stress of 500 psi. 1.2 1.0 C/C0 0.8 0.6 Fractured core, net stress = 1,000 psi Fractured core, net stress = 2,000 psi 0.4 Fractured core, net stress = 500 psi Fractured core, net stress = 500 psi (after 2,000 psi) 0.2 Unfractured core, net stress = 500 psi 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4 4.5 5 PV Fig. 7—Breakthrough/elution curves comparing the NaI concentration in the fractured core under different net stresses of 500, 1,000, 2,000, and then returning to 500 psi and the unfractured core under net stress of 500 psi. Another fractured core from the same specimen of the plug handled in the SI experiments was used to conduct new tests placing a high permeable woven wire mesh in the center of the core to keep the fracture open. The permeability of this core may be considered to be very similar to the previous one since the two cores were originally one large core 3.8  30 cm2 cut in two small plugs of 3.8  13 cm2. Fig. 8 shows the detail of the wire mesh. Its thickness is 150 mm with approximately 145 mesh/in. and 80 mm wire diameter. Tests were repeated applying a net stress from 500 to 3,500 psi. Fig. 9 shows breakthrough curves of the unfractured core, fractured core, and fractured core with mesh under a net stress of 500 psi. Fig. 10 depicts the tracer test in the fractured core with mesh under different net stresses: 500, 2,000, and 3,500 psi. We observe the same breakthrough time in the experiments with and without mesh under a net stress of 500 psi (Fig. 9). This suggests that when the fracture is kept open with the wire mesh, we recover its original average hydraulic conductivity, which is much higher than the matrix. We also note (Fig. 10) that the application of different confining pressures does not change the profile of the tracer curve when we keep the fracture open with the mesh. This suggests that the mesh keeps the fracture open at the stress ranges considered in this study, and the fracture dominates the flow behavior. Waterflooding in the Fractured Core with Mesh One cycle of water injection was performed in the fractured core with mesh and compared with the oil recovery of the unfractured core to evaluate if the mesh was working as a barrier or if it was helping to keep the fracture open. First, the total permeability was measured, and it has increased to 715 md, almost 10 times higher than the total permeability of the fractured core without mesh (75 md). The same procedure described to establish Swc for the SI experiments was performed here, but the system was not heated, that is, the test 2020 SPE Reservoir Evaluation & Engineering 5 was performed at room temperature. Fig. 11 shows the recovery factor vs. PV, and it is clear that the volume of oil produced is lower in the fractured core. One can see that the injected fluid (synthetic brine) flows quickly through the fracture and by-passes the resident oil, leading to poor sweep efficiency and low recovery. The early breakthrough of injected water is common during water injection in naturally fractured reservoirs, where most of the matrix oil production occurs due to capillary imbibition (Fernø 2012). This poses a challenge in the application of EOR techniques in naturally fractured reservoirs, requiring the development of new techniques to improve oil production. Fig. 8—Wrapped fractured core with a woven wire mesh placed in the center of the fracture. 1.2 1.0 C/C0 0.8 0.6 0.4 Unfractured core, net stress = 500 psi 0.2 Fractured core, net stress = 500 psi Fractured core with mesh, net stress = 500 psi 0 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 PV Fig. 9—Breakthrough/elution curves of the unfractured core (dark blue), fractured core (green), and fractured core with mesh (red) under net stress of 500 psi. It would have been ideal to repeat the SI experiment using the fractured core with mesh to evaluate its performance in comparison with the imbibition displacement of the other samples, but it was not possible because the aluminum wrap required to keep the mesh inside the core would be difficult to remove to open the lateral faces for the brine flow. Micro-CT Analysis of the Fractured Core Micro-CT was performed in order to decrease the uncertainty associated with the fracture aperture and to investigate the pores of the matrix after the SI experiments. Due to the size of the core, it was scanned at 23.5-mm resolution as shown in Fig. 12. The porosity and pore space were segmented (Figs. 13 and 14), and the pore connectivity was calculated (Fig. 15). The porosity was computed for each single XY plane of the micro-CT images (i.e., each one voxel size long) and a variation from approximately 8.5% to 12% with a total average of 10.51% was observed, indicating a fairly homogeneous matrix with no secondary porosity at this scale. We believe that the difference between the average porosity measured using the micro-CT analysis and the laboratory measurement might be explained by connected microporosity that is not captured by the spatial resolution of the micro-CT scan. The cross sections of the core are illustrated in Figs. 16 through 19. These figures also show the segmented pore space and the connected pores. Figs. 16 through 19 show that it is challenging to identify the fracture by simply analyzing the two-dimensional images. Some of the cross sections look actually like an unfractured core (see, for instance, Fig. 18). In other cross sections, however, it is possible to identify the fracture with a heterogeneous aperture that reaches a maximum value of 1.76 mm (see Fig. 19). 6 2020 SPE Reservoir Evaluation & Engineering 1.2 1.0 C/C0 0.8 0.6 0.4 Fractured core with mesh, net stress = 2,000 psi Fractured core with mesh, net stress = 500 psi Fractured core with mesh, net stress = 3,500 psi 0.2 0 0 0.5 1.0 1.5 2.5 2.0 3.0 3.5 4.0 4.5 5.0 PV Fig. 10—Breakthrough/elution curves of the fractured core with mesh under three different net stresses: 500 (red), 2,000 (yellow), and 3,500 psi (light green). Oil Recovery (OOIP %) 60 50 40 30 20 Unfractured carbonate core Fractured carbonate core with mesh 10 0 0 1 2 3 4 5 6 7 PV Fig. 11—Waterflooding results for the unfractured core (green) and fractured core with mesh (red). (mm) 41.83 (mm) 0 0 153.4 Fig. 12—3D view of the fractured carbonate core scanned at 23.5 lm. Thin Section Petrography Analysis In this section, we present the results of the petrographic analysis carried out after the SI experiments. The analysis aimed at comparing the matrix heterogeneity and visible porosity of the cores and at identifying possible damages to the matrix and other pore-scale phenomena that may have affected fluid flow during the SI experiments. Large-format 3  2 in.2 thin sections were prepared from the unfractured and the fractured plugs with and without mesh. High-resolution low-power photographs of the entire thin section were taken with a magnification of 2.4 (Fig. 20), while some areas were evidenced with a magnification of 60 (Fig. 21). 2020 SPE Reservoir Evaluation & Engineering 7 13 Porosity (%) 12 11 10 9 8 7 0 20 40 60 80 100 120 140 Distance Along the Core (mm) Fig. 13—Porosity profile with a total average of 10.51%. (mm) 41.83 (mm) 0 0 153.4 Fig. 14—3D view showing the pore space segmented through the fractured core. (mm) 41.83 (mm) 0 0 153.4 Fig. 15—Pore connectivity map. Red represents connected porosity. Petrographic descriptions were prepared for the thin sections, and photomicrographs were taken under low magnification to illustrate the general features and textures of the samples. The three samples appear to be fairly similar in terms of petrography and porosity. All limestones are classified as bioclastic grainstone according to the industry standard of Dunham (1962). Visible porosity is moderate and mainly comprises primary interparticle porosity and biomouldic porosity created by the dissolution of aragonitic fragments. Secondary porosity has also been created by the dissolution of micritic cortices, and it is hosted by secondary circumgranular pores surrounding allochems. Bioclastic micrite may host microporosity, and primary porosity is considered lowered by compaction and by block calcite cementation. Figs. 21a and 21b consist of two photomicrographs taken at low magnification (60) from the fractured carbonate core with mesh. The fracture aperture in this section is typically 0.5–1.0 mm. Fig. 21a shows the induced fracture filled with the woven wire 8 2020 SPE Reservoir Evaluation & Engineering mesh and a microfracture between the two yellow arrows. We believe that this fracture was created by failure and cleaving of the sample when the main fracture was generated. Fig. 21b shows detached micrite envelopes (mi) apparently accumulated as pore fills. These micrites at the right side are locally cemented by mosaic calcite (mc), suggesting that if they are indeed allochthonous pore fills, transportation and accumulation of the micrite envelopes took place before the cementation. The yellow arrows highlight a grain column with mildly sutured contacts between the allochems. (mm) (mm) (mm) 132.7 132.7 132.7 (mm) 0 0 35.32 (mm) 0 35.32 0 (mm) 0 0 35.32 Fig. 16—Cross sections from the center of the core showing the pore space (left), the normal image of the core with the fracture inside the red polygon (center), and the connected pores (right). (mm) 38.58 0 0 (mm) 38.58 (mm) 37.5 0 0 (mm) 37.5 Fig. 17—Cross section showing the fracture inside the red polygon (left) and the connected pores (right). 2020 SPE Reservoir Evaluation & Engineering 9 (mm) 38.58 0 (mm) 38.58 (mm) 37.5 0 0 0 (mm) 37.5 Fig. 18—Cross section where the fracture is almost imperceptible. XY view (left) and the pore space (right). (mm) 38.58 0 (mm) 38.58 (mm) 37.5 0 0 0 (mm) 37.5 Fig. 19—Cross section showing a fractured segment with an aperture of 1.76 mm (left) and the connected pores (right). 10 mm 10 mm 10 mm Fig. 20—Low-power thin section micrograph with magnification 32.4 and bedding rotated through 458: unfractured (left) and fractured cores with mesh (center) and without mesh (right). 10 2020 SPE Reservoir Evaluation & Engineering (b) (a) mi mc mi mi mi 500 µm (c) 500 µm (d) o cr 2 rf cr o 1 cr en rf o rf cr 1 o cr 1 o en rf 500 µm 500 µm Fig. 21—Plane polarized light at low magnification (360). Fractured core. with mesh (a and b) pointing out the microfracture formed next to the main fracture (a) and detached micrite envelopes (mi) and mildly sutured contacts between allochems (b). Fractured core without mesh (c and d) showing the view across the induced fracture (c) and the “rock flour” (rf) accumulated during testing (d). Figs. 21c and 21d are low-power shots taken from the fractured core without mesh. Here, the fracture seems to have propagated through the fracturing of allochems along most its length, and the aperture ranges from 0.06 to 0.17 mm. Fig. 21c illustrates the induced fracture (Heavy Arrow 1) and a rare bifurcation (Arrow 2) along with a thin offshoot. It is possible to see block calcite, forming mainly as epitaxial overgrowths (o) nucleating on crinoid (cr) fragments. We can also observe an endothyracid foraminifera (en). In Figs. 21d and 21a sparse micritic interparticle component was distinguished coating a crinoid overgrowth (o), and it is interpreted as a nongeologic rock flour (rf). This photomicrograph is aligned parallel to the bedding, and the upper surface of the core is toward the right. The rock flour mostly drapes the floors of the pores in this view, proposing it was accumulated in the down-flow direction during the testing. In both fractured cores, offshoots were formed close to the main fracture, and it may impact porosity and permeability. In all cases (fractured and unfractured) the allochems meet at point, long or mildly sutured contacts, indicating relatively moderate compaction. The crushed leached bioclasts with their spalled micrite envelopes (Fig. 21b) are also attributed in part to compaction and were pointed out as formation damage representing “movement-of-fines” hazard, although some appear to have remained in situ. The deformation in this analysis is in principle considered as a geologic factor preblock calcite cementation. However, a comparison with the untested samples would be required to assess the original impact and actual formation damage. We leave this analysis for a future publication. Numerical Simulations In this section, we describe the numerical simulations that were performed to understand the behavior of the capillary imbibition process, as well as to history-match unknown fracture, matrix parameters, and saturation functions (e.g., relative permeability and capillary pressure). We represent the fracture explicitly via high-permeability low-thickness cells and model the Amott cell as a high-PV reservoir surrounding the computational model of the core. Model Description A 3D model of the core was built in the IMEX simulator (Computer Modelling Group, Calgary, Alberta, Canada) using a Cartesian grid. Two fluid phases (brine and oil) were considered. The core was modeled as a slab with the same vertical dimension of volume of the cylindrical core. We choose this simplified representation of the core, since it can be more easily discretized with a structured mesh. This simplification suffices for obtaining a qualitative understanding of the process and an estimate of relative permeabilities and capillary pressure, but a more detailed analysis would require the representation of the correct geometry of the core. A mesh of 18  18  30 cells was used in the discretization of the domain. The core dimensions and petrophysical properties are shown previously in Table 1. Remaining parameters used in the numerical simulations are shown in Table 2. The initial water saturation (Swi ) was obtained in a preprocedure of the SI experiment. Fig. 22 shows the 3D view of the block representing the fractured core immersed in the brine. Different scenarios were considered to find the optimal computational model that allowed us to history-match the imbibition experiments. The brine that imbibes the core comes from a high-PV region surrounding the core domain that is fully saturated with water. The displaced oil is also collected in this region. Note that the permeability value of the fractured core outlined in Table 1 corresponds to the total permeability of the core. It consists of a matrix and fracture flow. In the next section, we describe the history-matching procedure applied for the fractured and unfractured models, as well as the methodology applied to find the specific fracture permeability and aperture and how it was related to the stress applied before the SI experiment. 2020 SPE Reservoir Evaluation & Engineering 11 De scrip tio n V al u e Based on −6 Rock compressibility 2.90075×10 1/kPa Oliveira et al. (2016) Reference pressure for calculation of the effect of rock compressibility 2757.9 kPa Oliveira et al. (2016) Reservoir temperature 58.7°C Laboratory measurement Oil density at standard condition 817.1 kg/m Water density at standard condition 1006 kg/m Oil viscosity at standard condition 2 cp Geotechenv.com (n.d.) Water viscosity at standard condition 1.165 cp Laboratory measurement Laboratory measurement 3 Laboratory measurement 3 Brine permeability (high permeable fracture) 10,000 md Behbahani et al. (2006) Brine porosity (very porous fracture) 0.99 fraction Behbahani et al. (2006) Table 2—Input parameters used in the simulations. Porosity 0.99 Brine - 0.9 - 0.8 Matrix - 0.7 - 0.6 Fracture - 0.5 - 0.4 - 0.3 - 0.2 0.16 Fig. 22—3D view showing the computational model created to simulate the SI experiment. The color bar scale represents porosity. History Matching of Core Properties A first model was created to match the matrix properties with the SI experiment in the unfractured core. Values of permeability, porosity, and Swc were measured in the laboratory and are shown in Table 1. A residual oil saturation (Sor ) of 0.651 was calculated from the final readings of oil recovery obtained from the SI experiment (Fig. 5). The relative permeability to the oil and water phase was estimated using correlations available in IMEX [Eqs. 1 and 2 for water-wet limestones and dolomites, according to Honarpour et al. (1986)]. A linear relative permeability curve was considered for the brine phase. Manual tuning was conducted to match the parameters of relative permeability and capillary pressure curves to the experimental data. The parameters obtained in the history-matching procedure described above were then considered for the matrix cells in the history matching of the unfractured core SI experiment.  0:43 0:0020525ðSw  Swcrit Þ 1 ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð1Þ  0:051371ðS  S Þ krw ¼ w wcrit 2:15 k ð/ Þ a  2 1:2624ðSo  Sorw Þ ðSo  Sorw Þ ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð2Þ krow ¼ ð1  Sorw Þ ð1  Swcon  Sorw Þ where Sw is the water saturation, Swcon is the connate water saturation endpoint, Swcrit is the critical water saturation endpoint, So is the oil saturation, Sorw is the residual oil for water/oil table saturation endpoint, / is the porosity, and ka is Permeability I. The computational model for the unfractured core is shown in Fig. 23 where the Swi field is displayed showing the high-PV cells fully saturated by brine surrounding the matrix with a Swc of 0.21. The results of the history-matching procedure are shown in Fig. 24. An excellent match of the experimental data was achieved with the numerical model. The relative permeability and capillary pressure curves found with manual tuning are presented in Fig. 25. Fig. 26 shows the oil saturation fields at different times during the imbibition simulation. After estimating the parameters for the unfractured experiment, the next step was to build the fractured model considering the matrix relative permeability and capillary pressure obtained from the history-matching procedure outlined above. A fracture was created in the computational model by refining one entire row of the matrix gridblocks (from the base to the top), depending on the choice of the aperture. The refinement was made in the I and J directions to avoid numerical issues, and different relative permeability curves were considered for the matrix and fracture cells, assuming there are no capillary forces within the fracture (Fig. 27). 12 2020 SPE Reservoir Evaluation & Engineering Water saturation 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.21 Fig. 23—3D view of the computational mesh colored by water saturation (left) and the view from the base of the model showing how the core is positioned at the center (right). 6.0 Oil Volume SC SCTR (cm3) 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 Experiment, unfractured carbonate core Simulation, unfractured carbonate core 1.0 0.5 0 4 9 14 19 24 29 34 39 44 49 Time (days) Fig. 24—History matching of the SI experiments for the unfractured carbonate core. 0.40 krw vs. Sw krow vs. Sw 0.64 0.48 0.32 0.16 0 0.21 Pcow vs. Sw 0.32 Pcow (kPa) Relative Permeability, kr 0.80 0.24 0.16 0.08 0.33 0.44 0.56 0.67 0.79 Sw 0 0.21 0.33 0.44 0.56 0.67 0.79 Sw Fig. 25—Relative permeability and capillary pressure matched for the SI experiment of the unfractured core. In order to obtain an estimate for the fracture aperture and permeability, we consider a three-layer system (matrix/fracture/matrix, see Fig. 28) with total equivalent permeability given by the experimental value of Table 1. The expression that relates the permeability and thickness of each layer to the equivalent permeability is given by Xn kA ¼1 j j ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð3Þ kavg ¼ At where Aj ¼ hj wj , representing the cross-sectional area of layer j. 2020 SPE Reservoir Evaluation & Engineering 13 Oil saturation 0 days 4 days 8 days 16 days 49 days 0.79 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Fig. 26—Oil saturation fields at different times: 0, 4, 8, 16, and 49 days. The saturation scale varies from 0 to 0.79, and the first slabs of the model are filtered to show the external surface of the core. Matrix region Fracture region with aperture = 0.375 mm Gridblock refined in nine parts K J I J Fig. 27—IJ-2D aerial view (left) and JK-2D (right) showing the three different regions defining the water (light green), matrix (blue), and fracture (red). Flow direction P2 L k1 k2 Q1 k3 Q2 Q3 P1 W h1 h2 h3 Fig. 28—Schematic of linear flow through parallel layers. 14 2020 SPE Reservoir Evaluation & Engineering As with the unfractured model, a Sor of 0.566 was taken from the imbibition experiment. The total porosity measured in the entire sample (matrix þ fracture) was 16.31% and the total permeability 75 md. Since we model the fracture as thin computational cells, we consider a porosity of 99% for the fracture cells, assuming there is no cementing or mineral filling its pore space. The first simulation models were created with an explicit representation of the fracture tortuosity, as shown in Fig. 22. However, the permeability anisotropy created in these simulation models led to high computation times as the model was refined. Thus, the results shown in the remainder of this section considered a planar fracture as shown in Fig. 27. Consequently, permeability values found for the fracture cells should be interpreted as an equivalent reduced permeability that is negatively affected by the fracture tortuosity. Similar to the unfractured core, a manual tuning procedure was carried out to match the fracture aperture and permeability to the SI experiments. Using an initial aperture value of 1 mm, this value was decreased gradually to find an aperture that matched the experimental results with reasonable accuracy. The decrease is necessary to correct the transmissibility of the fracture to account for fracture tortuosity. The same procedure was conducted to find the fracture permeability. The values of aperture 0.135 mm, average permeability 7.1 md, and fracture permeability 32 md provided a reasonable match with the late-time behavior of the imbibition experiment (see Fig. 29). Note that the reduced core permeability is more consistent with the unfractured core value and confirms the healing of the fracture, as first indicated by the tracer experiments. However, it is possible to note from Fig. 29 that this simulation model was unable to provide a good match for the early time recovery. 6.0 Oil Volume SC SCTR (cm3) 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 Experiment, fractured carbonate core Experiment, fractured carbonate core: Aperture 0.135 mm/kavg 75 md/kf 17.007 md Experiment, fractured carbonate core: Aperture 0.135 mm/kavg 7.1 md/kf 32 md 1.0 0.5 0 4 9 14 19 24 29 34 39 44 49 Time (days) Fig. 29—Oil recovery 3 time with the experimental data (purple hexagons) and the simulation (green line). The solid green line shows the result considering the average permeability of 75 md and fracture permeability of 17,007 md. The dashed line shows the result with an average permeability of 7.1 md and fracture permeability of 32 md. One solution found to match the early time of the simulation with the experimental data was creating an artificial heterogeneity in the model (Fig. 30). This was done by modifying the relative permeability and capillary pressure in the area of the matrix surrounding the fracture. The reasoning behind this preliminary test was the observation that the fracturing process may have created a damage zone around the fracture. The rock flour created during the application of the confining stress (observed in the petrographic analysis) might have modified the pore connectivity by occluding some pores, potentially impacting the pore size distribution, which in turn affects the petrophysical curves (the relative permeability and capillary pressure). 2 3 1 4 K J Fig. 30—Regions defined in the new model: 1—matrix, 2—brine, 3—fracture (gridblock divided by 25), and 4—matrix with different relative permeabilites. The curve was matched with a fracture aperture of 0.135 mm, average permeability 7.18 md, and fracture permeability 52 md. The heterogeneous computational model provided a good match of the experimental data in both early time and late-time (Fig. 31). Fig. 32 shows the relative permeability and capillary pressure curves for the new computational model. Figs. 33 and 34 show the evolution of the oil saturation in both homogeneous and heterogeneous models. The good match obtained with the heterogeneous model gives us indications that the core samples may show strong heterogeneity, possibly due to the fracturing process. However, further analyses are required to confirm this hypothesis. 2020 SPE Reservoir Evaluation & Engineering 15 6.0 Oil Volume SC SCTR (cm3) 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 Experiment, fractured carbonate core Simulation, fractured carbonate core: Aperture 0.135 mm/kavg 7.18 md/kf 52 md/heterogeneous 1.0 0.5 0 4 9 14 19 24 29 34 39 44 49 Time (days) Fig. 31—Comparison of the production data obtained from the laboratory experiments in the fractured core (purple hexagon) and the simulation considering the heterogeneous model, matched with fracture aperture equal to 0.135 mm, fracture permeability 52 md, and average permeability 7.18 md. 0.40 kr – Matrix Region 1 0.64 0.48 0.32 krw vs. Sw krow vs. Sw 0.16 0 0.20 0.32 0.44 0.56 Pc – Matrix Region 1 0.32 Pcow (kPa) Relative Permeability, kr 0.80 0.68 0.24 0.16 Pcow vs. Sw 0.08 0 0.20 0.80 0.32 0.44 Sw 0.68 0.80 Sw 0.150 kr – Brine Region 2 and Fracture Region 3 0.80 0.60 krw vs. Sw krow vs. Sw 0.40 0.20 0 0 0.20 0.40 0.60 Sw 0.80 1.00 Relative Permeability, kr 1.00 Relative Permeability, kr 0.56 kr – Matrix Region 4 0.120 0.090 krw vs. Sw krow vs. Sw 0.050 0.030 0 0.20 0.32 0.44 0.56 0.68 0.80 Sw Fig. 32—Capillary pressure and relative permeability defined in the four regions of the heterogeneous model. Discussion The SI experiments reported in this study show a faster oil recovery from the fractured core when compared with the unfractured core due to rapid imbibition caused by the fracture. This result is often seen when running imbibition experiments with the fractured cores and is caused by an increase in the surface area open for imbibition. However, remarkably, the early time recovery rate for the fractured core is significantly lower than the unfractured core. This is seen when we look at the recovery curves, noting that the fractured core shows a nearly linear recovery profile with a “flat” early time behavior. This might have been caused by the damage induced by the applied stresses during the procedure that established the Swc . 16 2020 SPE Reservoir Evaluation & Engineering Oil saturation 0 days 4 days 8 days 16 days 32 days 49 days 1.00 0.90 0.80 0.70 0.60 0.50 0.40 K 0.30 0.20 0.10 0 J Fig. 33—JK-2D Plane 9: oil saturation evolution in the fractured core. Oil saturation 0 days 4 days 8 days 16 days 32 days 49 days 1.00 0.90 0.80 0.70 0.60 0.50 0.40 K 0.30 0.20 0.10 0 J Fig. 34—JK-2D Plane 9: oil saturation evolution in the fractured core with an artificial heterogeneity. Tracer tests in both fractured and unfractured cores were performed at different net stresses (500–2,000 psi) to evaluate the impact of the fracture in fluid flow. The concentration breakthrough curve of the unfractured core is similar to the breakthrough curve of the fractured core under a high net stress of 2,000 psi (Fig. 7). This suggests that at this confining pressure, the fracture closes and the fractured core behaves as an unfractured core. However, when returning the net stress to the previous initial value of 500 psi, we observe that the breakthrough curve remains almost unchanged. This implies that there may be a hysteretic effect in the deformation of the fracture asperities. The asperities may have undergone irreversible plastic deformation that kept the fracture closed when the confining pressure was relaxed to a lower value. This is a remarkable result that may impact our conceptual understanding of modeling of fractures under geomechanical effects. Fractures are typically modeled as elastic heterogeneities, but the experimental evidence of plastic deformation would require different models and change dramatically the results of fluid flow in the reservoir scale. Further tracer tests with a mesh inside the fracture were carried out to isolate the effect of the fracture, that is, to ensure that the matrix does not experience poroelastic deformation during the process. Indeed, when keeping the fracture open with a mesh, we observe that the breakthrough curves are not sensitive to different net stresses (Fig. 10) and that the fracture is the main conduit for fluid flow when it is kept open (Fig. 9). The micro-CT analysis shows that the fracture aperture is very small after the core has undergone high net stresses. The fractured core was scanned with a resolution of 23.5 mm, and this resolution was not enough to map the connection along the fracture. The fracture actually exists, and it is open since it is not cemented or mineral filled, but the tight apertures prevented the micro-CT scan from identifying the fracture pore space in most of the cross sections. This analysis was useful, however, to obtain a new estimate for the PV of the matrix that was different from the previous one obtained with the experiments. The thin petrography analysis was also requested to evaluate the matrix heterogeneity of the samples. While the samples are fairly similar, rock compaction and “movement-of-fines” hazard were pointed out as formation damage that can result in a slight reduction in permeability in both cores. The simulation of the SI experiments was history matched with a fracture aperture of 0.135 mm. It can be interpreted as an average aperture of the fracture that takes into consideration the aperture heterogeneity and the tortuosity of the fracture. Two models were considered in the history matching. A first model with homogeneous matrix matched the late-time recovery reasonably well (Fig. 29) but failed to capture the early recovery. For this model, a fracture permeability of 32 md was found. A second model considering a heterogeneous zone around the fracture (a “damage zone”) with different relative permeabilities and capillary pressure provided a good match in both early time and late-time recovery. For this model, a fracture permeability of 52 md was found. The good agreement in the second model gives us indications that heterogeneity in the matrix properties may explain the early behavior of the recovery. 2020 SPE Reservoir Evaluation & Engineering 17 Conclusions A few conclusions that can be drawn from this study are summarized below: 1. The stress applied during the preparation of the SI experiments caused permanent deformation of the fracture asperities, leading to decreased fracture transmissibility. This may impact the way we typically model fractures in coupled flow/mechanics simulators. 2. The woven wire mesh used in the fractured plug has proven to be a good solution for the core analysis maintaining a high fracture permeability even under stress conditions. 3. It was not possible to match the experimental results with simulation models that consider a homogeneous matrix and fracture. The inclusion of a heterogeneity zone in the computational model provided a good match of the experimental results. This gives us indications that heterogeneity caused by the applied stresses may play an important role in the limestone samples. However, a deeper analysis is recommended to fully understand the behavior of the imbibition experiments with numerical simulations. Nomenclature A ¼ cross-sectional area of the sample, cm2 h ¼ height, cm k ¼ permeability, darcy ka ¼ Permeability I, darcy kavg ¼ average permeability, darcy kf ¼ fracture permeability, darcy kr ¼ relative permeability, dimensionless L ¼ length, cm P ¼ pressure, psi Pc ¼ capillary pressure, Pa Sw ¼ water saturation, dimensionless Swc ¼ connate water saturation, dimensionless Swcrit ¼ critical water saturation endpoint, dimensionless Swcon ¼ connate water saturation endpoint, dimensionless Swi ¼ initial water saturation, dimensionless So ¼ oil saturation, dimensionless Sor ¼ residual oil saturation, dimensionless Sorw ¼ residual oil for water/oil table saturation endpoint, dimensionless V1,2,3 ¼ valves 1/2/3, dimensionless Vr ¼ reference volume, cm3 Vs ¼ expansion volume, cm3 w ¼ width, cm / ¼ porosity, percent Acknowledgments This research was cofunded by CNPq—Council for Scientific and Technological Development under the Ministry of Science, Technology and Innovation of the Brazilian federal government, through Science without Borders Programme and Shell Brazil, according to the ANP R&D levy as “Compromisso de Investimentos com Pesquisa e Desenvolvimento.” It has been performed in the Centre for EOR and CO2 Solutions at Heriot-Watt University. The first author also would like to thank the laboratory team for the support; Scott Parker, Christopher Brown (ALS Oil and Gas), Jukka Kuva (Geological Survey of Finland), and Christine Maier (HWU) for the valuable contributions; and for all the further incentive received during the elaboration of this work. References Ali, T. A. and Sheng, J. J. 2015. Evaluation of the Effect of Stress-Dependent Permeability on Production Performance in Shale Gas Reservoirs. Paper presented at the SPE Eastern Regional Meeting, Morgantown, West Virginia, USA, 13–15 October. SPE-177299-MS. https://doi.org/10.2118/ 177299-MS. Axelsson, G., Björnsson, G., and Montalvo, F. 2005. Quantitative Interpretation of Tracer Test Data. Paper presented at the Proceedings World Geothermal Congress, Antalya, Turkey, 24–29 April. Behbahani, H. S., Di Donato, G., and Blunt, M. J. 2006. Simulation of Counter-Current Imbibition in Water-Wet Fractured Reservoirs. J Pet Sci Eng 50 (1): 21–39. https://doi.org/10.1016/j.petrol.2005.08.001. Berard, T., Jammes, L., Lecampion, B. et al. 2007. CO2 Storage Geomechanics for Performance and Risk Management. Paper presented at the Offshore Europe, Aberdeen, Scotland, UK, 4–7 September. SPE-108528-MS. https://doi.org/10.2118/108528-MS. Chen, M. and Bai, M. 1998. Modeling Stress-Dependent Permeability for Anisotropic Fractured Porous Rocks. Int J Rock Mech Min Sci 35 (8): 1113–1119. https://doi.org/10.1016/S0148-9062(98)00167-3. Delshad, M., Najafabadi, N. F., Anderson, G. A. et al. 2006. Modeling Wettability Alteration in Naturally Fractured Reservoirs. Paper presented at the SPE/DOE Symposium on Improved Oil Recovery, Tulsa, Oklahoma, USA, 22–26 April. SPE-100081-MS. https://doi.org/10.2118/100081-MS. Dunham, R. J. 1962. Classification of Carbonate Rocks According to Depositional Textures. in Ham, W. E., ed., Classification of Carbonate Rocks: AAPG Memoir 1, p. 108–121. Tulsa, Oklahoma, USA: AAPG. Fernø, M. A. 2012. Enhanced Oil Recovery in Fractured Reservoirs. In Introduction to Enhanced Oil Recovery (EOR) Processes and Bioremediation of Oil-Contaminated Sites. Rijeka, Croatia: InTech. Gale, J. E. 1982. The Effects of Fracture Type (Induced Versus Natural) on the Stress-Fracture Closure-Fracture Permeability Relationships. Paper presented at the 23rd U.S. Symposium on Rock Mechanics (USRMS), Berkeley, California, USA, 25–27 August. ARMA-82-290. Geotechenv.com. n.d. Average Viscosities of Miscellaneous Liquids, http://www.geotechenv.com/Reference_Pages/average_viscosities_liquids.pdf (accessed 26 January 2019). Greenkorn, R. A. 1962. Experimental Study of Waterflood Tracers. J Pet Technol 14 (1): 87–92. SPE-169-PA. https://doi.org/10.2118/169-PA. Haghi, A. H., Chalaturnyk, R., and Geiger, S. 2018. New Semi-Analytical Insights into Stress-Dependent Spontaneous Imbibition and Oil Recovery in Naturally Fractured Carbonate Reservoirs. Water Resour Res 54 (11): 9605–9622. https://doi.org/10.1029/2018WR024042. 18 2020 SPE Reservoir Evaluation & Engineering Honarpour, M., Koederitz, L., and Harvey, A. H. 1986. Relative Permeability of Petroleum Reservoirs. Boca Raton, Florida, USA: CRC Press Inc. Huo, D., Li, B., and Benson, S. M. 2014. Investigating Aperture-Based Stress-Dependent Permeability and Capillary Pressure in Rock Fractures. Paper presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands, 27–29 October. SPE-170819-MS. https://doi.org/ 10.2118/170819-MS. Jiang, J., Shao, Y., and Younis, R. M. 2014. Development of a Multi-Continuum Multi-Component Model for Enhanced Gas Recovery and CO2 Storage in Fractured Shale Gas Reservoirs. Paper presented at the SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, 12–16 April. SPE169114-MS. https://doi.org/10.2118/169114-MS. Jones, F. O. Jr. 1975. A Laboratory Study of the Effects of Confining Pressure on Fracture Flow and Storage Capacity in Carbonate Rocks. J Pet Technol 27 (1): 21–27. SPE-4569-PA. https://doi.org/10.2118/4569-PA. Kumar, D., Gutierrez, M., Frash, L. P. et al. 2015. Numerical Modeling of Experimental Hydraulic Fracture Initiation and Propagation in Enhanced Geothermal Systems. Paper presented at the 49th U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, California, USA, 28 June–1 July. ARMA-2015-253. Latham, J.-P., Xiang, J., Belayneh, M. et al. 2013. Modelling Stress-Dependent Permeability in Fractured Rock Including Effects of Propagating and Bending Fractures. Int J Rock Mech Min Sci 57: 100–112. https://doi.org/10.1016/j.ijrmms.2012.08.002. March, R., Doster, F., and Geiger, S. 2018. Assessment of CO2 Storage Potential in Naturally Fractured Reservoirs with Dual-Porosity Models. Water Resour Res 54: 1650–1668. https://doi.org/10.1002/2017WR022159. Meshcheryakova, A., Lukin, S., and Rukavishnikov, V. 2015. Stress-Dependent Permeability Model of Naturally-Fractured Reservoir on the Example of the Field K. Paper presented at the Tyumen 2015-Deep Subsoil and Science Horizons, 23 March. https://doi.org/10.3997/2214-4609.201412054. Moortgat, J. and Firoozabadi, A. 2017. Water Coning, Water, and CO2 Injection in Heavy-Oil Fractured Reservoirs. SPE Res Eval & Eng 20 (1): 168–183. SPE-183648-PA. https://doi.org/10.2118/183648-PA. Morrow, N. R. and Mason, G. 2001. Recovery of Oil by Spontaneous Imbibition. Curr Opin Colloid Interface Sci 6 (4): 321–337. https://doi.org/ 10.1016/S1359-0294(01)00100-5. Ng, K. W., Poudel, R., Kyle, W. et al. 2017. A Laboratory Experimental Study of Enhanced Geothermal Systems. Paper presented at the 51st U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, California, USA. ARMA-2017-0415. Obeysekara, A., Lei, Q., Salinas, P. et al. 2018. Modelling Stress-Dependent Single and Multi-Phase Flows in Fractured Porous Media Based on an Immersed-Body Method with Mesh Adaptivity. Comput Geotech 103: 229–241. https://doi.org/10.1016/j.compgeo.2018.07.009. Olasolo, P., Juárez, M. C., Morales, M. P. et al. 2016. Enhanced Geothermal Systems (EGS): A Review. Renew Sustain Energy Rev 56: 133–144. https:// doi.org/10.1016/j.rser.2015.11.031. Oliveira, G. L. P. D., Ceia, M. A. R., Missagia, R. M. et al. 2016. Pore Volume Compressibilities of Sandstones and Carbonates from Helium Porosimetry Measurements. J Pet Sci Eng 137: 185–201. https://doi.org/10.1016/j.petrol.2015.11.022. Ramirez-S, J., Samaniego V, F., Rodriguez, F. et al. 1995. Tracer Test Interpretation in Naturally Fractured Reservoirs. SPE Form Eval 10 (3): 186–192. SPE-28691-PA. https://doi.org/10.2118/28691-PA. Rozhko, A., Jonoud, S., Wennberg, O. et al. 2017a. Modeling of Normal Net Stress Effect on Fracture Relative Permeability and Its Effect on Oil Recovery from Fractured Car. Paper presented at the First EAGE Workshop on Evaluation and Drilling of Carbonate Reservoirs, 4 October. https://doi.org/ 10.3997/2214-4609.201702365 Rozhko, A., Naumann, M., Wennberg, O. et al. 2018. Modelling Two-Phase Fluid Flow in a Natural Fracture in Chalk under Different Stress. Paper presented at the 80th EAGE Conference and Exhibition, 11 June. https://doi.org/10.3997/2214-4609.201801132. Rozhko, A., Wennberg, O., and Jonoud, S. 2017b. Modelling of Normal Net Stress Effect on Two-Phase Relative Permeability and Capillary Pressure of Rough-Walled Fracture. Paper presented at the IOR-19th European Symposium on Improved Oil Recovery, 24 April. https://doi.org/10.3997/22144609.201700274. Schmid, K. S., Alyafei, N., Geiger, S. et al. 2016. Analytical Solutions for Spontaneous Imbibition: Fractional-Flow Theory and Experimental Analysis. SPE J. 21 (6): 2308–2316. SPE-184393-PA. https://doi.org/10.2118/184393-PA. Teklu, T. W., Alameri, W., Graves, R. M. et al. 2012. Geomechanics Considerations in Enhanced Oil Recovery. Paper presented at the SPE Canadian Unconventional Resources Conference, Calgary, Alberta, Canada, 30 October–1 November. SPE-162701-MS. https://doi.org/10.2118/162701-MS. Vialle, S., Druhan, J. L., and Maher, K. 2016. Multi-Phase Flow Simulation of CO2 Leakage through a Fractured Caprock in Response to Mitigation Strategies. Int J Greenhouse Gas Control 44: 11–25. https://doi.org/10.1016/j.ijggc.2015.10.007. Zhou, Z., Jin, Y., Zeng, Y. et al. 2018. Experimental Study of Hydraulic Fracturing in Enhanced Geothermal System. Paper presented at the 52nd U.S. Rock Mechanics/Geomechanics Symposium, Seattle, Washington, USA, 17–20 June. ARMA-2018-148. Zimmerman, R. W. and Bodvarsson, G. S. 1996. Hydraulic Conductivity of Rock Fractures. Transp Porous Media 23 (1): 1–30. https://doi.org/10.1007/ BF00145263. SI Metric Units Conversion 145.038 psi ¼ 1 MPa 1 in. ¼ 2.54 cm 2020 SPE Reservoir Evaluation & Engineering 19