Oil Relative Permeability Research Articles

Analytical prediction model for edge water invasion flow rate in SAGD heavy oil reservoirs

SAGD (Steam Assisted Gravity Drainage) technology is a highly developed method for the extracting heavy oil. In the Liaohe Oilfield in China, there are 72 SAGD well groups within a massive heavy oil reservoir containing edge water and the risk associated with edge water invasion is substantial. Currently, the injected steam is less than 50 m away from the edge water, which increases the urgency to address the potential invasion of edge water. If the edge water flows into the reservoir, it will impact nearly 8.0 × 105 tons of crude oil production. Recognizing the importance of mitigating the edge water invasion, this paper proposes a prediction model for the edge water invasion flow rate in SAGD reservoirs. The model integrates mass and heat transfer dynamics between the steam chamber and edge water, the relative permeabilities of oil and water phases, and the viscosity-temperature relationship of water. The model is validated through numerical simulations and field data. The findings indicate that for SAGD reservoirs with a permeability greater than 1 D, maintaining a minimum distance of 25 m between the edge water and the steam chamber is advisable, especially when the pressure differential is 0.5 MPa. Furthermore, the prediction model is used to forecast the edge water breakthrough time and evaluate water invasion risk. A prediction chart for the edge water invasion flow rate is developed, providing a practical tool for estimating invasion flow rate curves. Also, a method of edge water invasion warning is established, with a corresponding chart that offers a quick assessment of water invasion risks in heavy oil reservoirs. Overall, this research lays a foundational framework for understanding and managing the edge water invasion in SAGD operations, offering critical insights for the future study aimed at addressing the challenge posed by edge water in heavy oil reservoirs.

Assessing the impact of geochemical mechanism and interpolation factor selection on the precision of low-salinity waterflooding modelling: a comparative study

ABSTRACT The efficacy of low salinity waterflooding (LSWF) as an enhanced oil recovery (EOR) method in carbonate formations has been well established; however, its geochemical modelling in such reservoirs remains insufficiently explored. This study aims to bridge this gap by conducting a comparative analysis of three well-recognised geochemical mechanisms including fines migration, rock dissolution/precipitation, and multi-ion exchange (MIE). Our research encompasses two parts: experimental and modelling. First, we conducted four coreflooding experiments to study the effect of LSWF on oil recovery in core scale as well as on rock wettability by measuring the contact angle of the crude oil-brine-rock system. In the next step, we created a one-dimensional compositional model in CMG-GEMTM for LSWF, validated it using the obtained experimental results, and compared the accuracy of the three geochemical mechanisms one-by-one. The results of the experimental section, confirm the positive effect of LSWF on oil recovery: 34.3% with seawater (40,000 ppm), 42.5% with LoSal-01 (10,000 ppm), 49.7% with LoSal-02 (5,000 ppm), and 60.9% with LoSal-03 (2,000 ppm). The experiments also show the wettability alteration through the reduction in the contact angle. Furthermore, the modelling results reveal that choosing MIE as the governing mechanism and sulphate concentration ([ S O 4 2 − ]) as the relevant interpolation factor (IF) leads to the most accurate LSWF model. After identifying the most accurate mechanism, we detected the wettability alteration in the model by showing the movement of oil and water relative permeability curves intersection point on the Kr-Sw diagram toward the right side.

Relative permeabilities for two-phase flow through wellbore cement fractures

Multiple fluids are likely to exist in fractures and flow paths associated with leaky wellbores, including liquids (e.g., crude oil) and gases (e.g., gas exsolved from liquid). These fluids occupy and move through different portions of the pore spaces within the fractures depending on many factors, including fluid properties, fracture size, and the amount of the different fluids. Upward leakage of any phase, through the fracture, can contaminate water-bearing formations, create hazardous surface conditions, and compromise the functionality of the wellbore. Early signs of wellbore leaks may be expressed by anomalous pressure behavior at surface monitoring points on cavern storage wells. These pressure anomalies are difficult to interpret, necessitating knowledge of the factors that affect the multiphase flow in fractures and porous media. These parameters are critical to modeling multiphase flow in fractures. This insight can guide further diagnosis and maximize leak remediation. Our study focuses on the relationship of the liquid–gas relative permeabilities for representative variable-aperture wellbore cement fracture. To obtain the relative permeability of each phase, two-phase flow tests were conducted where both fluids were flowing simultaneously through a fractured wellbore cement specimen under a range of factors, namely (1) aperture size, (2) capillary numbers, and (3) viscosity ratio. The flow experiments were conducted under a range of confining stresses and flow velocities, using nitrogen gas and silicone oils (of different viscosities) in a specially designed pressure vessel. The sum of gas and oil relative permeabilities were found to be less than one under all conditions, which indicates that the presence of one phase affects the permeability of the other phase, and vice versa. Since the gas phase flow conditions include a significant inertial flow component in addition to viscous flow, the inertial flow coefficients at different saturation states are presented. The factors affecting the relationship between the relative permeabilities are discussed in detail. A new mathematical model for estimating the relative permeability of wellbore cement fracture is presented and experimentally validated.

Research on Gas Injection Limits and Development Methods of CH4/CO2 Synergistic Displacement in Offshore Fractured Condensate Gas Reservoirs

Gas injection for enhanced oil and gas reservoir recovery is a crucial method in offshore Carbon Capture, Utilization, and Storage (CCUS). The B6 buried hill condensate gas reservoir, characterized by high CO2 content, a deficit in natural energy, developed fractures and low-pressure differentials between formation and saturation pressures, requires supplementary formation energy to mitigate retrograde condensation near the wellbore area through gas injection. However, due to the connected fractures, the B6 gas reservoir exhibits strong horizontal and vertical heterogeneity, resulting in severe gas channeling and a futile cycle, which affects the gas injection efficiency at various levels of fracture development. Based on these findings, we conducted gas injection experiments and numerical simulations on fractured cores. A characterization method for oil and gas relative permeability considering dissolution was established. Additionally, the gas injection development boundary for this type of condensate gas reservoir was quantified according to the degree of fracture development, and the gas injection mode of the B6 reservoir was optimized. Research indicates that the presence of fractures leads to the formation of a dominant gas channel; the greater the permeability difference, the poorer the gas injection effect. The permeability gradation (fracture permeability divided by matrix permeability) in the gas injection area should be no higher than 15; gas injection in wells A1 and A2 is likely to achieve a better development effect under the existing well pattern. Moreover, early gas injection timing and pulse gas injection prove beneficial in enhancing the recovery rate of condensate oil. The study offers significant guidance for the development of similar gas reservoirs and for reservoirs with weakly connected fractures; advancing the timing of gas injection can mitigate the retrograde condensation phenomenon, whereas initiating gas injection after depletion may reduce the impact of gas channeling for reservoirs with strongly connected fractures.

Low salinity water flooding: estimating relative permeability and capillary pressure using coupling of particle swarm optimization and machine learning technique

The reservoir’s properties are required for proper reservoir simulation, which also involves uncertainties. Experimental methods to estimate the relative permeability and capillary pressure data are expensive and time-consuming. This study aims to determine the relative permeability and capillary pressure functions of a sandstone core in the presence and absence of clay during low-salinity water floods. The data were provided by automatic history matching the results from previously lab-reported studies through coupling a simulator with the particle swarm optimization algorithm. Correlations were proposed using multiple-linear regression for relative permeability and capillary pressure parameters at low-salinity conditions. They were validated against experimental results of no clay and clayey formation with regression of 95% and 97%. To assign one curve of relative permeability and capillary pressure to the grid cells of the simulator, averaging techniques were implemented. The effect of salinity and clay content on the obtained curves was investigated. Changing salinity from 42000 to 4000 ppm, the reduction in water relative permeability appeared to be higher than the oil relative permeability increment. Moreover, a noticeable shift in the relative permeability curves toward the highest saturations related to the clay content was observed. The proposed hybrid method could be a suitable tool to estimate the relative permeability and capillary pressure functions of the water-based EOR methods.

Steady-state two-phase relative permeability measurements in proppant-packed rough-walled fractures

Understanding multiphase flow in fractures filled with minerals and proppants is vital in various subsurface applications. Limited experimental data have led to reliance on correlations lacking physical basis. We conducted experiments to characterize relative permeability in rough-walled fractures packed with unconsolidated porous media. We tested fractures packed with water-wet 40/70 sand (silica) and surface-coated ceramic proppants. Brine and mineral oil were used as the wetting and non-wetting fluid phases, respectively. Steady-state (SS) drainage (non-wetting-phase displacing wetting-phase) and imbibition (wetting-phase displacing non-wetting-phase) tests were performed under a wide range of saturation histories (full-cycle and scanning-curves) to study relative permeability hysteresis of the propped fractures. Every SS drainage or imbibition test consisted of several discrete points at which fluid saturations and the corresponding relative permeability were measured by varying the fractional flow rates of fluids whilst maintaining a constant total flow rate. We analyzed residual non-wetting phase saturations and relative permeability trends to understand two-phase flow behavior in each proppant pack. High-resolution x-ray microtomography was used to understand the pore-scale topology, wettability, and to provide insights about the pore-scale displacement mechanisms involved in this study. The results showed that commonly used models to estimate relative permeabilities of fractures significantly overestimated the SS brine and oil relative permeabilities (denoted as krw and kro) measured in this study. Further analysis unveiled that the kro values during imbibition exceeded their drainage counterparts in both proppants, the ceramic proppant exhibited a lower initial water saturation and a higher end-point kro permeability at the end of the drainage displacement, as well as higher krw across all flooding processes. Updated fitting parameters for a Brooks-Corey-type relative permeability correlation are introduced. This study presents improved insights, extensive experimentally generated relative permeability data, and an updated relative permeability correlation, which can be collectively utilized to reduce uncertainties associated with continuum-scale forecasts of multiphase flow behavior in fractured subsurface formations.

New Relative Permeability Models for North American Sandstone Utilizing Artificial Neural Networks

Mathematical models and machine learning applications such as Artificial Neural Networks (ANN) have been adopted in hydrocarbon exploration, drilling, production, and reservoir engineering. Thanks to ample data sets and computing power, statistical analysis, analytics, and model prediction replace time-consuming and expensive laboratory measurements. This study used ANN to create two models for predicting water (krw) and oil (kro ) relative permeability profiles for predominantly North American water-wet sandstone reservoirs. The developed model was compared to the Modified Corey and Ibrahim and Koederitz’s equations. The coefficient of multiple determination (R2 ) and Root-Mean-Square Error (RMSE) were used to evaluate the accuracy of the new model. The developed model showed a superior fit and can, therefore, be utilized to generate krw and kro profiles for North American water-wet sandstone reservoirs.

Impact of interfacial tension on oil-water flow in a narrow gap

Numerous researchers have examined the co-current flow of oil-water and aqueous solutions containing polymers and surfactants in thin gaps for oil recovery. While some have focused on charges and forces at the interfaces of oil-surfactant solutions during flow. The study of flow structures, interface behavior, and relative permeabilities of oil and aqueous phases of surfactant flow through thin gaps has been less explored. For the first time, this research aims to comprehensively investigate the flow of oil-water and oil-surfactant solutions through a thin gap (Hele-Shaw cell) with a particular focus on the impact of sodium dodecyl sulfate (SDS). The experiments reveal that SDS forms an emulsion near the oil-water interface, capturing oil droplets and enabling their flow along with the SDS solution. Microscopic studies confirm this, showing that when SDS contacts oil, it creates channels through the oil phase, leading to the accumulation and division of oil into small round-shaped droplets, resulting in an oil-in-water emulsion. The addition of SDS to the injecting water significantly enhances relative permeabilities, leading to a remarkable 90% increase in oil recovery from the cell. The research suggests that the optimal SDS concentration range for maximum oil recovery is between 1.5 and 2 wt%, as it achieves the minimum interfacial tension between oil and water.

Iso-Permeability Point Trail Method to Determine the Relative Permeability Curve for a New Amphiphilic Polymer Flooding

Amphiphilic-polymer flooding, which can increase water viscosity, decrease oil viscosity, and improve oil displacement efficiency, is a promising oil exploitation method for heavy oil. Due to oil–water emulsification, shear-thinning, and changes in oil viscosity when determining the relative permeability data of new amphiphilic polymers, the conventional J.B.N. method is not accurate. This paper presents a new method called the iso-permeability point trial method to determine the relative permeability curve by combining the J.B.N. method, the Corey model, and the relationship between water saturation and the relative permeability ratio. To avoid using polymer viscosity, a mathematical equation was derived based on the characteristics of the relative permeability curve. The results indicate that the new method is feasible and the obtained curve is more reasonable and smooth. The influence of concentration, permeability, and oil viscosity on amphiphilic-polymer displacement relative permeability was also analyzed, demonstrating that under the same water saturation, the water relative permeability is lower than that of water flooding but the oil relative permeability is bigger, which manifests as the iso-permeability point moves to the right and results in a lower residual oil saturation. In addition, the aforementioned trends are more obvious when the amphiphilic-polymer concentration is high, formation permeability is low, and oil viscosity is low.

Effective Relative Permeabilities Based on Momentum Equations with Brinkman Terms and Viscous Coupling

Summary The relative permeability expresses the mobility reduction factor when a fluid flows through a porous medium in the presence of another fluid and appears in Darcy’s law for multiphase flow. In this work, we replace Darcy’s law with more general momentum equations accounting for fluid-rock interaction (flow resistance), fluid-fluid interaction (drag), and Brinkman terms responding to gradients in fluid interstitial velocities. By coupling the momentum equations with phase transport equations, we study two important flow processes—forced imbibition (coreflooding) and countercurrent spontaneous imbibition. In the former, a constant water injection rate is applied and capillary forces are neglected, while in the latter, capillary forces drive the process and the total flux is zero. Our aim is to understand what relative permeabilities result from these systems and flow configurations. From previous work, when using momentum equations without Brinkman terms, unique saturation-dependent relative permeabilities are obtained for the two flow modes that depend on the flow mode. Now, with Brinkman terms included, the relative permeabilities depend on local spatial derivatives of interstitial velocity and pressure. Local relative permeabilities are calculated for both phases utilizing the ratio of phase Darcy velocity and phase pressure gradient. In addition, we use the Johnson-Bossler-Naumann (JBN) method for forced imbibition (with data simulated under the assumption of negligible capillary end effects) to calculate interpreted relative permeabilities from pressure drop and average saturation. Both flow setups are parameterized with literature data, and sensitivity analysis is performed. During coreflooding, Brinkman terms give a flatter saturation profile and higher front saturation. The saturation profile shape changes with time. Local water relative permeabilities are reduced, while they are slightly raised for oil. The saturation range where relative permeabilities can be evaluated locally is raised and made narrower with increased Brinkman terms. JBN relative permeabilities deviate from the local values: The trends in curves and saturation range are the same but more pronounced as they incorporate average measurements, including the strong impact at the inlet. Brinkman effects vanish after sufficient distance traveled, resulting in the unique saturation functions as a limit. Unsteady state (USS) relative permeabilities (based on transient data from single-phase injection) differ from steady-state (SS) relative permeabilities (based on SS data from coinjection of two fluids) because the Brinkman terms are zero at SS. During spontaneous imbibition, the higher effect from the Brinkman terms caused oil relative permeabilities to decrease at low water saturations and slightly increase at high saturations, while water relative permeability was only slightly reduced. The net effect was a delay in the imbibition profile. Local relative permeabilities approached the unique saturation functions without Brinkman terms deeper in the system because phase velocities (involved in the Brinkman terms) decreased with distance. In both systems, scaling and simulations demonstrate that the relative change in relative permeabilities due to Brinkman terms increases with the Brinkman coefficient, permeability, and inverse squared distance from the inlet.

Simulation study of affecting parameters during low salinity water injection in carbonate reservoirs: from core to field scale

Over the last decade, economic and environmental factors have led to low salinity water injection (LSWI) becoming one of the most important improved oil recovery methods. Although many results have been obtained from laboratory tests, only a few papers have been published regarding the modeling and simulating LSWI in carbonate reservoirs compared to sandstone reservoirs. This paper investigated the most affecting parameters on oil recovery during LSWI at the core and field scale. The published work focused more on the effective parameters related to ultimate oil recovery using LSWI. However, important parameters affecting the oil recovery rate were not investigated. We compared how important parameters affected the ultimate oil recovery factor and ultimate oil recovery rate. According to the results of this study, the salinity of injected water and curvature of oil relative permeability were the most important factors on the ultimate oil recovery factor. By reducing both of these parameters, more increment oil was recovered. By increasing the injection rate of water, the curvature of the water relative permeability, wettability, and the endpoint of oil relative permeability, the oil recovery rate also increased. Furthermore, threshold capillary pressure and the endpoint of relative permeability of water had inverse effects on oil recovery. Injecting low salinity water into the reservoir will change its wettability. As a result, it will change the properties of the reservoir and increase the production from the reservoir, resulting in more oil being produced. LSWI resulted in an increase of oil recovery factor of 5% and 11% respectively after 25 and 58 years in this case.

Performance evaluation of microemulsion acid for integrated acid fracturing in Middle Eastern carbonate reservoirs

Considering the characteristics of carbonate reservoirs in the Middle East, a low-viscosity microemulsion acid that can be prepared on site and has an appropriate retardation ability was developed. It was compared with four conventional acid systems (hydrochloric acid, gelled acid, emulsified acid and surfactant acid) through experiments of rotating disk, multistage acid fracturing and core flooding with CT scanning. The micro-etching characteristics and conductivity of fracture surfaces were clarified, and the variation of saturation field during water invasion and flowback of spent acid and the recovery of oil phase relative permeability were quantitatively evaluated. The study shows that the addition of negatively charged agent to the oil core of microemulsion acid can enhance its adsorption capacity on the limestone surface and significantly reduce the H+ mass transfer rate. Moreover, the negatively charged oil core is immiscible with the Ca2 + salt, so that the microemulsion acid can keep an overall structure not be damaged by Ca2 + salt generated during reaction, with adjustable adsorption capacity and stable microemulsion structure. With high vertical permeability along the fracture walls, the microemulsion acid can penetrate into deep fracture wall to form network etching, which helps greatly improve the permeability of reservoirs around the fractures and keep a high conductivity under a high closure pressure. The spent microemulsion acid is miscible with crude oil to form microemulsion. The microemulsion, oil and water are in a nearly miscible state, with basically no water block and low flowback resistance, the flowback of spent acid and the relative permeability of oil are recovered to a high degree.

Corner flow effect on the relative permeability of two-phase flow in nano-confined porous media

Relative permeability is a critical factor clarifying the multiphase flow behavior in nano-porous media. However, most studies have focus on the circle flow, neglecting the corner flow effect. Therefore, in this work, a comprehensive relative permeability model considering the corner flow effect is proposed. We integrated the corner flow with the immiscible flow model and the confined liquid-gas phase equilibrium with the near-miscible flow model. Then it was validated against the experimental measured data, indicating the proposed model can well describe the two-phase flow in the confined space. Subsequently, sensitivity analysis of corner number, fractal dimension, minimum radius, and viscosity ratio were conducted. Results show that the corner flow effect is noticeable when corner number is less than 8. Under the optimal pore radius of 2 × 10−5 m, the gas relative permeability increases from 0.4909 to 0.9274 with corner number raising from 4 to 10. Under critical oil phase saturation of 0.175, increase of fraction dimension, minimum radius, and viscosity ratio leads to the significant decrease of oil relative permeability and increase of gas relative permeability. In addition, nano-confinement effect and CO2 injection will reduce the interfacial tension and increase the near-miscible relative permeability. When CO2 injection increase to 100% under oil saturation of 0.4084, the increment of oil relative permeability is nearly 67.2%. Interfacial intension-based interpolation method indicates that the confined fluid is more likely to be miscible than the bulk fluid. This relative permeability model provides deeper understandings of two-phase flow in the nano-porous media, which is benefit for the better development of unconventional reservoirs.

Development of a numerical simulator for modeling seismic EOR

Natural earthquakes, culture noise, and artificially induced mechanical waves have been reported to affect the productivity of oil wells. Sources emitting waves in the seismic frequency range, between 1 and 1000 Hz, have been used as an enhanced oil recovery (EOR) tool for improving oil production rates. Theories suggest several mechanisms for the increased oil production rate including (AbuZaid et al., 2021): overcoming the capillary forces holding the oil phase in place (Alzahrani and Abbas, 2020), improving the relative permeability of oil, and (Ariadji, 2005) decreasing viscosity as temperature rises from waves attenuation. In this work, a fully implicit modified black oil simulator has been developed. The fluid flow simulator is coupled with a ray tracing module for simulating waves propagation in the model. Wave simulation is used to calculate the effect of seismic waves on capillary pressure, oil relative permeability, and reservoir temperature. It is also used to investigate the applicability of the proposed mechanisms for explaining the observed enhancement in oil recovery due to seismic waves. This seismic stimulation simulator can provide insights on the response of wells’ production rates at various field characteristics and seismic tool(s) operation conditions, explain field results, and design field implementation of seismic EOR.

Fundamentals-Based Alternative Addresses Issue With Three-Phase Permeability Model

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 205883, “Issue With Stone II Three-Phase Permeability Model and a Novel Robust Fundamentals-Based Alternative to It,” by Subodh Gupta, SPE, Heretech Energy. The paper has not been peer reviewed. _ The objective of this paper is to present a fundamentals-based, three-phase flow model consistent with observation that avoids the pitfalls of conventional models. Though the use of the Stone II model is very popular for three-phase flow across the industry, one issue in the context of gravity drainage is how it appears counterintuitively to limit the flow of oil when water is present near its irreducible saturation. The novelty of the work presented in the complete paper is in the development of a model based on fundamentals of flow in fine channels that better explains observed results in the context of flow in porous media. Problem Definition Residual oil saturation (So) from retrieved cores from oil-drained chambers of steam-assisted gravity drainage (SAGD) reservoirs invariably shows values as low as 1 or 2%, whereas reservoir simulations using Stone II-based relative permeabilities (an industrywide favorite) predict significantly higher numbers (14–18%). In previous work, the author and others, in an attempt to remedy the situation, extended the oil-phase relative permeability in the presence of the water phase (krow) and oil-phase relative permeability in the presence of the gas phase (krog) curves all the way to water and gas saturation values less than unity; however, they discovered that, in the presence of water saturation (Sw) near the irreducible water saturation (Swi), the use of the Stone II formula for oil relative permeability still resulted in high residual So. Correct estimation of residual oil-phase saturation is even more important for solvent/steam mixed thermal recovery processes such as solvent-aided processes, where a small amount of solvent is added with steam in SAGD, and significantly more important for solvent-dominated processes, where a small amount of steam or heat is added with a large amount of solvent. A large amount of residual oleic-phase saturation and associated pessimistic solvent-recovery prediction will lead to erroneous economic assessment of these processes. The discrepancy in residual So, as the author and coauthors discovered in previous work, stems from a peculiarity of the Stone II formulation given by Equation 1 of the complete paper. To model this 1D problem numerically, a program developed by the author for his PhD thesis for modeling of moving front reservoir processes with dynamic gridding was modified and run with constant fluid properties for hexane and water at constant pressure and temperature. It also incorporated the three-phase relative permeabilities given by Equation 1 and Table 1 of the complete paper. The results are shown in Fig. 1.

Issue with Stone-II three phase permeability model, and a novel robust fundamentals-based alternative to it

The objective of this paper is to present a fundamentals-based, consistent with observation, three-phase flow model that avoids the pitfalls of conventional models such as Stone-II or Baker's three-phase permeability models.While investigating the myth of residual oil saturation in SAGD with comparing model generated results against field data, Gupta et al. (2020) highlighted the difficulty in matching observed residual oil saturation in steamed reservoir with Stone-II and Baker's linear models. Though the use of Stone-II model is very popular for three-phase flow across the industry, one issue in the context of gravity drainage is how it appears to counter-intuitively limit the flow of oil when water is present near its irreducible saturation.The current work begins with describing the problem with existing combinatorial methods such as Stone-II, which in turn combine the water-oil, and gas-oil relative permeability curves to yield the oil relative permeability curve in presence of water and gas. Then starting with the fundamentals of laminar flow in capillaries and with successive analogical formulations, it develops expressions that directly yield the relative permeabilities for all three phases. In this it assumes a pore size distribution approximated by functions used earlier in the literature for deriving two-phase relative permeability curves. The outlined approach by-passes the need for having combinatorial functions such as prescribed by Stone or Baker.The model so developed is simple to use, and it avoids the unnatural phenomenon or discrepancy due to a mathematical artefact described in the context of Stone-II above. The model also explains why in the past some researchers have found relative permeability to be a function of temperature. The new model is also amenable to be determined experimentally, instead of being based on an assumed pore-size distribution. In that context it serves as a set of skeletal functions of known dependencies on various saturations, leaving constants to be determined experimentally.The novelty of the work is in development of a three-phase relative permeability model that is based on fundamentals of flow in fine channels and which explains the observed results in the context of flow in porous media better. The significance of the work includes, aside from predicting results more in line with expectations and an explanation of temperature dependent relative permeabilities of oil, a more reliable time dependent residual oleic-phase saturation in the context of gravity-based oil recovery methods.

Hydrogel nanocomposite network elasticity parameters as a function of swelling ratio: From micro to macro flooding

Gel flooding is one of the most important cEOR methods. In this study, a Co[AM-AMPS-MA-AAC]/PEI-MBA nanocomposite, using zirconium or zinc nanoparticles, was synthesized to improve the performance of traditional hydrogels. FTIR and XRD tests confirmed the three-dimensional structure and homogeneous distribution of nanoparticles. The SEM and ESEM images revealed a homogeneous and 3D structure with an average pore size of 35 nm. The sweep strain test showed that the maximum storage moduli of Zr and Zn nanocomposites are 21,300 and 7700 Pa, respectively. The frequency sweep test showed linear viscoelastic behavior at various frequencies. According to TGA results, less than 1% of the nanocomposites degraded at reservoir temperatures. Network parameter calculations revealed the average pore size for Zr and Zn nanocomposites was 35 and 27 nm, respectively, showing high agreement with ESEM. The micromodel test showed a 22% increase in oil recovery, and the core-flooding test showed that Zr-nanocomposite caused a 98% decrease in water production and lowered the relative permeability of water by 37 times that of oil's relative permeability reduction. According to the research results, the synthesized nanocomposites have good structural and thermal strength, increase oil recovery, and decrease water production, making them a promising candidate for EOR processes.

Effect of Heterogeneity on Capillary Pressure and Relative Permeability Curves in Carbonate Reservoirs. A Case Study for Mishrif Formation in West Qurna/1 Oilfield, Iraq

The special core analysis tests were accomplished on a set of core plugs for Mishrif Formation (mA, mB1, and mB2cde/mC units) in West Qurna/1 oilfield, southern Iraq. Oil relative permeability (Kro) data and the Corey-type fit of the data as functions of the brine saturation at the core outlet face for individual samples in the water-oil imbibition process to estimate relative permeability measurements by the centrifuge method were utilized. Identical correlations for oil and water relative permeabilities were extracted by steady-state and unsteady-state methods. For the mA samples, the gas-water capillary pressure curves were within a narrow range (almost identical) indicating that mA is a homogeneous unit. Kro curves for three mB2ab plugs were practically identical, that is referring to the homogeneity in the upper portion of the unit. The mB2 unit has a more solid‐phase concentration than other units. In addition, the general trend of low residual oil saturation is related to the raising in porosity but no reliable correlation between the residual oil saturation to water drive (Sorw) and Klinkenberg-corrected permeability (Kinf). Based on the correlation between the effective oil permeability at the initial water saturation [ko(Swi)] and (Kinf/f)1/2 for the high-permeability lithofacies mB1 plugs, ko(Swi) is approximately equal to or exceeds Kinf. While ko(Swi) was below Kinf for the other samples. New good empirical equations were obtained for effective gas permeability at final water saturation versus Kinf, as well as, for Kro and Krw versus saturation for all lithofacies.

Effect of Temperature on Two-Phase Gas/Oil Relative Permeability in Viscous Oil Reservoirs: A Combined Experimental and History-Matching-Based Analysis

Summary Thermal enhanced oil recovery (TEOR) is the most widely accepted method for exploiting the heavy oil reservoirs in North America. In addition to improving the mobility of oil due to its viscosity reduction, the high temperature down in the hole due to the injection of the vapor phase may significantly alter the fluid flow performance and behavior, as represented by the relative permeability to fluids in the formations. Therefore, in TEOR, the relative permeabilities can change with a change in temperature. Also, there is no model that accounts for the change in temperature on two-phase gas/oil relative permeability. Further, the gas/oil relative permeability and its dependence on temperature are required data for the numerical simulation of TEOR. Very few studies are available on this topic with no emerging consensus on a general behavior of such effects. The scarcity of such studies is mostly due to experimental problems to make reliable measurements. Therefore, the primary objective of this study was to overcome the experimental issues and investigate the effect of temperature on gas/oil relative permeability. Oil displacement tests were carried out in a 45-cm-long sandpack at temperatures ranging from 64°C to 210°C using a viscous mineral oil (PAO-100), deionized water, and nitrogen gas. It was found that the unsteady-state method was susceptible to several experimental artifacts in viscous oil systems due to a very adverse mobility ratio. However, despite such experimental artifacts, a careful analysis of the displacement data led to obtaining meaningful two-phase gas/oil relative permeability curves. These curves were used to interpret the relative permeability curves for gas/heavy oil systems using the experimentally obtained displacement results. We noted that at the end of gasflooding, the “final” residual oil saturation (Sor) still eluded us even after several pore volumes (PVs) of gas injection. This rendered the experimentally determined endpoint gas relative permeability (krge) and Sor unreliable. In contrast, the irreducible water saturation (Swir) and the endpoint oil relative permeability (kroe) were experimentally achievable. The complete two-phase gas/heavy oil relative permeability curves are inferred with a newly developed systematic history-matching algorithm in this study. This systematic history-matching technique helped us to determine the uncertain parameters of the oil/gas relative permeability curves, such as the two exponents of the Corey equation (No and Ng), Sor and krge. The history match showed that kroe and Swir were experimentally achievable and were reliably interpreted, except these four parameters (i.e., Corey exponents, true residual oil saturation, and gas endpoint relative permeability) were interpreted from simulations rather than from experiments. Based on our findings, a new correlation has been proposed to model the effect of temperature on two-phase gas/heavy oil relative permeability.

Correct relative permeability data from steady-state experiments for capillary end effects

Water-oil relative permeability curves can be obtained from co-injection experiments at steady-state (SS) conditions. The two-phase Darcy's law can be used to calculate the relative permeability directly only when water saturation is constant along the core. However, the capillary end effect (CEE) causes water accumulation or depletion at the end of the core depending upon the wettability. This work modifies the Intercept Method initially proposed by Gupta and Maloney. Similar to their work, we again envisage carrying out a steady-state (SS) co-injection experiment. For each ratio of water to oil flowrate (F=qwqo), we require experiments at different total flowrates. From each run, we obtain pressure drop across the core and average water saturation inside the core.We demonstrate mathematically that a plot of average water saturation vs. reciprocal of oil flowrate gives a straight line whose intercept is the water saturation in the unaffected region. A plot of pressure difference vs. oil flowrate yields a straight line whose slope gives the oil relative permeability which can be used to calculate water relative permeability. It is necessary to perform the SS experiment at least three times for the same F=qwqo (at different oil/water rates). The same procedure is used for other values of F to obtain more data points to construct the relative permeability curves. An experimental step-by-step procedure for experimental engineers to follow is given in appendix C.