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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Capillary Pressure to Relative Permeability: Task 7.3.4 Relative Permeability Analysis Final Report

Surface tension affects all aspects of fluid flow in porous media. Through measurements of surface tension interaction under multiphase conditions, a relative permeability relationship can be determined. Relative permeability is a numerical description of the interplay between two or more fluids and the porous media they flow through. It is a critical parameter for various tools used to characterized subsurface multiphase flow systems, such as numerical simulation for oil and gas development, carbon sequestration, and groundwater contamination remediation. Therefore, it is critical to get a good statistic distribution of relative permeability in the porous media under study. Empirical relationships for determining relative permeability from capillary pressure are already well established but do not provide the needed flexibility required to match laboratory derive relative permeability relationships. By expanding the existing methods for calculating relative permeability from capillary pressure data, it is possible to create both two and three-phase relative permeability relationships. Existing laboratory-measured relative permeability data along with mercury intrusion capillary (MICP) data coupled with interfacial tension and contact angle measurements were used to determine the efficacy of this approach to relative permeability curve creation. The relative permeability relationships determined with this method were fit to existing laboratory data to elucidate common fitting parameters that were then used to create relative permeability relationships from MICP data that does not have an associated laboratory-measured relative permeability relationship.

58 GEOSCIENCES↗
DOE OSTI2022

Fluid – Fluid Interfacial Area and Its Impact on Relative Permeability - A Pore Network Modeling Study

Abstract Relative permeability (kr) is commonly modeled as an empirical function of phase saturation. Although current empirical models can provide a good match of one or two measured relative permeabilities using saturation alone, they are unable to predict relative permeabilities well when there is hysteresis or when physical properties such as wettability change. Further, current models often result in relative permeability discontinuities that can cause convergence and accuracy problems in simulation. To overcome these problems, recent research has modeled relative permeability as a state function of both saturation (S) and phase connectivity (X). Pore network modeling (PNM) data, however, shows small differences in relative permeability for the same S-X value when approached from a different flow direction. This paper examines the impact of one additional Minkowski parameter (Mecke and Arns, 2005), the fluid-fluid interfacial area, on relative permeability to identify if that satisfactorily explains this discrepancy. We calculate the total fluid-fluid interfacial areas (IA) during two-phase (oil/water) flow in porous media using pore network modeling. The area is calculated from PNM simulations using the areas associated with corners and throats in pore elements of different shapes. The pore network is modeled after a Bentheimer sandstone, using square, triangular, and circular pore shapes. Simulations were conducted for numerous primary drainage and imbibition cycles at a constant contact angle of 0° for the wetting phase. Simultaneous measurements of capillary pressure, relative permeability, saturation, and phase connectivity are made for each displacement. Fluid-fluid interfacial area is calculated from the PNM capillary pressure, the fluid location in the pore elements, and the pore element dimensional data. The results show that differences in the relative permeability at the same (S,X) point is explained well by differences in the fluid-fluid interfacial area (IA). That is, for a larger change in IA at these intersection points, the permeability difference is greater. That difference in relative permeability approaches zero as the difference in IA approaches zero. This confirms that relative permeability can be modeled better as a unique function of S, X, and IA. The results also show that an increase in IA restricts flow decreasing the nonwetting (oil) phase permeability. This decrease is caused by an increase in the throat area fraction compared to the corner area as the total area IA increases. The wetting phase relative permeability, however, shows the inverse trend, in that its relative permeability is greater when IA becomes larger owing to a greater fraction of the total area associated with the corners. The area IA, however, impacts the nonwetting phase relative permeability more than the wetting phase relative permeability. Corner flow improves the wetting phase relative permeability because the wetting phase is continuous there. Finally, a sensitivity analysis shows that relative permeability a is more sensitive to change in S than they are for IA for the case studied implying that if only two parameters are used to model relative permeability it is better to choose S and X.

Engineering↗
DOE OSTI2025

Quantifying the Effect of Pore‐Size Dependent Wettability on Relative Permeabilities Using Lattice Boltzmann Simulation

Relative permeability is a crucial two-phase property in porous media that can be significantly impacted by wettability conditions. While traditional research has predominantly examined homogeneous wettability, this work explores the less studied pore-size dependent (PSD) wettability, featured by a pore-size dependent wettability distribution. Leveraging high-fidelity Lattice Boltzmann simulations on CT-scanned porous samples, we demonstrate how PSD wettability would impact relative permeability at the pore scale. Our findings reveal that the deviation of relative permeability from the homogeneous wettabilitity induced by PSD wettability can be 5%–20%. The deviation of relative permeability curves increases as the spanning range of the contact angle increases. We also find that this impact is less pronounced as the capillary number increases. By adopting a pore-size-dependent contact angle relationship, our approach provides a more accurate and nuanced understanding of how PSD wettability would impact two-phase flow. These findings discovered at the pore scale may also provide valuable insights on relative permeability at the core to reservoir scales.

25 ENERGY STORAGE↗
DOE OSTI2022

Sensitivity Analysis of Fluid–Fluid Interfacial Area, Phase Saturation and Phase Connectivity on Relative Permeability Estimation Using Machine Learning Algorithms

Recent studies have shown that relative permeability can be modeled as a state function which is independent of flow direction and dependent upon phase saturation (S), phase connectivity (X), and fluid–fluid interfacial area (A). This study evaluates the impact of each of the three state parameters (S, X, and A) in the estimation of relative permeability. The relative importance of the three state parameters in four separate quadrants of S-X-A space was evaluated using a machine learning algorithm (out-of-bag predictor importance method). The results show that relative permeability is sensitive to all the three parameters, S, X, and A, with varying magnitudes in each of the four quadrants at a constant value of wettability. We observe that the wetting-phase relative permeability is most sensitive to saturation, while the non-wetting phase is most sensitive to phase connectivity. Although the least important, fluid–fluid interfacial area is still important to make the relative permeability a more exact state function.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

An integrated approach to derive relative permeability from capillary pressure

Surface tension affects all aspects of fluid flow in porous media. Through measurements of surface tension interaction under multiphase conditions, a relative permeability curve can be determined. Relative permeability is a numerical description of the interaction between two or more fluids and the porous media. It is a critical parameter for various tools that characterize subsurface multiphase flow systems, such as numerical simulation for carbon sequestration, oil and gas development, and groundwater contamination remediation. Therefore, it is critical to get a good statistical distribution of relative permeability in the porous media under study. Empirical formula for determining relative permeability from capillary pressure are already well established but do not provide the needed flexibility that is required to match laboratory-derived relative permeability curves. By expanding the existing methods for calculating relative permeability from capillary pressure data, it is possible to create both two and three-phase relative permeability curves. Mercury intrusion capillary pressure (MICP) data from the Morrow 'B' Sandstone coupled with interfacial tension and contact angle measurements were used to create a suite of relative permeability curves. Furthermore, these curves were then calibrated to a small sample of existing laboratory curves to elucidate common fitting parameters for the formation that were then used to create relative permeability curves from MICP data that does not have an associated laboratory-measured relative permeability curve.

58 GEOSCIENCES↗
DOE OSTI2024

Quantifying the Effect of Pore‐Size Dependent Wettability on Relative Permeability Using Capillary Bundle Model

Abstract Relative permeability is a key parameter for characterizing the multiphase flow dynamics in porous media at macroscopic scale while it can be significantly impacted by wettability. Recently, it has been reported in microfluidic experiments that wettability is dependent on the pore size (Van Rooijen et al., 2022). To investigate the effect of pore‐size‐dependent wettability on relative permeability, we propose a theoretical framework informed by digital core samples to quantify the deviation of relative permeability curves due to wettability change. We find that the significance of impact is highly dependent on two factors: (i) the function between contact angle and pore size (ii) overall pore size distribution. Under linear function, this impact can be significant for tight porous media with a maximum deviation of 1,000%.

Yu, Siqin↗
DOE OSTI2022

Relative permeability of gas and water flow in hydrate-bearing porous media: A micro-scale study by lattice Boltzmann simulation

The water-gas relative permeability is an important parameter to characterize multiphase flow in sediments. To study the water-gas relative permeability of hydrate-bearing porous media, multiphase flow simulations were carried out at the pore scale using the lattice Boltzmann method. In this work, the effects of hydrate saturation and hydrate-growth habits on the water-gas relative permeability, which is scaled by the relative permeability considering the hydrate only, were evaluated in a two-dimensional porous medium. Results show that the increase of hydrate saturation causes the decrease of water-gas effective permeability as expected. However, the effect of hydrate saturation on the water-gas relative permeability is different from that of hydrate saturation on the water-gas effective permeability. The water-gas relative permeability increases with the increase of hydrate saturation in the pore-filling case. The water-gas relative permeability decreases with the increase of hydrate saturation in the grain-coating case. The wettability of solid phase has a different effect on the relative permeability of wetting phase and nonwetting phase. The Jamin effect (phase blocking) was observed and may exist in the production of gas from natural gas hydrate reservoirs. This seriously affects the multiphase flow characteristics. The changes of microscale fluid distribution effect the changes of water-gas relative permeability. The relationship between the water-gas relative permeability and the characterization parameters of microscale fluid distribution was analyzed.

58 GEOSCIENCES↗
DOE OSTI2020

An experimental system and procedure of unsteady-state relative permeability test for gas hydrate-bearing sediments

Reliable estimations of the relative permeability of gas and water in hydrate-bearing sediments (HBS) and the dependency of the relative permeability on hydrate saturation are critical to predict the productivity of a hydrate reservoir. Yet, this remains poorly estimated owing to lack of experimental data associated with difficulties in conducting multiphase flow experiments in HBS. Recognizing the experimental challenges, this study intends to develop and validate a new experimental system and procedure of unsteady-state relative permeability test that can generate reliable and reproducible flow measurements in HBS. Furthermore, gas hydrate is considered as a part of solid matrix in the sediment, so one of the challenges is to maintain a constant hydrate saturation, which is achieved in this experimental study using tight pressure-temperature (P-T) control near the hydrate stability boundary. The measured differential pressure across the specimen, methane injection flow rate, and volume of displaced brine are used to calculate the relative permeability by adopting a conventional Buckley-Leverett theory-based interpretation method. Residual brine saturation calculated for the hydrate-bearing specimen is higher than that of hydrate-free specimen, presumably due to decrease in pore size, increase in heterogeneity of solid matrix, and increase in size distribution of solid matrix and pore in the presence of hydrates. Further studies are necessary to represent the results of the unsteady-state flow experiment in HBS with a gas hydrate-dependent relative permeability model.

03 NATURAL GAS↗
DOE OSTI2021

Rapid determination of supercritical CO 2 and brine relative permeability using an unsteady-state flow method

In this study, relative permeability of supercritical CO 2 (scCO 2 ) and brine was determined in reactive and non-reactive rock cores using a combination of unsteady-state methodology and computed tomography. Experiments were conducted using a medical grade CT scanner to determine saturation using a custom Python script. The saturation and differential pressure across the core were then used to derive four empirical constants to calculate relative permeability. This methodology increases temporal efficiency while reducing experimental complexity. Additionally, we show that the method can be used to determine scCO 2 relative permeability in a wide range of lithologies and flow rates, and with the ability to account for matrix dissolution during scCO 2 flooding.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Relative permeability as a stationary process: Energy fluctuations in immiscible displacement

Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work, we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large length scales and relying on averaging in both space and time to homogenize the behavior. Explicit criteria are obtained to define stationary conditions: (1) there can be no net change for extensive measures of the system state over the time averaging interval; (2) the net energy inputs into the system are zero, meaning that the net rate of work done on the system must balance with the heat removed; and (3) there is no net work performed due to the contribution of internal energy fluctuations. Results are then evaluated based on direct numerical simulation. Dynamic connectivity is observed during steady-state flow, which is quantitatively assessed based the Euler characteristic. We show that even during steady-state flow at low capillary number ([Formula: see text]), typical flow processes will explore multiple connectivity states. The residence time for each connectivity state is captured based on the time-and-space average. The distribution for energy fluctuations is shown to be multi-modal and non-Gaussian when terms are considered independently. However, we demonstrate that their sum is zero. Given an appropriate choice of the thermodynamic driving force, we show that the conventional relative permeability relationship is sufficient to model the energy dissipation in systems with complex pore-scale dynamics that routinely alter the structure of fluid connected pathways.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A Novel Relative Permeability Model for Gas and Water Flow in Hydrate-Bearing Sediments With Laboratory and Field-Scale Application

In a producing gas hydrate reservoir the effective porosity available for fluid flow constantly changes with dissociation of gas hydrate. Therefore, accurate prediction of relative permeability using legacy models (e.g. Brooks-Corey (B-C), van Genuchten, etc.) that were developed for conventional oil and gas reservoirs would require empirical parameters to be calibrated at various S h over its range of variation, but such calibrations are precluded because of lack of experimental relative permeability data. This study proposes a new relative permeability model for gas hydrate-bearing media that is a function of maximum capillary pressure, capillary entry pressure, pore size distribution index, residual saturations, hydrate saturation, and four other constants. The three novel features of the proposed model are: (i) requires fitting its six empirical parameters only once using experimental data from any single S h , and the same set of empirical parameters predict relative permeability at all S h , (ii) includes the effect of capillarity, and (iii) includes the effect of pore-size distribution. From practical standpoint, the model can be used to simulate multiphase flow in gas hydrate-bearing sediments where the proposed relative permeability can account for the evolving hydrate saturation. The proposed model is implemented in a numerical simulator and the wall time required to perform simulations using the proposed model is shown to be similar to the time it takes to run same simulations with the B-C model. The proposed model is a step forward towards achieving the goal of physically accurate modeling of multiphase flow for gas hydrate-bearing sediments that accounts for the effect of gas hydrate saturation change on relative permeability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Scaling of two-phase water-steam relative permeability and thermal fluxes in porous media

Two-phase water-steam flow conditions are frequently encountered in many engineering applications, including geothermal reservoirs. Although routine calculations are based on the multiphase Darcy’s law, the role of the topology of the flowing phases at the pore-scale is usually neglected in the estimation of relative permeabilities. Instead, the latter are frequently computed using empirical models like the Corey correlation. In this work, we first apply the model for relative permeabilities based on pore-scale flow regimes developed by Picchi and Battiato (2019), Relative permeability scaling from pore-scale flow regimes, Water Resour. Res. 55, 3215–3233, to scenarios typical of geothermal reservoirs and then extend it by deriving the scaling laws for the transmissibilities and the thermal properties as a function of temperature. First, we discuss the scaling behavior of normalized relative permeabilities in terms of viscosity ratio and capillary number of water-steam systems and, then, we provide a validation of the model against experimental data available in the literature. The model captures well the data trends collected in real 3D porous media. These results suggest that water-steam relative permeabilities follow the same scaling behavior of gas-liquid systems where the non-wetting phase is much less viscous than the wetting phase. Finally, we investigate the impact that relative permeabilities have on heat transfer rates at two-phase flow conditions and the scaling of mass and energy transmissibility and thermal properties of the mixture. An estimation of the exergy carried by the two-phase water-steam mixture is also included.

42 ENGINEERING↗
DOE OSTI2025

Unsteady- and Steady-State Relative Permeability Study with X-ray and Acoustic Monitoring for CO 2 Storage in Deep Saline Aquifers

In this study, we link the multiphase flow measurements with controls of sedimentary structures (e.g., heterogeneity and anisotropy) on relative permeability to variations in ultrasonic velocities for two deep saline aquifer formations (Entrada and Bluff Sandstones) in the San Juan Basin of the Southwestern USA. The rock specimens were extracted from outcrop sites near Durango, CO, USA. They have distinct differences in grain size, cementation composition, and individual chemical amounts, despite both formations being eolian sandstones. We performed a series of unsteady- and steady-state CO 2 -brine relative permeability experiments under capillary-controlled displacement rates. Unsteady-state experiments were conducted at 71 °C and 9.65 MPa; steady-state experiments were conducted at 85 °C and 22.8 MPa and 89 °C and 24.1 MPa for the Bluff and Entrada Sandstones, respectively. During the unsteady experiments, X-ray computed tomography was used to visualize multiphase flow in porous media and quantify saturations during brine drainage under various flow rates. Scan images and saturation profiles indicate that the CO 2 distribution in the pore volume was strongly impacted by the presence of high-angle cross-laminations, heterogeneous rock structure, and direction of bedding orientation. Those factors contribute to dramatic and quick initial breakthroughs and affect the overall saturation dynamics. Steady-state relative permeability tests were conducted at net flow rates of 1 mL/min for both brine drainage and imbibition. During the experimental steps, the CO 2 fractional flow was increased and decreased for both drainage and imbibition scenarios to mimic the front when CO 2 contacts brine and behind the front when brine enters space previously occupied by CO 2 . It was found that compressional velocity decreased, while shear waves slightly increased as brine saturation decreased. The hysteresis effects for the relative permeability and acoustic velocities were distinct. Furthermore, the CO 2 /brine front stability is quantified by applying a mobility ratio approach to spot saturations at which the boundary line between fluids becomes uneven. The results presented in this work can potentially boost the quality and precision of forecasts for the CO 2 storage projects in which the vertical and horizontal core-scale heterogeneity and anisotropy impact the plume migration within host reservoirs.

carbon dioxide (CO2)↗
DOE OSTI2024

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. Here, 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.

58 GEOSCIENCES↗
DOE OSTI2020

Relative Permeability for Offshore Enhanced Oil Recovery

Relative permeability (k<sub>r</sub> ) is the description of <strong>multiphase transport through porous media </strong>that is most widely accepted and utilized to scale relationships up to the field scale through simulations. Previous research at NETL has shown a <strong>dependence of k</strong><sub><strong>r </strong></sub><strong>on the flow rates and porous media structure </strong>that is poorly captured in most descriptions of this process. Our project was originally scoped to be a 3-year project to (2019-2021): (1) determine if this poor literature description is true for offshore EOR; (2) collect data on the generation of relevant k<sub>r</sub> curves for offshore EOR; and (3) distribute this collected data, methodology and resultant curves.<br>

Crandall, Dustin↗
DOE OSTI2022

Simulated CO 2 storage efficiency factors for saline formations of various lithologies and depositional environments using new experimental relative permeability data

Saline formations are attractive geologic reservoirs for permanent carbon dioxide (CO 2 ) storage. Here, the U.S. Department of Energy's National Energy Technology Laboratory (DOE-NETL) has worked to develop and refine methods and tools for the calculation of CO 2 storage potential in subsurface reservoirs. DOE-NETL's CO 2 -SCREEN provides an online tool for executing these storage methods. CO 2 storage efficiency terms are input parameters in DOE-NETL's methods and equations embedded in the CO 2 -SCREEN, which assesses pore space available for CO 2 storage. In this work, a modeling workflow was initiated to refine two CO 2 storage efficiency terms - volumetric displacement (E V ) and microscopic displacement (E d ). The models are based on new experimental relative permeability data that are specific to homogenous lithology and depositional environments of key subsurface saline formations targeted for CO 2 storage. In future work, heterogenous features will be added to this initial modeling effort to update efficiency factors as described in DOE-NETL's methods and CO 2 -SCREEN tool. E V accounts for the volume utilized in the reservoir under the areal plume, while E d accounts for saturation values in the plume to assess efficiency of CO 2 storage at the pore scale. The results of this work are significant in that prior values were based on a limited geologically non-specific relative permeability data set that were collected prior to 2009. Specifically, we applied numerical simulations using TOUGH3 models to update CO 2 storage efficiency values for supercritical CO 2 injection into brine-saturated reservoirs for three lithologies (clastics, limestone, dolomite) and six depositional environments (Marginal Marine, Strand Plain, Deltaic Complex Fluvial, Aeolian, Shallow Marine, and Reef) that have a high potential for geologic CO 2 storage. Experimental relative permeability data in cores from these environments were utilized in the models with corresponding rock type/sedimentary environment. Results of this study showed that dolomite followed by limestone generated higher ranges of storage efficiency compared to clastics. The updated values provided a tighter efficiency range for clastics, lower P 10 but higher P 90 range for limestone, and higher P 10 and P 90 for dolomite. In general, tighter reservoirs with relatively low permeability and porosity were associated with higher E V and E d , showing efficient reservoir and pore utilization in these scenarios. High reservoir pressure and temperature associated with increasing depth increased the E V , and high CO 2 injection rates resulted in increases in E V and E d , while the impact of permeability anisotropy was minimal after the 30-year injection period.

03 NATURAL GAS↗
DOE OSTI2020

Influence of Clay Wettability Alteration on Relative Permeability

Abstract Understanding the wettability of porous materials is important to model fluid flow in the subsurface. One of the critical factors that influences wetting in real reservoirs is the composition of geologic materials. The wetting properties for clay minerals can have a particularly strong impact on flow and transport. In this work, we analyze the chemical composition of a Mt. Simon sandstone core to resolve the microscopic structure of clay regions and assess how alterations to the local wetting properties influence multiphase transport based on core flooding experiments and relative permeability simulations. We show that whichever fluid has greater affinity toward clay minerals will tend to accumulate within these high surface area regions, leading to dramatic shifts in the relative permeability. This work establishes the essential importance of the mineral composition and associated wetting properties in the modeling of flow and transport in reservoir‐scale systems.

Fan, Ming↗