Mohammad Piri

Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow

Pore-network models have been used to describe a wide range of properties from capillary pressure characteristics to interfacial area and mass transfer coefficients. The void space of a rock or soil is described as a network of pores connected by throats. The pores and throats are assigned some idealized geometry and rules are developed to determine the multiphase fluid configurations and transport in these elements. The rules are combined in the network to compute effective transport properties on a mesoscopic scale some tens of pores across. This approach is illustrated by describing a pore-scale model for two- and three-phase flow in media of arbitrary wettability. The appropriate pore-scale physics combined with a geologically representative description of the pore space gives a model that can predict average behavior, such as capillary pressure and relative permeability. This capability is demonstrated by successfully predicting primary drainage and waterflood relative permeabilities for Berea sandstone. The implications of this predictive power for improved characterization of subsurface simulation models are discussed. A simple example field study of waterflooding an oil-wet system near the oil/water contact shows how the assignment of physically-based multiphase flow properties based on pore-scale modeling gives significantly different predictions of oil recovery than using current empirical relative permeability models. Methods to incorporate pore-scale results directly into field-scale simulation are described. In principle, the same approach could be used to describe any type of process for which the behavior is understood at the pore scale.

Wettability of Supercritical Carbon Dioxide/Water/Quartz Systems: Simultaneous Measurement of Contact Angle and Interfacial Tension at Reservoir Conditions

Injection of carbon dioxide in deep saline aquifers is considered as a method of carbon sequestration. The efficiency of this process is dependent on the fluid-fluid and rock-fluid interactions inside the porous media. For instance, the final storage capacity and total amount of capillary-trapped CO2 inside an aquifer are affected by the interfacial tension between the fluids and the contact angle between the fluids and the rock mineral surface. A thorough study of these parameters and their variations with temperature and pressure will provide a better understanding of the carbon sequestration process and thus improve predictions of the sequestration efficiency. In this study, the controversial concept of wettability alteration of quartz surfaces in the presence of supercritical carbon dioxide (sc-CO2) was investigated. A novel apparatus for measuring interfacial tension and contact angle at high temperatures and pressures based on Axisymmetric Drop Shape Analysis with no-Apex (ADSA-NA) method was developed and validated with a simple system. Densities, interfacial tensions, and dynamic contact angles of CO2/water/quartz systems were determined for a wide range of pressures and temperatures relevant to geological sequestration of CO2 in the subcritical and supercritical states. Image analysis was performed with ADSA-NA method that allows the determination of both interfacial tensions and contact angles with high accuracy. The results show that supercritical CO2 alters the wettability of quartz surface toward less water-wet conditions compared to subcritical CO2. Also we observed an increase in the water advancing contact angles with increasing temperature indicating less water-wet quartz surfaces at higher temperatures.

The Effect of Saturation History on Three-Phase Relative Permeability: An Experimental Study

We investigate the effect of different saturation histories relevant to various oil displacement processes (including secondary and tertiary gas injections) on three-phase gas/oil/brine relative permeabilities of water-wet sandstone. It is found that three-phase water (wetting phase) relative permeability is primarily a function of water saturation and shows no dependency upon saturation history. Three-phase gas (nonwetting phase) relative permeability is also a function of gas saturation as well as the direction of gas saturation change. Three-phase relative permeability to oil (intermediate-wetting phase) appears to depend on all phase saturations, and saturation history have no significant impact on it. Three-phase oil relative permeability shows weak sensitivity to initial oil saturation prior to gas injection. The functional forms of oil relative permeability with saturation, particularly at low oil saturations, are also examined. It is observed that, at high oil saturations where networks of oil-filled elements govern oil flow, oil relative permeability exhibits a quartic form with oil saturation (kro∝So4) whereas, at low oil saturations where flow is believed to be controlled by layer drainage, it shows a quadratic form (kro∝So2). The quadratic form of three-phase oil relative permeability is consistent with the theoretical interpretation of layer drainage at the pore scale.

Pore-scale modeling of dispersion in disordered porous media

We employ a direct pore-level model of incompressible flow that uses the modified moving particle semi-implicit (MMPS) method. The model is capable of simulating both unsteady- and steady-state flow directly in microtomography images of naturally-occurring porous media. We further develop this model to simulate solute transport in disordered porous media. The governing equations of flow and transport at the pore level, i.e., Navier-Stokes and convection-diffusion, are solved directly in the pore space mapped by microtomography techniques. Three naturally-occurring sandstones are studied in this work. We verify the accuracy of the model by comparing the computed longitudinal dispersion coefficients against the experimental data for a wide range of Peclet numbers, i.e., 5×10(-2)<Pe<1×10(6). Solutions of full Navier-Stokes enable us to examine the impact of inertial forces at the very high Peclet numbers. We show that inclusion of the inertial forces improves the agreement between the computed dispersion coefficients with their experimental counterparts. We then investigate the impact of pore-space topology on the pre-asymptotic and asymptotic dispersion regimes by comparing solute dispersion in the three sandstones that possess different topological features. We illustrate how grain size and homogeneity of the two sandstones dictate the threshold and magnitude of the asymptotic regime.

Experimental Investigation of Dynamic Contact Angle and Capillary Rise in Tubes with Circular and Noncircular Cross Sections

An extensive experimental study of the kinetics of capillary rise in borosilicate glass tubes of different sizes and cross-sectional shapes using various fluid systems and tube tilt angles is presented. The investigation is focused on the direct measurement of dynamic contact angle and its variation with the velocity of the moving meniscus (or capillary number) in capillary rise experiments. We investigated this relationship for different invading fluid densities, viscosities, and surface tensions. For circular tubes, the measured dynamic contact angles were used to obtain rise-versus-time values that agree more closely with their experimental counterparts (also reported in this study) than those predicted by Washburn equation using a fixed value of contact angle. We study the predictive capabilities of four empirical correlations available in the literature for velocity-dependence of dynamic contact angle by comparing their predicted trends against our measured values. We also present measurements of rise in noncircular capillary tubes where rapid advancement of arc menisci in the corners ahead of main terminal meniscus impacts the dynamics of rise. Using the extensive set of experimental data generated in this study, a new general empirical trend is presented for variation of normalized rise with dynamic contact angle that can be used in, for instance, dynamic pore-scale models of flow in porous media to predict multiphase flow behavior.

Pore-Scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. I. Cusp Formation and Collapse

We present a pore-scale network model of two- and three-phase flow in disordered porous media. The model reads three-dimensional pore networks representing the pore space in different porous materials. It simulates wide range of two- and three-phase pore-scale displacements in porous media with mixed-wet wettability. The networks are composed of pores and throats with circular and angular cross sections. The model allows the presence of multiple phases in each angular pore. It uses Helmholtz free energy balance and Mayer–Stowe–Princen (MSP) method to compute threshold capillary pressures for two- and three-phase displacements (fluid configuration changes) based on pore wettability, pore geometry, interfacial tension, and initial pore fluid occupancy. In particular, it generates thermodynamically consistent threshold capillary pressures for wetting and spreading fluid layers resulting from different displacement events. Threshold capillary pressure equations are presented for various possible fluid configuration changes. By solving the equations for the most favorable displacements, we show how threshold capillary pressures and final fluid configurations may vary with wettability, shape factor, and the maximum capillary pressure reached during preceding displacement processes. A new cusp pore fluid configuration is introduced to handle the connectivity of the intermediate wetting phase at low saturations and to improve model’s predictive capabilities. Based on energy balance and geometric equations, we show that, for instance, a gas-to-oil piston-like displacement in an angular pore can result in a pore fluid configuration with no oil, with oil layers, or with oil cusps. Oil layers can then collapse to form cusps. Cusps can shrink and disappear leaving no oil behind. Different displacement mechanisms for layer and cusp formation and collapse based on the MSP analysis are implemented in the model. We introduce four different layer collapse rules. A selected collapse rule may generate different corner configuration depending on fluid occupancies of the neighboring elements and capillary pressures. A new methodology based on the MSP method is introduced to handle newly created gas/water interfaces that eliminates inconsistencies in relation between capillary pressures and pore fluid occupancies. Minimization of Helmholtz free energy for each relevant displacement enables the model to accurately determine the most favorable displacement, and hence, improve its predictive capabilities for relative permeabilities, capillary pressures, and residual saturations. The results indicate that absence of oil cusps and the previously used geometric criterion for the collapse of oil layers could yield lower residual oil saturations than the experimentally measured values in two- and three-phase systems.

Atomistic Molecular Dynamics Simulations of Crude Oil/Brine Displacement in Calcite Mesopores

Unconventional reservoirs such as hydrocarbon-bearing shale formations and ultratight carbonates generate a large fraction of oil and gas production in North America. The characteristic feature of these reservoirs is their nanoscale porosity that provides significant surface areas between the pore walls and the occupying fluids. To better assess hydrocarbon recovery from these formations, it is crucial to develop an improved insight into the effects of wall-fluid interactions on the interfacial phenomena in these nanoscale confinements. One of the important properties that controls the displacement of fluids inside the pores is the threshold capillary pressure. In this study, we present the results of an integrated series of large-scale molecular dynamics (MD) simulations performed to investigate the effects of wall-fluid interactions on the threshold capillary pressures of oil-water/brine displacements in a calcite nanopore with a square cross section. Fully atomistic models are utilized to represent crude oil, brine, and calcite in order to accommodate electrostatic interactions and H-bonding between the polar molecules and the calcite surface. To this end, we create mixtures of various polar and nonpolar organic molecules to better represent the crude oil. The interfacial tension between oil and water/brine and their contact angle on calcite surface are simulated. We study the effects of oil composition, water salinity, and temperature and pressure conditions on these properties. The threshold capillary pressure values are also obtained from the MD simulations for the calcite nanopore. We then compare the MD results against those generated using the Mayer-Stowe-Princen (MSP) method and explain the differences.

In situ characterization of wettability alteration and displacement mechanisms governing recovery enhancement due to low-salinity waterflooding

A series of micro-scale core-flooding experiments were performed on reservoir core samples at elevated temperature and pressure conditions to develop better insights into wettability alteration and pore-scale displacement mechanisms taking place during low-salinity waterflooding (LSWF). Two individual miniature core samples were cut from a preserved reservoir whole core, saturated to establish initial reservoir fluid saturation conditions, and subsequently waterflooded with low-salinity and high-salinity brines. A third miniature sister core sample was also cut, solvent-cleaned, and subjected to a dynamic wettability restoration process (to reestablish native state wettability) and then a low-salinity waterflood. All samples were imaged during the experiments using a micro-CT scanner to obtain fluid occupancy maps and measure in situ oil-water contact angles. The results of the experiments performed on the preserved core samples show a significantly improved performance of low-salinity waterflooding compared to that of high-salinity waterflooding (HSWF). Pore-scale contact angle measurements provide direct evidence of wettability alteration from weakly oil-wet toward weakly water-wet conditions during LSWF, whereas contact angles measured during HSWF remain unchanged. We believe that the reduction in oil-water contact angles toward increased water-wetness lowers the threshold water pressure needed to displace oil from some medium-sized pore elements. Contact angles measured during the dynamic wettability restoration process show an equilibrium wettability state very similar to the initial one observed in the preserved samples. This indicates that drilling fluid contaminants had a negligible effect on the reservoir rock wettability. The experimental results also reveal similarities between saturation trends for the preserved-LSWF and restored-LSWF tests.

Pore-scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. II. Results

We use the model described in Zolfaghari and Piri (Transp Porous Media, 2016) to predict two- and three-phase relative permeabilities and residual saturations for different saturation histories. The results are rigorously validated against their experimentally measured counterparts available in the literature. We show the relevance of thermodynamically consistent threshold capillary pressures and presence of oil cusps for significantly improving the predictive capabilities of the model at low oil saturations. We study systems with wetting and spreading oil layers and cusps. Three independent experimental data sets representing different rock samples and fluid systems are investigated in this work. Different disordered networks are used to represent the pore spaces in which different sets of experiments were performed, i.e., Berea, Bentheimer, and reservoir sandstones. All three-phase equilibrium interfacial tensions used for the simulation of three-phase experimental data are measured and used in the model’s validation. We use a fixed set of parameters, i.e., the input network (to represent the pore space) and contact angles (to represent the wettability state), for all experiments belonging to a data set. Incorporation of the MSP method for capillary pressure calculations and cusp analysis significantly improves the agreement between the model’s predictions of relative permeabilities and residual oil saturations with experimental data.

Introduction to special section on Modeling of Pore‐Scale Processes

[1] In recent years pore-scale modeling of flow through porous media has gained much popularity. This can be attributed to advances in visualization of the actual pore space (and fluid distributions), to very high image resolution, and to the steady increase in computing power. The latter allows the incorporation of processes on the scale of individual pores in models that are close to the continuum scale. At the same time, research into physical and chemical processes in the fluids occupying individual pores, and interactions with the solid phase, have continued. The visualisation capability has greatly contributed to the accurate modeling of the pore space. [2] The popularity of pore-scale modeling was reflected in a sizable special session at the XVIth Conference on Computational Methods in Water Resources (CMWR), which was held in Copenhagen in June 2006. Expanded papers from this conference have been submitted for inclusion in this special section on Modeling of Pore-Scale Processes. The selection of papers represents an excellent cross section of the current research in this area, as outlined below. Contributors to the section tend to work mainly in the areas of hydrocarbon recovery, water resources or both, although the applications of the presented research are significantly wider. [3] Pore-scale modeling began with the representation of a porous medium as an interconnected network of cylindrical tubes complemented with simple rules for flow through the tubes, to calculate macroscale flow and transport characteristics such as relative permeability and dispersion coefficients. These macroscopic properties were in turn taken as input in macroscopic or continuum-scale models for flow and transport. With respect to this basic goal, little has changed in the almost 60 year history of pore-scale modeling. Blunt [2001] and Blunt et al. [2002] have provided some excellent reviews of the corresponding literature. [4] However, what has changed in recent years is the level of detail at which various processes and also the pore space itself are modeled. Especially in the area of (multiphase) flow there has been a drive to predict flow characteristics starting from pore space information of high-resolution thin section and X-ray computed microtomography images. This stands in contrast to the more traditional methods, in which (idealized) geometrical and topological network characteristics are matched to relatively simple macroscale data, to predict more complicated properties. However, in practice the distinction between the two approaches is not as large as it appears. For example the detailed pore space is often mapped onto an idealized network and some information (such as wettability) is currently only available from macroscopic data. Both approaches are represented in this special section and prove to be equally useful. The above discussion of ‘‘detailed’’ versus ‘‘idealized’’ approaches reveals what is probably the most important question in pore-scale modeling: What are the really important characteristics and pore-scale processes that are both necessary and sufficient to predict certain macroscale properties? For a long time, in the absence of large computing power, the idealized approach has worked with a minimum number of necessary parameters, which are often not sufficient. However, the increase in computing power has allowed the incorporation of many features and additional parameters, some of which are probably not necessary for a given process. It may be clear that the requirements of, in particular, the detail in which the pore space is modeled, depends on the process in question. Moreover, investing computational resources in unnecessary details reduces the opportunity to scale up to a reasonable macroscopic scale. To answer the above problems, the often employed heuristic attitude to network modeling needs to be complemented by more rigorous mathematics, such as the upscaling methods described in some of the papers in this special section. [5] Apart from the papers that aim to work through the full prediction trajectory from pore space to macroscopic process, a number of other papers have taken a deliberately simplified approach to work out the unresolved details of a given process in, for example, a single pore, with the aim of incorporating these in a network model. In the overview of the papers in the special section, presented below, a broad distinction is made between the papers that deal with multiphase flow and those that deal with dispersion and reaction. [6] Finally, special mention needs to be made of the development and application of the lattice Boltzmann (LB) method in pore-scale modeling, which features more or less prominently in many of the papers. This method is used almost routinely to calculate single-phase flow patterns, hence absolute permeabilities, in irregular (pore) geometries. More sophisticated versions of the LB method are applied and developed for two-phase flow, as well as for Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, UK. Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, Wyoming, USA.