Pore-scale Network Model Research Articles

X-ray micro-CT based computation of effective diffusivity of metabolic gases in tomato fruit

The effective diffusivity is a key engineering property of fruit that affects transport of metabolic gases and, hence, ripening. It strongly depends on the microstructure of the fruit. In bulky fruit such as tomato, porosity and pore structure differ between tissues and change during maturation and ripening. Knowledge of the relationship between gas diffusivity and microstructure of tomato will aid management and control of postharvest operations. By using mathematical models of mass transport that incorporate the 3-D microscopic tissue geometry obtained from micro-computed tomography (μ-CT), the relationship between microstructural features and gas diffusivity may be computed in a direct way. In this study, a previously validated pore-scale network model (PNM) was used to simulate the effective gas diffusivity of O2, CO2 and ethylene for five types of tomato fruit tissues (i.e., outer mesocarp, inner mesocarp, septa, placenta and columella) at different maturation and ripeness stages. The effective gas diffusivity of the placenta and columella was large during the entire ripening process as these tissues contained more interconnected open intercellular spaces. The effective diffusivity of the inner mesocarp increased with increasing porosity during ripening while the microstructural changes of the outer mesocarp lagged compared to those of the inner mesocarp region, resulting in a delayed increase of the effective gas diffusivity with ripening. Regression models between the effective diffusivity of O2, CO2 and ethylene as a function of porosity, open porosity or tortuosity were established. This study provides a quantitative basis for further gas exchange modeling in intact tomato fruit to predict their ripening process.

Pore-scale network modeling approach to study the impact of Microporosity's pore space topology

Carbonates present a significantly important area for the research as classical empirical methods applied for sandstones characterization, may easily mislead when applied to carbonates. The impact becomes more protuberant when considering low resistivity pay carbonate formations where Archie's equation may yield higher than actual water saturation values, which, however, underestimate the hydrocarbon reserves. Especially, the bimodal pore sizes distribution makes carbonates extremely complicated for characterization through traditional digital rock physics applications. Unlike sandstone, for a given carbonate sample, it is almost impossible to have pore digital 3D images with minimum elementary volume (REV) to generate a standard pore-network model (PNM) due to the resolution and computational processing power limitations.

Microscale investigation of DNAPL displacement by engineered graphene quantum dots in heterogeneous porous media

This x-ray microtomography study investigates the dynamic pore-scale displacement of a dense non-aqueous phase liquid (DNAPL) such as heavy crude oil in a heterogeneous aquifer rock using carbonaceous nanoparticles. The nanoparticles were synthesized from Wyoming coal and consisted of a mixture of graphene quantum dots (GQD) and engineered graphene quantum dots (E-GQD) in equal proportions. Synergistic interactions between GQD and E-GQD at the oil/water interface reduced the DNAPL/brine interfacial tension (IFT) from 13.4 mN/m to 5.4 mN/m. In addition, the nanofluid mixture altered the wettability of the minerals found in the rock (quartz, carbonate, and feldspar) from oil-wet to water-wet with average contact angles of 66°, 51°, and 60°, respectively. The wettability alteration was more pronounced in carbonates due to the tendency of GQD to adsorb on these surfaces. Analyses of the saturation profiles and pore-scale fluid occupancy maps revealed that the wettability alteration was not instantaneous and required a short soaking time for the fluid-rock interactions to take place. IFT reduction alone was not enough to displace the DNAPL at the early stages of nanofluid flooding because of the high density and viscosity of the oil. As a result, the nanofluid did not outperform brine after 1 pore volume (PV) of injection. On the other hand, the nanofluid was able to invade small pores that were not accessible to brine after 3 PV of injection due to both IFT and contact angle reduction, which lowered the threshold capillary pressure of these pores. Subsequently, more medium and large pores were invaded by the nanofluid as the injection continued, leading to an 11% increase in DNAPL recovery after 20 PV of nanofluid injection, as compared to waterflooding. This incremental recovery is significant considering that the experiments were performed with a heavy oil at ambient temperature, which is more representative of aquifer conditions. Thus, the GQD-based nanofluid has the potential to achieve much larger recoveries in deeper heavy oil reservoirs provided enough soaking time is allowed. The insights provided by this study could be used to validate pore-scale network models or guide in the design and selection of more effective nanomaterials for aquifer remediation or enhanced oil recovery applications.

The Impact of Rheology on Viscous Oil Displacement by Polymers Analyzed by Pore-Scale Network Modelling.

Several experimental studies have shown significant improvement in heavy oil recovery with polymers displaying different types of rheology, and the effect of rheology has been shown to be important. These experimental studies have been designed to investigate why this is so by applying a constant flow rate and the same polymer effective viscosity at this injection rate. The types of rheology studied vary from Newtonian and shear thinning behavior to complex rheology involving shear thinning and thickening behavior. The core flood experiments show a significantly higher oil recovery with polyacrylamide (HPAM), which exhibits shear thinning/thickening behavior compared to biopolymers like Xanthan, which is purely shear thinning. Various reasons for these observed oil recovery results have been conjectured, but, to date, a clear explanation has not been conclusively established. In this paper, we have investigated the theoretical rationale for these results by using a dynamic pore scale network model (DPNM), which can model imbibition processes (water injection) in porous media and also polymer injection. In the DPNM, the polymer rheology can be shear thinning, shear thinning/thickening, or Newtonian (constant viscosity). Thus, the local effective viscosity in a pore within the DPNM depends on the local shear rate in that pore. The predicted results using this DPNM show that the polymer causes changes in the local flow velocity field, which, as might be expected, are different for different rheological models, and the changes in the velocity profile led to local diversion of flow. This, in turn, led to different oil recovery levels in imbibition. However, the critical result is that the DPNM modelling shows exactly the same trend as was observed in the experiments, viz. that the shear thinning/thickening polymer gave the highest oil recovery, followed by the Newtonian Case and the purely shear thinning polymer gave the lowest recover, but this latter case was still above the waterflood result. The DPNM simulations showed that the shear-thinning/thickening polymer show a stabilized frontal velocity and increased oil mobilization, as observed in the experiments. Simulations for the shear-thinning polymer show that, in high-rate bonds, the average viscosity is greatly reduced, and this causes enhanced water fingering compared to the Newtonian polymer case. No other a priori model of the two-phase fluid physics of imbibition, coupled with the polymer rheology, has achieved this degree of predictive explanation, of these experimental observations, to our knowledge.

Effect of Pore Structure on Slippage Effect in Unsaturated Tight Formation Using Pore Network Model

The gas slippage phenomenon under dry conditions has been investigated extensively both numerically and experimentally. However, very limited research has focused on gas slippage behavior under wet conditions. Unlike conventional formation, the influence of water on the gas transport process cannot be neglected in tight formations due to the comparable amount of thin water film attached along the rock surface. It is found experimentally that the gas slippage factor is positively related to water saturation if the water saturation is small, while it decreases with water saturation if it is larger than a critical value. Most of the existing models failed to capture the measured downtrend of the gas slippage factor with increasing water saturation, which resulted from water blocking or gas trapping phenomenon. In this work, a pore-scale network model is proposed to look at the water distribution characteristic and investigate the effect of water on the gas slippage factor. The proposed pore-scale model incorporates the capillary dominated multiphase fluid distribution, real gas effect, and gas transport mechanisms at pore scale. On the basis of our pore network model, the effect of pore structure characteristics including the frequency of mean pore radius, size of mean pore radius, aspect ratio, and coordination number on the gas slippage behavior are investigated and discussed in detail. Similar to previous experimental observations, the simulated gas slippage factor shows a non-monotonic increase trend with water saturation; it starts to decrease under high water saturation, and the critical water saturation depends on the pore structure factors. It increases with the mean pore radius and coordination number but decreases with the aspect ratio. We used the pore network model to investigate the effect of the water phase on the gas slippage behavior at the pore scale for the first time. It emphasized the predominance of water blocking and the gas trapping phenomenon in the estimation of the gas slippage factor at high water saturation.

Dynamic Pore-Scale Network Modeling of Spontaneous Water Imbibition in Shale and Tight Reservoirs

Spontaneous water imbibition plays an imperative role in the development of shale or tight oil reservoirs. Spontaneous water imbibition is helpful in the extraction of crude oil from the matrix, although it decreases the relative permeability of the hydrocarbon phase dramatically. The dynamic pore-scale network modeling of water imbibition in shale and tight reservoirs is presented in this work; pore network generation, local capillary pressure function, conductance calculation and boundary conditions for imbibition are all presented in detail in this paper. The pore network is generated based on the characteristics of Barnett shale formations, and the corresponding laboratory imbibition experiments are matched using this established dynamic pore network model. The effects of the wettability, throat aspect ratio, viscosity, shape factor, micro-fractures, etc. are all investigated in this work. Attempts are made to investigate the water imbibition mechanisms from a micro-scale perspective. According to the simulated results, wettability dominates the imbibition characteristics. Besides this, the viscous effects including viscosity, initial capillary pressure and micro-fractures increase the imbibition rate, while the final recovery factor is more controlled by the capillarity effect including the cross-area shape factor, contact angle and the average pore-throat aspect ratio.

Experimental Study and Pore Network Modeling of Formation Damage Induced by Fines Migration in Unconsolidated Sandstone Reservoirs

Abstract Fine migration is always considered as one of the major mechanisms that are responsible for formation damage. The unwanted reduction of reservoir permeability would result in the decline of water injection and consequent oil production, especially for the unconsolidated sandstone reservoir. For better understanding, the mechanisms of formation damage in pore-scale, a new three-dimensional pore-scale network model (PNM) is proposed and developed to simulate formation damage caused by particle detachment, migration, and capture in pore throats based on force analysis. Experiments are also conducted on the formation damage characteristics of an unconsolidated core. Both X-ray diffraction and scanning electron microscope (SEM) are applied to understand the microscopic reservoir properties. The experimental results show that the studied core has a strong flowrate sensitivity. A comparison between experimental results and PNM simulation results is conducted. The simulated results agree well with the experimental data, which approves the efficiency and accuracy of the PNM. Sensitivity analysis results show that larger particle sizes, higher flowrate, higher fluid viscosity, and lower ion concentration of the fluids would contribute to the formation damage, which could provide guidance for the development of unconsolidated sandstone reservoirs with strong sensitivity.

Impact of mineralogy and wettability on pore-scale displacement of NAPLs in heterogeneous porous media

Subsurface formations often contain multiple minerals with different wettability characteristics upon contact with nonaqueous-phase liquids (NAPLs). Constitutive relationships between microstructure heterogeneity and NAPL fate and transport in these formations are difficult to predict. Several studies have used pore-scale network models with faithful representations of rock pore space topology to predict macroscopic descriptors of two-phase flow, however wettability is usually considered as a spatially random variable. This study attempts to overcome this limitation by considering more realistic representations of rock mineralogy and wettability in these models. This is especially important for heterogeneous rocks where properties vary at the pore-scale. The work was carried out in two phases. First, pore-fluid occupancy maps during waterflooding were obtained by X-ray microtomography to elucidate the impact of pore wall mineralogy and wettability on water preferential flow paths and NAPL trapping within a heterogeneous aquifer sandstone (Arkose). Then, microtomography images of the rock were used to generate a hybrid pore network model (PNM) that incorporated both pore space topology and pore wall mineralogy. In-situ contact angles (CA) measured on the surface of different minerals were assigned to the network on a pore-by-pore basis to describe the exact wettability distribution of the rock (Pore-by-pore model). The equivalent network was used as input in a quasi-static flow model to simulate waterflooding, and the predictions of residual NAPL saturation and relative permeabilities were compared against their experimental counterparts. To examine the sensitivity of the model to the underlying fluid-solid interactions, we also used traditional methods of wettability characterization in the input data and assigned them randomly to the PNM. Wettability in this case was assessed from macroscale CA distribution of oil droplets on the surface of unpolished Arkose substrates released by spontaneous imbibition of water (Arkose model) and from pendant drop measurements on polished quartz (Quartz model). Our results revealed that the Pore-by-pore model predicted waterflooding with the highest accuracy among all three cases. The Arkose model slightly overestimated NAPL removal whereas the Quartz model failed to predict the experiments. More in-depth analysis of the Pore-by-pore and Arkose models showed that macroscopic transport quantities are less dependent to microstructure heterogeneity if minerals are distributed uniformly across the rock. The predictions herein indicate the importance of incorporating mineralogy and wettability maps to improve the prediction capabilities of PNMs especially in systems with high mineral heterogeneity, where minerals are nonuniformly distributed, or selective fluid-mineral interactions are targeted.

Pore network model for retrograde gas flow in porous media

Gas well deliverability in retrograde gas reservoirs is affected by the appearance of a liquid phase near the wellbore when the bottom-hole pressure is below the dew point. At low enough pressure gradients, the liquid phase may bridge the pore throats, blocking the gas phase flow, leading to what is known as condensate blockage. If the pressure gradient is above a critical value, the capillary forces cannot block the gas flow and the condensate bridges are displaced. Gas production can be estimated using reservoir-scale simulation of the retrograde gas flow near producing wells using relative permeability curves that take into account the different physical phenomena and their dependence on local pressure, temperature and pressure gradient (capillary number). Pore-scale simulators can be used to model retrograde gas flow through porous media and to determine the gas and liquid phases relative permeability curves as a function of different flow parameters. Here, a fully-implicit isothermal compositional pore-scale network model is presented for retrograde gas flow in porous media at high capillary number, at which capillary forces are neglected. The flow pattern in each capillary changes from a single-phase gas flow to a two-phase core-annular flow regime when the pressure and the fluid composition reach a critical condition based on the thermodynamics of the fluid mixture. Newton's method is used to solve the non-linear flow and thermodynamics equations to calculate the pressure distribution and the flow rate of each component through the network. The model was used to predict gas-liquid relative permeability at high capillary number from a depletion process in a 2D network. The results show the evolution of the condensate saturation at different conditions and how the gas permeability falls abruptly at a certain condensate saturation.

Pore-scale network modeling of microporosity in low-resistivity pay zones of carbonate reservoir

Archie's law is commonly used for the estimation of brine saturation using electrical conductivity of sedimentary rock. For a formation with narrow pore size distribution (PSD), low resistivity could mean high water saturation and hence, high water production. This, however, is not the case for many formations with wide PSDs, for which Low Resistivity Pay (LRP) zones have been reported with very low or none water cut production. One of the main causes resulting in LRP zones, especially in carbonates, is the existence of wide PSDs. Due to their small sizes, micro-pores have much higher threshold capillary pressures during drainage in a water-wet sample. In these systems, oil as the non-wetting phase preferably occupies larger pores leaving micro-pores saturated with brine. The existence of connected pathways through micro-pores that are fully saturated with a conductive phase (i.e., brine) creates ‘shortcuts’ for the electrical current which causes a short circuit and, ultimately, lowers rock resistivity measured from logs. Here in this work, we investigate the impact of microporosity on the electrical properties of porous media under multiphase flow conditions. We develop a pore-scale network model for the simulation of displacement sequences during drainage and imbibition in the presence of micro-pore networks. To do so, we first construct ‘macro’ networks on 2D rectangular lattices which are later altered to include micro-pores. A comprehensive set of sensitivity analyses is performed to assess the impact of various parameters including the tortuosity, geometry, and location of the microporosity (i.e., parallel or in series, continuous or non-continuous). Also, 3D networks for two different rock samples are used to investigate the effect of PSD on the electrical resistivity curves. This work helps to examine the use of Archie's equation for field applications, specifically, for evaluating formations with wide PSDs.

A Study to Investigate Fluid-Solid Interaction Effects on Fluid Flow in Micro Scales

Due to micro-nanopores in tight formation, fluid-solid interaction effects on fluid flow in porous media cannot be ignored. In this paper, a novel model which can characterize micro-fluid flow in micro scales is proposed. This novel model has a more definite physical meaning compared with other empirical models. And it is validated by micro tube experiments. In addition, the application range of the model is rigorously analyzed from a mathematical view, which indicates a wider application scope. Based on the novel model, the velocity profile, the average flow velocity and flow resistance in consideration of fluid-solid interaction are obtained. Furthermore, the novel model is incorporated into a representative pore scale network model to study fluid-solid interactions on fluid flow in porous media. Results show that due to fluid-solid interaction in micro scales, the change rules of the velocity profile, the average flow velocity and flow resistance generate obvious deviations from traditional Hagen-Poiseuille’s law. The smaller the radius and the lower the displacement pressure gradient (∇P), the more obvious the deviations will be. Moreover, the apparent permeability in consideration of fluid-solid interaction is no longer a constant, it increases with the increase of ∇P and non-linear flow appears at low ∇P. This study lays a good foundation for studying fluid flow in tight formation.

Gas-liquid membrane contactors: Modeling study of non-uniform membrane wetting

Current available models for simulation of the separation process in gas-liquid membrane contactor (MC) systems consider a uniform partial membrane wetting along the membrane length (Lmem). However, transmembrane pressure changes along the Lmem. Additionally, the available models usually consider a simplified uniform pore size to represent the micro-porous MC. Additionally, not all pores in a MC have the same size. In this study, a pore-scale network model is developed to simulate the physical separation of H2S using MCs by taking to account for (i) transmembrane pressure variation and (ii) pore size distribution of MC. The model results are compared with the experimental results of H2S separation. Modeling results indicate that membrane wetting is non-uniformly distributed along Lmem. The membrane wetting ratio is maximum at the inlet of the liquid phase, and it decreases toward the liquid outlet. Also, increasing the inlet gas pressure reduces the membrane wetting ratio, and leads to higher H2S separation. Moreover, the model results indicate that shifting of the pore size distribution of MC towards smaller pore size declines the membrane wetting ratio and increases the H2S separation efficiency.

Permeability prediction from a pore-scale network model constrained by low-pressure nitrogen sorption isotherms

The matrix permeability of shale is controlled by the microstructure of shale pore network. Therefore, a thorough understanding of shale pore structure is fundamental to the prediction of shale permeability. We constructed a physically representative pore network model for two Barnett Shale samples. We predicted a Darcy permeability of 7.19 nanodarcies (nd) and apparent permeability of 57.34 nd for these samples. We explored the pore structure of shale matrix with low-pressure nitrogen adsorption/desorption isotherms. The pore size distribution, the network connectivity, as well as pore spatial arrangement are determined for the organic matter and the whole matrix. We separated pores in the network model into two groups: the affiliated pores and the dominant pores. For these samples, the affiliated pores are pores with diameters smaller than 8 nm and the dominant pores are with diameters larger than 8 nm. The affiliated pores develop on the walls of the dominant pores. The cutoff value between affiliated pores and dominant pores may differ for different samples. The pore spatial arrangement is validated against previous literature resultsand a diagenetic explanation for development of shale pore system. The network model can be used to predict shale permeability and other petrophysical properties.

Study of formation damage caused by retention of bi-dispersed particles using combined pore-scale simulations and particle flooding experiments

The infiltration of solid particles (fines) into a reservoir during drilling or water reinjection is a long-standing problem in the petroleum industry because of the associated production decline or injectivity loss. Solid particle infiltration is also an active area of research in other fields such as waste water treatment and fines migration in clay-rich reservoirs.In this work, we perform experiments to study particle infiltration into sintered glass bead core plugs and measure the changes in porosity and permeability using computed tomography (CT) scanning and pressure transducers, respectively. Suspensions of prescribed bimodal particle sizes, concentrations, and flowrates are flooded through the core plugs. Permeability changes are measured continuously over time, and the porosity change is measured after flowing a fixed mass of invaded particles.A dual pore-scale numerical model approach (a combination of a direct pore-scale discrete element method (DEM) and a pore-scale network model) is used to predict permeability reduction by particle filtration in porous media. Large particle deposition is modeled using the DEM in a disordered sphere pack geometry; the result is a prediction of deposition as a function of large particle concentration. Small particle deposition is modeled using the network model; the result is a prediction of deposition as a function of small particle concentration. Crucially, the geometry of the network model depends on the amount of large particles deposited. In this way, the deposition of large and small sized particles is coupled together.The permeability and porosity reduction of the network due to the deposition of small and large particles are then calculated from the functions above. We compare the experimental results with simulation predictions and find that the dual pore-scale model is capable of predicting the permeability of the invaded core in the regions away from the injection face. Permeability prediction in the region adjacent to the injection face is improved by incorporating the influence of the external filter cake.

Dynamic pore-scale network model (PNM) of water imbibition in porous media

A dynamic pore-scale network model is presented which simulates 2-phase oil/water displacement during water imbibition by explicitly modelling intra-pore dynamic bulk and film flows using a simple local model. A new dynamic switching parameter, λ, is proposed within this model which is able to simulate the competition between local capillary forces and viscous forces over a very wide range of flow conditions. This quantity (λ) determines the primary pore filling mechanism during imbibition; i.e. whether the dominant force is (i) piston-like displacement under viscous forces, (ii) film swelling/collapse and snap-off due to capillary forces, or (iii) some intermediate local combination of both mechanisms.A series of 2D dynamic pore network simulations is presented which shows that the λ-model can satisfactorily reproduce and explain different filling regimes of water imbibition over a wide range of capillary numbers (Ca) and viscosity ratios (M). These imbibition regimes are more complex than those presented under drainage by (Lenormand et al. (1983)), since they are determined by a wider group of control parameters. Our simulations show that there is a coupling between viscous and capillary forces that is much less important in drainage. The effects of viscosity ratio during imbibition are apparent even under conditions of very slow flow (low Ca)–displacements that would normally be expected to be completely capillary dominated. This occurs as a result of the wetting films having a much greater relative mobility in the higher M cases (e.g. M = 10) thus leading to a higher level of film swelling/snap-off, resulting in local oil cluster bypassing and trapping, and hence a poorer oil recovery. This deeper coupled viscous mechanism is the underlying reason why the microscopic displacement efficiency is lower for higher M cases in water imbibition processes.Additional results are presented from the dynamic model on the corresponding effluent fractional flows (fw) and global pressure drops (ΔP) as functions of capillary number and viscosity ratio. These results indicate that unsteady-state (USS) relatively permeabilities in imbibition should be inherently rate dependent.

Multiscale modelling of dual-porosity porous media; a computational pore-scale study for flow and solute transport

Many environmental and agricultural applications involve the transport of water and dissolved constituents through aggregated soil profiles, or porous media that are structured, fractured or macroporous in other ways. During the past several decades, various process-based macroscopic models have been used to simulate contaminant transport in such media. Many of these models consider advective-dispersive transport through relatively large inter-aggregate pore domains, while exchange with the smaller intra-aggregate pores is assumed to be controlled by diffusion. Exchange of solute between the two domains is often represented using a first-order mass transfer coefficient, which is commonly obtained by fitting to observed data. This study aims to understand and quantify the solute exchange term by applying a dual-porosity pore-scale network model to relatively large domains, and analysing the pore-scale results in terms of the classical dual-porosity (mobile-immobile) transport formulation.We examined the effects of key parameters (notably aggregate porosity and aggregate permeability) on the main dual-porosity model parameters, i.e., the mobile water fraction (ϕm) and the mass transfer coefficient (α). Results were obtained for a wide range of aggregate porosities (between 0.082 and 0.700). The effect of aggregate permeability was explored by varying pore throat sizes within the aggregates. Solute breakthrough curves (BTCs) obtained with the pore-scale network model at several locations along the domain were analysed using analytical solutions of the dual-porosity model to obtain estimates of ϕm and α. An increase in aggregate porosity was found to decrease ϕm and increase α, leading to considerable tailing in the BTCs. Changes in the aggregate pore throat size affected the relative flow velocity between the intra- and inter-aggregate domains. Higher flow velocities within the aggregates caused a change in the transport regime from diffusion dominated to more advection dominated. This change increased the exchange rate of solutes between the mobile and immobile domains, with a related increase in the value of the mass transfer coefficient and less tailing in the BTCs.

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.

Effect of the Pore Size Distribution on the Displacement Efficiency of Multiphase Flow in Porous Media

Abstract Due to the complexity of porous media, it is difficult to use traditional experimental methods to study the quantitative impact of the pore size distribution on multiphase flow. In this paper, the impact of two pore distribution function types for three-phase flow was quantitatively investigated based on a three-dimensional pore-scale network model. The results show that in the process of wetting phase displacing the non-wetting phase without wetting films or spreading layers, the displacement efficiency was enhanced with the increase of the two function distribution’s parameters, which are the power law exponent in the power law distribution and the average pore radius or standard deviation in the truncated normal distribution, and vice versa. Additionally, the formation of wetting film is better for the process of displacement.

A dynamic pore-scale network model for two-phase imbibition

Pore-scale network modeling serves as an efficient tool for the simulation of multiphase flow in porous media, like carbon dioxide sequestration, enhanced gas/oil recovery and transport in fuel cell. To overcome the limitations of existing dynamic networks, we develop an alternative model for imbibition that accounts for the complex physical process of frontal displacement, film swelling, and snap off. The novelty of this model is that the outlet boundary is permeable to both wetting and non-wetting fluids before all the displaced phase is trapped. Instead of solving the nonlinear system of film pressure equations with conventional algorithms, a scale factor is employed to iteratively adjust the solutions estimated independently by mass conservation and the Young–Laplace equation until they are consistent with each other. To guarantee the effectiveness and accuracy, we also provide strategies for the selection of two significant considerations: scale factor and time-step size. This method is employed to study the effects of displacement rate and contact angle on waterflooding performance, relative permeabilities, as well as residual saturation. We believe this model can be further used to describe the distribution of slickwater in shale gas systems after hydraulic fracturing and predict water saturation based on the pore-scale topology of reservoirs.

The flow of power law fluids in elastic networks and porous media

The flow of power law fluids, which include shear thinning and shear thickening as well as Newtonian as a special case, in networks of interconnected elastic tubes is investigated using a residual-based pore scale network modeling method with the employment of newly derived formulae. Two relations describing the mechanical interaction between the local pressure and local cross-sectional area in distensible tubes of elastic nature are considered in the derivation of these formulae. The model can be used to describe shear dependent flows of mainly viscous nature. The behavior of the proposed model is vindicated by several tests in a number of special and limiting cases where the results can be verified quantitatively or qualitatively. The model, which is the first of its kind, incorporates more than one major nonlinearity corresponding to the fluid rheology and conduit mechanical properties, that is non-Newtonian effects and tube distensibility. The formulation, implementation, and performance indicate that the model enjoys certain advantages over the existing models such as being exact within the restricting assumptions on which the model is based, easy implementation, low computational costs, reliability, and smooth convergence. The proposed model can, therefore, be used as an alternative to the existing Newtonian distensible models; moreover, it stretches the capabilities of the existing modeling approaches to reach non-Newtonian rheologies.