Dynamic effects in capillary pressure-saturations relationships for two-phase flow in 3D porous media: implications of micro-heterogeneities

The capillary pressure–saturation (Pc–S) relationships are essential in characterising two-phase flow behaviour in porous media. However, these relationships are not unique and depend on the flow dynamics, i.e., steady state or dynamic, among other factors. It has been shown that empirical models describing two-phase flow processes in porous media may be inadequate to account fully for the physics of flow in dynamic conditions. New capillary pressure relationships have been proposed which include an additional term to account for the dependence of capillary pressure on saturation and time derivative of saturation (∂S/∂t)(∂S/∂t). This parameter is a capillary damping coefficient, also known as dynamic coefficient (τ)(τ), which establishes the speed at which flow equilibrium is reached. The dependence of Pc–SPc–S relationships on ∂S/∂t∂S/∂t is called dynamic effects. In most laboratory experiments for measuring two-phase flow properties, it is implicitly assumed that the sample is homogeneous. However, this is not the case and micro-heterogeneities with their distinct multiphase flow properties may exist within the domain. They affect the dynamics of the multiple fluid phases and saturation distributions in the domain. These issues have been studied individually but the combination of dynamic effects and micro-scale heterogeneities on the Pc–SPc–S relationships has not been quantified accurately, particularly in 3D domains. Consequently, there are significant uncertainties on the reported values of ττ in the literature. In this work, we have carried out a numerical study to investigate how the presence of micro-scale heterogeneities affects the dynamics of dense non-aqueous phase liquid (DNAPL) and water flow in porous domain. The relative significance of the variations in nature, intensity and distribution of micro-scale heterogeneities on dynamic flow conditions are manifested on Pc–SPc–S curves which are quantified in terms of the dynamic coefficient, ττ. There is a complex interplay of various factors (e.g., dynamic flow conditions, distribution and intensity of micro-heterogeneity, pore size distribution, domain size and geometry and media anisotropy) which affects Pc–SPc–S curves. However, our results show that as the intensity of heterogeneity increases the dynamic coefficient at a given saturation increases, provided all other factors remain the same. The effects of domain shapes (cylindrical vs. rectangle), aspect ratios, dimensionality (2D vs. 3D), permeability anisotropy on ττ are also analysed in order to generalise their effects as far as possible. We envisage that our simulations will minimise some of the inconsistencies on the reported data on ττ in the literature

Artificial neural network to determine dynamic effect in capillary pressure relationship for two-phase flow in porous media with micro-heterogeneities

An artificial neural network (ANN) is presented for computing a parameter of dynamic two-phase flow in porous media with water as wetting phase, namely, dynamic coefficient (τ), by considering micro-heterogeneity in porous media as a key parameter. τ quantifies the dependence of time derivative of water saturation on the capillary pressures and indicates the rates at which a two-phase flow system may reach flow equilibrium. Therefore, τ is of importance in the study of dynamic two-phase flow in porous media. An attempt has been made in this work to reduce computational and experimental effort by developing and applying an ANN which can predict the dynamic coefficient through the “learning” from available data. The data employed for testing and training the ANN have been obtained from computational flow physics-based studies. Six input parameters have been used for the training, performance testing and validation of the ANN which include water saturation, intensity of heterogeneity, average permeability depending on this intensity, fluid density ratio, fluid viscosity ratio and temperature. It is found that a 15 neuron, single hidden layer ANN can characterize the relationship between media heterogeneity and dynamic coefficient and it ensures a reliable prediction of the dynamic coefficient as a function of water saturation

Artificial neural network to determine dynamic effect in capillary pressure relationship for two-phase flow in porous media with micro-heterogeneities

Open access articleAn artificial neural network (ANN) is presented for computing a parameter of dynamic two-phase flow in porous media with water as wetting phase, namely, dynamic coefficient (τ), by considering micro-heterogeneity in porous media as a key parameter. τ quantifies the dependence of time derivative of water saturation on the capillary pressures and indicates the rates at which a two-phase flow system may reach flow equilibrium. Therefore, τ is of importance in the study of dynamic two-phase flow in porous media. An attempt has been made in this work to reduce computational and experimental effort by developing and applying an ANN which can predict the dynamic coefficient through the “learning” from available data. The data employed for testing and training the ANN have been obtained from computational flow physics-based studies. Six input parameters have been used for the training, performance testing and validation of the ANN which include water saturation, intensity of heterogeneity, average permeability depending on this intensity, fluid density ratio, fluid viscosity ratio and temperature. It is found that a 15 neuron, single hidden layer ANN can characterize the relationship between media heterogeneity and dynamic coefficient and it ensures a reliable prediction of the dynamic coefficient as a function of water saturation

A numerical study of capillary pressure - saturation relationship for supercritical carbon dioxide (CO2) injection in deep saline aquifer

Carbon capture and sequestration (CCS) is expected to play a major role in reducing greenhouse gas in the atmosphere. It is applied using different methods including geological, oceanic and mineral sequestration. Geological sequestration refers to storing of CO2 in underground geological formations including deep saline aquifers (DSAs). This process induces multiphase fluid flow and solute transport behaviour besides some geochemical reactions between the fluids and minerals in the geological formation. In this work, a series of numerical simulations are carried out to investigate the injection and transport behaviour of supercritical CO2 in DSAs as a two-phase flow in porous media in addition to studying the influence of different parameters such as time scale, temperature, pressure, permeability and geochemical condition on the supercritical CO2 injection in underground domains. In contrast to most works which are focussed on determining mass fraction of CO2, this paper focuses on determining CO2 gas saturation (i.e., volume fraction) at various time scales, temperatures and pressure conditions taking into consideration the effects of porosity/permeability, heterogeneity and capillarity for CO2-water system. A series of numerical simulations is carried out to illustrate how the saturation, capillary pressure and the amount of dissolved CO2 change with the change of injection process, hydrostatic pressure and geothermal gradient. For example, the obtained results are used to correlate how increase in the mean permeability of the geological formation allows greater injectivity and mobility of CO2 which should lead to increase in CO2 dissolution into the resident brine in the subsurface

Artificial Neural Network (ANN) modelling of scale dependent dynamic capillary pressure effects in two-phase flow in porous media

A number of numerical simulations and experimental investigations have reported the impact of specific domain size on the dynamic capillary pressure which is one of the forces that govern two-phase flow in porous media. These investigations are often achieved with time-consuming experiments and/or costly/complex computational methods. In view of this, a computationally efficient and simple alternative platform for the prediction of the domain scale dependence of the dynamic capillary pressure effects, defined in terms of a coefficient named as dynamic coefficient ( ), is developed using artificial neural network (ANN). The input parameters consist of the phase saturation, media permeability, capillary entry pressure, viscosity ratio, density ratio, temperature, pore size distribution index, porosity and domain volume with corresponding output obtained at different domain scales. Good generalization of the model was achieved by acquiring data from independent sources comprising experiments and numerical simulations. Different ANN configurations as well as linear and non-linear multivariate regression models were tested using a number of performance criteria. Findings in this work showed that the ANN structures with two hidden layers perform better than those with single hidden layer. In particular, the ANN configuration with 13 and 15 neurons in the first and second hidden layers, respectively, performed the best. Using this best-performing ANN, effects of increased domain size were predicted for three separate experimental results obtained from literature and our laboratory with different domain scales. Results showed increased magnitude of as the domain size increases for all the independent experimental data considered. This work shows the applicability and techniques of using ANN in the prediction of scale dependence of two-phase flow parameters

Unsaturated slopes behavior under antecedent intermittent rainfall patterns: centrifuge and numerical study

Antecedent rainfall is a prime factor for rainfall-induced landslides on unsaturated slopes. The effects of the intermittent behavior of antecedent rainfall on landslide initiation are uncertain. The work described here had the objective of showing the influence of antecedent intermittent rainfall patterns to predict landslide initiation. Soil slope models prepared from silty sand were tested in centrifuge model testing. At first, soil slopes experienced different antecedent rainfall patterns, namely, uniform gap, decreasing gap, and increasing gap, before they were exposed to continuous rainfall until the failure was initiated. The seepage and deformation behaviors of instrumented slopes were evaluated and back-analyzed with soil–water–air coupled hydromechanical finite element analysis using calibrated material parameters and suitable boundary conditions. The evolution of porewater pressure, displacements, and deviatoric strains was found to provide comparable responses. The analysis of incremental velocity clearly showed that times for landslide initiation follow the order of decreasing gap, uniform gap, and increasing gap antecedent rainfall patterns. The study identified that not only cumulative rainfall, but also antecedent intermittent rainfall patterns have a significant effect as a triggering agent and suggested incorporating it as a parameter for landslide early warning mechanisms

Centrifuge modeling of one-step outflow tests for unsaturated parameter estimations

International audienceCentrifuge modeling of one-step outflow tests were carried out using a 2-m radius geotechnical centrifuge, and the cumulative outflow and transient pore pressure were measured during the tests at multiple gravity levels. Based on the scaling law of centrifuge modeling, the measurements generally showed reasonable agreement with prototype data calculated from forward simulations with input parameters determined from standard laboratory tests. The parameter optimizations were examined for three different combinations of input data sets using the test measurements. Within the gravity level examined in this study up to 40 g, the optimized unsaturated parameters compared well when accurate pore pressure measurements were included along with cumulative outflow as input data. The centrifuge modeling technique with its capability to implement variety of instrumentations under well controlled initial and boundary conditions, shortens testing time and can provide significant information for the parameter estimation procedure

Scale dependency of dynamic relative permeability- satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

Capillary pressure–saturation-relative permeability relationships (Pc–Sw–Kr) are functions of importance in modeling and simulations of the hydrodynamics of two-phase flow in porous media. These relationships are found to be affected by porous medium and fluid properties but the manner in which they are affected is a topic of intense discussion. For example, reported trends in fluid viscosity and boundary conditions effects have been found to be contrary to each other in different studies. In this work, we determine the dependency of dynamic Kr–Sw relationships (averaged data) on domain scale in addition to investigating the effects of fluid viscosity and boundary pressure using silicone oil (i.e. 200 and 1000 cSt) and water as the respective non-wetting and wetting fluids with a view to eliminating some of the uncertainties reported in the literature. Water relative permeability, Krw, was found to increase with increasing wetting phase saturation but decreases with the increase in viscosity ratio. On the other hand, the oil relative permeability, Krnw, was found to increase with the increasing non-wetting phase saturation in addition to the increase in viscosity ratio. Also, it was found that with the increasing boundary pressure Krw decreases while Krnw increases. The influence of scale on relative permeability was slightly indicated in the non-wetting phase with Krnw decreasing as domain size increases. Effect of measurement location on dynamic relative permeability was explored which is rarely found in the literature. Comparison was also made between Kr–Sw relationships obtained under static and dynamic condition. Finally, mobility ratio (m) and dynamic coefficient (s) were plotted as a function of water saturation (Sw), which showed that m decreases as s increases at a given saturation, or vice versa

The behavior characteristics of a reservoir levee subjected to increasing water levels

Centrifugal model testing has been widely used to study the stability of levees. However, there have been a limited number of physical studies on levees where the velocity of increasing water levels was considered. To investigate the behavior characteristics of reservoir levees with different velocities of increasing water levels, centrifugal model tests and seepage-deformation coupled analyses were conducted. Through this study, it was confirmed that increasing water levels at higher velocities induces dramatic increases in the displacement, plastic volumetric strain and risk of hydraulic fracturing occurring in the core of the levee. Hence, real-time monitoring of the displacement and the pore water pres­sure of a levee is important to ensure levee stability