Capillary Pressure-saturation Relationship Research Articles

Pore network modeling of drainage process in patterned porous media: A quasi-static study

This work represents a preliminary investigation on the role of wettability conditions on the flow of a two-phase system in porous media. Since such effects have been lumped implicitly in relative permeability–saturation and capillary pressure–saturation relationships, it is quite challenging to isolate its effects explicitly in real porous media applications. However, within the framework of pore network models, it is easy to highlight the effects of wettability conditions on the transport of two-phase systems. We employ quasi-static investigation in which the system undergoes slow movement based on slight increment of the imposed pressure. Several numerical experiments of the drainage process are conducted to displace a wetting fluid with a non-wetting one. In all these experiments the network is assigned different scenarios of various wettability patterns. The aim is to show that the drainage process is very much affected by the imposed pattern of wettability. The wettability conditions are imposed by assigning the value of contact angle to each pore throat according to predefined patterns.

Laboratory study of geological carbon sequestration using surrogate fluids: Dielectric measurement and scaling of capillary pressure–saturation relationships

Multiphase flow models are powerful tools to understand and predict the flow and trapping of supercritical-CO2 (scCO2) in deep saline geologic formations. The constitutive relationship between capillary pressure (Pc) and saturation (Sw) is the essential input parameter into these multiphase models. By selecting surrogate fluids that match the density and viscosity ratios between scCO2 and brine, the behavior of scCO2 and brine may be reproduced under ambient conditions, making it possible to overcome the difficulty of conducting laboratory-scale experiments with scCO2. This paper presents the Pc–Sw relationship for the surrogate fluids of scCO2 and brine measured using the dielectric sensor method. To explore the necessity and applicability of measuring the entire Pc–Sw relationship, we compared the dielectric sensor results with those from two scaling methods: classical Leverett scaling and a novel entry pressure scaling method. Additionally, the obtained surrogate fluid Pc–Sw values were compared with experimental data of scCO2 and brine under high pressure. The dielectric sensor method successfully obtained the Pc–Sw relationship and produced more accurate measurements of residual and irreducible saturations compared to scaling methods.

Modeling air–water interface in disordered fibrous media with heterogeneous wettabilities

Considering the balance of mechanical forces across a meniscus anchored to two circular objects, we developed a CPU-friendly semi-analytical algorithm for tracking the instantaneous shape and position of the air–water interface inside microstructures that resemble a collection of disordered parallel cylinders, e.g., a bundle of fibers in a fiber-reinforced composite or microfabricated posts in a microfluidic system. In the context of fluid transport in fibrous media, in particular, the methodology presented in this paper provides a means for producing a relationship between capillary pressure and fluid saturation in media with heterogeneous wettabilities – often needed to predict the rate of fluid transport. In addition, we developed a conversion formulation that allows a capillary pressure–saturation relationship obtained for one combination of contact angles to be used to construct such a relationship for media with different combinations of contact angles, eliminating the need for additional simulations.

Hydraulic properties of partially saturated rock fractures subjected to mechanical loading

This study presents a methodology for estimating the unsaturated hydraulic properties of rock fractures under deformation conditions. The surface morphology of an artificial granite rock fracture was examined using a high-resolution three-dimensional laser scanner, and the aperture distribution of the fracture was found to follow a Gaussian distribution. By virtue of the aperture distribution function and applying the Young–Laplace equation to local apertures, a novel model was presented to predict the capillary pressure–saturation relationship and the relative hydraulic conductivity of rough-walled rock fractures subjected to normal and shear loading. The proposed model was partially validated against existing laboratory data on the unsaturated hydraulic properties of rock fractures, and can be readily applied to various engineering practices such as transport phenomena in fractures, landslide mitigation, or underground oil storage.

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.

On front solutions of the saturation equation of two-phase flow in porous media

We investigate the existence of “front” solutions of the saturation equation of two-phase flow in porous media. By front solution we mean a monotonic solution connecting two different saturations. The Brooks–Corey and the van Genuchten models are used to describe the relative-permeability – and capillary pressure–saturation relationships. We show that two classes of front solutions exist: self-similar front solutions and travelling-wave front solutions. Self-similar front solutions exist only for horizontal displacements of fluids (without gravity). However, travelling-wave front solutions exist for both horizontal and vertical (including gravity) displacements. The stability of front solutions is confirmed numerically.

Capillary Pressure Hysteresis Behavior of Three Sandstones Measured with a Multistep Outflow–Inflow Apparatus

Many phenomena of practical importance, such as water movement in soils and the recovery of oil and gas from subterranean reservoirs, involve capillary pressure hysteresis in natural porous materials. Experimental capillary pressure–saturation relationships provide important information on pore systems and multiphase displacements. Data, at various levels of detail, are available for strongly wetted soils and sphere packs, but very few detailed hysteresis data have been reported for consolidated porous media, such as rocks, at equivalent wetting conditions. A new porous plate apparatus and procedure have been used to give extensive capillary pressure hysteresis relationships within a few days, a significant improvement on previous methods. Air–brine data are presented for three types of consolidated sandstones. Rate of outflow and inflow were recorded for each data point. Imbibition scanning curves have been obtained starting from the primary and secondary drainage curves. Drainage scanning curves that branch from imbibition curves starting at different levels of initial water saturation have also been measured. The data met a stringent test of quality in that all hysteresis loops exhibited closure as predicted by theory and as usually reported for unconsolidated media. The overall form of the hysteresis curves is related to fluid distributions, percolation effects, and trapping. Initial wetting phase (WP) saturation versus residual nonwetting phase (NWP) relationships provide detailed information on the extent of trapping for imbibition starting at different initial saturations, a parameter of particular interest in carbon dioxide sequestration. Features of the dynamic outflow–inflow data provided indication of the differences in flow rates for drainage and imbibition.

A modeling approach to represent hysteresis in capillary pressure-saturation relationship based on fluid connectivity in void space

[1] This study presents a new model for description of hysteretic constitutive relationships between capillary pressure and saturation under capillary-dominated multiphase flow conditions in porous media. Hysteretic relationships are required for accurate prediction of spatial and temporal distribution of multiphase fluids in response to successively occurring drainage and imbibition events in porous media. In addition to contact angle effects, connectivity of the void space in the porous medium plays a central role for the macroscopic manifestation of hysteresis behavior and capillary entrapment of wetting and nonwetting fluids. The hysteretic constitutive model developed in this work uses void-size distribution and a measure of connectivity for void space to compute the hysteretic curves and to predict entrapped fluid-phase saturations. Two functions, the drainage connectivity function and the wetting connectivity function, are introduced to characterize connectivity of fluids in void space during drainage and wetting processes. These functions can be estimated through pore-scale simulations in computer-generated porous media or from traditional experimental measurements of primary drainage and main wetting curves. The hysteresis model results are verified by comparing the model predicted scanning curves with 3-D pore-scale simulations as well as with actual data sets obtained from column experiments found in the literature.

A two-dimensional model of the pressing section of a paper machine including dynamic capillary effects

Paper production is a problem with significant importance for society; it is also a challenging topic for scientific investigation. This study is concerned with the simulation of the pressing section of a paper machine. A two-dimensional model is developed to account for the water flow within the pressing zone. A Richards-type equation is used to describe the flow in the unsaturated zone. The dynamic capillary pressure–saturation relation is adopted for the paper production process. The mathematical model accounts for the coexistence of saturated and unsaturated zones in a multilayer computational domain. The discretization is performed by the MPFA-O method. Numerical experiments are carried out for parameters that are typical of the production process. The static and dynamic capillary pressure–saturation relations are tested to evaluate the influence of the dynamic capillary effect.

Experimental investigation of hysteretic dynamic effect in capillary pressure–saturation relationship for two‐phase flow in porous media

Well‐defined laboratory experiments have been carried out to investigate hysteretic dynamic effect in capillary pressure–saturation relationships for two‐phase flow in homogeneous and heterogeneous (layered) porous media. Conceptually, the dependence of the capillary pressure curves on the rate of change of saturation (dSw/dt) is defined as the dynamic effect in capillary pressure relationship, which is indicated by a dynamic coefficient, τ (Pa s) and it determines the rate at which two‐phase flow equilibrium is reached, i.e., dSw/dt = 0 where Sw and t are the water saturation and time, respectively. The dependences of τ on various fluid and porous materials properties have been studied in the context of drainage; but, there is limited study for imbibition and the hysteresis of τ−Sw relationships. As such, the emphasis in this article is on reporting τ−Sw curves for imbibition while also demonstrating the hysteresis in the τ−Sw relationships by comparing τ−Sw curves for drainage (previously reported) and imbibition (this study) in carefully designed laboratory experiments. Homogeneous sand samples composed of either fine (small particle size and lower permeability) or coarse (larger particle size and higher permeability) sand have been used for these experiments. Furthermore, a layered domain made of a find sand layer sandwiched between two coarse sand layers is used as a model of heterogeneous domain. The results of the study confirm that the τ−Sw relationships are hysteretic in nature and, as such, the speed to flow equilibrium should vary depending on whether drainage or imbibition takes place. At a particular water saturation, the magnitudes of the dynamic coefficient (τ) are found to be generally higher for imbibition, which imply that the speed to flow equilibrium at the same saturation will be slower for imbibition. © 2013 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 59: 3958–3974, 2013

Forward Prediction of Height‐Averaged Capillary Pressure–Saturation Parameters Using the BC‐vG Upscaler

There is ongoing interest in approaches for upscaling point (e.g., pixel or voxel scale) measurements of soil hydraulic properties to predict column‐scale behavior in the laboratory, or even field‐scale processes. We have developed the BC‐vG Upscaler for estimating the height‐averaged capillary pressure–saturation relationship, , for a given porous medium based on equations used in the TrueCell program. Whereas TrueCell inversely estimates point Brooks and Corey (BC) equation parameters from data, the BC‐vG Upscaler uses point BC parameters as inputs for the forward prediction of height‐averaged van Genuchten (vG) parameters. The BC‐vG Upscaler was verified using previously published, independent point and height‐averaged capillary pressure–saturation data sets for silica sand. The capability of the BC‐vG Upscaler was demonstrated in three separate applications. The first showed how the program can be used to predict height‐averaged vG equation parameters using three different relationships between n and m. The second explored the effects of varying column height on the predicted vG parameters for a hypothetical porous medium. The third used the BC‐vG Upscaler to predict height‐averaged vG parameters for a 50‐cm‐tall column based on previously published point BC parameters for a wide range of porous media. The BC‐vG Upscaler is available free upon request. It should prove useful for converting point BC parameters into height‐averaged vG parameters suitable for inclusion in numerical models for simulating variably saturated flow. The program could also be used to develop new scale‐dependent relationships between the parameters of the BC and vG equations.

Capillary Heterogeneity in Sandstone Rocks During CO2/Water Core-flooding Experiments

We have successfully applied a novel experimental technique to measure drainage capillary pressure curves in reservoir rocks with representative reservoir fluids at high temperatures and pressures. The method consists of carrying out 100% CO2 flooding experiments at increasingly higher flow rates on a core that is initially saturated with water and requires that the wetting-phase pressure is continuous across the outlet face of the sample. Experiments have been carried out on a Berea Sandstone core at 25 and 50°C and at 9MPa pore pressure, while keeping the confining pressure at 12MPa. Measurements are in good agreement with data from mercury intrusion porosimetry. The technique possesses a great potential of applicability due to the following reasons: (a) it can be applied in conjunction with steady-state relative permeability measurements, as it shares a very similar experimental configuration; (b) it is faster than traditional (porous-plate) techniques used for measuring capillary pressure on rock cores with reservoir fluids; (c) by comparison with results from mercury porosimetry, it allows for the estimation of the interfacial and wetting properties of the CO2/water system, the latter being unknown for most rocks; (d) by combination with X-ray CT scanning, the method allows for the observation of capillary pressure–saturation relationships on mm-scale subsets of the rock core. The latter are of high relevance as they directly and non- destructively measure capillary pressure curve heterogeneity in sandstone rocks.

Experimental characterization of the water transport properties of PEM fuel cells diffusion media

A full experimental characterization of the liquid water transport properties of Toray TGP-090 paper is carried out in this work. Porosity, capillary pressure curves (capillary pressure–saturation relationships), absolute permeability, and relative permeability are obtained via experimental procedures. Porosity was determined using two methods, both aimed to obtain the solid volume of the network of fibers comprising the carbon paper. Capillary pressure curves were obtained using a gas displacement porosimeter where liquid water is injected using a syringe pump and the capillary pressure is recorded using a differential pressure transducer. Absolute and relative permeability were also measured with an apparatus designed at Virginia Tech. Absolute permeability was calculated at different flow rates using nitrogen. On the other hand, relative permeability was a more complicated task to carry out giving the complexity (two-phase flow condition) of this property. All of the water transport properties of Toray TGP-090 were studied under the effects of wet-proofing (PTFE treatment) and compression. Some observations were that wet-proofing reduces the porosity of the raw material, increases the hydrophobicity (Pc–S curves), and reduces the permeability of the material. Similar effects were observed for compression, where compressed material exhibited trends similar to those of wet-proofing effects. The results presented here will allow a more accurate modeling of PEMFCs, providing an experimentally verified alternative to the assumptions frequently employed.

Uniqueness of Specific Interfacial Area–Capillary Pressure–Saturation Relationship Under Non-Equilibrium Conditions in Two-Phase Porous Media Flow

The capillary pressure–saturation (P c–S w) relationship is one of the central constitutive relationships used in two-phase flow simulations. There are two major concerns regarding this relation. These concerns are partially studied in a hypothetical porous medium using a dynamic pore-network model called DYPOSIT, which has been employed and extended for this study: (a) P c–S w relationship is measured empirically under equilibrium conditions. It is then used in Darcy-based simulations for all dynamic conditions. This is only valid if there is a guarantee that this relationship is unique for a given flow process (drainage or imbibition) independent of dynamic conditions; (b) It is also known that P c–S w relationship is flow process dependent. Depending on drainage and imbibition, different curves can be achieved, which are referred to as “hysteresis”. A thermodynamically derived theory (Hassanizadeh and Gray, Water Resour Res 29: 3389–3904, 1993a) suggests that, by introducing a new state variable, called the specific interfacial area (a nw, defined as the ratio of fluid–fluid interfacial area to the total volume of the domain), it is possible to define a unique relation between capillary pressure, saturation, and interfacial area. This study investigates these two aspects of capillary pressure–saturation relationship using a dynamic pore-network model. The simulation results imply that P c–S w relation not only depends on flow process (drainage and imbibition) but also on dynamic conditions for a given flow process. Moreover, this study attempts to obtain the first preliminary insights into the global functionality of capillary pressure–saturation–interfacial area relationship under equilibrium and non-equilibrium conditions and the uniqueness of P c–S w–a nw relationship.

On Mathematical Modeling and Simulation of the Pressing Section of a Paper Machine Including Dynamic Capillary Effects: One-Dimensional Model

This study presents the dynamic capillary pressure model (Hassanizadeh and Gray, Adv Water Resour 13:169–186, 1990; Water Resour Res 29:3389–3405, 1993) adapted for the needs of paper manufacturing process simulations. The dynamic capillary pressure–saturation relation is included in a one-dimensional simulation model for the pressing section of a paper machine. The one-dimensional model is derived from a two-dimensional model by averaging with respect to the vertical direction. Then, the model is discretized by the finite volume method and solved by Newton’s method. The numerical experiments are carried out for parameters typical for the paper layer. The dynamic capillary pressure–saturation relation shows significant influence on the distribution of water pressure. The behavior of the solution agrees with laboratory experiments (Beck, Fluid pressure in a press nip: measurements and conclusions, 1983).

Measurement of Capillary Pressure–Saturation Relationships Under Defined Compression Levels for Gas Diffusion Media of PEM Fuel Cells

Measurements of capillary pressure–saturation relationships under defined levels of compression for gas diffusion layers (GDL) of polymer electrolyte membrane fuel cells as thin, mixed-wettable porous media have been carried out in a newly constructed device. This article lines out the construction principle of the cell and the preconditioning procedure of the sample to measure the capillary pressure–saturation relationships under well-defined conditions and loads of compression. Three commercial GDLs (Freudenberg H2315T10A, H2315T10AC1, and SGL Carbon BA24) have been examined and a compression-depending hysteresis of the capillary pressure–saturation relationship has been measured and identified.

Dynamic effects on capillary pressure–Saturation relationships for two‐phase porous flow: Implications of temperature

AbstractWork carried out in the last decade or so suggests that the simulators for multiphase flow in porous media should include an additional term, namely a dynamic coefficient, as a measure of the dynamic effect associated with capillary pressure. In this work, we examine the dependence of the dynamic coefficient on temperature by carrying out quasi‐static and dynamic flow simulations for an immiscible perchloroethylene–water system. Simulations have been carried out using a two‐phase porous media flow simulator for a range of temperatures between 20 and 80°C. Simulation domains represent 3‐D cylindrical setups used by the authors for laboratory‐scale investigations of dynamic effects in two‐phase flow. Results are presented for two different porous domains, namely the coarse and fine sands, which are then interpreted by examining the correlations between dynamic coefficient(s) and temperature, time period(s) required for attaining irreducible water saturation, and the dynamic aqueous/nonaqueous phase saturation and capillary pressure plots. The simulations presented here maintain continuity from our previous work and address the uncertainties associated with the dependency of dynamic coefficient(s) on temperature, thereby complementing the existing database for the characterization of dynamic coefficients and subsequently enabling the users to carry out computationally economical and reliable modeling studies. © 2012 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 58: 1951–1965, 2012

Special Section on Landslides: Setting the Scene and Outline of Contributing Studies

The guest editors introduce the special section on landslides, including each of the contributions and implications for future research. Advances in our understanding will involve multidisciplinary research and applications with the goal of preventing damage to infrastructure and the environment.

Capillary Pressure Curve for Liquid Menisci in a Cubic Assembly of Spherical Particles Below Irreducible Saturation

The capillary pressure–saturation relationship, Pc(Sw), is an essential element in modeling two-phase flow in porous media (PM). In most practical cases of interest, this relationship, for a given PM, is obtained experimentally, due to the irregular shape of the void space. We present the Pc(Sw) curve obtained by basic considerations, albeit for a particular class of regular PM. We analyze the characteristics of the various segments of the capillary pressure curve. The main features are the behavior of the Pc(Sw) curve as the wetting-fluid saturation approaches zero, and as this saturation is increased beyond a certain critical value. We show that under certain conditions (contact angle, distance between spheres, and saturation), the value of the capillary pressure may change sign.

From Local Measurements to an Upscaled Capillary Pressure–Saturation Curve

Capillary pressure–saturation relationship plays an important role in the description of two-phase flow in porous media. Commonly, this relationship is determined in laboratory on a sample of few centimeters and it is then used in numerical modeling of two-phase in domain sizes of hundreds to thousands of meters. The correctness of such approach has been hardly ever questioned. In this study, an upscaled capillary pressure is determined from local pressure and saturation measurements employing a rigorous averaging procedure. Drainage and imbibition experiments were performed in a column of 21 cm long. The experiments were performed as a series of equilibrium steps; each time we changed the boundary pressures incrementally and then waited until an equilibrium distribution of fluids was reached. Phase pressures and saturation inside the column as well as external pressure and average saturation were recorded at each equilibrium step. Various averaging operators were considered: simple average, simple phase-average, intrinsic phase-average, and centroid-corrected average. Also, a potential-based average operator was introduced as reference curve to establish which operator gives the correct average pressure. Large differences were found for the average non-wetting phase pressure using different operators during primary drainage. However, when both phases were present throughout the domain (e.g. during main drainage) the differences between pressures obtained by various average operators were negligible. In such cases, the centroids of the two phases and the centroid of the averaging domain were close to each other. The comparison between averaged capillary pressure–saturation curves has shown that the centroid-corrected averaging operator is the most appropriate operator.