Multiple Fluid Phases Research Articles

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

The capillary pressure–saturation ( P c – 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 ) . This parameter is a capillary damping coefficient, also known as dynamic coefficient ( τ ) , which establishes the speed at which flow equilibrium is reached. The dependence of P c – S relationships on ∂ 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 P c – S relationships has not been quantified accurately, particularly in 3D domains. Consequently, there are significant uncertainties on the reported values of τ 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 P c – S curves which are quantified in terms of the dynamic coefficient, τ . 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 P c – 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 τ 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 τ in the literature.

Liquid immiscibility and its role at the magmatic–hydrothermal transition: a summary of experimental studies

Several types of fluid immiscibility may affect the evolution of volatile-rich magmatic systems at the magmatic–hydrothermal transition. The topology of silicate–salt–H 2O systems implies that three-fluid immiscibility (silicate melt+hydrosaline melt+vapour) should be stable in a broad range of compositions and P– T conditions. The most important factor controlling the immiscibility appears to be the Coulombic properties (electric charges Z and ionic radii r) of the main network-modifying cations and the capacity for immiscibility appears to decrease in the following sequence: Mg>Ca>Sr>Ba>Li>Na>K. Liquid immiscibility is enhanced in peralkaline compositions and in the presence of nonsilicate anions such as F −, Cl −, CO 3 2− and BO 3 3−. In volatile-rich magmatic systems, the H 2O is likely to react with the chloride, fluoride, borate and carbonate species and the chemical effects of high-temperature hydrolysis may be greatly enhanced by phase separation in systems with multiple immiscible fluid phases. Natural granitic magmas can thus exsolve a range of chemically and physically diverse hydrosaline liquids and the role of these fluid phases is likely to be especially significant in pegmatites and Li–F rare-metal granites.

Polyamorphic transition of germanium under pressure

Pressure-induced transformations in the atomic and electronic structure of amorphous germanium $(a\ensuremath{-}\mathrm{Ge})$ have been investigated by using x-ray absorption spectroscopy (XAS) combined with energy-scanning x-ray diffraction. Our data show that an abrupt change in the local structure and in the electron states near the Fermi level occurs in evaporated $a\ensuremath{-}\mathrm{Ge}$ at a pressure of about 8 GPa. The transformation is clearly detectable by a change in the shape and energy shift in the near-edge structures and by an increase of the average first-neighbor distance measured by XAS. The occurrence of this polyamorphic transition is discussed in light of the recent advances in the study of multiple dense fluid phases.

Three-dimensional imaging of multiphase flow in porous media

This paper reports progress in the 3D pore-scale micro-CT imaging of multiple fluid phases during drainage experiments in porous materials. Experiments performed on a sintered monodisperse bead pack and a Berea sandstone sample are described. It is observed that the residual (trapped) wetting phase in the sintered bead pack is present as pendular rings, bridges between adjacent grains and lenses within pore throats. Estimates of the residual wetting phase saturation are in accord with previous experiments and predictions on model bead packs. Relative permeabilities computed directly on the digitised images of the fluid phases are in good agreement with experimentally measured values for Berea sandstone. Two simple numerical methods for estimating two phase drainage saturation distributions directly from images are compared. Both methods give good agreement with the bead pack experiment. The match for Berea sandstone is poorer; differences may be due to variable wettability.

Particle-Based Direct Numerical Simulation of Contaminant Transport and Deposition in Porous Flow

This work describes an approach to porous flow modeling in which the “micro-length scale to macro-length scale” physical descriptions are addressed as Lagrangian, pore-level flow and transport. The flow features of the physical domain are solved by direct numerical simulation (DNS) with a grid-free, hybrid smoothed particle hydrodynamics (SPH) numerical method (Berry, 2002) based on a local Riemann solution. In addition to being able to handle the large deformation, fluid–fluid and fluid–solid interactions within the contorted geometries of intra- and inter-pore-scale modeling, this Riemann–SPH method should be able to simulate other complexities, such as multiple fluid phases and chemical, particulate, and microbial transport with volumetric and surface reactions. A simple model is presented for the transfer of a contaminant from a carrier fluid to solid surfaces and is demonstrated for flow in a simulated porous media.

Particle‐Based Direct Numerical Simulation of Contaminant Transport and Deposition in Porous Flow

This work describes an approach to porous flow modeling in which the “micro‐length scale to macro‐length scale” physical descriptions are addressed as Lagrangian, pore‐level flow and transport. The flow features of the physical domain are solved by direct numerical simulation (DNS) with a grid‐free, hybrid smoothed particle hydrodynamics (SPH) numerical method (Berry, 2002) based on a local Riemann solution. In addition to being able to handle the large deformation, fluid–fluid and fluid–solid interactions within the contorted geometries of intra‐ and inter‐pore‐scale modeling, this Riemann–SPH method should be able to simulate other complexities, such as multiple fluid phases and chemical, particulate, and microbial transport with volumetric and surface reactions. A simple model is presented for the transfer of a contaminant from a carrier fluid to solid surfaces and is demonstrated for flow in a simulated porous media.

A forward model of three‐dimensional fracture orientation and characteristics

A new forward modeling approach to simulate the extension/closure and orientation statistics of evolving fracture networks is presented. The model is fully dynamical and couples fracturing to other processes. Thus, fracturing affects hydrology and, in turn, its development is affected by fluid pressure. In this way, highly pressured fluids can enhance their own migration while low‐pressured ones may become trapped. Fracturing affects the stress tensor through rock volumetric changes and stress affects fracture dynamics. Thus, to predict fracture dynamics, we coevolve a set of fracture variables simultaneously with mass, momentum, and energy conservation equations for the solid and multiple fluid phases. In our computational approach, a representative set of putative fractures of a range of orientations is introduced. The time‐dependent properties of each realized fracture is calculated by using the stress component normal to its fracture plane, pressure, and rock properties. The volumetric strain caused by fracturing allows for a self‐limiting feedback that we account for using a nonlinear incremental stress rheology. The anisotropic fracture permeability is obtained using the predicted fracture network statistics. Thus, the coupling between rock deformation, notably fracturing, and hydrology is accounted for as is that between fracturing and stress. The statistical aspect of fracture network dynamics is described by assuming a probability distribution characterizing variations in rock strength within a nominally uniform lithology. The dependence of fracture density and length on the rate of fluid pressure or stress variation is thereby captured. Embedding the model in a three‐dimensional basin finite element simulator, we illustrate the dynamical nature of the location and character of fracture zones in a sedimentary basin.

Distinguishing melt and fluid subduction components in Umnak Volcanics, Aleutian Arc

Plate processing at convergent margins plays a central role in the distribution of elements among major earth reservoirs. The mechanisms by which this distribution occurs, however, have remained poorly constrained. This paper provides new constraints through a detailed isotope and trace element study of volcanic rocks from Umnak Island, Central Aleutian Arc. The data require the addition of three distinct subduction components to the subarc mantle, which are characterized and quantified: (1) a hydrous fluid from subducted oceanic crust, with mid‐ocean ridge basalt (MORB)‐like isotopic compositions but high Pb/Nd; (2) a hydrous fluid from subducted sediment, with sediment‐like isotopic compositions and an enrichment in fluid‐mobile elements; (3) a sediment partial melt, with sediment‐like isotopic compositions and high Th/Nd and Th/Nb compared to both regional and global sediments. The sediment melt is depleted in fluid‐mobile elements, indicating loss of fluid prior to melting. The high Th/Nb of the sediment melt indicates presence of a Ti‐rich residual phase such as rutile during partial melting. The observation that sediment fluid and sediment melt can be distinguished in different volcanic rocks suggests that they arrive separately at the sites of arc magma formation. This indicates release of multiple discrete fluid and melt phases from sediment to the overlying mantle wedge, which can be viewed as a natural consequence of progressive metamorphism of the subducting slab.

Glass casts of rock fracture surfaces: A new tool for studying flow and transport

A method was developed for fabricating transparent glass casts of fractured rock pairs. These glass casts provide reproduction of surface topography and roughness of natural fractures, optical clarity, and representative wettabilities of mineral surfaces. The glass casts are an improved tool for studying flow and transport in fractures compared to previous approaches. The surface of a clean glass fracture has a contact angle near zero, and more importantly, the surface wettability can be intentionally altered with chemical treatment. Glass casts of rock fracture surfaces may be used for visually and quantitatively studying various physical, chemical, and microbial processes occurring in rock fractures, especially when multiple fluid phases are involved.

Estimation of porous media flow functions

Properties important for describing the flow of multiple fluid phases through porous media are represented as functions of state variables (fluid saturations). A generalized procedure is presented to obtain the most accurate estimates of the multiphase flow functions from the available experimental data. The procedure is demonstrated for several different experimental designs, including a novel experiment in which fluid saturations are measured using nuclear magnetic resonance imaging. A method to evaluate the accuracy of the estimates is presented, and its use for assessing experimental design is demonstrated.

On the Eulerian-Lagrangian formulation of balance equations in porous media

The article presents a general approach to modeling the transport of extensive quantities in the case of flow of multiple multicomponent fluid phases in a deformable porous medium domain under nonisothermal conditions. The models are written in a modified Eulerian–Lagrangian formulation. In this modified formulation, the material derivatives are written in terms of modified velocities. These are the velocities at which the various phase and component variables propagate in the domain, along their respective characteristic curves. It is shown that these velocities depend on the heterogeneity of various solid matrix and fluid properties. The advantage of this formulation, with respect to the usually employed Eulerian one, is that numerical dispersion, associated with the advective fluxes of extensive quantities, are eliminated. The methodology presented in the article shows how the Eulerian–Lagrangian formulation is written in terms of the relatively small number of primary variables of a transport problem. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 505–530, 1997

NMR Imaging of Immiscible Displacements in Porous Media

Summary We introduce a rapid, quantitative nuclear magnetic resonance imaging (NMRI) technique to resolve and measure multiple fluid phases in porous media. Liquids are resolved on the basis of their NMR spin-spin (T2) relaxation times, and their intensities are corrected by attenuation analysis. The phase-resolved and corrected NMRI intensities are normalized to yield fluid saturations. We present the procedure and limitations of this technique. We present in-situ saturation measurements for three immiscible (oil and water) displacements in the same Berea sandstone core. We compared NMRI and effluent recovery methods. T2 of the displacement fluids were sensitive to displacement conditions.

Potentials and Their Role in Transport in Porous Media

The concept of “capillary,” or “matric,” potentials is commonly used in soil physics to describe water movement in unsaturated soils. The rigorous definition of these and other potentials is presented from fundamental thermodynamic principles at the microscopic level and extended to the macroscopic level by averaging over a representative elementary volume. Of special interest is the treatment of adsorptive surface forces and their associated potentials. Porous medium potentials are extended to a domain containing multiple fluid phases and multiple components. A macroscopic motion equation for a fluid phase (Darcy's law) is derived, incorporating the effect of potentials and surface forces. It relates advective fluxes to gradients of macroscopic chemical potentials and temperature. It reduces to the usual form of Darcy's law only when the aqueous phase is sufficiently dilute and temperatures are uniform. Kelvin's law, which relates relative humidity to matric potential, is extended to the case of multiple multicomponent fluid phases in a porous medium domain. The concept of “irreducible” (or “residual”) wetting fluid saturation and its relationship to capillary pressure, surface forces, and the Gibbs chemical potential, are discussed. Common methods for determining the matric potential are reexamined in light of this work.

Solubility of Methane in Benzene, Naphthalene, Phenanthrene, and Pyrene at Temperatures from 323 to 433 K and Pressures to 11.3 MPa

Global energy concerns have prompted increasing efforts to develop processes to produce alternative forms of liquid fuels, such as those derived from coal. In such processes, multiple fluid phases are present in essentially all stages of feed preparation, conversion reactions, and product separation. The effective design and operation of such conversion processes require accurate knowledge of the phase behavior of the fluid mixtures encountered. Studies of the solubilities of light gases in heavy hydrocarbons are also of interest in the processing of petroleum products, enhanced oil recovery, and supercritical fluid processes. Solubility data are presented for methane in each of four aromatic hydrocarbons, including benzene, naphthalene, phenanthrene, and pyrene. The measurements cover temperatures from 323 to 433 K at pressures to 11.3 MPa. The data for methane in benzene are in reasonable agreement with the earlier measurements of Sage, while data for phenanthrene are in excellent agreement with those of Malone. The solubilities are described with a root-mean-squared error of 0.001 in mole fraction by the Soave-Redlich-Kwong and Peng-Robinson equations of state when one interaction parameter is used over the complete temperature range for each binary system. Henry's constant and partial molar volumes at infinite dilution were also calculated onmore » the basis of the Krichevsky-Kasarnovsky equation.« less

23Na microimaging of water phase in porous limestone

23Na microimaging has been investigated as a method for discriminating multiple fluid phases in porous media. Useful23 Na images from NaCl saturated brine in limestone were obtained in a few-minutes. Good images requires several hours.

Multinuclear NMR Imaging of Fluid Phases in Berea Sandstone

Multinuclear NMR of 7Li, 19F, and 1H has been investigated as a method for discriminating multiple fluid phases in porous rock. Good 7Li NMR images from LiCl brine in saturated Berea sandstone were obtained within a few hours at 1 × 1 × 5 mm 3 resolution using a low-TE, 3D volume imaging sequence. At 4.7 T, the 7Li T 1 was 750 ms, and T 2 was 10 ms. High-quality 19F and 1H images of a model fluorinated injectant (trifluorotoluene) in Berea were obtained at 0.4 × 0.4 × 3 mm 3 resolution in a few hours. Fluorine-19 imaging was found to be easier than 1H imaging due to the narrower 19F resonance and comparable T 1 and T 2 in Berea sandstone. Lithium-7 and 19F imaging offer alternatives for discriminating aqueous and organic phases unambiguously in flooded oil cores, especially where 1H signals for the two phases are unresolved.

Use of a Massively Parallel SIMD Computer for Reservoir Simulation

Summary Massively parallel single-instruction, multiple-data (SIMD) computers have shown much promise in solving numerically intensive problems ranging from molecular modeling to computational fluid dynamics. Much of the research on the use of parallel computing for reservoir simulation, however, has been limited to coarse-grain, shared-memory computers or medium-grain hypercubes. We report here on research performed on a massively parallel SIMD computer with 65, 536 processors. This work addresses issues in machine architecture, programming environment, and formulation of a reservoir simulator on SIMD computers. Toward this end, a three-phase, 3D, implicit-pressure, explicit-saturation (IMPES) compositional simulator was developed in FORTRAN 90. Problems associated with reservoir simulation on SIMD computers (such as an appropriate data structure for the SIMD architecture, treatment of multiple fluid phases, data communication, and the matrix solution) are addressed in this paper. In addition, table lookup poses a unique problem for SIMD computers because storage of large tables on each processor is impractical, as is the use of the front-end computer to perform this function. The problem is overcome through a novel use of local memory access. We found that massively parallel computers can be used to run very large reservoir models and that the cost of data transfer between processors need not be prohibitive. Reservoir models with two hydrocarbon components and up to 2, 097, 152 gridblocks were run successfully with this simulator. Computational speeds on the order of 1 GFLOP's (1 giga floating point operations) were achieved for the generation of the Jacobian matrix and the matrix solution with 65, 536 processors.

X-Ray CT and NMR Imaging of Rocks

Introduction In little more than a decade, X-ray computerized tomography (CT) and nuclear magnetic resonance (NMR) imaging have become the premier modalities of medical radiology. Both of these imaging techniques also promise to be useful tools in petrophysics and reservoir engineering, because CT and NMR can nondestructively image a host of physical and chemical properties of porous rocks and multiple fluid phases contained within their pores. The images are taken within seconds to minutes, at reservoir temperatures and pressures, with spatial resolution on the millimeter and submillimeter level. The physical properties imaged by the two techniques are complementary. CT images bulk density and effective atomic number. NMR images the nuclide concentration, Mo, of a variety of nuclei ( H, 19-F, 23-Na, 31-P, etc.), their longitudinal and transverse relaxation-time curves (t1 and t2 ), and their chemical shift spectra. In rocks, CT images both rock matrix and pore fluids, while NMR images only mobile fluids and the interactions of these mobile fluids with the confining surfaces of the pores. Principles CT uses an X-ray source that rotates around the sample to obtain one-dimensional projections of X-ray attenuation at different angles. From these projections, a crosssectional slice through the sample is reconstructed by computer. Finally. a three-dimensional image is reconstructed from sequential cross-sectional slices taken as the sample is moved through the scanner. To obtain both density and effective atomic number, CT images are taken at two X-ray energies. One energy is high enough for the X-rays to be predominantly Compton-scattered and one is low enough for them to be mostly photoelectrically absorbed. A combination of the two images in the computer. on a pixel-by-pixel basis, generates separate images of bulk density and effective atomic number. In NMR imaging, the sample is placed inside an intense, homogeneous, magnetic field, one preferably generated by a superconducting magnet. Radio frequency (RF) coils apply RF magnetic fields at the precise Larmor frequency to cause the particular nuclear species to precess. The RF coils then detect the signals generated by the precessing nuclei. Spatial localization within the sample is obtained by x. y, and z magnetic-field gradient coils that cause nuclei in different parts of the sample to precess at slightly different frequencies. The resulting frequency-modulated signal is Fourier-transformed to obtain the spatial distribution of nuclear-spin density. Unlike CT, an image is obtained of the entire sample volume within the RF coil. JPT P. 257^