Pore Space Geometry Research Articles

Pore geometry and transport properties of Fontainebleau sandstone

Quantitative characterization of pore geometry using laser scanning confocal microscopy and measurements of permeability, resistivity, and pore volume were performed on four samples of Fontainebleau sandstone with effective porosities ranging from 4% to 20% at confining pressures up to 70 MPa. Observed bench permeabilities and hydraulic radii for samples with porosities of 10%, 16%, and 20% agree well with those predicted using the equivalent channel model of Walsh and Brace [1]; however, there is more than an order of magnitude over estimation for a sample with a porosity of 4%. The relative pressure dependence of permeability and formation factor for this sample differs from that of the three more porous samples. We interpret the behavior to result from fundamental differences in the topology and geometry of pore space at low porosity. Comparison of our data with results in the literature for rocks synthesized by hot isostatic pressing suggests that the mechanism by which porosity reduction occurs strongly affects the pore geometry and transport properties of sedimentary rocks.

Magnetization evolution in connected pore systems. II. Pulsed-field-gradient NMR and pore-space geometry.

The time evolution of nuclear magnetization in a porous medium, e.g., proton dipole moments on water saturating a sandstone, can be described in terms of relaxation-operator eigenstates (modes of the magnetization). Decay of the magnetization in a pulsed-field-gradient NMR (PFGNMR) or stimulated-echo experiment is described by the intermediate scattering function (ISF). The ISF is a sensitive probe of the spatial structure of the modes of the magnetization. We have studied the time evolution of the magnetization and the behavior of the ISF by solving the relaxation-operator problem. A suitable set of PFGNMR measurements provides important information about the pore-space geometry, for example, the gradient-independent part of the spectrum of decay rates is contributed by large or isolated pores.

Magnetization evolution in connected pore systems. III. Fluid flow.

The time evolution of the magnetization in a fluid-filled porous medium is studied for the case in which the pore fluid carries a steady current. Both the mean lifetime and the spectrum of relaxation rates are calculated with effective-medium theory. The structure of the spectrum of relaxation rates is found to be very sensitive to the fluid flow. Thus the spectrum of relaxation rates is a valuable detector of fluid flow or of features of the pore-space geometry when the flow is known.

Magnetization isotherms and pore-space geometry.

A model of the magnetization response of a $^{3}\mathrm{\ensuremath{-}}^{4}$He mixture in a porous medium is studied as the $^{4}\mathrm{He}$ is carried through a capillary-condensation hysteresis loop. This response appears as a magnetization hysteresis loop that has important qualitative and quantitative features related to the geometry of the pore space. It is suggested that an experimental exploration of the magnetization isotherm can provide valuable information about pore-space geometry.

Geometry, dielectric response and scaling in porous media

Local porosity distributions and local percolation probabilities have been proposed as well defined and experimentally observable geometric characteristics of general porous media. Based on these concepts the dielectric response is analysed using the effective medium approximation and percolation scaling theory. The theoretical origin of static and dynamic scaling laws for the dielectric dispersion and enhancement including Archie's law in the low porosity limit are elucidated. These well known experimental facts are unified within a theoretical framework based on a quantitative characterization of the pore space geometry. In the high porosity limit the zero frequency real dielectric constant is predicted to diverge as ε'(0) ∝ (1 − ϕ)-m' where ϕ denotes porosity and m' is analogous to the cementation exponent.

Wettability effects on oil-water-configurations in porous media: A nuclear magnetic resonance relaxation study

1 H spin-lattice relaxation and other physical properties are compared to study the oil-water-surface interplay in suitably chosen and prepared natural porous media of different wettability. Whereas the water-oil arrangement is well established for both strongly water wet and strongly oil wet porous media, the problem is still open for intermediate wettability surfaces. Relaxation behavior reflects the pore space geometry and shows wettability effects on sweeping efficiency and on immiscible liquid arrangement in well-defined equilibrium situations. A simple picture at the pore-length scale is verified for strongly water wet samples, whereas a more complex picture arises for intermediate wettability samples.

Effects of compaction on the pore space geometry in sandy soils

The effects of compaction on the structure of sandy soils was analysed from a description of changes in pore space geometry in the field or in the laboratory. The results indicated that pores corresponding to the fabric of the elementary particles were modified by compaction. Only one passing over of tractor wheels induced a change in the fabric of elementary particles. The structure of the plough pan was characterized by discontinuity of the remaining large pores which indicated that compaction occurred for suctions > 1 kPa. Moreover, the fabric of elementary particles in the plough pan appeared to be very packed.

Abstract: Effects of packing on the pore space geometry of sandy soils. A contribution to the study of compaction mechanisms

Abstract: Effects of packing on the pore space geometry of sandy soils. A contribution to the study of compaction mechanisms

Laboratory experimental study of soil crusting: Relation between aggregate breakdown mechanisms and crust stucture

Crusts formation on cores of air-dry and prewetted aggregates was studied, using a laboratory rainfall simulator. Samples were taken out during the experiment, in order to study changes in water content and aggregates size distribution inside the crust and under the crust. Pore space geometry of the crusts is described using light optical microscopy and mercury porosimetry. In the case of air-dry aggregates, aggregates become micro-cracked. Macropores at the surface are quickly closed and ponding occurs rapidly. With prewetted aggregates, microcracking does not occur, and only a very slow abrasion of the aggregates is observed. Porosity remains high and no ponding excess occurs. The discussion of these results shows that it is the way of the wetting and the initial water content which determine the breakdown mechanism, and therefore, the behaviour of the aggregates submitted to rainfall.

Modelling pore-scale displacement processes at near-critical conditions

The importance of critical phenomena in EOR is reviewed and the merits and limitations of conventional experiments briefly discussed. In order to develop an adequate description of the significant flow phenomena involved in field-scale displacement processes the pore-scale mechanisms underlying the macroscopic behaviour must be identified and understood. Therefore, an approach which complements conventional experiments and provides the necessary insights into the pore-scale phenomenology is required: details of a new physical modelling approach are presented. The effects of near-critical behaviour (i.e. low interfacial tension and small density contrasts) on displacement processes are modelled by the critical solution behaviour of partially miscible binary liquids. In particular, the interfacial tension can be varied precisely, and over a wide range, by controlling the temperature deviation from the critical solution temperature. Micromodels, transparent networks etched in glass, replace cores as realisations of porous media. They permit great flexibility and control over the pore-space morphoogy, allow fluid distributions to be observed, and provide the best means of assessing the influence of the pore-space geometry and topology on the processes of interest. The key role of interfacial phenomena in determining the flow characteristics is emphasised. Experimental observations are presented which illustrate pore-scale behaviour when the interfacial tension is very low. In particular, the importance of gravity is highlighted; effects are seen even on the pore scale where the influence of gravity is usually ignored. Finally, the implications of these observations for EOR are discussed and further topics for study suggested, including the development of this versatile modelling approach.

Percolation theory of vapor adsorption—desorption processes in porous materials

A percolation model for adsorption—desorption phenomena in porous solids is developed. The model relates the sorption isotherm characteristics and the hysteresis observed to the pore space geometry (size distribution) and topology (connectivity) and the physical parameters of the process. Kelvin's equation is taken to represent the process at the local (pore) level, while the porous solid is represented by a network of pores. The statistics of the pores occupied by vapor during adsorption or desorption are determined from Kelvin's equation and the network properties. In contrast to adsorption, desorption processes (both primary and secondary) are strongly dependent on accessibility properties of the network. Exact analytical expressions are derived for the accessibility functions when the porous medium is represented by a Bethe lattice. These results generalize previous work in ordinary percolation. Alternatively, an algorithm is developed for regular lattices, and numerical results from Monte Carlo simulations in square lattices are also presented. The model is shown to predict major characteristics of both primary and secondary sorption isotherms and suggests methods for thei rinterpretation. This study is motivated and extends previous work by G. Mason ( Proc. R. Soc. London A 390, 47 (1983)).

Hydraulic Conductivity of a Sandy Soil at Low Water Content After Compaction by Various Methods

To investigate the degree to which compaction of a sandy soil influences its unsaturated hydraulic conductivity K, samples of Oakley sand (now in the Delhi series; mixed, thermic, Typic Xeropsamments) were packed to various densities and K was measured by the steady-state centrifuge method. The air-dry, machine packing was followed by centrifugal compression with the soil wet to about one-third saturation. Variations in (i) the impact frequency and (ii) the impact force during packing, and (iii) the amount of centrifugal force applied after packing, produced a range of porosity from 0.333 to 0.380. With volumetric water content θ between 0.06 and 0.12, K values were between 7 × 10−11 and 2 × 10−8 m/s. Comparisons of K at a single θ value for samples differing in porosity by about 3% showed as much as fivefold variation for samples prepared by different packing procedures, while there generally was negligible variation (within experimental error of 8%) where the porosity difference resulted from a difference in centrifugal force. Analysis involving capillary-theory models suggests that the differences in K can be related to differences in pore-space geometry inferred from water retention curves measured for the various samples.

The microgeometry and transport properties of sedimentary rock

Abstract This monograph describes recent progress in modelling the transport properties of sedimentary rock. Statistical descriptions are applied to the pore-space geometry and to the transport processes involving pore fluids. Fractals are used to quantify the pore geometry at length scales shorter than grain size. Percolation theory is applied to fluid flow. The permeability can be expressed in terms of a single effective pore diameter measured from mercury injection capillary pressure. This permeability relation is valid for essentially all porous rock and for a broad class of porous media. Mercury injection provides a powerful caliper of the geometry of a percolation cluster in a pore-space and supplies new information about pore space correlations and dynamics of fluid displacements. The statistical description of fluid transport in porous media has analogues in disordered electronic and magnetic materials. Future work may make substantial use of such analogues to solve more complex problems of direct...

Percolation processes and porous media: I. Geometrical and topological model of porous media using a three-dimensional joint pore size distribution

Three-dimensional information on the pore space in porous media, generated either in a continuous or in a discrete manner, was transformed into a geometrical-topological network system of intersecting ellipsoids, using random processes for the investigation of pore size and the reconstruction of the pore structure. It was assumed that: (i) pore space and pore size can be described by an orthogonal three-dimensional system; (ii) pore unit shape can be described by an ellipsoid; (iii) the reconstruction of the medium by randomly packing ellipsoids in space and allowing them to intersect will preserve the topological-geometrical properties of the original medium. The rationale for this approach lies in our inability to describe analytically the pore space geometry and topology of a natural porous medium. Even if this feat could be accomplished, the use of such information for fluid flow studies in porous media would be impractical or impossible because of the complicated boundary conditions imposed by the irregular geometry of the pore space. Instead, the natural pore geometry has been replaced with a geometry that can be handled mathematically, even if only approximately, and the network structure of the pore space is also replaced with a network that can be handled. These concepts find applications in Part II. The results presented here confirm that the proposed concepts have a sound basis. The advantage offered by this study with respect to research of pore space geometry and topology is that it offers an automated and computerized method for obtaining a relatively simple statistical representation of a porous medium.

Quantifying solid–fluid interfacial phenomena in porous rocks with proton nuclear magnetic resonance

The three order-of-magnitude variation in the proton nuclear magnetic resonance (NMR) longitudinal relaxation time T1 of water adsorbed on silica surfaces versus that of bulk water makes proton NMR studies of porous materials powerful tools to study the effects of adsorption. Recent theory permits the utilization of this different response to obtain pore space surface-to-volume (S/V) distribution functions by inverting the decay of the z component of magnetization of fully saturated porous rocks; information can likewise be obtained on the fluid distribution at partially saturated conditions. A computer program has been developed to invert the NMR relaxation curves for the S/V distribution function, assuming an isolated pore regime, the ramifications of which are examined. The program has been applied to experimental results from water, porous sandstones, and tight gas sands at various pore fluid saturations and varying electrolyte content. For the fully saturated case, the results show promise in the application of NMR to describing pore space geometries in rock samples with widely varying surface-to-volume ratios. For partially saturated rocks, the results reflect the preferential early draining of the large pores at high water saturations, connectivity percolation phenomena at intermediate saturations, and the dominating role of adsorbed water films at low water saturations. Experiments on rocks saturated with saline solutions disclose the importance of the effects of alteration of the active sites on the rock surfaces as well as the role of electrolytes in modifying the structural properties of bulk solution.

ONE- AND TWO-PHASE FLOW IN NETWORK MODELS OF POROUS MEDIA

Abstract We discuss the low Reynolds number flow of one or two immiscible Newtonian fluids in network models of microscopically random porous media. For the case of a single fluid, we reduce the flow problem to an analog random electrical resistor problem and use an 'effective medium theory' to express the permeability of such networks in terms of the pore space geometry. For the flow of two fluids we use the Washburn approximation to incorporate capillary pressure differences, and show that this problem may also be formulated as a random electrical network. In this case, the capillary menisci correspond to moving batteries, and we follow the motion of the fluid-fluid interface (the ensemble of analog batteries) by a time-step procedure. We study the time evolution of the interface and the dynamics of blobs of one fluid contained in the other, as a function of the network geometry.’

Role of CO2 in Evolution of Secondary Porosity in Pennsylvanian Morrow Sandstones, Anadarko Basin, Oklahoma: ABSTRACT

The Anadarko basin is one of the most outstanding hydrocarbon producers in the North American continent. Examination of more than 50 cores from the Pennsylvanian Morrow sandstones reveals a complex diagenetic history. Although quartzarenite is the major lithology, shell fragments, glauconites, and clayey matrix occur in considerable amounts throughout the section. This diagenetic complexity is a function of depositional environment and burial and thermal history of the basin. Most porosity in the Morrowan sandstones throughout the Anadarko basin is chiefly secondary. Such porosity results from the dissolution of clayey matrix, carbonate fragments and cement, glauconite, and quartz grains and their overgrowth. Evolution of secondary porosity is related directly to the generation of hydrocarbons. CO2 gas, with concentrations ranging from 0.3 to 4.7% by volume, was detected in more than 150 natural gas wells examined in the basin. Based on geothermal and geopressure gradients, and on experimental investigations of the solubility-potential of CO2 in formation fluids under elevated temperatures and pressures, a good estimate of solubility of CO2 in the Morrow Formation water may be attained. Because the concentration of CO2 appears to increase with depth in the basin, secondary porosity should not be restricted to a particular zone or to particular depths, but definitely would persist with depth. Organic acids at shallow depths and H2S in d eper zones may be important in enhancement of secondary porosity. Amounts of porosity and the geometry of pore space are directly related to the original lithology. A better understanding of lithofacies is very critical in evaluating reservoir quality. End_of_Article - Last_Page 412------------

Visual Examinations of Fluid Behavior in Porous Media - Part I

Abstract An exploratory study was made to examine the possibilities of a visual approach in investigations into microscopic mechanisms of fluid behavior in porous media. Appropriate apparatus and techniques were developed so that microscopic phenomena could he recorded on color movie film as well as be observed visually. The observation flow cells in which the fluid behavior studies were made were essentially single-layered matrices of spheres between plates, sometimes all-glass, sometimes all-Lucite and sometimes a combination of the two. The fluids were limited to water and a filtered crude oil. Two flow regimes were observed during the flow of the immiscible liquids: channel flow and slug flow. In the former, transport was effected through stable networks of interconnecting channels; and in the latter, part of the movement took place in the form of slugs. Under certain conditions, flood-front patterns were found to be different depending upon which liquids were the displacing and displaced phases and not depending upon whether the matrix was water-wet glass or oil-wet Lucite. Residual formations of oil and water were observed and are described. Some of the ramifications and significance of the observed phenomena are discussed. Introduction In recent years considerations of microscopic mechanisms of fluid flow in porous media have taken on greater significance. Much needs to be learned before the fundamentals of petroleum technology are completely established. For example, many unanswered questions exist in connection with relative permeability, displacement phenomena, residual fluid formations, flow structure, etc.; and further analytical mathematical formulations are seriously indicated. It is hoped that systematic investigations into the microscopic mechanisms connected with the behavior of fluids in porous media will shed some light on some of the problems extant. Until recently microscopic mechanisms have been considered almost exclusively as speculative hypotheses. Within the past few years, however, the problem has been submitted to a limited number of experimental investigations. Nuss and Whiting made some studies on the pore-space geometry of sandstones and limestones by impregnating cores with an inert plastic and leaching the solid matrices to leave behind plastic models of the pore spaces. Schaefer traced pore spaces microscopically through lengths of limestone cores by cutting away thin sections from the exposed faces normal to the line of view.