F. A. L. Dullien

Characterization of pore structure by a combination of quantitative photomicrography and mercury porosimetry

Abstract The methods of quantitative stereology have been applied to pore size distribution determination. In the sphere pore segment (SPS) model the pore structure is approximated by a three-dimensional network consisting of strings of touching spheres. The porous samples are saturated with Woods metal, and photomicrographs prepared of polished sections are scanned by an automatic image analyzing computer. The photomicrographic pore size distribution curves generally differ from and are more realistic than the mercury porosimetry curves. The SPS model has been applied successfully to the pore size distribution determination of a large number of sandstone samples. Comparison with the mercury porosimetry curves has resulted in an excellent correlation between petrography and tertiary oil recovery. For the case of strongly anisometric pores the general pore segment (GPS) model has been proposed. Equations have been developed and used for the photomicrographic size distribution determination of pores of arbitrary shape. Marked improvement has been observed over the SPS model in the case of the void size distribution in packed beds of spheres.

Three‐dimensional reconstruction of porous media from serial section data

Software has been developed, with the aid of data for a Berea sandstone sample, to partition the irregular, interconnected pore space of a porous medium into its constituent pores. Output includes the sizes (volumes) of the individual pores, the sizes (area and radii of curvature) of the individual necks (windows) between the pores, the order in which the pores and necks are connected, and the degree of interconnectedness.

The effects of surface roughness on the capillary pressure curves and the heights of capillary rise in glass bead packs

Abstract In this paper drainage and imbibition capillary pressure curves, obtained with various low viscosity oils by porous diaphragm tensiometry in packs of smooth and etched glass bead packs, are compared. Only in packs of smooth beads was there a definite irreducible wetting fluid saturation, whereas in packs of etched beads the wetting fluid saturation kept decreasing, without any apparent limit, with increasing applied capillary pressure. Residual wetting fluid saturations as low as 1% of the void space have been reached. Imbibition and drainage experiments have also been carried out in columns of both smooth and etched bead packs using molten paraffin wax. In the latter, the equilibrium heights were the same in drainage and in imbibition. The wetting liquid occupying the grooves in the surface of etched beads, which is responsible for these phenomena, was visualized by scanning electron microscopy and optical microscopy on samples in which styrene monomer was used in the drainage test and was subsequently polymerized.

Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network

A stochastic approach to network modelling has been used to simulate quasi-static immiscible displacement in porous media. Both number-based and volume-based network saturation results were obtained. Number-based results include: number-based saturation curves for primary drainage, secondary imbibition and secondary drainage, fluid distribution data, and cluster trapping history. Using pore structure data of porous media, it is possible to convert the number-based curves to capillary pressure — saturation relationships. Pore size distribution functions and pore shapes which are thought to closely represent Berea sandstone samples were used to predict the capillary curves. The physical basis of these calculations is a one-to-one correspondence between the cumulative node and bond index fractions in the network analysis, and the cumulative number-based distributions of pore body and pore throat diameters, respectively. The oil-water capillary pressure curve simulated for primary drainage closely resembles those measured experimentally. The agreement between the simulated and the measured secondary imbition and secondary drainage curves is less satisfactory.

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

Abstract 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.

Rate of capillary rise in porous media with nonuniform pores

Abstract An equation for the rate of capillary rise in porous media with nonuniform pores has been derived on the basis of a three-dimensional network model of pore structure, consisting of a repeating capillary element with step changes in its diameter. The measured rates of capillary rise of water in a number of sandstone samples have been accurately predicted by the model. The apparent capillary diameter for the rate of the capillary rise has been found to be several orders of magnitude smaller than the pore diameter corresponding to the peak of the mercury intrusion porosimetry curve. The permeability of the sandstone samples has been found to be approximately directly proportional to the apparent diameter of the rate of capillary rise. This approximate proportionality has been shown to follow from the capillary network model of the pore structure used in this work.

Hydraulic continuity of residual wetting phase in porous media

Abstract This paper presents results of drainage tests in Berea sandstone, thin glass bead packs, and a two-dimensional glass capillary micromodel, obtained at vanishingly small capillary numbers, using oil and water as the two fluids. The primary objective of the present tests was to investigate the pattern of near-stationary residual wetting fluid saturations reached in Berea sandstone samples at various applied pressure differentials, using a porous plate at the exit face of the sample. Pressures ranging up to about 30 times the threshold pressure of penetration and times on the order of 5 weeks were used. The results do not indicate a lower limit of the wetting phase saturation. The lowest saturation reached is under 10% which is much lower than the “irreducible” saturations reported previously in sandstones. The near-stationary saturation reached under a certain applied pressure differential decreased abruptly when the pressure differential was increased, resulting in a lower near-stationary value after each pressure increase. The performance of the porous plate used in these tests set a limitation to the maximum pressure differential that could be used without running the risk of starting to produce also the displacing nonwetting fluid. Model experiments were performed with thin bead packs contained between two parallel glass plates in an attempt to visualize various displacement mechanisms of water from pore clusters that appear to have been completely surrounded by oil. In these experiments the islands of water which were completely surrounded by oil were displaced and produced through a continuum of oil. When oil breakthrough was prevented by the application of a capillary barrier at the exit, the displacement of water occurred close to the displacement pressure estimated for the island of beads containing the “trapped” water. Without the application of a capillary barrier, however, very much higher pressures and hundreds of pore volumes of throughput of the displacing fluid were necessary for displacement of the “trapped” water. It is believed that the mechanism of displacement of the wetting phase through a continuum of the nonwetting phase consists of transport of the wetting phase on the solid surface in the form of rivulets. Pore wedges or edges, as well as surface capillary grooves which are present on rough surfaces, have been shown to result in surface capillary transport of a wetting fluid. For example, surface capillary rise of wax was observed on ground glass surfaces.

An experimental study of secondary oil migration

Experiments using long glass columns packed with glass beads or sand have been done to investigate secondary oil migration under hydrostatic conditions. Different combinations of bead sizes, oil densities, oil-water interfacial tensions, and column orientations have been tested. In some experiments, the oil was replaced by air. The observations included the oil migration pathway, the minimum oil column height needed for migration, and the rate of advance of the migration front. Migration was found to take place along restricted pathways and an imbibition front often formed at the bottom of the oil zone. The minimum oil zone height needed for migration can be predicted accurately if the values of the drainage and imbibition capillary pressures are known for the saturations at which the oil just becomes disconnected. In most experiments, the migration front advanced at a constant rate, which depended on the fluid properties, bead size, initial oil height, and pore structure. Migration rate is dependent on buoyant and capillary forces, but the dependence on capillary forces becomes weaker as the oil length increases. Column orientation also has been found to affect migration efficiency.

Bivariate pore-size distributions of some sandstones

Abstract Bivariate pore volume distributions a (D, Dc)dDdDe have been measured for a Bartlesville and a Berea sandstone. α(D, De)dDdDe gives the fraction of pore volume characterized by the diameter range D → D + dD and the pore entry diameter range De → De + dDe. The distribution were obtained with joint use of Woods metal porosimetry and quantitative photomicrography. The technique of Woods metal porosimetry is described in the text. The data show that entry pores in a given size range ΔDe control penetration into pores of a wide range of diameters D. No correlation between De and D is apparent.

Characterization of porous media - pore level

Pore size and pore size distribution are defined, 1-D pore structure models, 2-D and 3-D network models of pore structure are reviewed. Simulation of capillary pressure and relative permeability curves with the help of network models of pore structure is discussed. Pore structure determination from serial sections is outlined. Phase immobilization technique is reviewed.