A theory on the relationship between fonnation resistivity factor and porosity is presented. This theory considers that, from the standpoint of the flow of electric current within a porous medium saturated with a conducting fluid, the pore space can be divided into flowing and stagnant regions. This assumption leads to a general expression, and fonnulas currently used in practice are special cases of this expression. The validity of the new expression is established by the use of data correspond-. jng to sandstones and packings and suspensions of particles. For the case of natural rocks, the theory confinns Archie's equation and gives an interpretation of the physical significance of the so-called cementation exponent.

A theoretical and experimental study on electric resistivity of vuggy fractured media is presented. In order to have a rigorous control of the involved variables, a vuggy fractured medium is idealized by a cubic array of cubes having hemispherical cavities drilled in each cube face. In this model, the spaces between the cubes represent fractures and the hemispherical cavities represent vugs. The theoretical developments lead to a simple relationship expressing formation resistivity factor as the product of two factors, one depending on vug porosity and the other on fracture porosity. This formulation has been validated with experimental data obtained with a special resistivity cell. The proposed formulation can easily be generalized to be applicable to real rocks, and so it is a useful tool for interpretation of electric well logs of vuggy fractured formations. Introduction It is well known that an important part of the world oil production comes from vuggy fractured reservoirs. This type of reservoirs are commonly found in Saudi Arabia, Iran, Iraq, Mexico, Oman and Syria, hence the importance of developing reliable analytical formulations concerning the geometrical properties, storage capacity, and flow properties of the porous space. A practical way of knowing the internal geometry of a porous medium consists in using the so called formation resistivity factor.1 By knowing the formation resistivity factor, it is possible to determine, for instance, the magnitude and type of porosity, and the tortuosity. However, in the case of vuggy fractured media, no previous well established expressions relating formation resistivity factor and the various kinds of porosities have been proposed to date. In this paper, expressions for the formation resistivity factor of vuggy fractured media are developed in terms of fracture and vug porosities. To establish these formulations, the vuggy fractured medium is idealized by a cubic array of cubes with hemispherical cavities drilled in each face. In this model, the spaces between the cubes represent fractures, and the hemispherical cavities represent vugs.2 The theoretical work is based on the idea that, in a vuggy fractured medium saturated with a conducting fluid, the vugs are zones of very low resistivity (or very high conductivity) in comparison with that of the fractures. In this way, one arrives at an equation expressing formation resistivity factor as the product of two components, one depending exclusively on fracture porosity, and the other on vug porosity. This equation was validated with experimental data obtained with a special resistivity cell. The Fractured Medium Due to the geometrical complexity of a vuggy fractured medium, a rigorous analytical study of the formation resistivity factor is not an easy task; however, by making certain logical idealizations it is possible to manage this problem in a relatively simple way. But before entering the study of vuggy fractured media, the case containing no vugs will be considered in this section. The simple fractured medium (i.e., with no vugs), has previously been treated analytically by several authors. For its study, the following basic considerations are made:When a potential difference is applied across the medium saturated with a conducting fluid, the electric current flows much more easily through the fractures than through de matrix, so that the current through the matrix can be considered as negligible, andthe fractured medium can be idealized by a cubic array of cubes (Warren and Root model3), as shown in Fig. 1. This same model has been used by Towle4 and by Aguilera5 for studying the relationship that exists between porosity and formation resistivity factor of fractured media.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIn this paper experimental results obtained for the oil displacement by water within a two-dimensional vuggy fractured porous cell are presented. The experiments were carried out with an acrylic cell, where fractures were represented by channels of 1.6 mm wide, 1.2 mm deep and 19 cm long, whereas the vugs were represented by cylinders of 1 cm diameter and 1.2 mm deep.The experimental procedure is as follows: the cell, saturated 100% with oil was placed horizontally and at time t=0 water was injected at a constant rate. Photographs were taken to follow the water front in the cell; then, the area corresponding to oil and water was measured. In this way the water saturation in the cell was determined. This water saturation is equal to the oil recovery, considering oil and water as incompressible fluids.Based on the experimental results, a theoretical model was developed. This model considers that the porous space is constituted by two regions: one that can conduct fluids, called flow region and a stagnant region that interchange matter with the flow region through a diffusion-like process. Analytical solutions for water saturation and normalized oil recovery are presented.The model fitted in a reasonable way the experimental data of normalized oil recovery, indicating that the theoretical model can be a useful tool to explain oil recovery processes in vuggy fractured reservoirs.

A formula relating porosity and formation resistivity factor is presented.This equation is applicable not only to consolidated and unconsolidatedmaterials, but also to dispersive systems. A comparison of calculatedvalues with experimental data shows the equation yields satisfactory results. Introduction The formation resistivity factor of a porous sample hasbeen defined as the ratio of the resistivity of the samplewhen completely saturated with an electrolyte to theresistivity of the saturating electrolyte. One of thetheoretical expressions relating the formation resistivityfactor, F R, to porosity, phi, is known as the Maxwellequation. Its form is 3 −F = ---------- ...........................(1)R 2 This equation can be applied to dispersive systems ofspheres, where electrical interference among theelements is negligible. In practice, little attention has been paid to Eq. 1, mainly because its application is limited to idealizedsystems. However, contrary to other empiricalexpressions currently used, it has the virtue of having arigorous theoretical deduction. In view of the potential importance of Eq. 1, andbecause the idealizations made in its derivation are notwell known, a theoretical development is presented inthe Appendix, according to the ideas suggested byMaxwell. Theory Outstanding among the attempts to generalize theMaxwell equation is the work of Fricke, whotheoretically demonstrated that for dispersive systems of oblate and prolate spheroids (x + 1) −F = -------------,.........................(2)R x where x is a geometric parameter that is a function ofthe axial ratio of the spheroids, and whose value is lessthan 2. When x = 2, Eq. 2 reduces to Eq. 1. Fricke confirmed Eq. 2 by using experimental dataon the conductivity of blood. For this purpose, hetreated the red corpuscles as oblate spheroids. Furthermore, he made use of the fact that the redcorpuscles behave as perfect insulators for director low-frequency current; this behavior results frompolarization effects. It is interesting to note that Maxwell's formula forspheres and Fricke's equation for spheroids areequilateral hyperbolas that can be written as P(1−) F = 1 + -----------,.......................(3)R where P takes on the values of 1.5 and (1 + x)/x, respectively. Furthermore, P is a geometric parameterwhose value becomes larger as the sphericity becomessmaller. Similarly, it has been found that, in the caseof two-dimensional dispersive systems, a relationship ofthe form of Eq. 3 is also satisfied. However, it shouldbe noted that idealizations have been made in itsderivation that, in principle, do not allow its applicationto those cases where the elements are in contact or neareach other, or when they have irregular shapes. Therefore, Eq. 3 should be modified if it is to be applied to real cases. For this purpose, consider a system of spheres, whether disperse or in contact. Fig. 1 shows some ofthe flowlines in the neighborhood of two spheres incontact. JPT P. 819^

In this work the effective molecular diffusion in homogeneous porous media was studied. An experimental setup was constructed to measure the effective molecular diffusion coefficient in packed unconsolidated sands, which allowed to take samples of fluids at different positions and times. The fluid samples were analyzed by gas chromatography to determine fluid concentration; these data were analyzed using the Fick's second law to calculate the molecular diffusion coefficient. These results were compared with those obtained using a different methodology based in pressure changes developed by Luna et al. A good agreement between both methodologies was obtained. Introduction Most of the Mexican oil is produced from mature reservoirs located at the offshore Campeche zone; because of this, the implementation of enhanced oil recovery (EOR) technologies is becoming rapidly necessary and important. Due to the fractured carbonated rock structure of these reservoirs, one of the most recommended technique is the injection of gases, such as nitrogen or carbon dioxide. This was shown in the giant Cantarell reservoir, where a nitrogen injection process has a better performance than expected, or in the Artesa field where carbon dioxide has been successfully injected. From this point of view, the laboratory study of the behavior of these gases is very important before the implementation of any EOR process. When a gas is injected in a reservoir, its behavior is governed by convection, dispersion and diffusion. Dispersion and convection work together especially in the fracture network, whereas diffusion is important in the matrix where fluid velocities are small; in fact, mass transfer between the matrix and its surrounding fractures is governed by gravitational segregation at short times, and molecular diffusion at long times. Diffusion within porous media has been studied since the early years of the 20th century, especially in homogeneous media with intergranular porosity. Some works1,2 focused on finding the relationship between the molecular diffusion, tortuosity, formation resistivity factor and effective molecular diffusion coefficient (MDC); others, were interested in measuring the MDC using indirect methods.4,5,6,7 For example, one common methodology is to establish a gas flow at one end of a liquid saturated porous block, and measure the concentration changes in the resulting current flow. The problem here is that it is very difficult to measure the concentration variations in the current, because changes are generally very small. The main aim of the present paper is the molecular diffusion process of a gas within a liquid saturated porous media. In particular, sand of well defined size (0.032 - 0.051 cm) and porosity (0.44) was used.3 This work presents an experimental study to find the effective molecular diffusion coefficient in porous media and its relationship to free molecular diffusion. The measured concentration variations through the porous medium are coupled with the second Fick's law for diffusion, to obtain the effective MDC. Model Consider a PVT cell with a cylindrical geometry of internal radio r and height H, where constant temperature and volume are established. A cylindrical porous matrix of porosity f, was placed at the bottom of the cylinder (Fig. 1). The porous matrix height is hp< H and radio equal to that of the cylindrical cell. Initially a liquid (hexane) is saturating completely the porous medium and a gas (nitrogen) is occupying the free space at the top of the matrix, both at the same temperature and pressure. The height of the gas column is hg, and that of the liquid hl. Immediately two transport processes begin: the liquid molecules spread into the gas zone and those of gas go into the liquid. Both processes are governed by mechanisms of free diffusion and diffusion in porous media (effective diffusion), that are present until the thermodynamic balance is reached. Since the diffusive process is faster in the gaseous phase than in the liquid phase, thermodynamic stability in the former is reached first.