Experimental Study of Effective Diffusion in Porous Media

Abstract

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.

CO2 Diffusion and Dispersion in Porous Media: Review of Advances in Experimental Measurements and Mathematical Models

“…He used a diffusion cell to measure binary molecular diffusion coefficients of gas mixtures at reservoir conditions. Juarez et al 100 measured the effective diffusion coefficient of a gas, i.e., nitrogen, in a sand-packed setup saturated with hexane by directly measuring the concentrations of fluid samples collected at various times and distances during the running of the test. The direct method for estimating the gas effective diffusion coefficients in hexane showed acceptable results compared to a non-conventional method, i.e., pressure decay method, that will be explained in the next section.…”

Drilling and Completing Horizontal Wells in Unconsolidated Sandstone Reservoir in Saudi Arabia; A Rock Mechanics View

“…Diffusion flow: This is the flow of solutes from high concentration to low concentration based on Fick's law 8 . This flow is effective in high permeability shale as the large size solutes are able to flow through the porous structure of the formation.…”

Methodology for using prompt gamma activation analysis to measure the binary diffusion coefficient of a gas in a porous medium

“…The ability to measure gas concentrations with sufficient spatial and temporal resolution is essential for determining diffusion coefficients [10,11]. Common methods for doing this include gas chromatography, mass spectroscopy [10,12,13], photothermal deflection [14], and nuclear magnetic resonance [15,16]. Of these, the mass spectroscopy (sometimes combined with gas chromatography analysis) is arguably most preferred technique.…”