Wicke–Kallenbach and Graham's diffusion cells: Limits of application for low surface area porous solids

The Role of Diffusivity in Oil and Gas Industries: Fundamentals, Measurement, and Correlative Techniques

The existence of various native or nonnative species/fluids, along with having more than one phase in the subsurface and within the integrated production and injection systems, generates unique challenges as the pressure, temperature, composition and time (P-T-z and t) domains exhibit multi-scale characteristics. In such systems, fluid/component mixing, whether for natural reasons or man-made reasons, is one of the most complex aspects of the behavior of the system, as inherent compositions are partially or all due to these phenomena. Any time a gradient is introduced, these systems try to converge thermodynamically to an equilibrium state while being in the disequilibrium state at scale during the transitional process. These disequilibrium states create diffusive gradients, which, in the absence of flow, control the mixing processes leading to equilibrium at a certain time scale, which could also be a function of various time and length scales associated with the system. Therefore, it is crucial to understand these aspects, especially when technologies that need or utilize these concepts are under development. For example, as the technology of gas-injection-based enhanced oil recovery, CO2 sequestration and flooding have been developed, deployed and applied to several reservoirs/aquifers worldwide, performing research on mass-transfer mechanisms between gas, oil and aqueous phases became more important, especially in terms of optimal design considerations. It is well-known that in absence of direct frontal contact and convective mixing, diffusive mixing is one of most dominant mass-transfer mechanisms, which has an impact on the effectiveness of the oil recovery and gas injection processes. Therefore, in this work, we review the fundamentals of diffusive mixing processes in general terms and summarize the theoretical, experimental and empirical studies to estimate the diffusion coefficients at high pressure—temperature conditions at various time and length scales relevant to reservoir-fluid systems.

A Diffusion Cell for the Mass Transfer Investigation in the Solid Porous Media

A diffusion cell for the mass transfer investigation of the gases through the solid porous media is developed. The diffusion cell may be configured in two different ways. One configuration corresponds to the reflecting boundary condition, whereas another configuration satisfies the absorbing boundary. The mass balance equations for different cell configurations are provided. The mass balance equations are applicable for the calculations of the diffusate quantity decays. The latter are suitable for the mass transfer parameters estimation using the solutions of the transport equations, obtained for the boundary conditions that correspond to the diffusion cell configurations. Accounting for the impact of the apparatus function of the diffusion cell on the experimental data is also revisited. In addition, the practical use of the diffusion cell based on the installation of the cell into the gas chromatograph for the investigation of the methane transport through the porous silica pellet as an example is demonstrated.