Dear Colleagues,

Diffusion is a core transport process that plays a very important role in various disciplines of science and engineering such as chemical engineering, petroleum engineering, biology, ocean engineering, and civil engineering. In particular to petroleum engineering, especially in the oil recovery processes, it may be the dominant process where convective forces are weak or absent (e.g., far in the reservoir, or ahead of the moving fronts) or when direct frontal contact and mixing is not possible. Examples include gas injection in unconventional reservoirs, heavy oil and bitumen recovery, compositional grading, and characterization of materials for various applications. Diffusive mixing may be a relatively slow process as compared to convective mixing and might be ignored for certain cases; however, it might be important in geological timescales. Therefore, the applications of diffusion and the outcome, especially in multiphase and multicomponent systems, become important for a wide spectrum of problems, from large-scale subsurface applications to the design of porous materials for various purposes. For example, in the application of gas injection in unconventional reservoirs for recovery enhancements, it is crucial to understand the mass transfer between gas and the oil in a composite acting as a porous medium to design and evaluate the performance of the recovery processes. Similarly, in heavy oil and bitumen recovery, injected light hydrocarbons can diffuse into the oil beyond the potential fronts and/or convective zones and promote the effectiveness of the displacement process, therefore reducing in situ viscosities, which in turn enhances the oil recovery. In addition, in other processes such as CO₂ sequestration, it is important to know the timescale of CO₂ being trapped in the geological structures, which is governed mainly by the diffusivity of CO₂ in the formation. Further, in gas re-dissolution processes, such as in lighter hydrocarbon systems, aqueous systems, or depleted reservoirs, the diffusivity and solubility control how much gas will be dissolved in oil and/or water and how long it will take to dissolve in the absence of mechanical/convective mixing, as well as the pressure history during the process. Thus, accurate determination of these parameters is essential for understanding and designing these processes.

Generally, diffusion in multiphase, multicomponent, or composite systems is not well understood, especially in terms of real industrial applications. From that point of view, this Special Issue will focus on multicomponent systems and consider the multiscale, multiphysics aspects of the problems. Thus, the topics of interest include but are not limited to the following:

• Application of diffusivity for subsurface processes and implications:
  1. Recovery processes;
  2. Pressure history;
  3. CO₂ sequestration;
  4. Gas storage.
• Experimental processes:
  1. Parameter estimation;
  2. Experimental data and methodologies;
  3. CO₂ and reactive transport.
• Porous material design:
  1. Gas or liquid permeation or penetration in porous materials;
  2. Treatment of porous materials (increasing/decreasing the permeation);
  3. Adsorption, phase behavior, and diffusive transport in unconventional reservoirs.
• Mathematics of diffusion subsurface engineering applications:
  1. Natural gases and oils;
  2. CO₂ dissolution and propagation.

Dr. Birol Dindoruk
Dr. Ram Ratnakar
Guest Editors

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• gas diffusivity in porous systems
• multicomponent multiphase mass transfer
• compositional grading in reservoir systems
• pressure decay
• measurement techniques for diffusivity
• mathematics of diffusivity
• diffusivity applications in porous media
• CO₂ propagation and dissipation in reservoirs

Title: Diffusion Coefficients in Systems Related to Reservoir Fluids: Available Data and Evaluation of Correlations
Authors: Yibo Yang; Erling H. Stenby; Alexander A. Shapiro; and Wei Yan
Affiliation: 1 Department of Chemistry, Technical University of Denmark 2 Department of Chemical Engineering, Technical University of Denmark
Abstract: Molecular diffusion determines the time to reach local equilibrium in a reservoir. It can be a main production mechanism in scenarios like production from fractured reservoirs or tight for-mation. However, there is a lack of high-pressure diffusion coefficients for reservoir fluids and its related systems. Many correlations exist but there is no consensus on their accuracy for these sys-tems. We provide a systematic review of the available data for systems related to reservoir fluids and a comprehensive comparison of five commonly used correlations for hydrocarbon mixtures, incl. the extended Sigmund correlation, the Riazi-Whitson correlation, the Leahy-Firoozabadi correla-tion, the Wilke-Chang correlation, and the Hayduk-Minhas correlation. We collected extensive data of diffusion coefficients in binary mixtures related to petroleum fluids and established a database of over 80 binaries and over 1500 data points. We also collected the data for gas diffusion in different oils and reservoir fluids but the data in high-pressure live oils are extremely scarce. The five cor-relations were evaluated using the binary database, and a few selected correlations using the oil database. They show similar overall deviations for the binary mixtures although for particular groups/regions, one may identify better correlations. For reservoir fluids, the predictions differ sig-nificantly among the correlations, and it is difficult to recommend a particular model due to the scarcity of data. The findings underscores the need for more accurate measurement and modeling of gas diffusion in mixtures more representative of reservoir fluids at high pressures.

Title: The Role of Diffusivity in Oil and Gas Industries: Fundamentals, Measurement, and Correlative Techniques
Authors: Dindoruk, Birol; Ram Ratnakar
Affiliation: 1 Department of Petroleum Engineering, University of Houston 2 Department of Chemical and Biomolecular Engineering, University of Houston
Abstract: Existence of various native or nonnative species, fluids and phases in the subsurface and in 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 systems behavior, as inherent compositions are partially or all due to the outcomes of this phenomena. Anytime a gradient, naturally or artificially, is introduced, these systems try to converge thermodynamically to an equilibrium state at some point in time while being in the disequilibrium state at scale during transitional processes. These disequilibrium gradients create diffusive forces, which in the absence of flow, control the mixing processes leading to equilibrium at a certain time scale, which could also be function of the other time and length scales of the system. In some of the cases, such diffusive systems can even lead to the onset of convection/fluid movement. Therefore, it is crucial to understand these aspects, especially when technologies are in development phase or need of development is of prime focus. 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, the research of the mass-transfer mechanisms between gas and oil and aqueous solutions have become of significant importance, especially in optimal design of these processes. It is well known that in absence of direct frontal contact and convective mixing, diffusive mixing is one of the dominant, and perhaps the only, mass-transfer mechanisms, which promotes the effectiveness of the oil recovery and/or CO2 and injection processes. Therefore, in this work, we review the fundamentals of diffusive mixing processes in general 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.