Linking up pressure, chemical potential and thermal gradients

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 42; no. 5; pp. 65 - 10
• Main Authors: Montel, François, Hoang, Hai, Galliero, Guillaume
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2019; Springer Nature B.V; EDP Sciences: EPJ
• Subjects: Biological and Medical Physics; Biophysics; Chemical potential; Complex Fluids and Microfluidics; Complex Systems; Composition; Computer simulation; Condensed Matter; Condensed matter physics; Entropy; Equations of state; Fluid pressure; Molecular dynamics; Nanotechnology; Organic chemistry; Other; Permeability; Physics; Physics and Astronomy; Polymer Sciences; Porous media; Potential gradient; Regular Article; Separation; Soft and Granular Matter; Surfaces and Interfaces; Temperature gradients; Thermal Non-Equilibrium Phenomena in Soft Matter; Thin Films; Topical issue: Thermal Non-Equilibrium Phenomena in Soft Matter
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/i2019-11821-0

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Petroleum reservoirs are remarkable illustrations of the impact of a thermal gradient on fluid pressure and composition. This topic has been extensively studied during the last decades to build tools that are required by reservoir engineers to populate their models. However, one can get only a very limited number of representative samples from a given reservoir and assessing connectivity between all sampling points is often a key issue. In some extreme cases, the whole reservoir fluid properties must be derived from a single point to define the field development plan. To do so, available models are usually not satisfactory as they need too many parameters and so cannot be considered as predictive tools. We propose in this work a comprehensive approach based on the irreversible thermodynamics principles to derive the relationships between pressure, chemical potentials and thermal gradients in porous media. It appears that there is no need for additional assumptions, it is just a matter of a making the right choices along theoretical developments. One of the most important steps is to express the full pressure gradient. As a final result, we obtain the chemical potential gradients for all components of the mixtures that can be easily translated in term of compositions through Equation of State modelling. The most important features of the final expressions are: i) the species relative separation in a thermal field is sensitive to the relative diffusion coefficients at stationary state. In porous media, the separation is sensitive to the permeability when the overall mobility is similar to diffusive mobility; ii) the magnitude of the separation depends on the residual entropy of the species; iii) the separation is not simply balanced by the average residual entropy. The balance is modified by the relative diffusion mobility of the components; iv) in low permeability porous media, the thermal gradient induces a pressure gradient proportional to the fluid residual entropy. As a validation, the proposed approach has been applied on a reservoir fluid subjected to a geothermal gradient and compared with non-equilibrium molecular dynamics simulation results at the stationary state.
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