Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media

This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for m...

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Autor principal:	Ruud Weijermars
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	diffusion pressure transient gaussian solutions reservoir modeling Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
Acceso en línea:	https://doaj.org/article/4d1b5a2a39924578bafa70744a5970ec
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spelling	oai:doaj.org-article:4d1b5a2a39924578bafa70744a5970ec2021-11-25T17:31:26ZDiffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media10.3390/fluids61103792311-5521https://doaj.org/article/4d1b5a2a39924578bafa70744a5970ec2021-10-01T00:00:00Zhttps://www.mdpi.com/2311-5521/6/11/379https://doaj.org/toc/2311-5521This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for molecular diffusion is applied to pressure diffusion in porous media. The pressure drop (by fluid extraction) or increase (by fluid injection) due to the production system may start with a simple pressure step function. The pressure perturbation imposed by the step function (representing the engineering intervention) will instantaneously diffuse into the reservoir at a rate that is controlled by the hydraulic diffusivity. Traditionally, the advance of the pressure transient in porous media such as geological reservoirs is modeled by two distinct approaches: (1) scalar equations for well performance testing that do not attempt to solve for the spatial change or the position of the pressure transient without reference to a well rate; (2) advanced reservoir models based on numerical solution methods. The Gaussian pressure transient solution method presented in this study can compute the spatial pressure depletion in the reservoir at arbitrary times and is based on analytical expressions that give spatial resolution without gridding-meaning solutions that have infinite resolution. The Gaussian solution is efficient for quantifying the advance of the pressure transient and associated pressure depletion around single wells, multiple wells and hydraulic fractures. This work lays the basis for the development of advanced reservoir simulations based on the superposition of analytical pressure transient solutions.Ruud WeijermarsMDPI AGarticlediffusionpressure transientgaussian solutionsreservoir modelingThermodynamicsQC310.15-319Descriptive and experimental mechanicsQC120-168.85ENFluids, Vol 6, Iss 379, p 379 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	diffusion pressure transient gaussian solutions reservoir modeling Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
spellingShingle	diffusion pressure transient gaussian solutions reservoir modeling Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85 Ruud Weijermars Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media
description	This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for molecular diffusion is applied to pressure diffusion in porous media. The pressure drop (by fluid extraction) or increase (by fluid injection) due to the production system may start with a simple pressure step function. The pressure perturbation imposed by the step function (representing the engineering intervention) will instantaneously diffuse into the reservoir at a rate that is controlled by the hydraulic diffusivity. Traditionally, the advance of the pressure transient in porous media such as geological reservoirs is modeled by two distinct approaches: (1) scalar equations for well performance testing that do not attempt to solve for the spatial change or the position of the pressure transient without reference to a well rate; (2) advanced reservoir models based on numerical solution methods. The Gaussian pressure transient solution method presented in this study can compute the spatial pressure depletion in the reservoir at arbitrary times and is based on analytical expressions that give spatial resolution without gridding-meaning solutions that have infinite resolution. The Gaussian solution is efficient for quantifying the advance of the pressure transient and associated pressure depletion around single wells, multiple wells and hydraulic fractures. This work lays the basis for the development of advanced reservoir simulations based on the superposition of analytical pressure transient solutions.
format	article
author	Ruud Weijermars
author_facet	Ruud Weijermars
author_sort	Ruud Weijermars
title	Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media
title_short	Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media
title_full	Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media
title_fullStr	Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media
title_full_unstemmed	Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media
title_sort	diffusive mass transfer and gaussian pressure transient solutions for porous media
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4d1b5a2a39924578bafa70744a5970ec
work_keys_str_mv	AT ruudweijermars diffusivemasstransferandgaussianpressuretransientsolutionsforporousmedia
_version_	1718412221729472512

Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media

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