scholarly journals Analytical Solutions of Carbonate Acidizing in Radial Flow

2021 ◽  
Author(s):  
Polyneikis Strongylis ◽  
Euripides Papamichos
Keyword(s):  
Analytical Solutions ◽  
Moving Boundary ◽  
Radial Flow ◽  
Fluid Velocity ◽  
Boundary Problems ◽  
Reactive Infiltration ◽  
Closed Form Solutions ◽  
Engineered Systems ◽  
Carbonate Acidizing ◽  
Reactive Fluids

AbstractThe flow of reactive fluids into porous media, a phenomenon known as reactive infiltration, is important in natural and engineered systems. While most of the studies in this area cover theoretical and experimental analyses in linear acid flow, the present work concentrates on radial flow conditions from a wellbore in the field and on finding exact analytical solutions to moving boundary problems of the uniform dissolution front. Closed-form solutions are obtained for the transient convection–diffusion which allow the demarcation of the range of applicability of the quasi-static limit. The fluid velocity dependency of the diffusion–dispersion coefficient is also examined by comparing results from analytical solutions from constant and velocity-dependent coefficients. These contributions form the basis for linear stability analyses to describe acid fingering encountered in reservoir stimulation.

Applied Mechanics in Moving Boundary Problems of One-Dimensional Non-Darcy Flow in Semi-Infinite Long Porous Media

2014 ◽  
Vol 977 ◽  
pp. 399-403
Author(s):  
Jia Hang Wang ◽  
Lei Wang ◽  
Duo Kai Zhou
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Mathematical Models ◽  
Analytical Solutions ◽  
Moving Boundary ◽  
Boundary Problems ◽  
Threshold Pressure Gradient ◽  
Depression Cone ◽  
Boundary Distance ◽  
Pressure Propagation

Dimensionless mathematical models of the fluid flow in the semi-infinite long porous media with constant production pressure on the inner boundary conditions are built, which include the effect of threshold pressure gradient (TPG). The analytical solutions of these dimensionless mathematical models are derived through new definitions of dimensionless variables. Comparison curves of the dimensionless moving boundary under different values of dimensionless TPG are plotted from the proposed analytical solutions. For the case of constant production pressure, a maximum moving boundary exists, beyond which the fluid flow will not occur. The value of maximum boundary distance decreases with increasing TPG. However, the velocity of pressure propagation decreases with time. The larger the TPG is, the steeper the curve of pressure depression cone is and the shorter the distance of the pressure propagation is.

scholarly journals On the Transient Atomic/Heat Diffusion in Cylinders and Spheres with Phase Change: A Method to Derive Closed-Form Solutions

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
I. L. Ferreira ◽  
A. Garcia ◽  
A. L. S. Moreira
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Single Phase ◽  
Moving Boundary ◽  
Error Function ◽  
Solid State Diffusion ◽  
Two Phase ◽  
Closed Form Solutions ◽  
State Diffusion ◽  
Cylinders And Spheres

Analytical solutions for the transient single-phase and two-phase inward solid-state diffusion and solidification applied to the radial cylindrical and spherical geometries are proposed. Both solutions are developed from the differential equation that treats these phenomena in Cartesian coordinates, which are modified by geometric correlations and suitable changes of variables to achieve closed-form solutions. The modified differential equations are solved by using two well-known closed-form solutions based on the error function, and then equations are obtained to analyze the diffusion interface position as a function of time and position in cylinders and spheres. These exact correlations are inserted into the closed-form solutions for the slab and are used to update the roots for each radial position of the moving boundary interface. The predictions provided by the proposed analytical solutions are validated against the results of a numerical approach. Finally, a comparative study of diffusion in slabs, cylinders, and spheres is also presented for single-phase and two-phase solid-state diffusion and solidification, which shows the importance of the effects imposed by the radial cylindrical and spherical curvatures with respect to the Cartesian coordinate system in the process kinetics. The analytical model is proved to be general, as far as, a semi-infinite solution for diffusion problems with phase change exists in the form of the error function, which enables exact closed-form analytical solutions to be derived, by updating the root at each radial position the moving boundary interface.

USNCCM-11: Computational fluid mechanics for free and moving boundary problems

2013 ◽  
Vol 87 ◽  
pp. 1
Author(s):  
Rekha R. Rao ◽  
S.A. Roberts ◽  
David R. Noble ◽  
Patrick D. Anderson ◽  
Jean-Francois Hétu
Keyword(s):  
Fluid Mechanics ◽  
Moving Boundary ◽  
Computational Fluid Mechanics ◽  
Moving Boundary Problems ◽  
Boundary Problems

Solving moving boundary problems with an adaptive moving grid method

1998 ◽  
Vol 53 (19) ◽  
pp. 3393-3411 ◽  
Author(s):  
Jörg Frauhammer ◽  
Harald Klein ◽  
Gerhart Eigenberger ◽  
Ulrich Nowak
Keyword(s):  
Moving Boundary ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Moving Grid ◽  
Boundary Problems
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