Analytical Solutions of Carbonate Acidizing in Radial Flow

Polyneikis Strongylis,Euripides Papamichos

doi:10.1007/s11242-021-01657-4

Polyneikis Strongylis, Euripides Papamichos

Open Access

https://doi.org/10.1007/s11242-021-01657-4

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Abstract

The 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.

Highlights

Reactive infiltration is the phenomenon where fluids enter the free space of a porous solid, while their components react with the solid matrix and result in changes to its porosity and permeability
Most of the research focuses on analyzing either theoretically or experimentally the pattern formation in rocks created by the reactive infiltration instability, a self-organizing system where the interplay between convective and diffusive fluxes sculpts the shape of the dissolution profile in the rock (e.g., Ortoleva et al 1987; Papamichos et al 2020)
A novel closed-form analytical solution was extracted for the initial transient convection–diffusion equation

Summary

Introduction

Reactive infiltration is the phenomenon where fluids enter the free space of a porous solid, while their components react with the solid matrix and result in changes to its porosity and permeability. The development of this more general closed-form solution allows the analytical validation of the approximate steadystate solution and the demarcation of its range of applicability. It examines the effect of this dependence on the propagation velocity of the reaction front and the fluid flux and acid concentration profiles.

Governing Equations

Solution for Transient Convection–Diffusion

Solution for Velocity‐Dependent Diffusion–Dispersion Coefficient

Conclusions