A Comprehensive Model of Matrix Acidization
Authors: Fan Yong , Wang Yuqin , Bryant R.S. 
Published: December 2007

Abstract
Matrix acidization is a widely practiced stimulation method to remove near-wellbore damage. Previous acidization models attempted to relate the amount of acid injected to the overall increase in permeability. Little attention was given to chemical reactions and physical changes occurring in damaged zones. In field evaluation of acidizing treatments, all the tools available today use the concept of evolving skin factor, implicitly assuming that the acid reaction rate is infinitely fast and that no matrix minerals react with acid. This is not true in acidizing operations. This paper, incorporating chemical reaction kinetics with fluid mechanics, describes a model for flow of reactive fluids through composite reservoirs and presents simultaneous solutions to the depth of effective acid penetration and fluid pressure that reflect the continuous changes in formation properties subject to acidizing.
The physical model considered is a composite reservoir where the damaged zone has different mineral compositions and formation properties than the undamaged formation. During treatment, acids react simultaneously with invaded particles and matrix minerals at different reaction rates, resulting in multiple reaction zones in the formation. The changes in porosity and permeability caused by dissolution of invaded particles and matrix minerals are modeled as a function of injection time and radial space. At the same time, a transient flow model is developed to simulate the pressure distribution and wellbore pressure response that reflect the interactions between the flow and the reactions occurring in the composite reservoir. The characteristic parameters are Damkohler and acid capacity numbers, which can be determined by using measured pressure inversion. Since chemical reactions and the reservoir model are incorporated into one comprehensive model, this work allows for better prediction of optimal acid injection rates, volume, and stimulated well productivity.

Introduction
Matrix acidization is a process where acid solutions are injected into the formation porosity at a pressure less than fracture initiation pressure. The goal of the treatment is to recover and enhance the formation permeability by selectively dissolving some of the minerals present in the near-wellbore vicinity. When compared to hydraulic fracturing, matrix acidizing is a low-cost operation, particularly attractive in treating highly permeable, but damaged formations. Despite wide usage of matrix stimulation, the physical and chemical phenomena occurring during acidization have not been fully understood in the oil industry. Optimization of treatments is seldom practiced. The failure rates of treatments are high because of inappropriate formations treated, wrong acid used, incorrect treatment procedure, and incorrect design. In a viewpoint of engineers, the important issues involved before, during, and after acidizing include (1) causes of formation damage, (2) selection of acid type and amount, (3) pumping schedule, (4) optimal injection rates for the given volume, and (5) stimulation ratio.
Many experimental, theoretical, and field studies have been conducted by researchers and engineers to address some of these issues and to improve acidizing treatments. The published work has covered several aspects of matrix acidizing, including heterogeneous reactions between the fluid and solid phase, homogeneous reactions in the fluid phase, fluid flow and mass transfer, the changes in pore structure from acid injection, and field treatment evaluations. Although some mathematical models were proposed for job design and stimulation forecasting, the approach, regardless of the simplicity or sophistication of the model, usually started with a linear geometry, leaving some unknowns as adjustable parameters.