Simulation of Sandstone-Matrix Acidizing in Heterogeneous Reservoirs
Authors: Taha R. , Hill A.D. , Sepehrnoori K. 
Published: December 2007

Summary
A numerical simulator wigs developed to predict porosity and permeability changes and the resulting effect on well productivity in permeability changes and the resulting effect on well productivity in sandstones subject to matrix acidizing. While earlier acidizing models are based on homogeneous porous media, here vertical variation in permeability was accounted for by consideration of several noncommunicating zones or layers with different overall permeability-height (Kh) products. Each layer, in turn, may have radial permeability variations and different physical and chemical properties. In this manner, the presence of a damaged physical and chemical properties. In this manner, the presence of a damaged zone can be incorporated by a change in near-wellbore properties.
During acidizing, the permeability change at a given vertical location depends on factors that affect acid penetration rate, such as initial acid concentration, mineral composition, temperature, flow rate, and cumulative acid injected at that location. Because the reservoir is vertically heterogeneous, initial distribution of injected acid will be nonuniform, with the majority of the flowing acid tending to enter zones with higher permeabilities. This is unfavorable because the lower-permeability zones permeabilities. This is unfavorable because the lower-permeability zones are of interest in a stimulation treatment. Adding diverting agents to the acid solutions, however, tends to decrease the flow rate of higher-permeability areas and helps to distribute fluid uniformly. The effect of organic resin diverting agents (added continuously) on vertical fluid distribution in a wellbore is also modeled.
With our model, the effect of injection rate on acid penetration distance and on diverting-agent efficiency was investigated. Acidization results in a heterogeneous porous medium are compared with results obtained for a vertically homogeneous porous medium. Finally, the design of optimal diverting strategies in matrix stimulation of heterogeneous formations is described.

Introduction
Sandstone-matrix acidizing is a process aimed at increasing the formation permeability in the vicinity of the wellbore by dissolving some formation material with a mixture of hydrofluoric and hydrochloric acid. Several investigators have developed models of this process that consider flow through the porous media with simultaneous heterogeneous reactions between acid and the solid matrix. These models provide a means for estimating volumes of acid needed for provide a means for estimating volumes of acid needed for desired levels of stimulation, depth of penetration of acid, and the resulting changes in permeability for matrix acidization in homogeneous reservoirs.
Our objective is to extend these models to simulate acidization in heterogeneous reservoirs where formation properties may vary both radially and vertically. Because properties may vary both radially and vertically. Because the presence of formation damage is known to be an important consideration in matrix acidizing, a near-wellbore region with properties different from the rest of the reservoir is included. Vertical reservoir heterogeneity is included in the model by division of the reservoir into multiple, noncommunicating layers with various properties. properties. Another important factor influencing sandstone-acidizing results is the vertical distribution of the injected acid. The effect of organic resin diverting agents on acid distribution was included in the model by use of the model of diverting-agent behavior presented by Hill and Galloway. Gravity segregation effects, which can have a significant impact on acid placement, were not considered in this study.
The results of any particular acidizing treatment will, of course, depend on such factors as the mineral properties of the sandstone being treated, the acid properties of the sandstone being treated, the acid concentration used, and the treating temperature. In this study, conditions representative of a typical treatment were chosen. The mineral properties of a sample of Berea sandstone were used to represent the formation. An acid concentration of 3 wt% HF/12 wt% HCl was used, and, when included, the organic resin diverting agent was assumed to be 0.1 vol %. Reaction kinetics were based on a temperature of 77F [25C]. It was also assumed that carbonate minerals had been removed by an HCl preflush so that only HF reactions could be considered. preflush so that only HF reactions could be considered. The results obtained here are not intended to be representative of acidizing in a particular formation; rather, they serve to illustrate important factors that can significantly affect any matrix-acidizing treatment.
The model developed was a versatile tool for studying the factors important in acidizing heterogeneous sandstone reservoirs.
JPT
P. 753