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Summary

A mathematical model was developed to study the effect of acidizing on the productivity of a single perforation penetrating a sandstone reservoir as a function of the distribution of damage around the perforation. Assuming the perforation to be ellipsoidal, we derived a 2D model that describes the single-phase flow of an acid through a perforated sandstone that contains two pseudochemical minerals dissolving perforated sandstone that contains two pseudochemical minerals dissolving at different rates. This paper presents cases that show the effectiveness of acidizing in removing both drilling-fluid damage and perforation damage. The most effective stimulation occurs when the perforation damage is removed by the acid.

Introduction

In this study, a mathematical model was developed to facilitate the investigation of the flow field and the dissolution pattern around a single perforation during sandstone acidizing. Previously, efforts have been made to investigate the mechanisms involved in the acid/mineral reactions occurring in sandstone acidizing. Experimental data obtained from acid reactions with rock minerals and core acidization and from chemical kinetic studies were combined with theoretical models to determine the reaction characteristics. The important parameters identified from these analyses were then applied to predict the movement of acid fronts and mineral reaction fronts in linear and radial models. General guidelines were drawn to aid in the design of an acid treatment. In a perforated downhole system, the wellbore interacts with the surrounding formation only through the perforations. As the injected fluids flow across the perforation surfaces, a sharp pressure drop occurs in the unpenetrated formation beyond the end of the perforation, resulting in high velocity through the perforation tip. Along the perforation surface behind the tip, fluid velocity decreases toward the wellbore. After the acid fluids have propagated a short distance into the formation, the high-velocity flow from the tip area diverges spherically into a broader region, and its velocity significantly. Fluids from other portions of the perforation penetrate more radially around the perforation itself and move deeper into the formation with less reduction in velocity. Thus the movement of the acid front around the perforation is a function of position and time. Formation properties also have a significant effect on position and time. Formation properties also have a significant effect on the flow behavior in the near-wellbore region. Drilling-fluid damage and perforation damage commonly occurring around the perforation impair the perforation damage commonly occurring around the perforation impair the flow capacity of the perforation and redistribute flow around the perforation in different ways. A crushed zone, which often completely perforation in different ways. A crushed zone, which often completely surrounds the perforation, tend to spread flow over the perforation surface evenly. While shallow drilling-fluid damage diverts the flow away from the wellbore and therefore enhances tip flow. Earlier acidizing models, which were based on 1 D flow in linear or radial systems, cannot be used to evaluate the uneven acid penetration pattern in a perforated system. Assuming the perforation to be ellipsoidal, we derived a 2D model to describe the single-phase flow of an acid through a perforated sandstone that contains two pseudochemical minerals perforated sandstone that contains two pseudochemical minerals (representing quartz and aluminosilicates) dissolving at different rates. The pressure and concentration distributions over the region of interest are obtained by solving the system of governing equations in ellipsoidal coordinates. Fig. 1 shows the perforation ellipsoid and the ellipsoidal flow field. First, the numerical studies have focused on the volumetric movements of acid fronts and mineral reaction fronts in an ellipsoidal flow field under the assumption of constant permeability and constant porosity. The results appear to agree reasonably well with Scbechter's analytical solutions. Empirical equations relating permeability changes to the dissolution of sandstone minerals were incorporated into the model to help examine the consequences of changes in flow patterns and the efficiency of acidizing in removing near-wellbore damage. Perforation skin factor, sp, is used to evaluate the severity of the damage and the effectiveness of a stimulation treatment in our single-perforation system.

Mathematical Model

When an acid flows through a porous medium, it dissolves rock minerals and displaces formation fluids. During this process, the chemical components in the flowing and stationary phases must be conserved. The equation of motion, provided by Darcy's law, is incorporated into the water- and acid-continuity equations to obtain the working equations that we call the pressure equation and the acid-balance equation.