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Summary

Acidizing of sandstones with HF/HCl mixtures is most frequently applied to remove near-wellbore damage, often in reservoirs with considerable vertical heterogeneity. A previously presented model for such processes in which an organic resin diverting agent was used has been extended to account for any type of particulate diverting agent and to allow for injection of multiple sequences of acid and diverting agent at either constant rates or constant bottomhole pressures (BHP's). When used to design treatments for a typical U.S. gulf coast reservoir, the model has shown that the optimal treatment strategy depends on both diverting-agent efficiency and the desired depth of live acid penetration and that relatively high injection rates appear advantageous for the conditions imposed by the model.

A general model of diverting-agent behavior was developed from filtration theory. A single parameter, the specific cake resistance, is needed to model the diverting-agent behavior in the acidizing simulator. Calculation procedures to determine this parameter from laboratory tests of diverting agents were developed. These tests are either constant-rate, constant-pressure, or variable-rate and variable-pressure experiments; in each case, the specific cake resistance can be extracted from the experimental data. These procedures allow the efficiencies of various diverting agents to be compared on an equal basis.

The sandstone acidizing model was used to design a treatment for a typical gulf coast sandstone reservoir. On the basis of an overall skin factor for the well, various assumptions were made about the distribution of formation damage around this multilayered completion. Treatment results were found to be fairly sensitive to the details of the damage distribution, suggesting that the skin factor alone may not be an adequate design parameter.

Introduction

Removal of near-wellbore damage may be achieved through matrix acidizing where mixtures of HF and HCl are injected into the formation below fracture pressures to react with formation minerals and materials deposited during the production process. Such treatments are usually conducted in reservoirs exhibiting contrasting vertical injectivity, consequently causing uneven placement of treating fluid. Diverting agents are commonly used in this situation to reduce the natural flow of fluid into sections of higher injectivity, thus ensuring a more even distribution. Particulate solids specifically were found to be excellent diverting agents. These cakeforming diverters demonstrated high resistance to flow, resulted in better diversion, and possessed good cleanup characteristics.

A single-well model developed previously simulates the acidization process in heterogeneous reservoirs. By dividing the formation into multiple, noncommunicating layers of various properties, we accounted for vertical reservoir heterogeneity. These layers, in turn, were subdivided radially into concentric cylinders of various physical and chemical properties to allow for incorporation of formation damage by changing near-wellbore properties. This model also included the effect of diverting agent on acid distribution through use of the model equation for the behavior of organic resin diverters presented by Hill and Galloway. From this work, we concluded that the pressure drop across the diverting-agent cake must be comparable to the pressure drop in the formation before effective diversion can happen.

In the diverting-agent model used previously, the pressure drop through a cake was dependent only on the amount of cake deposited. This explains another earlier conclusion that low injection rates promote efficient diversion because at such rates the pressure drop in the formation is low but the pressure drop in the diverting agent remains unaffected (regardless of rate). Using filtration theory, Doerier and Prouvost later offered a more general model of diverting-agent behavior. The equation showed the dependence of the cake pressure drop on the product of flux and amount of cake deposited. The current study uses the same theory to characterize different types of diverting agents and introduces interpretation techniques for the various laboratory tests normally performed in the industry.

From interpretation of test data, a parameter called the specific cake resistance, which directly reflects the efficiency of a given diverting agent, can be computed. This parameter is related to cake and particle properties so that it can render a means of scaling up test data to field situations. We have included this feature in the existing model to enable the prediction or evaluation of treatments aided by any particulate diverting agent. Furthermore, with the added ability to handle multiple sequences of fluids injected at either constant rates or constant BHP'S. this generalized model will be able to simulate normally encountered field conditions. The utility of the acidizing model in designing a treatment for a typical sandstone reservoir is demonstrated.

Characterization of Diverting Agents From Laboratory Data

in general, materials with particle size of less than 5 Am are thought to constitute the class of materials that form compressible filter cakes. The materials used as diverting agents have been reported to have particle sizes ranging from 5 to 44 mum. From this observation, diverting-agent materials may be expected to behave as incompressible cakes and the underlying approach is derived as such.

Ruth et al. depicted the flow through a filter cake as equivalent to that of a bundle of parallel, circular capillaries of equal diameter with length equal to the cake thickness. In doing so, they have assumed that the end effects and wall roughness are negligible and that the cake particles are of the same size and shape, packed randomly without any preferred orientation. Such a model lends itself to the theoretically proven Poiseuille's equation, the derivation of which is also restricted to Newtonian fluid of constant viscosity and density. In addition, if fluid velocity is low, inertial forces will be insignificant, and the driving force is opposed only by viscous shear present between the fluid layers.

By equating surface areas of capillaries to surface areas of bed particles and replacing capillary radii by equivalent hydraulic radii of the irregular pore spaces, we can give the resulting pressure drop across a cake as

(1)

Grouping the intrinsic cake properties on one side of the equation and the measurable quantities on the other side yields the definition for the specific cake resistance, alpha:

(2)

The specific cake resistance is intrinsically related to the ability of a cake to impede flow. It forms an equal basis on which various cake-forming materials can be compared.

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