Role of Acid Diffusion in Matrix Acidizing of Carbonates
Authors: Hoefner Mark L. , Fogler H. Scott 
Published: December 2007

Summary.
To increase the efficiency of matrix treatments in carbonates, a new type of retarded acid-in-oil microemulsion system has been developed. The microemulsion is of low viscosity but can exhibit acid diffusion rates two orders of magnitude lower than aqueous HCl. Decreased acid diffusion delays spending and allows live acid to penetrate the rock matrix more uniformly and to greater distances. Coreflood results show that the microemulsion can stimulate cores in fewer PV's and under conditions of low injection rates where aqueous HCl fans completely. The microemulsion could also conceivably increase acid penetration along any natural fractures and fissures that may be present, thus increasing acidizing efficiency in this type of treatment. The relationship between the acid diffusion rate and the ability of the fluid to matrix-stimulate limestone is investigated.

Introduction
The ability to achieve increases in productivity or injectivity by matrix acidizing in carbonate formations is strongly related to the radial distance away from the wellbore to which stimulation occurs. (In this sense. matrix acidizing refers to the treatment of homogeneous rock that is free of natural, interconnected vugs and fractures. ) Because acid penetration and the subsequent enhanced flow of oil or water occur through dominant channels ("worm-holes") that are etched in the rock by flowing acid, stimulation efficiency is controlled by the extent to which channels propagate radially away from the wellbore and into the formation. Under certain acidizing conditions, these channels may not propagate to a significant distance or they may not form at all. Muskat showed the dependence of productivity increase on the radius of the stimulated zone. In wells not affected by near-wellbore damage, stimulation must occur to a distance on the order of 10 ft [3 m] from the wellbore to achieve a 100% productivity (or injectivity) increase. This means that a significant amount of unconsumed acid must penetrate to this distance to bring about the permeability increase. In formations affected by near-wellbore damage, the distances will be smaller. Nevertheless, it is recognized that damage in carbonates beyond about 1 to at most 3 ft [0.3 to 1 m] from the well-bore generally cannot be removed by matrix treatments with aqueous HCl. Here, acid is completely consumed before significant penetration is achieved because the dissolution rate of calcite and other carbonates in aqueous HCl is extremely rapid. In fact, calcite dissolution is transport-limited in HCl at temperatures above 32 degrees F [0 degrees C]; consequently, acid is consumed almost immediately upon flowing from the wellbore into the formation.
Any acid penetration that is achieved is a result of a phenomenon called wormholing that results in the phenomenon called wormholing that results in the formation of dominant channels through which acid can flow. Wormholes form because rock heterogeneity causes some pores or groups of pores to experience pores or groups of pores to experience greater-than average acid flow, and as result, some areas experience accelerated dissolution. Permeability increases because of partial dissolution of the porous matrix, and flow to the partial dissolution of the porous matrix, and flow to the region increases even more. A channel, or wormhole, will form very quickly. Wormholes originate at the wellbore and extend radially in random directions into the formation. The efficiency of the stimulation is determined by the structure of the channels (frequency, length, and direction) because, once formed, the wormholes carry virtually all the flow. Not all the factors that affect wormholing are known, and this random process is extremely difficult to model mathematically. Other investigators have likened wormholing to the flow and reaction that take place in a fracture during fracture-acidizing treatments. This earlier work concludes that there is no way to predict the number of wormholes that will form. It is proposed, however, that if an average wormhole diameter and an acid flow rate per wormhole are assumed (equivalent to guessing the number of wormholes), then a maximum expected wormhole length can be determined. This is achieved by calculating the distance some fraction of the original acid will reach in the channel before spending. This distance. it is concluded, is probably limited by the rate of acid leakoff from the channel to the formation and not by the rate of chemical reaction.
Application of fracture-acidizing concepts to wormholing can be helpful in understanding the effects of such factors as the heterogeneous reaction rate and fluid loss on acid transport in the channels. In fracture treatments, it is usually desirable to try to reduce the rate of acid spending by artificially increasing the viscosity of the fluid.
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