A kinetic model for the reaction of Hydrochloric acid with limestone bas been determined. Reaction order and rate constant for this model were calculated from experiments where acid reacted with a single calcium carbonate plate. Experiments were performed so that acid flow past the plate and mass transfer rate to the rock surface could be calculated theoretically. The resulting model, therefore, accurately represents the acid reaction process at the rock surface and is independent of mass transfer rate. Combination of this model with existing theory allows prediction of acid reaction during acid fracturing operations. A model for acid reaction in wormholes created during matrix acidization treatments is presented along with data for reaction of hydrochloric, formic and acetic acids in a wormhole. Factors limiting stimulation in acid fracturing or matrix acidizing treatments are then discussed. Introduction To predict the stimulation ratio resulting from acid fracturing or matrix acidizing treatments it is necessary to know the rate of acid reaction under field conditions. In acid fracturing treatments, for example, reaction occurs as acid flows through a narrow fracture. Reaction in a matrix treatment occurs during flow through wormholes (channels of roughly circular cross-section) created by acid reaction. In both treatments, a large amount of mixing occurs during flow through the fracture or channel as a result of tortuosity and wall roughness. Reaction rate can be obtained from experiments, or predicted by theoretical calculations that accurately model field conditions. In general a theoretical procedure is preferred since it can be used without recourse to laboratory testing. Acid-reaction-rate data have been reported from a number of experiments intended to simulate acid reaction in field treatments. Tests most often used are:the static reaction rate test, in which a cube of limestone is contacted with unstirred acid at a known ratio of rock surface area to acid volume;flow experiments, where acid is forced to flow between parallel plates of limestone; anddynamic tests, whine limestone specimens are rotated through an agitated acid solution. In general, these tests model some aspects of the reaction process, such as area to volume ratio, or acid flow velocity, but do not accurately model all field conditions. To obtain an accurate mathematical model for field treatments, assuming fracture or wormhole geometry is known, it is necessary to characterize acid reaction kinetics at the limestone surface, rate of acid transfer to the surface, and rate of fluid loss from the fracture or wormhole. (Each of these processes is shown schematically in Fig. 1.) processes is shown schematically in Fig. 1.) Reaction kinetics are independent of the geometry in which reaction occurs; therefore, once kinetics have been determined for a given acid-rock system field treatments can be simulated by prediction of the rate of acid transfer to the surface and fluid loss to the formation. Unfortunately, experiments reported to dare do not allow determination of a kinetic model. SPEJ P. 406

A model has been developed that accurately predicts acid penetration distance; it allows the effects of fracture geometry, acid injection rate, formation temperature, acid concentration, and rock type to be included in the treatment design. Results predicted by the model can be used in modifying acid treatments to maximize the stimulation ratio. Introduction Acid fracturing is a production stimulation technique that has been widely used by the oil industry. In such a treatment, acid or a fluid used in a pad ahead of the acid, is injected down the well casing or tubing at rates greater than the rate at which the fluid can flow into the reservoir matrix. This injection produces a buildup in wellbore pressure sufficient to overcome compressive earth stresses and the formation's tensile strength. Failure then occurs, forming a crack (fracture). Continued fluid injection increases the fracture's length and width. Acid injected into the fracture reacts with the formation to create a flow channel that remains open when the well is put back on production. To achieve reservoir stimulation, an acid fracturing treatment must produce a conductive flow channel long enough to alter the flow pattern in the reservoir from a radial pattern to one that approaches linear flow. McGuire and Sikora conducted an analog simulation of the productivity of a fractured well that serves as the basis productivity of a fractured well that serves as the basis for predicting the stimulation achievable with vertical fractures. Their study indicated that the variables that determine stimulation ratio are the ratio of fracture length to drainage radius, L/re, and the ratio of fracture conductivity to formation permeability, wkf/k. To design an acid fracture treatment, therefore, it is necessary to predict the fracture geometry during the treatment, the predict the fracture geometry during the treatment, the conductive fracture length, and the fracture conductivity created by acid reaction. A number of authors have studied various aspects of acid fracturing treatment design. Methods for predicting fracture geometry were first proposed by Howard and Fast. Techniques that give improved results have recently been presented by Keel and Geertsma and de Klerk. Although presented by Keel and Geertsma and de Klerk. Although these last two calculation procedures differ somewhat in formulation, the resulting geometry predictions are in agreement. Either procedure, therefore, can be used to predict the dynamic fracture geometry in acid fracturing predict the dynamic fracture geometry in acid fracturing treatments. Acid reaction characteristics have been studied in static reaction tests by several authors and design procedures using data from these tests were proposed procedures using data from these tests were proposed by Hendrickson et al. Use of the static test to design acid fracturing treatments is of marginal value since the test models only the ratio of fracture area to acid volume. An improved design procedure was presented by Barron et al., who studied acid reaction by flowing acid through a channel between limestone plates and derived a correlation to relate acid penetration distance along a fracture to treatment variables. The usefulness of the correlation is limited, however, since the experiments were run in a smoothwalled fracture, at room temperature, and with the fracture oriented in a horizonal plane. Smith et al. studied acid reaction at high temperatures in a reaction cell where reactive plates of limestone were rotated through acid and noted the effect of velocity on acid spending time and acid penetration. JPT P. 849

Dynamic fluid loss tests provide the best method for simulating the fluid loss process during hydraulic fracturing. Through the use of these tests and a reasonable theoretical model for the rate of fracture growth, fracture length can be predicted with acceptable accuracy. Introduction Successful design of hydraulic fracture treatments depends upon accurate knowledge of the fluid loss properties of the fracturing fluid. Howard and Fast properties of the fracturing fluid. Howard and Fast gave the first description of the fluid loss process and developed equations relating fracture area to fluid and formation properties and treating data. This development was based upon static filtration tests similar to the API mud filtration test. More recently, Hail and Dollarhide have shown that the static fluid loss test does not adequately represent conditions under which additives perform in a fracture treatment. They suggest using a dynamic fluid loss test to determine fluid loss parameters, and they develop an alternative form of the Howard and Fast equation for fracture area. In addition, they give data demonstrating some of the effects found in dynamic tests that are not present in static tests."Dynamic fluid loss" in this paper refers to fluid leakoff from a fracture when a high flow velocity along the fracture exists at the point where fluid leak-off occurs. This is the normal situation since hydraulic fracturing produces a long, narrow crack along which fluid flows at velocities up to several hundred feet per minute. High velocity is maintained far down the fracture even though volumetric flow rate decreases as the fracture becomes progressively more narrow. When additives are used, laboratory fluid loss data based on the older "static" test (no flow across the surface at which fluid leakoff occurs) are not representative and a "dynamic" fluid loss test should be run. In a dynamic fluid loss test, a high-velocity stream of fluid, which inhibits thick filter cake formation, moves past the rock surface at the same time fluid enters the core. As shown in Figs. 1 and 2 fluid loss during this test can be divided into three regimes:control by reservoir properties,control by reservoir properties and filter cake, andcontrol by steady-state filter cake. Initially, pressure drop is totally dissipated across the core and fluid leakoff occurs as if no additive were present. Next, a filter cake begins to form and leakoff present. Next, a filter cake begins to form and leakoff velocity is lower because some pressure drop occurs across the cake. Finally, a steady state is reached at which the cake has a constant thickness and fluid leakoff velocity is constant. Flow velocity through the steady-state cake is dependent upon flow velocity across the rock surface, upon fluid and additive properties, and upon rock pore size. In this paper the properties, and upon rock pore size. In this paper the volume of fluid loss required to allow formation of a steady-state filter cake is termed the -spurt lose' (denoted Vsp), and the steady-state cake is described by the leakoff velocity, V(L). Filter cake thickness formed in a dynamic test is limited since particles outside the matrix are subjected to large shearing stresses. To illustrate the type of cake formed, Fig. 3A shows the face of a core exposed to a granular additive in oil and Fig. 3B shows one exposed to gelled water-silica flour (in these tests, additive contacted only a 0.75-in. strip across the core). These photographs show that cake formed by Use additive used in oil is almost entirely within the rock, since all rock characteristics observable outside the test zone are visible inside the test zone. JPT P. 882

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A procedure is developed for predicting changes in the porosity distribution in a sandstone resulting from reaction with hydrofluoric acid. This procedure is based on a theory for slow heterogeneous reactions in a porous solid where the solid matrix is consumed in the reaction Process. Reaction-rate data for use in this theory are obtained from experiments where acid is injected through short cores and effluent concentration measured using a fluoride specific ion electrode. This rate is found to be first order in hydrofluoric acid concentration. Variations in rate with temperature and quantity of rock dissolved are shown. Introduction Mixtures of hydrofluoric and hydrochloric acid are used to stimulate gas and oil production from sandstone reservoirs by increasing formation porosity and permeability near the wellbore. This porosity and permeability near the wellbore. This acid will react with almost all constituents of naturally occurring sandstones, such as silica, feldspar, clays, and calcareous material. In order to utilize this acid effectively, it is necessary to predict where acid reacts and changes that occur predict where acid reacts and changes that occur with reaction. Chemical reactions between hydrofluoric acid and silica or calcite in the rock matrix are simple, well known reactions. However, reactions with silicates such as clays or feldspars are complex since these minerals occur as three-dimensional lattices with only average empirical formulas. Examples are kaolinite ([A Fe +3 Mg]-Si O1.8 0.1 0.1 2 5 [OH]. Ca), montmorillonite (A Mg Si4 0.05 1.67 0.33 4 O [OH] . NA), and feldspars such as albite10 2 0.33 ([NaSi A ]). In the reactions shown below the3 8 reaction of sodium silicate is used to represent hydrofluoric acid reaction with silicates found in the matrix. REACTION WITH SILICA SiO + 4HF SiF + 2H O2 4 2 SiF + 2HF H SiF4 2 6 REACTION WITH SILICATES (FELDSPAR OR CLAYS) Na SiO + 8HF SiF + 4NaF + 4H O4 4 4 2 2NaF + SiF Na SiF4 2 6 2HF + SiF H SiF4 2 6 REACTION WITH CALCITE CaCO + 2HF CaF + H O + CO3 2 2 2 Reaction of HF-HCl mixtures with silicates and quartz has been the subject of studies by Blumberg, Blumberg and Stavinou, Gatewood et al. and Smith and Hendrickson. These studies indicate that the reaction is first order in HF concentration and that reaction rate with silicates is at least 10 times faster than reaction with silica. To dare, a reliable method for relating reaction data taken on finely ground silica, dispersed clays, or glass slides to the acidization process in a sandstone formation has not been developed Figs. 1 and 2 are photomicrographs of a Berea sandstone core illustrating the system in which acid reaction occurs. In these photomicrographs silica grains are black, and a few feldspar grains are apparent because of their internal porosity, which gives a streaked appearance. Unfortunately, clay or calcite cannot be differentiated from the pore space since all appear as an area shading from pore space since all appear as an area shading from gray to white. It is apparent that the heterogeneous nature of the porous material greatly complicates the reaction problem. For this reason, a theory including mass problem. For this reason, a theory including mass transport, surface kinetics, and a statistical representation for the porous material is required to describe acid reaction. SPEJ P. 306