A new mathematical model has been developed which considers more of the variables encountered during fracture acidizing treatments than previous models. In particular the variables include, wellbore cooldown, temperature profile of fluid in the fracture, the fracture geometry created by both non-reactive and reactive fluids the spending of the leading edge of the acid, and the conductivity of the etched fracture faces. Productivity increases calculated by the new program correlate more closely with actual field results than those calculated by previous programs. This paper describes the previous programs. This paper describes the method of handling the variables in setting up the new model and presents the equations used to describe the reaction rate of the acid. Introduction Fracture acidizing has been used for stimulating wells for over 25 years. The techniques used have developed more as an art, than a science, often based on intangible ideas, rather than on predictable facts. Although a mathematical model has been available since the early 1960's, little correlation has been observed between predicted and field results. One reason for this undoubtedly was due to the use of the acid as both the hydraulic fracturing fluid and as the reactive fluid. Another was the inadequacy of the model to describe the rheological and physical properties of the fluids in the fracture. properties of the fluids in the fracture. Only when treating techniques changed, in which better results were obtained by creating the fracture with a non-reactive pad fluid ahead of the acid, was serious effort directed toward describing the conditions or properties of the fluids in the fracture. Equations were developed first to describe the cooldown of the wellbore area, as illustrated by Ramey's "Wellbore Heat Transmission" equations in the Appendix. Then, Whitsett and Dysart, and later Sinclair, proposed methods for describing the proposed methods for describing the temperature profile of fluids within a hydraulic fracture. Hall and Dollarhide provided basic equations for considering the fracture geometry created by more than one fluid within the fracture.

The placement of a propping agent in hydraulically created fractures is a more adequate basis for predicting the folds of increase after a job. This is based on the premise that all unpropped areas of the created fracture eventually heal. Thus, the penetration of the prop pack into the reservoir and the amount of fill-up in the fracture determine the stimulation results. INTRODUCTION PRESENT METHODS of predicting the results of stimulation treatments are based on the productivity index ratios developed by McGuire and Sikora(1) (Figure 1). The predicted folds of increase are in relation to the conductivity ratio before and after fracturing and the penetration of the producing formation. This assumes that the propping agent supports the entire area of the hydraulically created facture(2). Although the industry has recognized for some time that the propping agent neither penetrates the full length of the fracture nor gives complete fill-up, the complexities of describing the placement of the prop have prevented using this feature in the treatment design. Limited use has been made of the settling-rate method for describing the extent which the prop pack penetrates the vertical fracture. The quotient of the vertical extent of the fracture and the settling rate gives the maximum time the prop is suspended by the fluid. The product of this time and the velocity of the fluid in the fracture gives the maximum distance the prop penetrates the fracture. Stokes Law can be used to predict the settling rate in Newtonian fluids, but is not applicable for non-Newtonian or power-law fluids. Kerns(3) et al. and Babcock(4) et al. have made studies on the transport of prop in vertical fractures, introducing the term ?equilibrium velocity' to the industry. Equilibrium velocity is the minimum linear velocity required to keep the prop moving through the fracture. A comparison of the settling-rate method and the equilibrium-velocity method is illustrated in Figure Z. However, as is known, little has been done toward using these methods for predicting the placement of prop in the fracture. One reason for this is that most of the fluids employed in these studies have been Newtonian, and the majority of the fracturing fluids are non-Newtonian. For this reason, a study was undertaken to expand the available information on commonly used fracturing fluids, such as gelled water. Laboratory tests were run in a plexiglas model of fixed, but variable, fracture width. The simulated vertical linear fracture was 2 ft in height by 6 ft long. Fracture widths were variable from 0.1 to 0.5 inch. Prop-laden fluids passing through this fracture exhibited the same general phenomena. While pumping down the pipe, the prop is fairly evenly dispersed in the fracturing fluid. However, as the fluid 'turns the corner, going into the fracture, centrifugal force and gravity concentrate the prop in the fluid moving through the lower part of the fracture. The bulk of the prop moves along the bottom of the fracture, as a fluidized bed.

models where no leak-off occurred as well "as in a vertical model with leak-off through one Production increases resulting from face. Other authors 192s3,4 have demonstrated fracture treatments should be based on the the same phenomena. To the best of our knowconductivity and location of the propping ledge no one has published model studies which agent -not on the area created by the frac demonstrate that mono-layer or partial monofluid. Model studies show that in conven-layers are obtained in conventional frac tio"nalfracture treatments propping agents treatments, i.e., where low viscosity gelled settle to the bottom of a fracture forming oil or water is used as the fracturing fluid. a packed pile of prop. The location and dimensions of the pack are dependent on the With few exceptions field treatments physical properties of the prop, fluid and designed on the basis of mono-layer or partial formation, the geometry, volume and length monolayer concepts have not responded any of the fracture, and the pump rate.better than conventionally designed treatments. Lab studies, on the other hand, show f~acture This paper presents a mathematical conductivities of partial monolayer are much procedure for predicting the location and greater than conductivities of a pack. We dimensions of the prop pack -ina vertical believe this inconsistency is evidence a pack linear fracture. A computer program has occurred. been prepared and is currently being used in designing fracture treatments.Our model studies supplied a considerable amount of equilibrium velocity data. INTRODUCTIONEarlier work had described the areal extent of a prop pack where no leak-off occurred. Studies we have made in models of Our goal was to describe both the areal exvertical and horizontal fractures show that tent and location of the prop pack under in convectional frac treatments props end up conditions where leak-off occurred, in a multilayer packs. We observed this in

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ABSTIUCTExtremely viscous fracture fluids have provided a new tool for stimulation of wells which previously have not been considered good candidates for conventional fracturing techniques. Soft sands and more permeablẽ omaticrl~~re~he~rim=ry t2rget~for the super thick fluids, but they have also performed well in retreatment and other applications.Super thick fluids function by creating wider fractures and providing better prop 2fi~tE~CiO~Of theẽSl WQill.The extremely high injection rates and large volumes of present treatments are not required. l%is paper will discuss the various oilbase and water-base fluids currently available. A theoretical comparison of fracture area, conductivity increase, and productivity increase obtained by conventional and super thick fluids under similar conditions is presented. Comparative field results of conventional and super thick fluids are also shown.