Determination of Proppant and Fluid Schedules From Fracturing-Pressure Decline

Abstract

Summary A procedure is presented for designing a fracture treatment when little or no information is available. This procedure is based on fluid efficiency, which is defined as the fracture volume divided by the injected fluid volume. The fluid efficiency for a treatment was found determine the pad size and optimum proppant schedule completely without any assumption of the appropriate fracture-geometry model or associated parameters. The efficiency was also found to determine the fluid's parameters. The efficiency was also found to determine the fluid's exposure time to temperature. This determination requires an assumption for the portion of the fracture face that is cooled during a treatment. The exposure is important for defining the fluid additives of relatively large and high-temperature treatments. The fluid efficiency can be determined from a pressure-decline analysis for a calibration treatment performed between the actual stimulation treatment. In addition, if the performed between the actual stimulation treatment. In addition, if the appropriate geometry model is assumed, the decline analysis of the calibration treatment provides inferred values of fluid-loss coefficient and fracture width and penetration. Also, for the case when the calibration treatment is smaller than the actual stimulation, analyses are presented for predicting the relative change in efficiency, width, and presented for predicting the relative change in efficiency, width, and penetration for the treatments. penetration for the treatments. Introduction The analysis of the fracturing-pressure decline after a fracturing treatment is given in Ref. 1 for the Perkins and Kern (PK) model of a fracture. This analysis provided predictions of the fracture's penetration, width, fluid-loss predictions of the fracture's penetration, width, fluid-loss coefficient, time of closure, and fluid efficiency on the basis of pressure response during the period from the end of injection to the time the fracture closes. Later, the analysis was generalized 3 for the Khristianovic, Geertsma, and de Klerk (KGD) model and for the penny or radial Model; consideration was also given to the effect of closure pressure (i.e., in-situ rock stress) changes during the decline period. The fluid efficiency is the fraction of the injected volume that is in the fracture at the time injection stops, and the remaining fraction is lost to the formation by fluid loss. Important conclusions were (1) that the fluid efficiency could be found fromexpressions either in terms of the time for the fracture to close or in terms of the ratio of net pressure (i.e., excess pressure above closure pressure) to a pressure characteristic pressure above closure pressure) to a pressure characteristic of the rate of decline (i.e., match pressure), (2) that these expressions were independent of any fracture model, and (3) that the expression based on time to close was independent of any potential changes in the closure pressure. Because fluid efficiency can be determined for a fracture treatment independent of any fracture model, the prospect arises that the efficiency for a calibration prospect arises that the efficiency for a calibration treatment could be used to design a subsequent stimulation treatment without the need for a model and such associated parameters as height, loss coefficient, and viscosity. This parameters as height, loss coefficient, and viscosity. This would be especially desirable for treatments in new prospect areas where little if any information may be prospect areas where little if any information may be available to determine what model or associated parameters are appropriate. The information desired includes the fluid volume to be injected, the rate of injection, the proppant addition schedule, the resulting propped width and length, and the time that the fluids would be exposed to temperature. The exposure time is required for selecting the type and amount of fluid additives. The rate of injection is generally prescribed on the basis of horsepower requirements and/or pressure limitations of the wellbore tubulars or wellhead. For a new area, the volume would generally be based on an estimate or on budget considerations, but after some experience in the area, it would be based on the requirements to achieve a relative change in penetration from that of earlier treatments. The proppant penetration from that of earlier treatments. The proppant schedule for a treatment in a new area is critical for an effective treatment and accurate appraisal of the prospect; an optimum proppant schedule, however, is the most difficult and critical of any of the required information to obtain. The proppant-free pad could range between 20 and 60% of the total volume with a significant error leading to less than the potential penetration because of a screenout or a significant portion of the fracture with no or with insufficient proppant. In the following sections, equations and procedures are developed that indicate that the optimum pad size, proppant schedule, and fluid exposure time for a stimulation proppant schedule, and fluid exposure time for a stimulation treatment can be obtained from the efficiency of a relatively smaller calibration treatment, and that this can be achieved without any assumptions concerning the appropriate fracture model (slight dependence of exposure time on the model), associated parameters, or a computer. SPEPE p. 255