A Computer Study of Horizontal Fracture Treatment Design
Authors: Lowe D.K. , McGlothlin B.B. , Huitt J.L. 
Published: December 2007

Abstract
Published correlations for the principal aspects of hydraulic fracturingwere combined into a digital computer program to facilitate the study ofinterrelated variables. The computer program includes individual relationshipsfor fracture width during pumping, fracture area generated, propping agentembedment, flow capacities of propped fractures and transport of proppingagents in horizontal fractures. The effects of more than 20 treatment andformation parameters on the predicted results of hydraulic fracturingtreatments were studied. The effects of these parameters were determined forfracture width during injection,fracture width after the overburdencomes to rest on the propping agents, assumed not to be crushed,generatedand propped fracture area,location and concentration of propping agents inthe fracture when injection ceases,flow capacities of the various proppedsections of the fracture andexpected increase in the well productivity.
The effects of propping agent, formation and fracturing fluid parameters onwell productivity are discussed. The parameters that were found to have themost pronounced effects on hydraulic fracturing treatments are injection rate, treatment volume, fracturing fluid coefficient, size and amount of proppingagent, spearhead volume, well damage radius and formation capacity.

Introduction
Many correlations have been published for predicting effects of variousparameters that are considered in the design of hydraulic fracturingtreatments. The Carter equation can be used to predict generated fractureradius as a function of fracture width, fracturing fluid leakoff and otherparameters. Fracture width can be determined by use of the Perkins and Kerncorrelation in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et al. have reported methods of predicting the location ofpropping agents in fractures when pumping ceases. The former study isapplicable to the case where the ratio of propping agent diameter to fracturewidth is less than 0.1. The latter is applicable when this ratio is greaterthan 0.1. These studies showed that the propping agent placement inhorizontal-radial fractures depends principally on how the individual particlesare transported in the fracture by the carrying fluid. Particle transport infractures is determined by local fluid velocity in the fracture, fluid andparticle properties, and the size of the particle relative to the fracturewidth. The distribution of propping agents, effective overburden pressure andformation rock strength control the propped fracture width by controlling theextent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated for the various regions of thefracture. The flow capacities and the radial extent of these regions can becombined with reservoir information to predict the productivity increases forfractured wells. In all these studies, the effects of certain treatment and/orreservoir parameters on one facet of fracturing can be predicted only if otherfacets which the parameters affect are fixed. For instance, fracture width andradius are interrelated; that is, to calculate the value of one, the value ofthe other must be known. Also, some parameters influence more than one aspectof fracturing. For example, proppant transport is a function of both fracturewidth and fluid viscosity, but fracture width is itself a function of fluidviscosity. Since these calculations are complex and the parametersinterrelated, it is not possible to write an equation with which the over-alleffects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are mostsignificant in hydraulic fracturing treatments have been incorporated into adigital computer program.

Computer Program
The program, which was written for an IBM 7094 computer, can be used topredict results of most of the combinations and values for the treatmentparameters that are ordinarily considered for fracturing treatments. Aspearhead of fracturing fluid and a propping agent-carrying fluid withdifferent fluid properties can be taken into account. Also, the total volumesand relative amounts of the spearhead and carrying fluids can be varied. Twodifferent propping agents (as used in tail-in operations) and a wide range offormation properties and injection rates are considered. The computer program(Fig. 12) consists of several sets of calculations. First, the final floodedfracture radius and average fracture width at the cessation of pumping arecalculated. This is done by simultaneous solution of the Perkins and Kernfracture width equation and the Carter equation for flooded fracture radius(equations used in the computer program appear in the Appendix). The next stepis to determine local fluid velocity in the fracture as a function of time andradius. Since it is, not possible to write this function in closed formexpression, a table of velocity values is generated by the program and storedfor subsequent use.