Date of Graduation

1999

Document Type

Thesis

Degree Type

MS

College

Statler College of Engineering and Mineral Resources

Committee Chair

John Loth

Committee Member

Shahab Mohaghegh

Committee Member

Gary J. Morris

Abstract

Hydraulic fractures are created to increase the productivity of oil and gas wells. The extent of improvement depends on the formation permeability, fracture conductivity and the fracture geometry, specifically the fracture length. The cost of fracturing is directly proportional to the volume pumped and the rate of pumping, respectively depending on the amount of proppant and horsepower available. In the design of a well fracturing job, many critical decisions have to be made, related to the desired length, width and height of the fractures to be created. The design specifies the type of fluids pumped and the pumping rate schedule. The pumping rate affects the fluid efficiency FE, which is the ratio between fracture volume created to that of the fluid volume pumped. During the job the bottom hole pressure is monitored online. This signal probably contains high frequency waves, which acoustically define the shape and length of the created fracture. The time required to characterize these high frequency acoustic waves will be less than a few seconds. They may be produced by the stop and start motion of the fluid at the tip, associated with the intermittent finite length crack propagation. The objective of this thesis is to develop a 2-D fracture formation computer code to calculate in real time, the characteristic fracture parameters as a function of position and time such as: width, pressure, fluid leakage and velocity. Then the fracture geometry is frozen in time for a few seconds, while the characteristic shape of the high frequency acoustic waves is being calculated using the method of characteristics. A finite element 2-D fracture-formation computer code was written with the objective of calculating the fracture geometry. In each time step t(j), a new fracture segment is formed. The first segment, with a triangular tip of length xtip(j=i), formed has a closed form solution based on defined inputs and boundary conditions. All other sections require an iterative estimate of the increase in fracture width w(i=1,j) at the casing. The fracture tip pressure is found by calculating segment by segment the: friction pressure loss, fluid wall leakage, inlet velocity, fluid storage due to segment width growth, and outflow rate. When the fracture tip is reached, its length xtip(j) is calculated to satisfy continuity. A special predictor corrector scheme had to be developed to insure convergence to the tip pressure boundary condition, as this method of solution is highly unstable.

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