Determining an optimal fracture design can be a complex process, involving large amounts of computer and engineering process, involving large amounts of computer and engineering time. This paper describes a method that utilizes mixed integer-linear programming to adjust a treatment's fluid selection, pump rate, proppant volume, and frac dimensions to arrive at an optimal design. This method can be readily adapted to most any fracture design model.
The optimization method presented in this paper has shown to be able to design less expensive fractures for a given stimulation ratio in less time than a trial and error approach. In the examples presented, variable stimulation costs (proppant, fluid, and presented, variable stimulation costs (proppant, fluid, and hydraulic horsepower charges) were reduced by 50% compared to trial-and-error-derived designs.
This paper is divided into two portions to separate the applicability of this method from the rather dry linear programming formulation. The main section of the paper provides an overview of the method and an example application. The second section covers the detailed derivations in 2 appendices. Appendix 1 describes the linear program formulation. Appendix 2 describes the methodology used to convert the optimal frac selections into a treatment schedule.
Linear Programming Overview. Linear programming (LP) is not a computer programming language, but rather a mathematical technique derived in the 1930's. The purpose of linear programming is to maximize or minimize some desired objective subject to certain constraints. For this paper', LP is used to determine the most economic combination of fluid type, fluid volume, pump rate, and proppant volume. This paper presents the formulation of the LP model, and includes presents the formulation of the LP model, and includes references for LP software.
The Problem. Normally, a frac design is based on a combination of an engineer's experience and a number of design sensitivities. These sensitivities may evaluate relationships such as the cost I performance tradeoff of different frac fluids. The frac designer can find that while a high viscosity fluid may be very efficient, its high friction pressure may make it an expensive choice due to high hydraulic horsepower requirements. Additionally, it may be found that fracs of different dimensions give the same performance, but at widely different costs. The resulting design problem represents a 5 dimensional "Rubik's Cube" that an engineer must manipulate to determine the best design.
The final-frac design may eventually be based more on relieving "calculation fatigue" than designing a cost-effective treatment. The final design will get the job done and certainly be profitable, but perhaps a treatment exists that will accomplish the same job with less cost. To do this, an LP technique is needed that will investigate all possible combinations of design parameters to determine the most cost-effective design.
The Solution. The method presented in this paper does not replace any established frac design methods, but rather seeks to augment existing methods. To optimize a treatment, the following 3 steps are taken:
A series of calculations are made to determine the performance of each fluid "candidate" at different pump rates. performance of each fluid "candidate" at different pump rates. P. 161