Optimum Fractures in High Permeability Formations
Authors: Morales R.H. , Norman W.D. , Ali Syed , Castille C. 
Published: December 2007

Abstract
This paper describes an analytical model that combines the design of tip screen out (TSO) fractures with estimates of reservoir production to determine the optimum propped length for high permeability formations. The model is validated with reservoir simulations. The model has been used to perform sensitivity studies on frac-packing candidates (fracturing combined with gravel packing) to determine the influence of the propped fracture width and length on the production. A field example is included to demonstrate the benefit of appropriate fracture design.

Introduction
The frac-packing completion of moderate to high permeability formations in the Gulf of Mexico, North Sea, Alaska, Indonesia and other regions, have increased dramatically over the last five years. The early frac-packing attempts had limited analytical basis. A better understanding of the influence of reservoir mechanical properties, tubular configuration, and damage mechanisms has emerged over the last few years.
While exceeding production of similar wells completed with conventional gravel packing techniques, the performance of the fractured wells has not always fulfill the expectations of negative skin completions. This is partially due to the lack of scrutiny for optimum parameters in the design phase, or placement problems during the treatment execution. Fracture length, conductivity (proppant concentrations and fluid damage), production and pressure behavior have all been studied to describe and evaluate the disparities with field results. Some conclusions of these studies are that the damage (mechanical and fluid induced) will impair production if the fracture is not properly designed. Certain aspects of radial flow (high pressure drops and high reservoir fluid velocities) create an environment for fines migrations, scale, asphaltene, and paraffin deposition. These problems can be mitigated by proper placement of high conductivity fractures which minimize pressure drop and the fluid velocities.
Evaluations of fracture performance using Cinco-Ley et al.'s indicate that maximizing the fracture conductivity is the first priority in the designing of fracture treatments. This implies that limited benefit is gained by fractures in high permeability formations where Fcd&lt;1. However, this paper shows that when fracture conductivity is coupled to the production forecast, there is an optimum fracture geometry and that the lower Fcd fractures can have a significant impact on the economics of the completion.
The proper design of any fracture should consider the optimum proppant concentrations in the fracture and corresponding optimum propped length.
The model described in this paper combines the fracture conductivity concept with production forecast to obtain an economical TSO design.

Description of the model
The equations used in the model are described in the Appendix. The following three steps outline the basis of the model:Analytical solutions given by Eqs. A-1 (or A-2) and A-3 determine the time to TSO and the fracture fluid efficiency for several fracture lengths. Figure 1 shows the relationship between fluid efficiency and tip screen-out time (given by Eqs. A-1 and A-3) for fracture half-lengths of 20 ft and 40 ft for the parameters listed in Table 1.An analytical solution based on fracture volume balance during post injection decline (Eq. A-5) determines the final pumping time for each fracture length. Figure 2 shows a relationship between the final pumping time and prescribed proppant concentration. The results in Figure 2 are independent of fracture length.
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