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SPE 159687

Productivity Index and Inflow performance of Hydraulically FracturedFormationsS. Al Rbeawi, SPE, D. Tiab, SPE, University of Oklahoma

Copyright 2012, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 8-10 October 2012.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not beenreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, itsofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission toreproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

AbstractProductivity index and inflow performance of horizontal wells intersecting multiple hydraulic fractures are of great

importance. This importance comes from the fact that the fracturing process has become a common stimulation technique in

the petroleum industry. However, few models for the productivity index and inflow performance have been presented in theliteratures due to the complexity governing this topic.

This paper introduces a new technique for estimating the pseudo-steady state productivity index of horizontal wellsintersecting multiple hydraulic fractures. Based on the instantaneous source solutions for the diffusivity equation, seven

analytical models have been derived for different source solutions. Four of them represent the effect of the formation height

and fracture height (the vertical direction), while the other three represent the solution for the horizontal plane. For vertical

hydraulic fractures, the four solutions of the vertical direction, representing the pseudo-skin factor, are almost neglected. Thethree horizontal plane solutions are the main parameters that control the productivity index and inflow performance of the

fractured formations. In this technique, the horizontal wells are acting in finite reservoirs where the pseudo-steady state flow

is expected to develop. Reservoir geometry, reservoir properties, and fracture dimensions were considered in this technique.

The number of fractures and the spacing between them were also investigated in this study. A new analytical model forestimating the required number of hydraulic fractures has been introduced in this study based on the reservoir drainage areaand the surface area of fractures.

The models have been used to establish several plots to estimate the shape factor group based on the number of fractures

and the half fracture length. This group is one of the main terms in the productivity index model. Several plots for the shapefactor of fractured formations have been introduced in this study. The results obtained from the new technique have been

compared with the results from previous models. Several numerical examples will be included in the paper.

IntroductionHydraulic fracturing is an important stimulation technique that has been widely used in conventional and unconventional

oil and gas reservoirs all over the world. The technique involves the creation of a fracture or fracture system in porous

medium to 1) increase the contact area between reservoir matrix and the wellbore, 2) overcome wellbore damage, 3) improve

oil and gas productivity in low permeability and tight gas reservoirs, 4) enhance the connectivity of naturally fracturedreservoirs, and 5) facilitate the production from shale gas reservoirs. During the last two decades, horizontal wells with multi-

stage hydraulic fractures have become a common applied completion technology in the petroleum industry. Because of the

large reservoir contact area connected to the wellbore, hydraulic fractures can greatly improve a wells productivity.The productivity index is a critical parameter in the oil and gas production process and its management. Regardless of

the type of formation and the type of wellbore, the index is defined as the amount or volume of reservoir fluids that can be

produced daily by one psi pressure drop at the sand face. For a horizontal well with multiple hydraulic fractures, the

productivity index is influenced by several factors such as the number of fracture, the spacing between them and the fracturedimensions. Reservoir permeability and reservoir fluid properties have great influence on the productivity index as well as

the geometry of the drainage area. Several models have been introduced during the last two decades for the productivity

index of fractured formations. The high cost of the fracturing process and the serious need for a technique that can help in

evaluating the benefits of the continuously increasing number of fractures are the two motivating factors to develop the

productivity index models for fractured formations.Raghavan and Joshi (1993) presented a method to evaluate the productivity of wells with hydraulic fractures. A general