Gas Well Deliverability Prediction - For Hydraulically Fractured (Vertical) Wells In Tight Reservoirs
Authors: Sinha M.K. , Furlong K.D. 
Published: December 2007

Abstract
A procedure has been developed for predicting the deliverability of a gas well which has been completed in a tight-gas reservoir and hydraulically fractured. This prediction procedure is based on the theoretical considerations of a single plane hydraulically created fracture of limited length (penetration). This procedure also assumes that the fracture is properly propped.
Use is made of the Russel-Truitt and Gringarten-Ramey-Raghavan dimensionless pressure drop functions for an infinitely conductive fracture. Fracture length is determined by the Fibonnaci Search Technique to minimize a least square function. The Search Technique is designed to determine the minimum value of a non-linear single variable objective function, where the single variable is the fracture penetration. This is accomplished by creating the objective function which is the sum of the squares of the differences between the calculated flow rates and the actual flow rates during the extended flow portion of the potential test.
The additional pressure drop near the fracture face caused by formation damage due to fracture fluid invasion is accounted for by using a Van Everdingen type dimensionless skin factor, S, for a linear flow system. The dimensionless skin factor is determined from the pressure buildup data collected following the potential test.
The well unloading effects during the early test flow periods are taken into account by utilizing Ramey's approach.

Introduction
The estimation of future production rates of gas wells plays a very important role in the natural gas industry. An accurate and reliable estimate of future deliverability of the well is needed for efficient long range operational planning, compliance with contractual committments, scheduling of facility installation and other investment decisions.
Traditionally, short term flow test data has been used along with some theoretical considerations to predict the future performance of a well. Test data predict the future performance of a well. Test data from a short-term back pressure test has been used since 1940 to estimate the deliverability of gas into a pipeline at a predetermined line pressure. This traditional method consists of using the characteristics of the back pressure equation,
......................(1)
and the gas material balance equation,
............(2)
The characteristics of the back pressure equation are governed by the values of 'Cs' and 'n' which are termed the stabilized performance coefficient and the back pressure exponent, respectively. The values of 'Cs' and 'n' are determined from the actual flow test. The original test procedure for determining 'Cs' requires that the data be obtained under stabilized flow conditions; that is, after the pressure transients have reached the no-flow boundary and the well is flowing in a stabilized or so-called semi-steady state condition. Under this condition the value of 'Cs' does not change with time. In highly permeable formations, only a very short period of time is required to reach these stabilized conditions. In the case of low permeability or tight formations, however, it may take permeability or tight formations, however, it may take months of flow to reach these stabilized conditions and the direct determination of the stabilized flow coefficient 'Cs' by actually flowing the well would be extremely time consuming and wasteful of gas.
In 1959, Poettman and Schilson suggested using the Isochronal test procedure with an extended flow to establish the slope, or exponent 'n' and the stabilized performance coefficient 'Cs'. The variation of the performance coefficient, C with time is used to determine 'Cs', the stabilized coefficient using theoretical considerations.
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