Analysis of Commingled Gas Reservoirs With Variable Bottom-Hole Flowing Pressure and Non-Darcy Flow
Authors: El-Banbi Ahmed H. , Wattenbarger Robert A. 
Published: December 2007

Abstract
This paper presents an extension of the Layered Stabilized Flow Model (LSFM) previously presented by the authors for commingled gas wells. The LSFM gives a method for reserve estimation and production forecasts. The extension in this paper takes into account bottom-hole flowing pressure (pwf) variations and non-Darcy flow. Simulator verifications and field examples are given.
The LSFM couples a material balance equation and the stabilized gas flow equation, including non-Darcy flow, for each layer of the commingled well. The method is simple and lends itself to spread-sheet applications. Only the flow rate and the pwf (or at least the surface pressure) history need to be known, along with the initial reservoir pressure and gas properties. The LSFM parameters are determined by history-matching the well's production rate over a selected calibration period.
The method shows excellent results for moderate to high permeability reservoirs, even with long shut-ins and considerable variation in pwf. (The model accounts for backflow between layers during shut-in periods.) The results of several simulated and field cases are reported.
The results of the LSFM provide estimates of OGIP and the two flow equation parameters for each layer. These values can then be used for forecasting.

Introduction
Decline curve analysis is sometimes a very practical tool for reserve estimation and performance prediction. It started as a rate forecasting technique by extrapolating the production trend as early as the beginning of the century. Later, Arps presented empirical equations that express the rate performance as a function of time. Fetkovitch combined some analytical solutions for transient flow with Arps empirical equations on a log-log graph and developed a type-curve matching technique for production data. Carter developed other type curves specific for gas wells to take into account the variation of gas properties with pressure. Fraim and Wattenbarger developed a pseudo-time function to force the production data of gas wells to match the liquid solution (b=0) for constant pwf production. This work was followed by other pseudo-time approaches that account for variation in pwf Different approaches of combining M.B equation with the gas flow equation for single-layer reservoirs were also presented by different authors. Similar techniques were used by others to solve the single-layer gas reservoir problems for production at variable pwf. Fetkovich et al. used type-curve matching to analyze commingled gas reservoirs. El-Banbi and Wattenbarger used the approach of combining the gas M.B equation with the stabilized flow equation to analyze commingled gas reservoirs producing at constant pwf.
The current paper extends the method used in Ref. 1 to include the variation in pwf and non-Darcy flow. This method can be used in analyzing production data and gives estimates of OGIP and flow coefficients for each layer in commingled reservoirs.
The Layered Stabilized Flow Model (LSFM) Background. Traditionally for oil wells, engineers estimate the productivity index of a well, j, from long shut-in tests. This productivity index (assumed constant with time) gives the relationship between the production rate and the "draw-down", (p - pwf), of the well:
(1)
The equivalent relationship for a gas well is
(2)
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