Type Curves for Finite Radial and Linear Gas-Flow Systems: Constant-Terminal-Pressure Case

Carter, Robert D., SPE, Amoco Production Co. Abstract This paper presents gas-production-rate results in type curve form for finite radial and linear flow systems produced at a constant terminal (bottomhole) pressure. These produced at a constant terminal (bottomhole) pressure. These results can be used in the analysis of actual gas and oil rate/time data to estimate reservoir size and to infer reservoir shape. The type curves are based on dimensionless variables that are a generalized form of those presented previously. In addition, an approximate drawdown previously. In addition, an approximate drawdown parameter is presented. Example applications that parameter is presented. Example applications that demonstrate the applicability of the type curves to a variety of reservoir configurations are given. The Appendix contains derivations of the dimensionless variables and the drawdown parameter. Introduction The gas-bearing rock in some low-permeability gas fields consists of sandstone lenses of uncertain but limited size. In such fields, the reservoir area and volume drained by individual wells cannot be inferred from well spacing. Moreover, good reserve estimates using plots of p/z vs. cumulative production are often not possible because of the difficulty of obtaining reservoir pressure from buildup tests. Therefore, reserve estimation techniques that use performance data, such as production rate as a function performance data, such as production rate as a function of time, are needed. Although this problem has been recognized, the techniques proposed in the past for application to gas reservoirs have been mostly empirical. The present work offers a method that is consistent with the basic theory of gas flow in porous media for analyzing production data to estimate reserves. This method will also provide some inference about reservoir shape. Type Curves Basic Assumptions Six basic assumptions are made in generating the type curves.The flow geometry is radial; therefore, the reservoir either is circular and is produced by a concentrically located well of finite radius or is a sector of a circle produced by the corresponding sector of the well (Fig. 1). produced by the corresponding sector of the well (Fig. 1). In the limit as, the flow regime becomes a linear one.Permeability, porosity, and thickness are constant throughout the reservoir.The pressure at the well radius (usually corresponding to the bottomhole flowing pressure CBHFP]) is held constant.The initial reservoir pressure is constant (independent of position).Non-Darcy flow is neglected.The flowing fluid is either a gas with viscosity and compressibility that vary with pressure or an oil with a constant viscosity/compressibility product. Definitions. The type curves are based on specially defined dimensionless time (tD), dimensionless rate (qD), a flow geometry parameter ( ), and a drawdown parameter ( ). These variables are defined by the following parameter ( ). These variables are defined by the following equations, which are derived in the Appendix. ............................ (1) ................................(2) ...............................(3) .....................(4) Results The type curves for rate as a function of time are presented in Fig. 2. A finite-difference radial-gas-flow simulator was used to generate the data for constructing the type curves. Two flow periods can be identified. The infinite-acting (or transient) period is that period before which the curves become concave downward. The transient period ends at to values ranging from about 0.15 to about 1.0, depending on the value of 17 that characterizes the curve. The curves are concave downward during the late-time or depletion period. Notice that the primary characterizing parameter during the infinite-acting period is, and is parameter during the infinite-acting period is, and is the characterizing parameter for late-time behavior (tD >1). The curves for = 1.234 (linear flow) are straight lines with a negative half-slope during the infinite-acting period. SPEJ p. 719