Standard decline curve equations can by used outside their normal range of application to give accurate and theoretically valid projections of tight gas well performance. This approach is preferable to the use of the reciprocal square-root of time as a preferable to the use of the reciprocal square-root of time as a tight gas well "type curve".
Low permeability fractured gas wells, when produced without constraint, typically exhibit a characteristic decline curve shape: a steep initial decline followed by a long well life at low producing rates relative to the initial potential. The common producing rates relative to the initial potential. The common methods of forecasting production from these wells vary in complexity and in the amount of detail required. Decline curves and mathematical curve fitting require only monthly production data; no knowledge of reservoir properties is necessary. The problem with these techniques it that, especially at early times, problem with these techniques it that, especially at early times, virtually any curve can give a reasonable fit to monthly data. On the other hand, log-log type curves and mathematical simulation require knowledge of the fracture and reservoir geometries as well as a detailed history of flowing rates and pressures. As a practical matter, this kind of detail is often unavailable practical matter, this kind of detail is often unavailable The utility of decline curves can be enhanced by recognizing the influence of the physics of reservoir fluid flow on the resulting semi-log plot. The characteristic tight gas well decline shape is a predictable result of the flow from a low permeability reservoir into a more conductive fracture.
The Arps Equation
The Arps equation is the most commonly used ratetime decline relationship:
Arps treated the equation as empirical, but noted that the exponent can be influenced by the reservoir flow conditions. The value of b determines the degree of curvature of the semi-log decline, from a straight line (exponential decline) at be = 0.0 to increasing curvature at higher values of b. He stated that the value of b varies between zero and 1.0, with no discussion of the possibility of b greater than 1.
There is no theoretical basis for limiting the exponent to values less than 1. Using numerical simulations, Gentry and McCray showed that reservoir heterogeneity (e.g., layered reservoirs) can result in a hyperbolic exponent exceeding 1.
A single decline equation with b less than 1 cannot approximate a typical tight gas decline shape as shown in Figure 1. Bailey used mathematical curve fitting to determine the "best fit" hyperbolic equation for wells in three tight has basins. For his representative group of fractured Wattenberg Field wells, the optimized exponent exceeds 1 in all but a few cases, and ranges as high as 3.5 in one case.
In practice, many engineers avoid the use of hyperbolic decline curves. Some use a favorite French curve to approximate tight gas well declines. Another common approach is to assume a decline shape composed of a series of straight line segments: for example, 50% exponential decline for two years, then 20% decline for three years, followed by 8% decline to an economic limit. While these methods may give satisfactory results for a group of similar wells, one must ask: Why do these wells follow a decline shape which is apparently arbitrary?
The Inverse Square-Root of Time Equation
In search of an equation which explains the influence of low permeability and flow geometry on the shape of the decline curve, permeability and flow geometry on the shape of the decline curve, some recent papers and articles have proposed the following equations for use with tight gas well declines:
The argument for this equation is based on the physics of linear flow and on observations from log-log type curves for fractured wells.