Applicability of the Arps Rate-Time Relationships for Evaluating Decline Behavior and Ultimate Gas Recovery of Coalbed Methane Wells

Abstract

This paper presents results of a simulation study designed to evaluate the applicability of Arps' [1945] decline curve methodology for assessing reserves in coalbed methane reservoirs. We simulated various coal properties and well/operational conditions to determine their impact on the production decline behavior as quantified by the Arps decline curve exponent, b. We then evaluated the simulated production with Arps' rate-time equations at specific time periods during the well's production decline period and compared estimated reserves to the "true" value (defined in this paper as the 30-year cumulative production volume). To satisfy requirements for using Arps' models, all simulations were conducted using a constant bottomhole flowing pressure condition in the wellbore. The significant results from our study include: All of the computed values of the long-term decline exponents were within the limits originally defined by Arps, i.e., 0.0 < b < 1.0. Agreement between Arps' recommended b-exponent range and our results using simulated performance data also suggests that, if applied under the correct conditions, the Arps rate-time models are appropriate for assessing reserves in coalbed methane reservoirs; The Arps b-exponents were not constant during the production decline period. For many simulated cases, the early decline behavior (within a few years after reaching the peak production rate) appeared to have exponential decline but eventually became more hyperbolic later in the well's life. Use of Arps' exponential model early in the production history in those wells with long-term hyperbolic decline behavior tended to underestimate gas reserves; The largest reserve estimate errors typically occurred during the first few years after reaching the peak production rate and during the initial production decline period. For those wells exhibiting long-term hyperbolic behavior, the initial reserve estimate errors underestimated reserves by as much as 20 to 30 percent; Heterogeneities in coal properties cause the production declines to deviate from exponential to hyperbolic. Properties having the largest impact on the production decline behavior include the shape of the adsorption isotherm, cleat permeability anisotropies, the shape of cleat gas-water relative permeability curves, stress-dependent cleat permeability and porosity, and layered coal seams with differences in initial reservoir pressures; We also observed a strong influence of well flowing pressure conditions as modeled with a bottomhole flowing pressure constraint. For all other properties and conditions being equal, wells with lower bottomhole flowing pressures exhibited more long-term hyperbolic behavior as defined by higher Arps b-exponents.

Laboratory Study of Gas Permeability and Cleat Compressibility for CBM/ECBM in Chinese Coals

“…In permeability calculation and reservoir simulation, cleat compressibility was often treated as constant (McKee et al, 1988;Pekot and Reeves, 2003;Pomeroy and Robinson, 1967;Puri and Seidle, 1991). However, other studies have shown that cleat compressibility is not constant with respective to pore pressure and effective stress (Palmer and Mansoori, 1996;Palmer and Mansoori, 1998;Rushing, 2008;Palmer, 2009;Shi and Durucan, 2010) and cleat compressibility may change exponentially with respect to effective stress change for some coals (McKee et al, 1988;Zhou et al, 2011). Thus, better understanding of how permeability and cleat compressibility change with respect to gas species, pore pressure and effective stress is of great interest, since they are key parameters for CBM/ECBM processes.…”

Production Behavior of Fractured Horizontal Well in Closed Rectangular Shale Gas Reservoirs

“…Gas adsorption is a surface phenomenon and is predominately a physical bond caused by the intermolecular attractive forces, such as Van der Waals forces, while desorption is the converse process of adsorption [18].…”

Differences and Similarities in the Stimulation and Production of Shale Gas Reservoirs and Other Tight Formations

“…The volume of adsorbed gas at a given pressure and under isothermal conditions, as shown in Figure 3, is given by (Rushing et al, 2008):…”