When tight gas sand reserves are assessed using the Arps rate-time equations, the decline behavior is typically defined in terms of the Arps decline exponent, b. The original Arps paper indicated that the b-exponent should lie between 0 and 1.0 on a semilog plot. However, in practice we often observe values much greater than 1.0, especially prior to the onset of true boundary-dominated flow. Unfortunately, the correct b-exponent is difficult (if not impossible) to identify during the early decline period — and (obviously) the selection of the wrong b-exponent will have a tremendous impact on reserve estimates, particularly when the b-exponent estimate is too high. As an exercise to evaluate the b-exponent as a continuous function of time, we have used synthetic and field production profiles. We then compare the computed b-exponent trend graphically to assess the "hyperbolic" nature of each case (recall that the b-exponent should be constant for a given hyperbolic rate decline). The field data cases used in this study were selected from a tight gas reservoir that has been previously evaluated on a per well basis using the production model based on the elliptical flow concept. These cases indicate that only portions of the production history are matched by the hyperbolic rate decline relation — suggesting that using the hyperbolic relation by itself may not be appropriate for reserves extrapolations in tight gas reservoirs, or at least that great care must be used in creating production forecasts based on the hyperbolic rate decline relation. In addition to the hyperbolic rate decline relation we have also developed and employed a new "power law loss-ratio" rate relation that has more generality than the hyperbolic rate decline relation. This new model tends to match production rate functions much better than the hyperbolic rate decline relation for tight gas and shale gas applications, but we must stress that at this time, the "power law exponential decline" rate relation is empirically derived from only tight gas/shale gas performance cases. We have applied the new model as well as the hyperbolic rate model to two synthetic (simulated) and field (tight gas well) cases for production forecast. Furthermore, the results of our synthetic performance cases do suggest that layered reservoir behavior can be accurately represented by the hyperbolic rate decline relation. Unfortunately, as other studies have shown, multilayer reservoir performance can be extremely difficult to generalize — particularly when layers in transient and boundary-dominated flow are in communication. Hyperbolic rate decline relation might be considered as an acceptable mechanism for estimating reserves in tight gas/shale gas systems, however we urge extreme caution as the hyperbolic relation must be constrained to a relative small duration production forecast. The major impact of this work is that it enables the analyst to have a diagnostic understanding of the hyperbolic rate decline relation (in terms of the D and b-parameters). Further, we also provide an alternative to the hyperbolic rate decline relation that appears to be substantially more robust, and the new "power law loss-ratio" rate relation can be validated and calibrated directly using rate functions.

Decline curve analysis using the Arps rate-time equations has historically been the primary tool used for reserve evaluations in tight gas sands. However, characteristic tight gas sand properties often preclude accurate assessments using only or primarily decline curve analysis — especially early in the productive life. Moreover, the Arps models are essentially used as curve-fitting devices with (very) limited theoretical basis. As such, this paper presents a reserves appraisal process that complements traditional decline curve analyses with theoretically-based production analysis techniques. Specifically, we incorporate multiple reserves estimation techniques ranging from simple extrapolation techniques to rigorous model-based analysis/interpretation methods, including:Arps exponential and hyperbolic relations — rate-time and rate-cumulative plots, as well as other auxiliary plots,Semi-analytical rate-cumulative techniques for boundary-dominated flow,The "flowing material balance" approach in its various formulations, andModel-based analysis ("rate-transient" or "model-matching" approaches). We provide both separate and combined analysis, including "diagnostic" plots which guide the evaluation process and help prevent erroneous reserve estimates resulting from use of single methods. Implementation of the proposed workflow will prevent unrealistic (either too low or high) reserve bookings by integrating multiple production analysis techniques. We demonstrate where and how each component technique should be used as well as their limitations. We also demonstrate how each technique can be used to reinforce/validate results from other techniques (i.e., multiple redundancies of methods). The primary objectives of this work are to:Provide a consistent workflow for integration of multiple reserve estimating techniques for tight gas sands,Provide an assessment of strengths and weaknesses of individual reserves estimation techniques, and.Provide demonstrative examples for implementing this workflow (including diagnostics).

This paper presents the results of a simulation study designed to evaluate the applicability of an Arps 1 decline curve methodology for assessing reserves in hydraulically-fractured wells completed in tight gas sands at high-pressure/high-temperature (HP/HT) reservoir conditions. We simulated various reservoir and hydraulic-fracture properties 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 productive life and compared estimated reserves to the true value. To satisfy requirements for using Arps' models, all simulations were conducted using a specified constant bottomhole flowing pressure condition in the wellbore. Our study indicates that the largest error source is incorrect application of Arps' decline curves during either transient flow or the transitional period between the end of transient and onset of boundary-dominated flow. During both of these periods (principally the transient period), we observed bexponents greater than one and corresponding reserve estimate errors exceeding 100 percent. The b-exponents generally approached values between 0.5 and 1.0 as flow conditions approached true boundary-dominated flow. Agreement between Arps' suggested b-exponent range and our results using simulated performance data also indicates that, if applied under the correct conditions, the Arps rate-time models are appropriate for assessing reserves in tight gas sands at HP/HT reservoir conditions.

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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.