Exponential vs. Hyperbolic Decline in Tight Gas Sands — Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves

Abstract

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.

Characteristic Production Decline Patterns for Shale Gas Wells in Barnett

“…It has been claimed that the Arps decline curves encounter problems when used in "unconventional" formations, particularly with regards to overestimation of reserves. When traditional Unit: bcf per day decline curve models are used on shale formations, Arps' values for larger than 1 are commonly obtained yielding infinite cumulative production [24]. As the importance of shale gas has increased over the last decade new methods have been proposed to model the behavior exhibited by long horizontal wells with multistage hydraulic fractures in shale reservoirs.…”

“…As the importance of shale gas has increased over the last decade new methods have been proposed to model the behavior exhibited by long horizontal wells with multistage hydraulic fractures in shale reservoirs. These methods include, but are not limited to, the Stretched Exponential (SE) model [25,26], the Power Law model [24], and Duong's model [27]. Two decline curve analysis models are used in the study -the Arps Hyperbolic model and the Stretched Exponential model.…”

An approach to modeling production decline in unconventional reservoirs

“…1 that returned a b value [1 is a consequence of flow that is still dominated by transient effects. Several authors (Can and Kabir 2014;Ilk et al 2008;Rushing et al 2007) have pointed out that Eqs. 1 and 2 will yield optimistic results when applied to unconventional formations.…”

“…Clark et al (2011) introduced the logistic growth model, which has the desirable property of yielding physical values of reserves recovery. Ilk (2010), after analyzing production (rate) data from shale gas wells, developed a power-law model and a method of applying the model that arbitrarily switched from the power-law decline behavior to an exponential decline behavior. Duong (2011) also observed that a loglog plot of q/N p versus time was a straight line.…”

Statistical, Data-Driven Approach to Forecasting Production from Liquid-Rich Shale Reservoirs

“…Over the years, several empirical decline curve analysis (DCA) models have been used to forecast reservoir production such as the Arps' hyperbolic decline model [1], Duong's model [2], the Stretched Exponential Production Decline (SEPD) model [3], the power-law model [4] and more recently the YM-SEPD model [5]. All these models have limitations, which have made them not entirely satisfactory for forecasting production from unconventional reservoirs, especially when production history is short.…”