The motivation for this work is straight-forward — simply put, there is need in the upstream oil and gas industry to properly forecast production rate performance in unconventional reservoirs. At present, this need is being met by an ever-growing inventory of time-rate (decline curve analysis (or, DCA)) relations of various constructs and purposes — this has led to inconsistent and somewhat contradictory results. The overall purpose of this work is to put forth an examination of the validity of the most common of these time-rate models via the use of high-resolution reservoir simulation.
As such, this work is constructed in 2 parts. The first part of this work is focused on the creation of a very high precision reservoir simulation model that is of sufficient accuracy and flexibility to model the well performance for the primary types of unconventional reservoirs (e.g., gas-water and oil-gas-water systems). The reservoir simulation model is validated against analytical models for the single-phase case (to ensure validity), then tested with numerous synthetic field cases (to ensure applicability to most types of unconventional reservoir systems).
The second part of this work focuses on the use of the common DCA relations (Arp's Modified Hyperbolic model, the stretched/power law exponential model, the Duong model, and the Logistical Growth model (a population model)) to correlate against reservoir simulation results to establish the "most appropriate" model(s) for which to history match actual field cases.
Based on the synthetic performance cases considered in the first portion of this work, a new time-rate (DCA) model is proposed based on the K1(x) Bessel Function (i.e., the Modified Bessel Function of the second kind). In form, this result is quite compact and has the general performance characteristics of the modified-hyperbolic model at early times and the stretched/power law exponential model(s) at intermediate and late times — that is, the rate and the decline parameters D(t) and b(t) for the K1X model closely match these functions for the aforementioned DCA models and the reservoir simulation performance results. In this sense, the K1X model is a sort of "hybrid" which represents the combined behavior of the modified-hyperbolic model and the stretched/power law exponential model(s).