Quantifying Uncertainty in Rate Transient Analysis for Unconventional Gas Reservoirs
Authors: Anderson D. M. , Liang P. 
Published: September 2011

The purpose of Rate Transient Analysis (RTA) is to extract useful information about a well/reservoir system from its dynamic well performance data, usually for the purpose of forecasting production and determining expected recovery. The approach can be said to be deterministic because it usually concludes with finding a model that provides the best possible fit of the data. In wells exhibiting boundary dominated flow (BDF), RTA typically provides a reliable characterization of hydrocarbon pore volume (HCPV), which in turn gives expected ultimate recovery (EUR). However, in the presence of long-term transient flow there is often significant uncertainty associated with those parameters, even if the quality of the history match is excellent. If the flow is transient, the source of uncertainty is the indeterminacy of the hydrocarbon pore volume beyond some minimum value. This uncertainty can be easily expressed by plotting EUR against HCPV for a range probable HCPV values (Stotts et al., 2007).

The primary assumption of the previous example is that the reservoir is simple (homogeneous and bounded). In unconventional reservoirs, the well/reservoir models that best describe observed field performance have been shown to be somewhat more complex, including tight unstimulated matrix rock surrounding a limited region of higher effective permeability (referred to as the Stimulated Reservoir Volume) itself containing a horizontal well with multiple hydraulic fractures. Due to the very low matrix permeability, boundary dominated flow is not likely a consideration and thus total HCPV is not a performance driver. However, effective fracture length, effective permeability, fracture conductivity and matrix permeability each contribute to long term performance and EUR. The deterministic RTA approach described earlier may lead to a satisfactory history match, but can be shown to be non-unique in most cases. In the simple model described previously, uncertainty is primarily limited to one parameter (total HCPV). However, in a more complex unconventional reservoir model, there is uncertainty associated with multiple input parameters, the combined effect of which is not easily determined.

In this paper, we propose a simple probabilistic approach to reservoir characterization and forecasting that is suitable for unconventional (or other complex) reservoirs. The approach can be applied to any reservoir model for which there are more unknown input parameters than there are performance based relationships available to constrain them. In this work, we will limit our investigation to one specific analytical model, the "Tri-linear Flow" Model. The probabilistic approach differs from the conventional deterministic approach of well performance modeling in which a single "best fit" model (and its associated forecast) is the final result. The probabilistic approach acknowledges that there may be multiple sets of input model parameters for which a satisfactory history match is available and provides multiple realizations for both the input and output terms using simplified uncertainty modeling.