Numerical investigation of limitations and assumptions of analytical transient flow models in tight oil reservoirs

Abstract

The complex fracture network created by multistage hydraulic fracturing has been recently described by triple porosity models. Existing triple porosity models typically assume sequential flow from matrix to micro fractures and from micro fractures to hydraulic fracture. Modeling simultaneous depletion of a matrix block into both micro and hydraulic fractures entails solution of a two dimensional continuity equation that is challenging by analytical or even semi-analytical methods. In addition, analysis with analytical models and type-curves provides deterministic and homogeneous estimates, rendering uncertainty analysis of fracture properties difficult.In this paper, we use a commercial reservoir simulator to compute the transient response in a segment of a hydraulically fractured horizontal well with a triple-porosity model, where matrix and fracture elements are explicitly discretized. Some limitations in analytical models such as sequential flow, single-phase flow and fully-connected symmetric fractures are investigated using the actual rate data from two tight oil wells completed in the Cardium and Bakken formations. An early drop in production, as commonly observed in many tight oil wells, could be attributed to gas dissolution with pressure decline and multiphase flow effects. Impacts of pressure interference between natural fractures and inter-well fracture communication are also investigated. Uncertainty in model parameter estimation is studied by assuming that results obtained from analytical solutions would characterize the mean estimate of the corresponding fracture parameters, additional heterogeneous models of natural/induced micro-fracture properties including its total number and intensity (spacing) are assigned stochastically. These models are subsequently subjected to flow simulations, and the variability in production performance captures the sensitivity due to model parameter uncertainties. Our results highlight the non-uniqueness of fracture characterization in production data analysis. It is demonstrated that ignoring the uncertainty in history-matched parameters and assumptions associated with analytical models could potentially over- or under-estimate production by up to 30%. The analysis workflow adopted in this study presents a practical framework for integrating numerical simulations with analytical solutions to study the limitations of analytical transient flow models and to quantify the uncertainty in production performance predictions.