Generalized analytical model of Transient linear flow in heterogeneous fractured liquid-rich tight reservoirs with non-static properties

• Published in: Applied Mathematical Modelling 2019-12, Vol.76, p.632-654
• Main Authors: Yuan, B., Zhang, Z., Clarkson, C.R.
• Format: Article
• Language: English
• Subjects: Analytical Model; Computer simulation; Diffusivity; Exact solutions; Fluid pressure; Heterogeneity; Hydraulic fracturing; Mathematical models; Permeability; Porosity; Pressure dependence; Pressure Dependency; Properties (attributes); Rate-Transient Analysis; Reservoir Heterogeneity; Reservoirs; Transient analysis; Transient Linear Flow; Workflow
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.06.036

•New analytical transient linear flow is rigorously modeled in heterogeneous fractured liquid-rich tight reservoirs with non-static properties.•Improved rate-transient analysis workflow is proposed to estimate reservoir/fracture properties.•Three liquid-rich shale field examples in North America are analyzed to demonstrate the practical applicability of new model. The industry is increasingly reliant on rate-transient analysis (RTA) to extract valuable information about the reservoir and hydraulic fractures. However, the application of current, commercially-available RTA models can lead to incorrect estimates of reservoir/fracture properties, potentially causing costly mistakes to be made in capital planning and reserve estimation. The root cause of these errors is that currently-available analytical solutions used in RTA models largely ignore reservoir heterogeneities, and assume static reservoir properties. In this work, a new transient linear flow is rigorously modeled in unconventional reservoirs with (1) pressure-dependent rock and fluid properties and (2) both continuous and discontinuous (heterogeneous) porosity and permeability. To achieve this, new transformations of pseudo-pressure, pseudo-time and pseudo-distance are first introduced to reduce the temporal and spatial non-linear diffusivity equation to that with approximately constant coefficients. Both a Laplace-domain solution and approximate analytical solution to the diffusivity equation are verified against a series of fine-grid numerical simulations for the assumption of fractal-based reservoir heterogeneity (over a wide range of stress-dependent rock and fluid properties). The results indicate that reservoir heterogeneity can result in nonlinear square-root-of-time plots. Further, rock and fluid pressure-dependencies act to decrease the slope of the square-root-of-time plot and affect reservoir/fracture property evaluations. Three liquid-rich shale (LRS) field examples in North America are analyzed to demonstrate the practical applicability of the new RTA models. Additional value of new RTA models over the sophisticated numerical simulation is to provide us an improved backforward-analysis workflow that can be used to quantify both effective fracture half-length and non-uniform permeability distribution around the fractures. The major contribution of this work is the introduction of a new analytical model for evaluating the transient linear flow period for the cases of arbitrary reservoir