Modeling The Fluid Flow in Low-Permeability Unconventional Reservoirs Across Scales

Abstract

In the last decade low-permeability unconventional reservoirs (i.e., shale and tight formations) become an increasingly important source of oil and especially gas supply in the world. Low permeability reservoirs are characterized with small grain sizes (m), low permeability (< 0.1mD), small porosity (<10%) and high total organic carbon (TOC) (0.8-20wt%). The productivity of shale and tight reservoirs heavily depends on the interaction between reservoir rock matrix and multi-stage fractured horizontal wells (MFHWs). To predict and optimize unconventional reservoirs’ production behavior, this study tries to model the fluid flow across scales-from the pore scale to the reservoir- scale. Shale matrix permeability is important in interpreting permeability measurement experiments as well as modeling the reservoir-scale flow in shale reservoirs. This study utilizes 2D SEM images and the process-based modeling approach to reconstruct 3D multi-scale shale pore networks. When compared with pore models in the literature, the pore network model is advantaged in describing a realistic, wide range of pore size distribution from micrometer (m) to several nanometers (nm) in a sub-millimeter-sized rock volume. The porescale no-slip flow modeling on pore networks provides intrinsic matrix permeabilities under the effect of multi-scale pore structures and different geological-forming processes. The intrinsic matrix permeability cannot fully represent the gas transport capability of an unconventional reservoir rock when the gas flow velocity at pore surfaces is no longer zero. Unified models are developed for the rarefied gas flow in single conduits of various cross-sections at elevated pressure. Apparent permeabilities are calculated with running unified models on all throats of pore networks. The relationship among pore space structures, gas pressure and apparent permeability reveals the limitation of Klinkenberg equation in describing the high-pressure rarefied gas flow in shale matrix. This study further develops a new equation of apparent permeability vs. pore pressure. Hydrocarbon flows out of rock matrix and then flows into hydraulic fractures then to the horizontal wellbore. Models of coupled flow in matrix and hydraulic fractures can be applied to interpret and/or predict the flow rates/pressure at wellbore vs. time. Distinguished from most models in the literature, this study develops a semi-analytical model with considering the dynamic declining rates of hydraulic fracture conductivity vs. increasing effective stress. This study validates that ignoring such fracture stress-sensitivity can underestimate MFHWs’ productivity at late-time stage. Many low-permeability unconventional reservoirs have a mixture of various conditions, such as rarefied flow, fracture and matrix stress-sensitivity, reservoir heterogeneity and gas adsorption/desorption. In order to easily model multiple flow phenomena, this work develops a composite methodology that combines simple linear flow, radial flow and/or source/sink flow equations. One of this composite method’s applications is validated by the fast and accurate composite modeling of the fluid flow in heterogeneous unconventional reservoirs. In the future work, the composite methodology will be applied in the modeling of gas adsorption/desorption and the rarefied flow in stress-sensitive reservoirs.