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.