Coupled fluid flow and geomechanics modeling of stress-sensitive production behavior in fractured shale gas reservoirs

Abstract

Compared with conventional reservoirs, gas flow in shale formation is affected by additional nonlinear coupled processes such as matrix/fracture deformations. We present a fully-coupled fluid flow and geomechanics model to accurately characterize the complex production behaviors of fractured shale gas reservoirs. The flow equations are discretized using a mimetic finite difference method, and poro-elasticity equations by a Galerkin finite-element approximation. A unified apparent-permeability model is implemented to quantify the combined impacts of the non-Darcy flow, adsorbed layer and pore-structure alterations on matrix permeability.

The discrete fracture-matrix (DFM) model based on a conformal unstructured grid is employed to explicitly represent fractures. The nonlinear contact problem between the two fracture surfaces is introduced to describe the fracture mechanics behavior. A splitting-node technique is used to deal with the discontinuities in the displacement field across the fracture interface. Under the effects of pressure decline and high confining stresses on the fracture faces, proppant compaction and embedment may occur, causing fracture closure and thus substantial production loss. Hence we also develop a comprehensive proppant-fracture model which is based on the theories of elasto-plastic contact mechanics, to capture the complex interactions between proppant and fracture.

The multiphysics numerical model enables us to investigate which factors have the most influential effect on the gas recovery of shale formations. High fidelity numerical solutions are provided to characterize the rate-transient signatures in the presence of the different flow and geomechanical mechanisms.

Introduction

Due to the rapid depletion in conventional resources of natural gas, unconventional reserves such as shale gas reservoirs have become more and more important for the energy industry in North American and have gradually turned into a major supplier of world energy demand in recent years. Shale gas production can be economically viable if sufficient stimulation of ultra-tight formation is achieved through the technologies of horizontal drilling and hydraulic fracturing. In order to obtain optimal management plans for shale gas reservoirs, there is considerable interest in numerical modeling approaches which can adequately characterize the complicated production behaviors.¹ Compared with conventional reservoirs, gas flow in shale formation is affected by additional nonlinear coupled processes including gas adsorption, low-permeability non-Darcy flow and matrix/fracture deformations.2., 3., 4., 5.

Darcy's law, which describes viscous flow driven by pressure gradient, is applicable to porous media where continuum theory holds and fluid velocity could be approximated as zero at the pore wall.⁶ However, the fluid-continuum theory is no longer valid for shale reservoirs with pore radius in the range of nanometers.⁷ Dynamic apparent permeability models are extensively employed to reflect the flow regimes associated with the non-Darcy effect.¹ The adsorbed gas layer on the pore surface occupies the pore space, resulting in the variations of the gas apparent permeability.8., 9.

In addition, stress-sensitivity is another active phenomenon in shale gas reservoirs. During reservoir depressurization, the pore pressure decline leads to a rise in the effective stress which, subsequently compacts pore-structure geometry and reduces formation porosity and intrinsic permeability.¹⁰ In the meantime, gas desorption triggers matrix shrinkage, whose effect is contrary to the pore pressure decrease.11., 12. Consequently, the net change in porosity and permeability accompanying gas extraction is controlled by the several competing processes.¹³ The nonlinear and stress-sensitive flow phenomena can be further aggravated by the generation of complex fracture network with non-ideal geometries after the fracturing treatment. It has been reported that the sharp decline of the gas rate within the first few months of production is one of the distinguishable features exhibited by the fractured stimulated wells.¹⁴ The stimulation process involves injecting high-pressure fracturing fluid, together with proppants which are usually sand or ceramic particles, into shale reservoir to break down the rock. Proppants play the role of keeping the fracture open after pumping stops and fracturing fluid flows back to the surface.¹⁵ The proppant layers filling the fracture channels can create highly conductive flow paths for gas production.¹⁶ Under the effects of pressure decline and high confining stresses on the fracture faces, proppant compaction, embedment into shale rock, and even crushing may occur, causing fracture closure and thus substantial production loss. Several studies have proposed the purely elastic models for the contacts between proppant and fracture.16., 17., 18., 19. Hertzian theory is widely applied for purely elastic contacts,²⁰ but in most cases there are plastically deforming behaviors which extremely complicate the contact force-displacement relationship.²¹ Under high compressive stress, the failure of shale rock can be initiated. Hertzian theory does not work properly when the vertical displacement is large relative to the radius of proppant sphere. Therefore in this work we develop a comprehensive proppant-fracture model which is based on the theories of elasto-plastic contact mechanics, to accurately capture the proppant embedment phenomena.

A fully coupled fluid flow and geomechanics model is developed to simulate the stress field and gas production in fractured shale reservoirs. A unified model for gas flow in organic nanopores is implemented, accounting for the coupling mechanisms of the non-Darcy flow regimes, adsorption layer and stress dependence. The flow equations are discretized using a mimetic finite difference method, and the poro-elasticity equations by a Galerkin finite-element approximation. The discrete fracture-matrix (DFM) model based on a conformal unstructured grid is employed to represent a fracture as the interface between two neighboring cells. The nonlinear contact problem between the two fracture planes is introduced to describe the fracture mechanics behavior. A splitting nodes technique is used such that each node along the fracture interface is assigned to double nodes with the same coordinates, for overcoming the presence of explicit discontinuities in the fractured domain.²²

The developed multiphysics simulator allows us to examine which factors have the most significant impact on the gas recovery of shale formations. High fidelity numerical solutions are provided to characterize the rate-transient signatures in the presence of the different flow and geomechanical mechanisms.