Prof. Marcio A. Murad

Professor Marcio A. Murad, from National Laboratory for Scientific Computing LNCC/MCTI (Brazil), gave two presentations on the 16th and on the 17th of September 2014.


“A New Class of Locally Conservative Numerical Schemes for Coupling

Multiphase Flows and Reservoir Geomechanics”



We propose a new iterative coupled formulation based on Biot’s theory of poroelasticity for multiphase flows of linear compressible fluids in strongly heterogeneous carbonated rocks including the geomechanics of theadjacent impermeable geological formations. Within the framework of the so-called iteratively coupled methods and fixed-stress split algorithm we develop mixed finite element methods for the flow and geomechanics subsystems which furnish locally conservative Darcy velocity and total Lagrangian fluid mass content in the sense of Coussy, Such fields are input for the transport problem for the water saturation which is formulated in terms of the Lagrangian porosity. The numerical resolution of the saturation equation is accomplished within a fractional step method. The predictor step is discretized by a higher-order non-oscillatory finite volume central scheme whereas the corrector based on Godunov or Strang splittings. The geomechanics step is solved in larger domains including the over-burden, up to the surface, under-burden and side-burdens up to the far field where boundary conditions are enforced. Numerical simulations of a water-flooding problem in secondary oil recovery are presented in domains characterized by images provided by seismic data processing . In addition simulations including the nonlinear stress-strain behavior of the adjacent rocks are performed showing the effects of irreversible deformation upon finger grow and breakthrough curves.


“A New Multi-scale Computational Model for Flow and

Transport in Shale Gas Reservoirs”


The macroscopic behavior of gas flow and transport in multi-porosity shale gas reservoirs is rigorously derived within the framework of the reiterated homogenization procedure applied to the Thermodynamics of inhomogeneous gases in nanopores. At the finest nanoscale the Density Functional Theory is applied to construct general adsorption isotherms and local density profiles of pure methane which reflect both repulsive hard sphere effects and Lennard-Jones attractive intermolecular interactions between fluid-fluid supplemented by a fluid-solid exterior potential. Such local description reproduces the monolayer surface adsorption ruled by the Langmuir isotherm in the asymptotic regime of large pore size distributions. The nanoscopic model is upscaled to the microscale where kerogen particles and nanopores are viewed as overlaying continua forming the organic aggregates at thermodynamic equilibrium with the free gas in the micropores. The resultant reaction/diffusion equation for pure gas movement in the aggregates is coupled with both Fickian diffusion of dissolved gas in water and free gas flow in the micropores along with the inorganic solid phase (clay, quartz, calcite) assumed impermeable. By postulating continuity of fugacity at the interface between free and dissolved gas in micropores and neglecting the water movement, we upscale the microscopic problem to the mesoscale, where both organic, inorganic solids and micropores are homogenized. The upscaling entails a new characteristic function which arises from the jumps in concentrations across the kerogen/micropore interface and leads to a new nonlinear pressure equation for gas hydrodynamics in the micropores including a new storage parameter strongly dependent on the total carbon content (TOC). When coupled with the nonlinear single phase gas flow in the hydraulic fractures the mesoscopic model leads to a new macroscopic triple porosity model with mass transfer functions between the different levels of porosity. Computational simulations illustrate the potential of the multiscale approach in numerically constructing accurate gas production curves in different regimes of gas flow.