Numerical Models in the Oil Industry

In this talk I will present an overview of the state of the art simulation technology used now-a-days in the industry.

Reservoir simulation is used in the oil industry to support strategic economic decisions by running numerical reservoir models to predict the results of various depletion strategies. This technology has evolved in the last 50 years combining mathematics and computers to assist the oil industry in the development of more and more complex fields using increasingly sophisticated recovery processes.

A numerical reservoir simulation model consists essentially of 1) a representation of the reservoir geology and petrophysics in terms of cells and interfaces 2) a flow model and 3) a well model implemented to reflect the possible depletion processes.

In this presentation we first cast reservoir simulation models as the result of a complex process where information from various sources and scales is collected to provide a quantitative, digital, representation of the subsurface. This includes a geophysical framework, flow relevant geological and petrophysical features, constitutive relations between fluids and porous media, and a fit for purpose representation of the phase behaviour of reservoir fluids. For computational purpose, the reservoir is represented by means of a geo-cellular grid consisting of cells filling the rock volume included inside a structural framework. In this grid information from different scales are integrated, and both upscaling and down-scaling play key roles.

Then we present the flow model, that is to say the set of partial differential equations suited to describe the behaviour of reservoir fluids during depletions. In the numerical simulator these flow equations are discretised in a mass conservative manner using cells as control volumes and interfaces as connections. Wells are included by means of dedicated models connected in a fully implicit manner with the reservoir equations.

The numerical model is advanced in time by means of a proper time marching scheme, balancing efficiency and accuracy. In this process the computational burden is given by the solution of large scale sparse linear systems, deriving from the discretisation of the mass balance equations, which represent a mix of parabolic and hyperbolic equations. In a typical reservoir simulation run, sparse linear systems are solved tens of thousands of times, and they are often ill conditioned because of extreme permeability contrasts, non linearity in the flow models or in the constitutive relations, time-variable degree of implicitness, critical well models or complex grid developed to account for, e.g., highly faulted/fractured reservoirs.

The numerical technology is now evolving from solvers suited for logically cartesian grids towards scalable solvers based on the decoupling of parabolic and hyperbolic components in the linearised system. Nonetheless, grid developed to capture heterogeneity and structural features may still be too detailed to suit numerical simulation, and this may require an upscaling towards coarser grids.

The talk will covers the main components of the simulation technology using some real life cases as examples. A view on the future, with emphasis on modelling of heterogeneous and fractured reservoirs, will finally be provided.


CONTACT: edie.miglio@polimi.it