Christophe Preux

An analysis of physical models and numerical schemes for polymer flooding simulations

Chemical-enhanced oil recovery (CEOR) processes are nowadays commonly used by engineers to improve the recovery factor of an oil field. In this paper, we propose to investigate the physical and numerical singularities arising in the numerical simulation of polymer-enhanced oil recovery technique for oil fields. We assume that the polymer is only transported in the water phase or adsorbed on the rock. The polymer reduces the water-phase mobility and can change drastically the behavior of water oil interfaces. Due to its size, the polymer flows faster than water so that an inaccessible pore volume must be added in the model. After a brief description of different models for polymer adsorption, mobility reduction, and inaccessible pore volume, we discuss the mathematical singularities of the obtained system. In the framework of industrial reservoir simulators, we focus on a constant inaccessible pore volume model which may lead to severe mathematical and numerical singularities. We consider an IMPES scheme; we propose approximate Courant-Friedrichs-Levy (CFL) criteria which are required to obtain some numerical stability of the simulation. 1D numerical polymer flooding experiments are computed with a complete reservoir simulator to illustrate the validity of our approximate CFL criteria.

An Analysis of Physical Models and Numerical Schemes for Polymer Flooding Simulations

Chemical Enhanced Oil Recovery processes (CEOR) are nowadays commonly used by engineers to improve the recovery factor of an oil field. In this paper, we propose to investigate the physical and numerical singularities arising in the numerical simulation of polymer enhanced oil recovery technique for oil fields. We assume that the polymer is only transported in the water phase or adsorbed on the rock. The polymer reduces the water phase mobility and can change drastically the behavior of water oil interfaces. Due to its size, the polymer flows faster than water so that an inaccessible pore volume must be added in the model. We propose to review the various physical models for adsorption, mobility reduction and inaccessible pore volume. Then, a mathematical study of the simplified system will be carried out to identify its singularities and their impact on the numerical resolution. Then, considering an IMPES scheme, we propose approximate CFL (Courant-Friedrichs-Levy) criteria which are required for the numerical stability of the simulation. 1D numerical polymer flooding experiments are computed with a complete reservoir simulator to illustrate the validity of our approximate CFL criteria.

A Connectivity Criterion to Select the Best Coarse Reservoir Model

Reservoir models are commonly built to represent hydrocarbon reservoirs and study fluid flows. To properly capture reservoir heterogeneity and to account for resolution data, engineers build very detailed geological models. However, this contributes to strongly increase the number of grid blocks, hence the computational overburden. A possibility to circumvent this weakness is upscaling: it consists in converting the fine geological model into a coarser reservoir model. The resulting decrease in the number of grid blocks makes it possible to perform flow simulation in a reasonable amount of time. The coarse reservoir model does not reproduce exactly the dynamic behavior of the fine geological model as upscaling induces a loss of information. An issue is the choice of the upscaling techniques. Distinct criteria have been proposed to evaluate the information loss induced by upscaling without performing flow simulation, but none of them has focused on connectivity. We introduce a new quality indicator depending on reservoir connectivity, the leading idea being that upscaling must preserve connectivity between wells. The potential of such a criterion to evaluate the value of upscaled reservoir models is investigated by considering two types of numerical experiments inspired by the SPE10 case.

Relative Permeability Homogenization by a Regression Technique

Geological and geophysical expertise coupled to numerical simulation allow the petroleum industry to build increasingly detailed reservoir models. These models integrate the whole set of available data but involve geostatistics and stochastic approach. A large number of simulations is required to estimate hydrocarbon reserves and optimize oil recovery. Geoscientists begin by building a geological model respecting the real geometry of the reservoir and containing possibly million of cells. A reservoir model containing less cells is then built in order to ensure that numerical simulation is feasible within a reasonable time. Upscaling is the link between the geological model and the reservoir model. Multiphase flows upscaling is still an actual issue. In particular, relative permeability curves are characteristic of twophase flow equations. Upscaled relative permeabilities are called pseudo-functions. These functions are often computed for each different case, assuming special flow conditions. The purpose here is to propose a homogenization method for relative permeability by an optimization approach. Non-linear regression analysis can also generate pseudo-relative permeabilities. Such a method is here adopted. Production curves are to be matched by an optimization algorithm in order to generate a homogenized relative permeability model.