A Cell-Centred CVD-MPFA Finite Volume Method for Two-Phase Fluid Flow Problems with Capillary Heterogeneity and Discontinuity

A novel finite-volume method is presented for porous media flow simulation that is applicable to discontinuous capillary pressure fields. The method crucially retains the optimal single of freedom per control-volume being developed within the flux-continuous control-volume distributed multi-point flux approximation (CVD-MPFA) framework (Edwards and Rogers in Comput Geosci 02(04):259–290, 1998; Friis et al. in SIAM J Sci Comput 31(02):1192–1220, 2008) . The new methods enable critical subsurface flow processes involving oil and gas trapping to be correctly resolved on structured and unstructured grids. The results demonstrate the ability of the method to resolve flow with oil/gas trapping in the presence of a discontinuous capillary pressure field for diagonal and full-tensor permeability fields. In addition to an upwind approximation for the saturation equation flux, the importance of upwinding on capillary pressure flux via a novel hybrid formulation is demonstrated

Numerical Modeling of Thermal EOR: Comprehensive Coupling of an AMR-Based Model of Thermal Fluid Flow and Geomechanics

La modélisation du procédé SAGD (Steam Assisted Gravity Drainage) peut impliquer un temps de calcul important lorsque l’écoulement thermique et la géomécanique sont couplés pour tenir compte des variations de perméabilité et de porosité à l’intérieur du réservoir induites par l’évolution des contraintes. Une procédure numérique qui effectue des simulations thermo-hydro-mécaniques, d’une manière efficace, est présentée. Cette procédure repose sur un processus de couplage itératif entre un simulateur réservoir thermique basé sur la méthode des volumes finis et un simulateur géomécanique basé sur une discrétisation par éléments finis. Une caractéristique forte de cette procédure est qu’elle permet de traiter des cas où les simulations de réservoir sont réalisées en utilisant un raffinement de maillage adaptatif. Elle fournit ainsi une description précise de l’évolution du front de vapeur d’eau et permet de prendre en compte les effets géomécaniques sans effectuer les simulations géomécaniques sur un maillage raffiné. L’efficacité de cette procédure de couplage est illustrée sur un cas SAGD synthétique mais réaliste

Sensitivity Analysis and Optimization of Surfactant-Polymer Flooding under Uncertainties

Chemical flooding is currently one of the most promising solution to increase the recovery of mature reservoirs. In Surfactant-Polymer (SP) processes, several parameters should be taken into account to estimate the return on investments: concentrations of the injected chemical species, slug sizes, initiation times, residual oil saturation, adsorption rates of the chemical species on the rock, etc. Some parameters are design parameters whereas other ones are uncertain. For operators, defining the optimal values of the first ones while considering the uncertainties related to the second ones, is not an easy task in practice. This work proposes a methodology to help handle this problem. Starting from a synthetic reservoir test case where an SP process is set up, we select design and uncertain parameters which may impact the production. In the reservoir simulator, for the sake of flexibility, some of them are tabulated functions, which enables the user to input any data coming from any system. However, point-wise modifications of these curves would soar the number of parameters. Therefore, a particular parameterization is introduced. We then propose a methodology based on Response-Surface Modeling (RSM) to first approximate the oil production computed by a reservoir simulator for different values of our parameters and identify the most influential ones. This RSM is based on a Karhunen-Loève decomposition of the time response of the reservoir simulator and on an approximation of the components of this decomposition by a Gaussian process. This technique allows us to obtain substantial savings of computation times when building the response surfaces. Once a good predictability is achieved, the surfaces are used to optimize the design of the SP process, taking economic parameters and uncertainties on the data into account without additional reservoir simulations

Integrating Data of Different Types and Different Supports into Reservoir Models

In this paper, we focus on the joint integration of production and 4-D inverted seismic data into reservoir models. These data correspond to different types and different scales. Therefore, we developed two-scale simulation workflows making it possible to incorporate data at the right scale. This issue also emphasized the need for adapting traditional history-matching methodologies. For instance, the formulation of the objective function and the development of customized parameterization techniques turned out to be two key factors controlling the efficiency of the matching process. Two application examples are presented. The first one is a small-size synthetic field case. It aims to build a set of reservoir models respecting either production data only or both production and 4-D seismic-related data. It is shown that the incorporation of 4-D seismic-related data in addition to production data into reservoir models contributes to reduce the uncertainty in production forecasts. The second example is a field in the North Sea offshore Norway operated by Statoil. It stresses difficulties in conditioning reservoir models to both real production and 4-D inverted seismic data among the very large number of uncertain parameters to handle and the comparison of real noisy data with numerical responses