Stephan K. Matthai
University of Melbourne, Australia (Chair of Reservoir Engineering)
Friday 27th May 2016
Aula Seminari Saleri VI Piano Mox-Dipartimento di Matematica, Politecnico di Milano
Understanding multiphase fluid flow in Naturally Fractured Reservoirs (NFRs) is important because much of the world’s remaining oil reserves reside in rocks the flow through which is fracture dominated [1,2]. Geologically realistic models of NFRs are rare, probably due the multidisciplinary nature of the subject matter1. In stead, “effective” or “dual continua” models are abundant [e.g, 3,4]. Their averaging of fracture permeability and block size makes it impossible to compare simulated saturation patterns with observations on the real system. Yet, such comparisons are important because, in contrast to experiments, observability of a well-matched realistic numerical model is complete and one can incrementally turn component physics off until the behaviour of interest vanishes. This allows elimination of ambiguities in cause and effect chains. The physics underpinning multiphase flow in NFRs are reasonably well understood [5-7].Governing partial differential equations were presented already in the nineteen sixties  and have been modified relatively little since then. Computation and analysis of fracture-matrix ensemble behaviour, however, remain challenging due to scale-dependent nonlinear constitutive relationships, the couplings among the variables, order of magnitude variations in key material properties, and the scale-variant heterogeneity of the fractured porous matrix system. These nonlinear couplings imply that the knowledge of the component physics is insufficient to predict characteristic NFR states and responses. While these could in theory be revealed in the laboratory, experimental setup and monitoring appear too challenging . This presentation is underpinned by computational results obtained on discrete fracture and matrix models (DFMs), discretized with unstructured grids, and flow simulated with a hybrid finite-element (FEM) – finite volume method (FVM) . Using operator splitting, the fluid pressure equation is solved with the FEM and the hyperbolic transport equation including gravitational terms with the FVM . Both methods are used in concert to compute nonlinear capillary diffusion in parallel with gravitational segregation of water and oil in zones of mixed saturation. All equations are solved with a parallelized algebraic multigrid method [12,13]. A decisive feature of the simulation approach is the treatment of the finite volumes at fracture-matrix interfaces [14,15]. New methods support saturation discontinuities and counter-current imbibition can therefore be modeled accurately using a Newton’s-method based implementation of the semi-analytical method proposed by VanDuijn and DeNeef . All these methods are implemented in the CSMP++ application programmer interface [17,18] which will be introduced in the course of this presentation. Several simulation examples will be used to compare the behaviour of the DFMs with conventional dual continua simulations [19-21]. The results show that - beyond benchmarking and the demonstration of numerical methods on simple flow geometries - the decisive step necessary to gain the insights needed for accurate NFR prediction is the application of stateof-the-art simulation methods to relevant realistic non-trivial models. Once the controls on their behaviour have been clarified this way, simplifications can be made by elimination of non-influential features and processes. Idealised models only serve the purpose of component algorithm testing. Where analytic calculations can be applied, sophisticated numerical simulations are not needed. References 1Physicists and applied mathematicians rarely have enough earth-science background to understand the heterogeneity and scale-variance of geological media; earth scientists lack the computational skills to build computer models.