Salinas, Pablo (Imperial College London) | Jacquemyn, Carl (Imperial College London) | Kampitsis, Andreas (Imperial College London) | Via-Estrem, Lluis (Imperial College London) | Heaney, Claire (Imperial College London) | Pain, Christopher (Imperial College London) | Jackson, Matthew (Imperial College London)
The use of dynamic mesh optimization (DMO) for multiphase flow in porous have been proposed recently showing a very good potential to reduce the computational cost by placing the resolution where and when necessary. Nonetheless, further work needs to be done to prove its usability in very large domains where parallel computing with distributed memory, i.e. using MPI libraries, may be necessary. Here, we describe the methodology used to parallelize a multiphase porous media flow simulator in combination with DMO as well as study of its performance. Due to the peculiarities and complexities of the typical porous media simulations due to its high aspect ratios, we have included a fail-safe for parallel simulations with DMO that enhance the robustness and stability of the methods used to parallelize DMO in other fields (Navier-Stokes flows). The results show that DMO for parallel computing in multiphase porous media flows can perform very well, showing good scaling behaviour.
Two new Non-Intrusive Reduced Order Modelling approaches to estimate time varying, spatial distributions of variables from arbitrary unseen inputs are introduced. One is a generalization of an existing'dynamic' approach which requires multiple surrogate evaluations to model the solutions at different time instances, the other is a'steady-state' approach that evaluates all time instances simultaneously, reducing the local approximation error. The ability of these approaches to estimate the water saturation distributions expected during a gas flood through a 2D, dipping reservoir is investigating for a range of unseen input parameters. The range of these parameters has been chosen so that a range of flow regimes will occur, from a gravity tongue to a viscous dominated Buckley-Leverett displacement. A number of practically relevant model error measures were employed as opposed to the standard L2 (Euclidean) norm. The influence of the number and the structure of training simulations for the model was also investigated, by employing two simple experimental design methods. The results show that POD based NIROM approaches are prone to significant deviations from the true model. The main sources of error are due to the non-smooth variation of system responses in hyperspace and the transient nature of the flows as well as the underlying dimensionality reduction. Since the first two sources are properties of the physical system modelled it may be expected that similar problems are likely to arise independently of the interpolation method and the reduction process used.
Zhang, Zhao (Heriot-Watt University) | Geiger, Sebastian (Heriot-Watt University) | Rood, Margaret (Imperial College London) | Jacquemyn, Carl (Imperial College London) | Jackson, Matthew (Imperial College London) | Hampson, Gary (Imperial College London) | Carvalho, Felipe Moura De (University of Calgary) | Silva, Clarissa Coda Marques Machado (University of Calgary) | Silva, Julio Machado (University of Calgary) | Sousa, Mario Costa (University of Calgary)
Flow-diagnostics are a common way to rank and cluster ensembles of reservoir models based on their approximate dynamic behaviour prior to commencing full-physics reservoir simulation. Traditionally, flow diagnostics are carried out on corner-point grids inherent to geocellular models.
The novel "Rapid Reservoir Modelling" (RRM) concept enables fast and intuitive prototyping and updating of reservoir models. In RRM, complex reservoir heterogeneities are modelled as discrete volumes bounded by surfaces that can be modified using simple sketching operations in real time. The resulting reservoir models are discretized using fully unstructured 3D meshes where the grid conforms to the reservoir geometry.
This paper presents a new and computationally efficient numerical scheme that enables flow diagnostic calculations on fully unstructured grids. Time-of-flight and steady-state tracer distributions are computed directly on the grid. The results of these computations allows us to estimate swept reservoir volumes, injector-producer pairs, well-allocation factors, flow capacity, storage capacity and dynamic Lorenz coefficients which all help approximate the dynamic reservoir behaviour.
We use the Control Volume Finite Element Method (CVFEM) to solve the elliptic pressure equation. A scalable matrix solver (SAMG) is used to invert the linear system. A new edge-based CVFEM is developed to solve hyperbolic transport equations for time-of-flight and tracer distributions. An optimal reordering technique is employed to deal with each control volume locally such that the hyperbolic equations can be computed in an efficient node-by-node manner. This reordering algorithm scales linearly with the number of unknowns.
The total CPU time, including grid generation and flow diagnostics, is typically below 3 seconds for grids with 50k unknowns. Such fast calculations provide, for the first time, real-time feedback on changes in the dynamic reservoir behaviour while the reservoir model is updated.
Jackson, Matthew (Imperial College) | Percival, James (Imperial College) | Mostaghimi, Peyman (Imperial College) | Tollit, Brendan (Imperial College) | Pavlidis, Dimitrios. (Imperial College) | Pain, Christopher (Imperial College) | Gomes, Jefferson (Imperial College) | Elsheikh, Ahmed H. (Imperial College) | Salinas, Pablo (Imperial College) | Muggeridge, Ann (Imperial College) | Blunt, Martin (Imperial College)