Upscaled modeling of well singularity for simulating flow in heterogeneous formations

Subsurface flows are affected by geological variability over a range of length scales. The modeling of well singularity in heterogeneous formations is important for simulating flow in aquifers and petroleum reservoirs. In this paper, two approaches in calculating the upscaled well index to capture the effects of fine scale heterogeneity in near-well regions are presented and applied. We first develop a flow-based near-well upscaling procedure for geometrically flexible grids. This approach entails solving local well-driven flows and requires the treatment of geometric effects due to the nonalignment between fine and coarse scale grids. An approximate coarse scale well model based on a well singularity analysis is also proposed. This model, referred to as near-well arithmetic averaging, uses only the fine scale permeabilities at well locations to compute the coarse scale well index; it does not require solving any flow problems. These two methods are systematically tested on three-dimensional models with a variety of permeability distributions. It is shown that both approaches provide considerable improvement over a simple (arithmetic) averaging approach to compute the coarse scale well index. The flow-based approach shows close agreement to the fine scale reference model, and the near-well arithmetic averaging also offers accuracy for an appropriate range of parameters. The interaction between global flow and near-well upscaling is also investigated through the use of global fine scale solutions in near-well scale-up calculations.     

Multiscale finite-volume method for density-driven flow in porous media

The multiscale finite-volume (MSFV) method has been developed to solve multiphase flow problems on large and highly heterogeneous domains efficiently. It employs an auxiliary coarse grid, together with its dual, to define and solve a coarse-scale pressure problem. A set of basis functions, which are local solutions on dual cells, is used to interpolate the coarse-grid pressure and obtain an approximate fine-scale pressure distribution. However, if flow takes place in presence of gravity (or capillarity), the basis functions are not good interpolators. To treat this case correctly, a correction function is added to the basis function interpolated pressure. This function, which is similar to a supplementary basis function independent of the coarse-scale pressure, allows for a very accurate fine-scale approximation. In the coarse-scale pressure equation, it appears as an additional source term and can be regarded as a local correction to the coarse-scale operator: It modifies the fluxes across the coarse-cell interfaces defined by the basis functions. Given the closure assumption that localizes the pressure problem in a dual cell, the derivation of the local problem that defines the correction function is exact, and no additional hypothesis is needed. Therefore, as in the original MSFV method, the only closure approximation is the localization assumption. The numerical experiments performed for density-driven flow problems (counter-current flow and lock exchange) demonstrate excellent agreement between the MSFV solutions and the corresponding fine-scale reference solutions.     

Lithofacies modeling by multipoint statistics and economic evaluation by NPV volume for the early Cretaceous Wabiskaw Member in Athabasca oilsands area,Canada

The static modeling and dynamic simulation are essential and critical processes in petroleum exploration and development. In this study, lithofacies models for Wabiskaw Member in Athabasca, Canada are generated by multipoint statistics(MPS) and then compared with the models built by sequential indicator simulation(SIS). Three training images(Tls) are selected from modern depositional environments;the Orinoco River Delta estuary, Cobequid bay-Salmon River estuary, and Danube River delta environment. In order to validate lithofacies models, average and variance of similarity in lithofacies are calculated through random and zonal blind-well tests.In random six-blind-well test, similarity average of MPS models is higher than that of SIS model. The Salmon MPS model closely resembles facies pattern of Wabiskaw Member in subsurface. Zonal blind-well tests show that successful lithofacies modeling for transitional depositional setting requires additional or proper zonation information on horizontal variation, vertical proportion, and secondary data.As Wabiskaw Member is frontier oilsands lease, it is impossible to evaluate the economics from production data or dynamic simulation. In this study, a dynamic steam assisted gravity drainage(SAGD)performance indicator(SPIDER) on the basis of reservoir characteristics is calculated to build 3 D reservoir model for the evaluation of the SAGD feasibility in Wabiskaw Member. SPIDER depends on reservoir properties, economic limit of steam-oil ratio, and bitumen price. Reservoir properties like porosity,permeability, and water saturation are measured from 13 cores and calculated from 201 well-logs. Three dimensional volumes of reservoir properties are constructed mostly based on relationships among properties. Finally, net present value(NPV) volume can be built by equation relating NPV and SPIDER. The economic area exceeding criterion of US$ 10,000 is identified, and the ranges of reservoir properties are estimated. NPV-volume-generation workflow from reservoir parameter to static model provides costand time-effective method to evaluate the oilsands SAGD project.