Interpretation of well-cell pressures on hexagonal grids in numerical reservoir simulation

Peaceman’s equivalent well-cell radius for 2D square grids has been generalized to 2D grids consisting of regular hexagons. The development consists of the following steps. Firstly, the analytical solution for the pressure drop between injector and producer for wells in a seven-spot pattern is determined. Secondly, this solution is compared with the numerical solution on hexagonal grids for a sixth of a seven-spot pattern. Finally, the equivalent well-cell radius is calculated, and its asymptotic behavior for infinitely fine grids is derived. The results are valid for both steady-state and unsteady-state conditions.     

A method for automatic history matching of a compositional reservoir simulator with multipoint flux approximation

A method for history matching of an in-house petroleum reservoir compositional simulator with multipoint flux approximation is presented. This method is used for the estimation of unknown reservoir parameters, such as permeability and porosity, based on production data and inverted seismic data. The limited-memory Broyden–Fletcher–Goldfarb–Shanno method is employed for minimization of the objective function, which represents the difference between simulated and observed data. In this work, we present the key features of the algorithm for calculations of the gradients of the objective function based on adjoint variables. The test example shows that the method is applicable to cases with anisotropic permeability fields, multipoint flux approximation, and arbitrary fluid compositions.     

Current-depth refraction of water waves

Surface gravity waves propagating on large-scale currents over a gently sloping sea bed are considered. Assuming irrotational flow a general proof is given of the existence of a mean energy level, leading directly to the current wave set-down. The complete set of conservation equations describing combined current-depth refraction is presented and solved in two special ssituations. Also a case with a rotational current is considered. Dissipation is neglected.