ECMOR VII - 7th European Conference on the Mathematics of Oil Recovery

The control-volume schemes are discussed for the modelling of vertical wells. The key problem of the well modelling is the accurate fluid flow calculation in the well vicinity. In this paper, the flux truncation errors are analyzed on the gridblocks in the near well region. It is shown that truncation errors of the standard approach might be large in the near well region due to the well singularity, and new numerical scheme is needed to be developed to reduce these errors. In this paper, a multi-point flux approximation scheme is presented for the flow modelling in the well vicinity. This scheme can take into account the particular well flow pattern, grid distortion and heterogeneity. It is suitable for any kinds of grids and heterogeneous media

In this paper, we focus on iterative optimization processes based upon the gradual deformation method. It is shown that such processen converge exponentiatly to the global minimum, at least for linear problems. Additionally, we evidence that the gradual deformation method does not preserve the spatial variability for great numbers of iterations. However, this bias is negligible for practical reservoir engineering problems.

We have considered the mathematical properties of the filtration equations and demonstrated that there are finite velocities of the shock waves and contact discontinuities of the saturations and phase concentrations. These features are the same ones as tor hyperbolic equations.

This paper presents finite volume schemes adapted to a new hybrid mesh model. The hybrid mesh is composed of: 1/ a global structured CPG grid describing the reservoir field, 2/ a structured radial grid around each well, 3/ an unstructured polyhedral grid connecting the two previous ones.

Streamline methods have been used for numerical approximation of the mathematical model for fluid flow since the 1800's and have been applied in petroleum engineering since the late 1950's. For reservoir simulation, however, finite differente simulators have always been the norm. Recently, streamline methods have emerged as an alternative to finite differente simulation for large, heterogeneous modeas that are difficult for traditional simulators to model adequately. 1,2,3,4,5

In the proces of quantifying hydrocarbon production forecast of reservoirs the pertinent questions are: • How do we parameterize reservoirs both meaningfully and efficiently ? • Which criterion should be used in determining how good a history match really is? • How do we search/characterize the parameter space of a reservoir efficiently and in an unbiased manner? • How do we perform forward modeling of the hydrocarbon recovery efficiently, yet with good accuracy?

The reservoir characterisation methods are still improving the integration of all available data for more accurate predictions, but the litmus test remains the history-matching confrontation, after a period of production, between observed data and simulated data as predicted by the numerical model of the reservoir.

Computer-aided history matching of oil production data requires the solution of a challenging minimization problem. Usually, gradient based techniques have been applied to this aim: starting from an initial guess of the solution, these methods converge to the closest local minimum, along specified descend directions. Typically, however, the parameter space is populated by many, local minima, each giving a different response in terms of forecasted production profiles. Theoretically, it is thus important to identify the lowest possible minimum among all candidates.

The issue of honouring reservoir characterisation in a 3D simulation model is a critical aspect of reservoir modeping. Hence, a computer calculation procedure has been devised to suitably determine grid block properties.