Abstract

Modeling Middle East giant carbonate reservoirs with fractures and stratiform super-k intervals present unique challenges to conventional simulation approaches. Several methods have been used in the representation of conductive faults and fractures for reservoir simulation. Broadly speaking, they can be classified as either single medium approaches or dual media approaches. In single medium approaches, the fault/fracture grids, local grid refinements, and pseudo relative permeability curves have been used. In the dual medium approach, the dual porosity dual permeability (DPDP) formulation has been applied. It should be noted that the classical dual porosity model for naturally fractured reservoir (NFR) is not suitable here. This is because the fracture zones in these reservoirs can be several times larger than the length of a grid cell and the matrix is quite permeable.

The DPDP system is numerically challenging as the two media representing the matrix and the fracture can have very high contrast in porosity and permeability. Since the matrix-fracture transfer terms in the solution matrix can be very large, their numerical treatment is important for the stability and efficiency of the solution method. In this paper, a parallel highly-scalable iterative solution method is introduced to address this problem. The method involves the ordering of the system Jacobian matrix such that each column of cells can be factorized exactly. This is then imbedded in a preconditioning step by calculating approximate inverse matrix using the truncated Neumann series and is iteratively solved using a generalized conjugate residual (GCR) method.

Introduction

Peripheral water injection has been practiced for a number of years in some giant carbonate reservoirs. It has been observed that significant unstable water encroachment has developed in some parts of the field. This can potentially lead to early water breakthrough in some wells and must be properly managed. Recent advances in geologic characterization in these reservoirs have identified that conductive faults or fractures in combination with stratiform super-k intervals may be a key contributor to these abnormalities. An example of a delineated fracture pattern is illustrated in Fig. 1 which areally represents tens of kilometers of the reservoir in question. It is of significant interest to correctly simulate the water movement in these reservoirs.

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