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Using Percolation Theory to Estimate Recovery from Poorly Connected Sands Using Pressure Depletion
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery, Sep 2014, Volume 2014, p.1 - 13
Abstract
In conventional waterflooding of low to intermediate net to gross reservoirs there is always some oil unswept even in the sands connected to both injection and production wells. This is oil trapped in “dangling ends”: flow units only poorly connected to the main flow path. In many cases the unswept volumes can be very large, depending on the properties of the reservoir and fluids and the well locations.
In this paper we show how percolation theory can be used to estimate the volumes of oil recovered and those left behind in these dangling ends following a conventional waterflood, without recourse to large scale simulation. Percolation theory is a general mathematical framework for connectivity and has been used previously to investigate the connectivity of flow units. The structure of these connected clusters in terms of backbones and dangling ends has not been previously studied. The results are also used to estimate the recovery of the unswept oil from dangling ends by a waterflood with a voidage replacement ratio <1.
We use a simple model of stochastically-distributed sandbodies to describe the reservoir. Many realizations for a range of net to gross ratio values and sandbody:system sizes were generated. In each realization the clusters connecting the injection and production wells were identified. These spanning clusters were subdivided into backbones and dangling ends. The volume fractions of the backbone and dangling end were then obtained. The statistical average and standard deviation of the volumes association with these clusters were obtained from the ensemble of realisations. These were used to determine the percolation scaling relationships in terms of simple algebraic formulae that cover the whole range of net to gross ratio and system sizes.
Our results show that the fraction of dangling ends can reach 20% of the clusters, and 80% among the spanning clusters, indicating a major proportion of the oil would be unswept by conventional waterflood. Recovery is improved for voidage replacement ratios less than 1 when the dangling ends are drained by oil expansion and solution gas drive.