Simulating Karstic Conduits as Wells in a Commercial Reservoir Simulator
Authors: Herriou Monia , Barker John Wilson 
Published: February 2016

Abstract
Karst is a generic term for the effects of meteoric (rain) water on carbonate rocks. Resulting features include rock dissolution, conduits, sink-holes, etc, which may have extremely high permeability. Fluid flow simulations in such environments are therefore very challenging - conventional reservoir simulators often experience convergence problems and run times of several days are not uncommon even for models with a modest number of grid cells.
We propose a method in which the conduits are represented as long horizontal wells with no net production to the surface, but in which cross-flow can occur. We present tests that demonstrate the efficiency of the method, first on a conceptual model then on a full field model of a particular carbonate reservoir.
The results obtained with the conceptual model confirm that a substantial (3-fold) reduction in CPU time could be achieved, compared to a conventional approach using high permeability values to represent the conduits.
The full field model was built using proprietary geo-statistical techniques developed by Total. It included a large number of conduits, represented as lines of grid blocks of very high permeability (pseudo relative permeability curves were also used). The models suffered from convergence difficulties and extremely long simulation times. Using our proposed method, a 6-fold reduction in CPU time was achieved for the history match period, with no significant difference in the results. For the predictive simulations, the results were different but further analysis led us to conclude that those obtained with our approach are the more accurate, because of a better representation of injection potential.
The method is potentially applicable to all reservoirs containing Karstic conduits.

Introduction
Karst is a generic term for the effects of meteoric (rain) water on carbonate rocks. Karstification may occur in reservoir rocks as a result of sea-level variations during deposition, for example. Resulting features include rock dissolution, conduits, sink-holes, etc, which may have extremely high permeability.
The representation of such features in a reservoir simulation model is problematic. One approach is to set a high permeability in the grid blocks affected by dissolution or through which conduits pass. An example is shown in Figure 1.
Conduits are generally much smaller in width and thickness than the simulator grid blocks, although they may extend over several grid blocks in length. A pseudo relative permeability curve may thus also be needed for flow in the direction of the conduits (see Figure 2). The pseudos represent the fact that water will flow rapidly through the conduits, so that a high fractional flow of water into the next block downstream will occur even at very low average water saturation in the block itself (when water has swept only the conduits).
Simulation models built using this approach often suffer from convergence difficulties and extremely long simulation times. In the case of one particular reservoir operated by Total, the full field model contained only 125 000 active grid blocks. However, simulating 28 years of production took up to 14 days of cpu time using a conventional, commercial reservoir simulator.
In this paper, we propose an alternative way of representing the conduits - as long horizontal wells with no net production to the surface but in which cross-flow can occur.
In the following sections, we outline the motivation behind the proposed approach, then present tests that demonstrate the efficiency of the method, first on a conceptual model then on a full field model of a particular carbonate reservoir.