This paper describes the current level of tracer flow modelling. A separate module for tracer flow calculation is incorporated in a state-of-the-art reservoir chemical-thermal simulator. The paper outlines what the tracer module is and why it is needed and used. Following a brief history of tracer simulation and a general description of the tracer module, the simulation application section describes the use of the tracer module. The section discusses and summarizes tracer simulations performed on several field cases and on a laboratory case. The paper includes example field-scale cases with a sensitivity study showing effects on reduction of numerical dispersion by improved gridding techniques. Obtained results are confirming the benefit of advanced solution methods for tracer flow with tracer grids finer than the phase grid. The tracer numerical dispersion is reduced significantly.
The tracer module was developed during a multiclient tracer research project in 1991-1993. In the recent years it has been further developed and upgraded. The coupling to a black oil simulator and a compositional simulator is progressing.
Assuming that tracers do not affect the flow of other fluids in the reservoir, the calculation of tracer flow may be performed in a module separated from the rest of the reservoir simulator. The module then needs flow parameters such as grid block pressures, phase velocities and saturations to be transferred from the host reservoir simulator at each timestep. The advantage of such an implementation is to use the available options for predicting reservoir fluid flow together with advanced numerical methods for the tracer flow calculation.
To be able to resolve the influence of reservoir heterogeneities on the measured tracer responses, an accurate numerical treatment of the tracer equations is needed. This is specially important when narrow tracer slugs are injected in a reservoir. It therefore seems feasible to build a separate module which to some extent is portable to other simulators. The tracer module calculates tracer flow by using an explicit method for integration of the convection part of the tracer equation. In order to reduce numerical smearing of the tracer pulses, the timestep for the tracer calculation is chosen as large as possible within the CFL criterion, but may still be much smaller than the timestep of the host reservoir simulator, which most often uses an implicit formulation. In the tracer module the main tool for reducing numerical dispersion is the use of a 2nd order numerical scheme for integrating the tracer equations. A separate grid refinement option for the tracer calculation is available. In combination, these methods lead to a good resolution of narrow tracer slugs propagating in a reservoir. The method of separate grid refinement is far less time consuming than performing the whole reservoir simulation on a refined grid.
In reservoirs tracers may be subjected to adsorption to the rock, partitioning between the phases, dispersion and molecular diffusion. Dispersion effects are introduced by using a full dispersion tensor, and the calculation is performed by using a fractional step method (operator splitting) between the convection term and the dispersion term of the tracer equation. The advantage of using this method is that the timesteps for the convection equation and the dispersion equation may be chosen individually. This means that the timestep for the convection equation may be chosen optimally to reduce numerical smearing effects even when physical dispersion/diffusion effects are included. Both explicit and implicit integration methods are available for the dispersion/diffusion calculation.
Partitioning between the phases and adsorption to the reservoir rock may lead to a significant delay of the tracer pulse. This is seen quite clearly for an adsorbing water tracer in a 1-dimensional plug at residual oil level (assuming 1-phase incompressible flow):
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