PORO software applicability

PORO is a semi-analytical simulator for tracer flux in an oil reservoir that supposes homogeneous and non-isotropic horizontal layers in which several vertical sources and sinks are present. The conceptual model is based on the analytical solutions of Darcy and convention diffusion equations. This simple model is more applicable than a more detailed one because of the high level of uncertainty in the reservoir description, especially after the water flooding in oil secondary recovery projects. The quality of the results was checked by comparing the simulator predictions with experimental results from laboratory and field exercises under different conditions.

How does PORO work?

The PORO simulator allows the evaluation of the principal parameters of the watered layers, by matching the experimental data on the basis of:

• A number of vertical injector wells (with arbitrary coordinates);

• A number of vertical producer wells (with arbitrary coordinates);

• Uniform water flow rates;

• Homogeneous horizontal layers;

• Non-lateral boundaries or sealing faults as boundaries;

• Anisotropy (the Kmax/Kmin ratio and the direction of Kmax must be specified,

K being the permeability).

The PORO simulator works by taking into account:

• That the wells are ‘vertical lines’ sources or sinks (cylindrical geometry);

• Analytical solutions for the velocity field (and the superposition principle);

• The generation of the streamlines between each injector and the connected

producers;

• The solution of the convection diffusion equation on each streamline and

computing the overall concentration in each producer.

For solving the convection diffusion equation, PORO converts the time into frequency (by Fourier transform) and transforms the space into a discrete one along each streamline. Finally, a simple scheme of finite differences is employed.

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Prior to starting the simulation, the following information has to be entered:

• The type (injector or producer) and the coordinates of the wells;

• The water flow rates of each well;

• The layer thickness, porosity and water saturation;

• The layer dispersivity (in oilfield scale, it is in the order of 10% of the distance between wells);

• The anisotropy ratio (Kmax/Kmin ) and the direction of Kmax;

• The sealing faults, if any;

• The time and frequency ranges (between 0.00001 and 1 for the conventional oilfield scale);

• The number of streamlines and the distance between consecutive points in each streamline.

Preparation of a software package for covering the tracer dynamics in all rock reservoir situations is a difficult, but necessary task. The most frequent cases include water stationary fluxes in which a conservative tracer moves in approximately horizontal and homogeneous layers (with simple primary porosity). These cases can be interpreted acceptably by the methods discussed here. Also, absorption, partition in the hydrocarbon phase, radioactive decay and tracers in stationary gas flows can be easily included in the models. However, it is very frequent to find cases in which the tracer moves in rocks with double porosity, particularly along conductive fractures [41-45]. Other anomalous cases are related to the tracer flow in ‘wormholes’, which are typical in unconsolidated sands and heavy oil reservoirs [46, 47]. Finally, it is necessary to include other geometries for covering 3-D flows and 2-D special cases, such as flow in horizontal wells.

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