This paper describes a two dimensional three phase numerical model for simulating two or three-phase coning behavior. It is a fully implicit model with respect to all variables by using the simultaneous solution of the different equations describing the multiphase flow.

For determining well flow rates as closely as possible for all the perforated grid blocks, particular attention has been paid to the well boundary condition which is physically taken into can sideration, with the well thus being a physical boundary. The model described is appreciably different in this respect from previous models in which the well is represented by Source point and in which the flow terms are calculated by using various simplifications.

The model is checked by the simulation of a three-phase coning case which had previously been studied on a physical model.

The simulation of an actual field case having a long production history is described. The geometric and influx characteristics of the well are in good agreement with a radial circular geometry. The model restores the production history very correctly.

An analysis of sensitivity to some poorly understood petrophysical parameters (capillary pressure, relative permeabilities, anisotropy) ha been performed. Results (breakthrough time, oil recovery) generally are:

  1. hardly affected by an error in estimating the anisotropy value

  2. highly sensitive to the shape of capillary-pressure and relative-permeability curves


Multiphase numerical models have usually employed finite difference approximations in which relative permeabilities are evaluated explicitly at the beginning of each time step. But simulators of this type are not capable of solving problems characterized by high flow velocities, such phenomena as well coning, except perhaps at extremely high cost.

Recently some papers1, 2, 3, 4 were published describing a method that employs semi- implicit relative permeabilities and uses the simultaneous solution of multiphase equations. This method is very efficient.

In these simulators, the well is represented by source points and flowrate terms are calculated by using various simplications (mobility or potential methods).

The numerical part of the model described in this paper is similar to those in the latest. models, but its representation of wellbore conditions is quite different and comes closer to expressing physical phenomena caused by end effects. The well is represented full-scale and not by source points.

The model is checked by the simulation of a laboratory three-phase experiment.

Fitting field results with a numerical model usually requires a great many parameter adjustments. In the last section of this paper we describe how in a field case where most of the characteristics are well known, we have succeeded in recreating the production history while modifying only the following parameters:

Equation (Available In Full Paper)

Shapes of capillary-pressure and relative-permeability curves and we describe their influence on the results.


The numerical model described in this paper is a two-dimensional one with radial symmetry. A compressible three-phase system is considered with possible exchange between the gas and oil phase independently oil the composition.

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