This paper describes a three-dimensional mathematical model for analyzing individual well behavior in asymmetric regions. It is especially useful for treating pressure transient test results in a multiwell environment typical of offshore or Arctic drilling platforms.

The model rigourously accounts for spatial variation of reservoir properties~ the effect of formation compaction associated with fluid withdrawals, non-Darcy flow, skin and wellbore storage effects, interlayer flow through the wellbore, and interference effects resulting from production in other wells. A completely implicit formulation together with a direct solution technique assures unconditional stability and rapid convergence.

The results of an application to single wells on a new drilling platform are presented. Comparisons of the model results with a conventional buildup analysis are given and the importance of accounting for formation compaction and turbulence is demonstrated. We also present the results of a hypothetical multiwell problem where interference effects are important. It is concluded that conventional analysis techniques are limiting and may lead to erroneous conclusions, particularly in analysing platform systems where well drainage areas are irregular and indeterminate.


Pressure transient testing has been extensively applied to gas wells to determine reservoir anomalies and pertinent formation characteristics. Analytical methods exist to account for turbulent flow, wellbore storage effects, skin effects, and interference from other wells.l-5 However, one frequently encounters peculiar pressure behaviour in gas wells where these techniques do not provide adequate interpretations. The peculiarities may arise from anyone or combination of the effects cited above and can be further complicated by reservoir heterogeneities; the existence of faults, flow through more than one layer, recirculation, asymmetric well locations, etc. This is especially true for platform type developments in heterogeneous formations where deviated, partially penetrating wells having irregular and indeterminate well drainage areas invalidates the assumptions made in conventional analytical techniques.

This paper describes a numerical well test model (capable of handling liquid or gas) that accounts for many or the factors neglected in conventional well analysis. We have adopted techniques previously presented by Coats, et al.6 to treat wellbore storage, turbulence, skin effects, cross-flow between layers, recirculation through the wellbore, partial penetration, and pressure-dependent permeability. A similar feature in our model is the ability to simulate shutin at the wellhead and observe the afterflow. Unlike their work, however; we have incorporated three-dimension capabilities and can handle problems in either cylindrical or cartesian (x, y, z) coordinate systems. Thus it is possible in the r, q, z system, for example, to simulate translent, his flow in a single well while simultaneosly accounting for interference effects from adjacent. Anymetrically located wells. This is especially useful in analyzing well test data from drilling platforms having a multiplicity of wells. In such cases the well test model can be used to match the flowing and static pressures, and determine the pertinent reservoir parameters and flow characteristics. The model is also useful for forecasting long-time de1iverability in tight gas reservoirs. Furthermore, it can adequately handle a dual porosity system characteristic of fractured or vugular resorvoirs in a manner similar to that presented by Agrawal and Beveridge.7

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