When a reservoir is bounded, well productivity is affected in the long time according to the nature of the boundary. The length of time for oil production is strongly affected by well location with respect to the boundary, whether the boundaries are single, paired and vertical or paired and inclined. It therefore becomes important that well location is guided to achieve prolong oil production. The guide may be achieved from solution to a specific flow equation describing pressure distribution. The solution prescribes rates and well location for available reservoir system properties. In this paper, dimensionless pressure derivatives of a vertical oil well are studied to search for optium well location that can guarantee satisfactory oil production without premature influence of the external boundaries. The external boundaries are sealing and are considered to be inclined. The solution to this dimensionless diffusivity equation is utilized. The derivatives are computed from the total dimensionless pressure expression summing all the image wells by superposition principle. The Python and Excel softwares were deployed to compute all the dimensionless pressures for the different well designs. Larger magnitudes of dimensionless pressure derivatives would indicate higher oil production for any well design and inclination of the sealing faults. The optimum well location from the sealing faults is inversely proportional to the inclined angles. This implies that nearer wells to faults produce optimally at a given time of production. Furthermore, the relationship between well distance and productivity has no maximum or minimum points. Therefore there is no particular optimum location distance from the faults for optimum productivity. Optimum well location for sealing boundaries depends on many factors, such as production profile, well design, faults angle, fluid type and lease size. Furthermore, it was also observed that the wellbore radius has no significant effect on the dimensionless pressure derivative, optimum well location and the optimum time of production.
In this study, a simpler numerical model for calculating inter-well distance was developed. This model was developed as an alternative to the Ei-function used for computing pressure drops. The mainobjective of developing this model is tomake resolution of pilfering issues easyto resolve. With the developed model, calculations relating to pressure drops and more specifically, inter-well distance, can be done with greater ease and accuracy. In developing this model, the integral equation of the Eifunction in the pressure drop equation was solved numerically. The numerical solution reduced thepressure drop equation to a polynomial equation which is much easier to solve. The developed model was used to solve real problems. Results generated from it were compared with those obtained using previous approaches. Important informationsuch as well configuration, region of the reservoir, and transient history wherethe work is valid are stated. The development of the correlations and tables forthe range of validity and values of the Ei-function is a major quantum leap in well testing and analysis. It will be quite cumbersome to resolve integrals with unknowns, hence, methods of trials and errors have been resorted to over the years. However, this new approach resolved the pressure drop equation into a systemof polynomials which is much easier to solve. Consequently, the distance betweenpossibly interfering wells (which is an important variable during interference test) can now be gotten with ease. The developed model is valid within the range of validity of the Ei-function. Without doubt, this work will help redefine the pressure drop equation into a polynomial equation which can easily be resolved using any of the known approaches to solving problems involving polynomials. More so, getting the correct distance betweenthe two wells in question is pivotal to the test. With the model developed in this work, getting inter-well distance is now easier and more accurate.
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