PHD-Department of Mathematics

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Browsing PHD-Department of Mathematics by Subject "Completely Bounded Reservoir"

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    Well Test Analysis of a Horizontal Well in a Completely Bounded Reservoir
    (Kenyatta University, 2022) Kitungu, Nzomo Timothy; Kennedy Awuor; Stephen Ezizanami; Daniel Okang'a Oyoo
    Well test analysis as an important part of reservoir engineering has gone through tremendous improvement through the years since the discovery of oil. This is in terms of the tools used, the technology involved, and the mathematical modeling involved. Since most oil reservoirs are underground and in some cases thousands of feet from the surface, it’s impossible to physically observe them and see how they behave or determine their character. Mathematical models play an important role in reservoir system characterization by predicting the well and reservoir behaviour and properties. Over the years horizontal wells have proved that they are more productive compared to vertical wells. In this dissertation, possible mathematical models that can be applied in well test analysis for horizontal wells in a completely bounded oil reservoir are developed. In developing the models, source and Green’s functions are used. Using these functions, dimensionless pressure and dimensionless pressure derivative distributions in real time are derived. Mathematical analyses of the models developed and how they can be applied to characterize a completely bounded oil reservoir penetrated with a horizontal well are presented. All possible flow periods and the effects of reservoir, fluid properties and well design on horizontal well performance are investigated and presented. The effects of reservoir anisotropy on well performance are also investigated. The results of this study show that assuming isotropic cases might reduce the accuracy and reliability of the results obtained and thus recommend consideration of anisotropy in computations. This should be in all the three directions. Further, the results of this study show that well design, directional permeability and reservoir geometry will affect the horizontal well performance differently at early flow time. This applies when the infinite-acting flow is considered as compared to the pseudosteady state flow at late time. It is also noted that the number of flow periods can be many; four full and at least three transitional flow periods from inception of early transient, when the well is infinite-acting, to late transient, when all the external reservoir boundaries are felt. The results also suggest that oil wells that are in the same reservoir and closely spaced will experience pressure communication (interference) faster and vice-versa. Thus, well pressure interference affects well performance. The results obtained in this study can be used for complete reservoir system characterization and to investigate the best well design for optimum oil recovery in a bounded well reservoir penetrated with a horizontal well.