Mathematical description of a bounded oil reservoir with a horizontal well

Abstract

When horizontal wells are compared with verticals wells, their production is always higher. If their performance can be improved, they can even be more productive. Considering a horizontal well in a completely bounded oil reservoir, when the well has been producing for some time and the effect of the boundaries is evident on the flow, the pressure distribution can be approximated by considering the effects of the boundaries on the flow. Considering when a pseudosteady state flow is attained this study presents a mathematical model for approximating pressure distribution for late time for a horizontal well in an oil reservoir with sealed boundaries. We use appropriate Source and Green’s functions to develop the model. The model developed show that when the flow reaches all the boundaries a pseudosteady state flow is attained and thus pressure distribution is influenced by the oil reservoir geometry especially its width and length. Considering that the thickness of the oil reservoir will be small compared to the length of the well, the oil reservoir width and length will determine the pressure response. This will influence the flow period occurring. By considering all aspects of the flow, the model can be applied to approximate the pressure distribution for as long as the well can continue producing.