Comparative evaluation of pressure distribution between horizontal and vertical wells in a reservoir (edge water drive)

Abstract Dimensionless pressure gradients and dimensionless pressure derivatives characteristics are studied for horizontal and vertical wells completed within a pair of no-flow boundaries inclined at a general angle ‘θ’. Infinite-acting flow solution of each well is utilized. Image distances as a result of the inclinations are considered. The superposition principle is further utilized to calculate total pressure drop due to flow from both object and image wells. Characteristic dimensionless flow pressure gradients and pressure derivatives for the wells are finally determined. The number of images formed due to the inclination and dimensionless well design affect the dimensionless pressure gradients and their derivatives. For n images, shortly after very early time for each inclination, dimensionless pressure gradients of 1.151(N+1)/LD for the horizontal well and 1.151(N+1) for vertical well are observed. Dimensionless pressure derivative of (N+1)/2LD are observed for central and off-centered horizontal well locations, and (N+1)/2 for vertical well are observed. Central well locations do not affect horizontal well productivity for all the inclinations. The magnitudes of dimensionless pressure drop and dimensionless pressure derivatives are maximum at the farthest image distances, and are unaffected by well stand-off for the horizontal well.

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Mathematical description of a bounded oil reservoir with a horizontal well

African Journal of Pure and Applied Sciences ◽

10.33886/ajpas.v2i1.190 ◽

2021 ◽

Vol 2 (1) ◽

pp. 67-76

Author(s):

T. N. Nzomo ◽

S. E Adewole ◽

K. O Awuor ◽

D. O. Oyoo

Keyword(s):

Pressure Distribution ◽

Effective Permeability ◽

Horizontal Well ◽

Horizontal Wells ◽

Oil Reservoir ◽

Vertical Wells ◽

Anisotropic Permeability ◽

Time Approximation ◽

Reservoir Geometry ◽

Short Time

Horizontal wells are more productive compared to vertical wells if their performance is optimized. For a completely bounded oil reservoir, immediately the well is put into production, the boundaries of the oil reservoir have no effect on the flow. The pressure distribution thus can be approximated with this into consideration. When the flow reaches either the vertical or the horizontal boundaries of the reservoir, the effect of the boundaries can be factored into the pressure distribution approximation. In this paper we consider the above cases and present a detailed mathematical model that can be used for short time approximation of the pressure distribution for a horizontal well with sealed boundaries. The models are developed using appropriate Green’s and source functions. In all the models developed the effect of the oil reservoir boundaries as well as the oil reservoir parameters determine the flow period experienced. In particular, the effective permeability relative to horizontal anisotropic permeability, the width and length of the reservoir influence the pressure response. The models developed can be used to approximate and analyze the pressure distribution for horizontal wells during a short time of production. The models presented show that the dimensionless pressure distribution is affected by the oil reservoir geometry and the respective directional permeabilities.

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