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.
Mean square numerical solution of stochastic differential equations by fourth order Runge-Kutta method and its application in the electric circuits with noise