APPLICATION OF GAUSS-LAGUERRE QUADRATURE FORMULA IN DETERMINATION OF DIMENSIONLESS PRESSURE DISTRIBUTION IN A VERTICAL WELL

¹Oloro J, ²Adewole E.S and ³Olafuyi.O.A

¹Petroleum Engineering Department, Delta State University, Oleh Campus

²Petroleum Engineering Department, University of Benin

³Petroleum Engineering Department, University of Benin

ABSTRACT

In this paper, application of Gauss-Laguerre quadrature formula was used to determine dimensionless pressure distribution in a vertical well based on the following assumptions: *Infinite acting reservoir that is, the reservoir is infinite size. *The well is producing at constant flow rate. *The reservoir is at a uniform pressure, when production begins. *The well, with a wellbore radius of radius of r_w is cantered in a cylindrical reservoir of radius r_e *No flow across the outer boundary. In work, the result shows that as r_D increases,  P_D decreases. This indicates that when the radius of wellbore is increasing, productivity decreases for a vertical well and also at early t_D the productivity is very insignificant. When P_D and t_D was plotted on log-log at late time the slope was 1.1513.This indicates that fully penetrating vertical well in an infinite reservoir and boundaries have been felt. The values of E_i at various r_D, shows that as r_D increases, E_i decreases. The results also shows that dimensionless pressure P_D increases with dimensionless time t_D and log approximation was applied when ≥0.25 and the smaller alpha, the higher the productivity. This method has ability to handle all homogeneous porous media, ability to handle all shapes of boundaries, regular or irregular and ability to eliminate trial-and error procedure.

Key words: Dimensionless, reservoir, wellbore, pressure, radius