Analytical investigation of steady flow around a circular wellbore in an elliptical domain

Abstract

Flow behavior thmugll a porous med,um depend, on fluid propetties as well as the chara~teri,ti~, (}fthe medium, In a homogeneou., and i~otropic porous m(:dium. now around a wellb",e i, gener~lly radial llI' lincar. In -lOme~a.,e,. flow "round a wellbore may ulso become elliptical in,te"d of rudial or linear, Many authors di.,cu,,,ed the elliptical flow behavior a«uming a vertical fracture at the center of the reservoir, Elliptical flow may also be observed around a circular weJlbore at the center of an anisotropi~ re,ervo;r even if thcre is no vert;eal fracture. Elliptical flow situation around a circular wellb",e al,o occurs dllring the producl;on pha'E of cyclic .<te~mstimulmlOn (CSS) when a ,hear lOne of enh~nced permcl1bdLtyl,\ crealed around the wellbol'e during the injection pha,e of thb process, No dlScussion is found in petroleum literatlll'e on elliptical Ilow hehavior with circular wcllbore at the center. This study modified the analytical Sollilions available in litera1llre to Investigate sleady flow "round a circular wellbore in an elliptical d()m~in. The new model i., u.'ed 10~nnlyzc the effect of eccentricity of the elliptical domain on ilow Me, It w~s found thm radial flow model WIll produce as much as nine percent errol' in flow calculatioil if it is used ill ellJptical,'yslem, Using "Continuous Succe,,,ion of Steady St~te.\" (CSSS) method. the model 1,\al,o applied to e~timme tilc depth of inveslJgation for a 'y,tem with elliptical flow domain, Tile depth of investig"tilm in nldi~l "nO elliplical sy'tem, ~re alw compared in thi, study. The elliptical model wa, linLlldIn accordance with the radial model Jt eccentricity equal to zero. The Jretl of dminage WJ~Jl<o founo to be independent of the flow mte. pressure level and ,hape of tilCeIlipt1cnidomain.