Semianalytic Solutions for a Well With a Single Finite-Conductivity Vertical Fracture

In 1his ~·we develop a simple, closed fonn approximation for the Laplace uansf orm solution for the case of a well with a finite eond~tivity vertical fracture in an infmite-acting reservoir. Our hf~nd sol~tion ls b~ on !l coupling of the solution for a uilincar finite conductiVlty vc11icll fraclUIC model (which docs not model radial flow) and the solution for a unif onn flux/inf mite conductivity vertical fractwc (which does model pseudoradial tlow). 'lbesc solu1ions are readily oblained from the literature. Overall. we consider our solution to be valid for CJD~.S and we show that our solution gives leas than 1 pcICCnt error in both PD an~fD' for CJQ>2. We suggest that our hybrid solution is not vali for CJD<.O.S and do not recommend its use for CJD,jKLJlsl,yD=O) = §ii[err( ..!::!IL}+ erf ( ~ }~ 2 21tLID 2'/tUD ~ l-%D E ( (l-x0 ) 2 ) l+xp E ( (l+x0 ) 2 ) (l) +4 14, +4 14, .... LID LID where die well ~ting derivative~~= t0 t:} is given by Houze,