... simulation results to establish the "most appropriate" model(s) for which to history match actual field cases. Based on the synthetic performance cases considered in the first portion of this work, a new time-rate (DCA) model is proposed based on the K 1 ( x ) Bessel Function ( i.e. , the Modified Bessel...

... & Gas vertical fracture Artificial Intelligence drillstem/well testing Bessel function application composite reservoir boundary circular composite reservoir aquifer boundary condition composite system algorithm horizontal well Drillstem Testing spatial position pressure-transient...

... variable, f(r′) is the known function for temperature distribution at t = 0, and I 0 is the zeroth order modified Bessel function of the second kind. Applying this solution to the shut-in well temperature problem, we introduce t s and t c , which represent well shut-in time and well production time...

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... is numerically solved. rafael rodríguez-n fernando samaniego-v linear probability function probability function pressure transient testing héber cinco-l fractured reservoir characterization complex reservoir bessel function reservoir upstream oil & gas variable block size model drillstem...

.... Asymptotic approximations for well responses at early and late times are provided. Computational issues are addressed and example applications are discussed. society of petroleum engineers bessel function drillstem/well testing hydraulic fracturing ozkan slab reservoir point-source solution exp...

... Abbreviation Expansion B formation volume factor and special function ( Eq. 14 ) c t system compressibility D special functions ( Eqs. 15 – 17 ) h formation thickness I 0 modified Bessel function of order 0 I 1 modified Bessel function of order 1 k...

... with the addition theorem for Bessel functions. It is shown, both analytically and numerically, that the new model contains several well-known solutions as subsets of the general solution. reservoir configuration boundary active well subregion coefficient boundary condition analytical solution...

... distribution is computed during two-phase flow. production logging upstream oil & gas wellbore fluid radial distance reservoir surveillance society of petroleum engineers temperature distribution diffusion bessel function enhanced recovery expression boundary condition differential...

... employs the Laplace transformation and the addition theorem for Bessel functions, is new and is different from past works. This solution is a subset of a generalized multi-well composite-reservoir solution. 1 An analysis technique, both predictive and interpretive, for detecting an impermeable linear...

... modified, first kind, zero order Bessel function I 1 modified, first kind, first order Bessel function I 2 modified, first kind, second order Bessel function J 0 first kind, zero order Bessel function J 1 first kind, zero order Bessel function J 1 first kind...

... buildup behavior approximation drillstem/well testing semi-log straight line infinite-acting period reservoir property spe 10325 bessel function upstream oil & gas skin factor unequal initial pressure drillstem testing reservoir horner plot initial pressure two-layer reservoir spe 10325...