...) 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 Function of the second kind). In form, this result is quite...

... reservoir thickness, h D = 1/L D = h/L c I 0 = Modified Bessel function of first kind, order 0 I 1 = Modified Bessel function of first kind, order 1 I n ' = Modified Bessel function of first kind, integer order n I n = derivative of Modified Bessel function of first...

... Oil & Gas well shut-in Bessel function wellbore production logging fluid temperature semi-analytical solution heat transmissibility coefficient application shut-in time heat conduction shut-in period Introduction K 0 is the zeroth order modified Bessel function of the second...

... for input into the engineering design of future carbon dioxide facilities and the use of surface pressure for interpreting reservoir behavior. drillstem testing spe 134881 temperature difference downhole pressure bessel function downhole gauge upstream oil & gas gauge crc-1 injection well...

... 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 exhibition...

... = ρ D 2 + ρ ′ D 2 − 2 ρ D ρ ′ D cos φ , where φ is the angle POP ′ and (9) cos φ = cos θ cos θ ′ + sin θ sin θ ′ cos ( ϕ − ϕ ′ ) . Using the addition theorem of Bessel functions 3 , 4 we have (10) exp...

..., with problems associated with Bessel functions overcome (see the next section), using the formula is straightforward, with little computer time involved. Closed-form approximations have also been presented in the literature for calculator use, e.g., by Papatzacos 5 and Vribik. 8 These approximations...

... experimental set-up, analytical solutions of the governing equation and applications of them to performed measurements. bessel function spe 22688 boundary condition artificial intelligence society of petroleum engineers early time solution positive root determination permeability order bessel...

... 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 coefficient subregion boundary condition transient pressure analysis drillstem...

... 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...

... temperature distribution diffusion bessel function enhanced recovery ramey flow rate heat flow assumption heat transfer dimensionless time production control production monitoring INTRODUCTION The importance of various aspects of heat transfer between wellbore fluid and the earth has...

... . To consider the accuracy of Eq. 25 , note that its derivation is based on approximations of Bessel functions, which restricts its validity at early times. With t Dj denoting dimensionless time of layer j, based on the apparent wellbore radius , we can confidently use Eq. 25 if t Dj ≥ 25 for j=l and 2...