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Green���s function for solving transient flow problems

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Proceedings Papers

Paper presented at the Canadian International Petroleum Conference, June 8–10, 2004
Paper Number: PETSOC-2004-048
...-analytical model coupling the reservoir/wormhole flow has been developed to study the effects of wormholes. This model is based on the source and Green s functions method, which has been widely practiced in horizontal and multilateral well analyses to solve the unsteady flow problems. This model is also...
Proceedings Papers

Paper presented at the The 29th International Ocean and Polar Engineering Conference, June 16–21, 2019
Paper Number: ISOPE-I-19-684
... is , 1 1 , , f b c d d d q q qS S S q t p p t q t ds n r n r (5) Where, 1/r is Rankine source Green function and r is distance between field point p and source point q; denotes solid angle. Boundary integral equation of outer domain...
Proceedings Papers

Paper presented at the SPE California Regional Meeting, March 27–29, 1985
Paper Number: SPE-13627-MS
... the calculation of the qs.f'D because there is no wellbore contribution to the total flow rate (qs.f'D 1 . 0). Therefore, in many cases, the Stehfest algorithm W"ill not even be used. The use of Green' s func tiona in pressure transients analysis has been originally presented by Gringarten and Ramey (1973...
Proceedings Papers

Paper presented at the The Nineteenth International Offshore and Polar Engineering Conference, July 21–26, 2009
Paper Number: ISOPE-I-09-221
.... Wehausen, JV, and Laitone, EV (1960). "Surface Waves," In: S. Flugge (eds Handbuch Der Physik Vol 9. New York: Springer-Verlag, pp 446-778. 575 A time-domain model for radiation and diffraction problems based on 3D finite water depth transient Green function is developed by a higher order boundary...
Proceedings Papers

Paper presented at the The Twenty-fourth International Ocean and Polar Engineering Conference, June 15–20, 2014
Paper Number: ISOPE-I-14-369
... Abstract The time-domain hybrid method which combined of Rankine source method and transient Green function method is used to solve sea-keeping problem in this paper. In order to validate the time-domain hybrid method and the quality of free surface and control surface simulation, numerical...
Proceedings Papers

Paper presented at the SPE Annual Technical Conference and Exhibition, October 2–5, 1988
Paper Number: SPE-18169-MS
... this, Gringarten and Ramey rediscovered the possibilities of Green's function theory with respect to potential flow. Following these ideas, Cinco-Ley et al. set out to solve the transient flow problem for a hydraulically fractured reservoir, and problem for a hydraulically fractured reservoir, and derived...
Proceedings Papers

Paper presented at the SPE Production and Operations Symposium, March 23–25, 2003
Paper Number: SPE-80911-MS
.... : "The Use of Source and Green Functions in Solving Unsteady-Flow Problems in Reservoirs," paper SPE 1973. Earlaugher , R.C ., JR : "Advances in Well Test Analysis, Monograph Volume 5 , Society of Petroleum Engineers, Richardson 1977. Mathematical Table of Integrals and formulae...
Proceedings Papers

Paper presented at the SPE Reservoir Simulation Symposium, February 14–17, 1999
Paper Number: SPE-51924-MS
... , H.J. : " The Use of Source and Green Functions in Solving Unsteady Flow Problems in Reservoir ", SPEJ ( October 1973 ) 285 – 96 ; Trans, AIME, 255 . Hayes , L. , Kendall , R.P. and Wheeler , M.F. : " Treatment of source and sinks in steady state reservoir engineering...
Proceedings Papers

Paper presented at the Latin American and Caribbean Petroleum Engineering Conference, May 31–June 30, 2009
Paper Number: SPE-122055-MS
.... References References a. Gringarten , A. C. and Ramey , H. J. Jr. : " The Use of the Point Source Solution and Green's Functions for Solving Unsteady Flow Problem in Reservoir ," SPEJ ( Oct. 1973 ) 285 – 296 . b. Liggett , J. A. and Liu , P.L-F. : " Unsteady Free Surface...
Proceedings Papers

Paper presented at the ADIPEC, October 31–November 3, 2022
Paper Number: SPE-211564-MS
..., the coefficients in the equation are functions of unknown influxes), the approach of Newton-Raphson is often used to solve this type of problem. For pseudo-radial flow in a slab reservoir, and using Ozkan & Raghvan solutions (1993) using the method of source and sinks and Green's function...
Proceedings Papers

Paper presented at the Canadian International Petroleum Conference, June 12–14, 2001
Paper Number: PETSOC-2001-006
... of the fluid within the fracture. As shown in Refs. 2, 3, this approximation is reasonable for most practical purposes. The solution for the flow within the fracture does not have to be expressed in terms of Green s function but can rather be calculated by other methods of solving ODE. Coupling of Reservoir...
Proceedings Papers

Paper presented at the PSIG Annual Meeting, May 5–8, 2020
Paper Number: PSIG-2001
... the flows using a steady-state formulation (DT-SS) given by (21) where we assume that each operational period is at steady state. The steady-state formulation is typically used to solve expansion planning problems or develop operational policies when the network transient is minimal. A key advantage...
Proceedings Papers

Paper presented at the SPE California Regional Meeting, March 27–29, 1985
Paper Number: SPE-13626-MS
... Engineers of AIME SPE 13626 Green's Functions for Solving Unsteady Flow Problems in Naturally Fractured Reservoirs With Arbitrary Fracture Connectivity: Part 1-Theory by A.M. Wijesinghe, Lawrence Livermore Nat/. Laboratory SPE Member Copyright 1985, Society of Petroleum Engineers This paper was presented...
Proceedings Papers

Paper presented at the Abu Dhabi International Petroleum Exhibition and Conference, October 13–16, 1996
Paper Number: SPE-36231-MS
... Clonts, M. D., Ramey, H. J. Jr. 1986 Pressure Transient Analysis for Wells with Horizontal Drainhole. paper SPE 15116, presented at the 1986 SPE Annual California Regional Meeting, Oakland, CA, April 2-4 Gringarten, A. C., Ramey, H. J. Jr. 1973 The Use of Source and Green s Functions in Solving...
Proceedings Papers

Paper presented at the The 32nd International Ocean and Polar Engineering Conference, June 5–10, 2022
Paper Number: ISOPE-I-22-315
... used method for solving certain solution problems in the three-dimensional frequency domain. Green s theorem and the distribution of singularities are discussed in Newman (1977). Garrison (1984) gave a method of using Green's function to represent the source potential when calculating the wave load...
Proceedings Papers

Paper presented at the SPE Annual Technical Conference and Exhibition, October 3–5, 2022
Paper Number: SPE-210402-MS
... Flow rate, stb/d r wD Dimensionless wellbore radius, dimensionless r w Wellbore radius, ft s Laplace transform variable t Time, hr t D Dimensionless time, dimensionless v i Parameter in Green's function x = Coordinate, ft x D...
Proceedings Papers

Paper presented at the SPE Annual Technical Conference and Exhibition, October 1–4, 2000
Paper Number: SPE-62916-MS
... D s ) The right hand side of Equation (15) includes both the singular and nonsingular solutions. This does not present a problem however since the singular solution is known and can be incorporated easily into the boundary element solution. Green Element Method To transform...
Proceedings Papers

Paper presented at the PSIG Annual Meeting, May 5–8, 2020
Paper Number: PSIG-2003
... functions. The solution of the PDE in (1.3.1) given initial conditions (1.3.2) and boundary conditions (1.3.3) is based on the structural theory of distributed systems [26], [27]. The theory concerns the use of Green s functions to solve linear PDEs for given forms of initial and boundary conditions...
Proceedings Papers

Paper presented at the The 27th International Ocean and Polar Engineering Conference, June 25–30, 2017
Paper Number: ISOPE-I-17-303
... seakeeping with transient Green s function. Rankine source method employs basic solution 1/r of Laplace equation as Green s function. Dawson (1977) first applied Rankine source method to compute steady ship wave. Nakos (1990) studied on steady and unsteady ship wave problems by quasi-linear formulation...
Proceedings Papers

Paper presented at the SPE International Petroleum Conference and Exhibition in Mexico, February 1–3, 2000
Paper Number: SPE-59012-MS
... ) G ( 1 , 1 ) − s { − ∫ 1 ∞ [ G r D ( ξ , r D ) ] r D = 1 ξ p i D ( ξ ) d ξ + h ( u ) [ G r D ( 1 , r D ) ] r D = 1 Substituting the Green's function into Eq. (A-13...

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