J. Douglas, Jr., F. Furtado, and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Computational Geosciences, 1 (1997), 155--190.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....characteristics with adjusted advection (MMOCAA) and locally conservative Eulerian Lagrangian method (LCELM) and applied to various reservoir simulations. MMOCAA preserves the global form of the identity associated with conservation of mass, but does not preserve a localized form of the identity [12, 15, 20, 42]. LCELM has been designed to satisfy the local conservationofmass[17,21,22] However, LCELM is very expensive, in particular, in 3D# mass conservative incomplete characteristic methods (ICMs) are being developed to overcome the high cost of LCELM [16] The main purpose of the section is to present ....

J. Douglas, Jr., F. Furtado, and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Computational Geosciences, 1 (1997), pp. 155--190.

....characteristics with adjusted advection (MMOCAA) and locally conservative Eulerian Lagrangian method (LCELM) and applied to various reservoir simulations. MMOCAA preserves the global form of the identity associated with conservation of mass, but does not preserve a localized form of the identity [12, 15, 20, 42]. LCELM has been designed to satisfy the local conservation of mass [17, 21, 22] However, LCELM is very expensive, in particular, in 3D; mass conservative incomplete characteristic methods (ICMs) are being developed to overcome the high cost of LCELM [16] The main purpose of the section is to ....

J. Douglas, Jr., F. Furtado, and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Computational Geosciences, 1 (1997), pp. 155--190.

....properties. Errors of this magnitude obscure the relevance of computed approximations to an unacceptable level and motivated the search for a version of the MMOC that both conserves and is at most very little more expensive computationally than the MMOC. Recently, Douglas, Furtado, and Pereira [2] formulated a variant of the MMOC called there the modified method of characteristics with adjusted advection (MMOCAA) which is a new, naturally parallelizable, accurate numerical method for the solution of the transport dominated diffusion processes in heterogeneous porous media. The MMOCAA does ....

....media. The MMOCAA does preserve the desired conservation law and also preserves the conceptual and computational advantages of the MMOC. The alteration in the procedure is solely with the transport part of the saturation calculation. However, there no formal analysis of the MMOCAA was given in [2]. To this end, I co authored a paper [5] with Douglas and Pereira that begins the analysis of the new method MMOCAA. We are concerned with the numerical approximation of the solutions of convection diffusion problems in which the convection or transport dominates the diffusion. We begin by ....

J. Douglas, Jr., F. Furtado, and F. Pereira. On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Computational Geosciences, 1, pp. 155-190 (1997). Chieh-Sen Huang 4

....by now well known, advantages and one fundamental flaw, the failure to preserve as an algebraic identity a desired conservation law associated with the underlying physical problem; in this case, the preserved quantity is supposed to be the water volume. Recently, Douglas, Furtado, and Pereira [8] formulated a variant of the MMOC called there the modified method of characteristics with adjusted advection (MMOCAA) which does preserve the desired conservation law and also preserves the conceptual and computational advantages of the MMOC. The formal analysis of the MMOCAA will be given here. ....

....equation analogous to (1.12) required that the Jacobian of the map (2.2) be identically one; this cannot be expected to hold for even the single space variable immiscible displacement problem. In particular, use of the traditional MMOC procedure has been shown by Douglas, Furtado, and Pereira [8] to lead to a failure to conserve mass by as much as 10 in two space variable simulations involving stochastic rock properties and about half that much with uniform rock properties. Errors of this magnitude obscure the relevance of computed approximations to an unacceptable level and motivated ....

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J. Douglas, Jr., F. Furtado, and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs. Computational Geosciences, 1 (1997), 155-190. 14

....the pressure calculation in the fractures from that of the saturation, and another operator splitting to handle the interaction of the matrix blocks and the fractures. The method in its final form as described here was developed in a series of papers by the authors and their collaborators [4, 6, 9, 10, 11]. We now turn to a description of the governing system of partial differential equations for the medium block model along with boundary and initial conditions. The model is formulated on a two sheeted covering of the domain Omega ae R representing the reservoir, with the flow in the ....

.... o rP c ) o (ae Gamma ae o )grK Delta rz = ae (1 Gamma )q q mf; x; t) q 0; q mf; x; t) q 0; 8) the right hand side of (8) results from assuming that only water is injected and, at a production point, the flow splits according to mobilities between water and oil (see [4]) The boundary conditions for each matrix block require continuity of the phase potentials: ff (x; y; t) Psi ff (x; t) for x ; y 2 B x ; ff = o: 9) We assume the boundary of the reservoir to be impermeable and require that the normal components of both water and oil fluxes across ....

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J. Douglas, Jr., F. Furtado, and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, Computational Geosciences, 1 (1997), 155--190.

....has several, by now well known, advantages and one fundamental flaw, the failure to preserve as an algebraic identity a desired conservation law associated with the underlying physical problem. Recently, in the simulation of two phase, immiscible flow in porous media, Douglas, Furtado, and Pereira [6] formulated a variant of the MMOC called there the modified method of characteristics with adjusted advection (MMOCAA) which does preserve the desired conservation law and also preserves the conceptual and computational advantages of the MMOC. No formal analysis of the MMOCAA was given in [6] ....

....[6] formulated a variant of the MMOC called there the modified method of characteristics with adjusted advection (MMOCAA) which does preserve the desired conservation law and also preserves the conceptual and computational advantages of the MMOC. No formal analysis of the MMOCAA was given in [6]; that analysis will be provided here, along with the presentation of the method of deriving appropriate forms of the MMOCAA, for several model convection diffusion problems. We note that there are a collection of finite element methods, called generically ELLAM , that address the conservation ....

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J. Douglas, Jr., F. Furtado, and F. Pereira. On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs. To appear in Computational Geosciences, 1997.

....on the ff side of R k . Then, the second equation of (2.12) can be written as q L q R q B q T huC = hf: 3.1) Then, in the first equation of (2.12) apply a trapezoidal rule to the (q n 2 ; v) Omega 2 term. This allows us to write the discrete problem in a particularly simple form [4]; similar relations hold for the realizations of (2.11) and (2.12) Thus, we can write (2.12) in the form q ff = 1 h (u C Gamma u ff ) ff = L; R; B; T ; 3.2) except along the interface Gamma, where we have q Delta j = 2 h (uC Gamma ji ) if R k ae Omega j ; 3.3) and along Gamma 1 ....

J. Douglas, Jr., F. Furtado, and F. Pereira. On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs, to appear in Computational Geosciences (1997).

....by now well known, advantages and one fundamental flaw, the failure to preserve as an algebraic identity a desired conservation law associated with the underlying physical problem; in this case, the preserved quantity is supposed to be the water volume. Recently, Douglas, Furtado, and Pereira [8] formulated a variant of the MMOC called there the modified method of characteristics with adjusted advection (MMOCAA) which does preserve the desired conservation law and also preserves the conceptual and computational advantages of the MMOC. No formal analysis of the MMOCAA was given in [8] an ....

....[8] formulated a variant of the MMOC called there the modified method of characteristics with adjusted advection (MMOCAA) which does preserve the desired conservation law and also preserves the conceptual and computational advantages of the MMOC. No formal analysis of the MMOCAA was given in [8]; an analysis of an application of the MMOCAA to a linear problem was given in [9] and a nonlinear example will be treated in this paper, where we would like to analyze a single space variable waterflood for which the total volumetric flow rate is piecewise constant, so as to concentrate attention ....

[Article contains additional citation context not shown here]

J. Douglas, Jr., F. Furtado, and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs. Computational Geosciences, 1 (1997), 155-190.

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