... 1984 9 1 1985 1 12 1985 1 12 1985 Copyright 1985, Society of Petroleum Engineers skin effect flow rate type curve inner boundary condition storage pressure drop boundary condition sandface flow rate phase redistribution drillstem testing approximation coefficient...

... communication and document the usefulness of these solutions, which enable us to obtain increased physical understanding of the performance of fractured wells in layered reservoirs. The influence of vertical variations in fracture conductivity is also considered. Example applications of the approximations...

... coefficient equilibrium difference equation pressure equation differential equation artificial intelligence application primary variable timestep equation of state reservoir simulation calculation equation approximation hungarian hydrocarbon inst flow in porous media fluid dynamics petroleum...

... or wellbores, it is possible to generate many common type curves. The procedure can be developed in an exact manner, in which case it is equivalent to existing techniques; however, a simple approximation step makes possible the generation of common solutions without recourse to numerical or ornate analytical...

... of the flow domain into computational volume elements is based on. the criterion of approximate thermodynamic equilibrium at all times within each element. The thermodynamic conditions in the rock matrix are assumed to be controlled primarily by the distance from the fractures, which leads to the use...

... fracture system observation well matrix system well response early time type curve warren approximation reservoir characterization hydraulic fracturing production monitoring dimensionless time reservoir surveillance complex reservoir reservoir drillstem/well testing production control...

... injection average steam saturation lsfd steam-assisted gravity drainage sagd fluid dynamics quasisteady-state approximation upstream oil & gas oil recovery saturation distribution steam zone volumetric velocity injection quality thermal method flow in porous media steam saturation...

...B. L. Darlow; R. E. Ewing; M. F. Wheeler Effective numerical simulation of many EOR problems requires very accurate approximation of the Darcy velocities of the respective fluids. In this paper we describe a new method for the accurate determination of the Darcy velocity of the total fluid...

...G. Chavent; G. Cohen; J. Jaffre; M. Dupuy; I. Ribera A new method to simulate incompressible diphasic flow in two dimensions (2D) is presented. Its distinctive features include (1) a reformulation of the basic equation using the premise of a global pressure and (2) approximation of convective terms...

... the derivatives of that function. The functions may be constructed by interpolation or by smoothing. When interpolation is used, a function is chosen that represents the data values exactly. In the smoothing method, a smooth function that only approximates each data value is chosen. In this work, we...

... is considered, with stresses symmetrical about both the pay-zone axis and the wellbore. An elliptical fracture perimeter is assumed. Fluid flows are one-dimensional (ID) Newtonian in the direction of the pay zone. Two models, FL1 and FL2, are developed. In FL1, a discontinuous stress variation is approximated...

... simplifying assumptions and approximations are made. We assume that the interface separates dissimilar but adhering materials that are elastic to first order. We consider only differences in material properties and take stresses to be locally uniform. Approximations are made that reduce the fourth-order...

... 17 9 1981 1 6 1983 1 6 1983 Copyright 1983, Society of Petroleum Engineers simulator timestep saturation equation pore finite-difference equation matrix gridblock approximation resolution iteration jacobian matrix upstream oil & gas reservoir simulation pvt...

.... Reviews of the approaches generally used have been given by Hogben et al ., 1 Isaacson, 2 and Sarpkaya and Isaacson. 3 To account more realistically for the effect of large wave heights, research recently has been directed primarily toward developing a second approximation based...

...V. Casulli; D. Greenspan Fast, economical, and accurate finite-difference numerical methods are developed for approximating continuum models of both miscible and immiscible fluid flows in porous media. The methods apply to very general systems of equations and boundary configurations. Computer...

... to be the sum of contributions from each phase, where in each phase the flux is proportional to the concentration gradient timestep flux upstream oil & gas approximation concentration velocity algorithm vtu simulation overshoot numerical dispersion flooding flow in porous media fluid...

... 4 1981 1 12 1981 1 12 1981 Copyright 1981, Society of Petroleum Engineers injection production rate composition fussell co 2 upstream oil & gas relative permeability time step iteration approximation equation psia saturation pressure equation execution time...

...James W. Watts This paper describes a way of solving the reservoir simulation pressure equation using preconditioned conjugate gradients. The preconditioning is based on an approximate inverse using a diagonal ordering of the difference equations. The new method has been tested and compared...

... (or indeed any orthogonal curvilinear coordinate system). ssip coefficient procedure approximation solution method drillstem testing diagonal residual term nonlinearity tolerance formulation equation drillstem/well testing fracture pwell reservoir simulator grid block matrix...

... 1981 17 12 1980 1 6 1981 1 6 1981 Copyright 1981, Society of Petroleum Engineers drillstem testing two-porosity system approximation permeability fractured reservoir type curve initial decline upstream oil & gas flow rate equation cumulative production decline...