... testing approximation coefficient wellbore storage laplace transformation dimensionless sandface flow rate equation artificial intelligence dimensionless time spherical flow drillstem/well testing pressure transient analysis reservoir surveillance expression upstream oil & gas...

... 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...

... reservoir simulation calculation equation approximation hungarian hydrocarbon inst flow in porous media fluid dynamics petroleum engineer journal thermodynamic property fluid system compositional model pressure difference A common feature of the models presented previously is that all use...

... 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...

... 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 distribution...

...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...

.... The fully implicit approximation assumes that all well and flow terms can be regarded as constant throughout the duration of each timestep, and in certain problems this approximation can result in appreciable time-truncation errors—e.g., when large time-steps are chosen near to breakthrough periods...

... conditions. (2) ∂ Φ ∂ z = 0     at     z = − D . 8 5 1981 21 9 1982 12 3 1982 1 2 1983 1 2 1983 Copyright 1983, Society of Petroleum Engineers lan offshore structure integral equation body surface time step approximation isaacson...

...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...

... independent components. Eq. 6 then becomes timestep flux upstream oil & gas approximation concentration velocity algorithm vtu simulation overshoot numerical dispersion flooding flow in porous media fluid dynamics gridblock dispersion reservoir simulation enhanced recovery...

... 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...

... of the system as included in the shape factor, α. 8 7 1980 2 3 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...

...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...

... 1979 1 6 1981 1 6 1981 Copyright 1981, Society of Petroleum Engineers (3) B o q well  =  constant  = q storage  + q res , where ssip coefficient procedure approximation solution method drillstem testing diagonal residual term...