A numerical procedure for the determination of equivalent grid block permeability tensors heterogeneous porous media is presented. The method entails solution fine scale pressure equation subject to periodic boundary conditions yield, upon appropriate averaging velocity field, coarse or permeability. When region over which this computed constitutes a representative elementary volume (REV), resulting may be interpreted as effective region. Solution on accomplished through application an...

Summary A simplified discrete-fracture model suitable for use with general-purpose reservoir simulators is presented. The handles both 2- and 3D systems includes fracture-fracture, matrix-fracture, matrix-matrix connections. formulation applies an unstructured control volume finite-difference technique a two-point flux approximation. implementation generally compatible any simulator that represents grid connections by connectivity list. specialized treatment based on "star-delta"...

A general method for computing the hydrodynamic interactions among N suspended particles, under condition of vanishingly small particle Reynolds number, is presented. The accounts both near-field lubrication effects and dominant many-body interactions. reproduce screening characteristic porous media 'effective viscosity' free suspensions. accurate computationally efficient, permitting dynamic simulation arbitrarily configured many-particle systems. calculated are shown to agree well with...

The fundamental solution or Green’s function for flow in porous media is determined using Stokesian dynamics, a molecular-dynamics-like simulation method capable of describing the motions and forces hydrodynamically interacting particles Stokes flow. By evaluating velocity disturbance caused by source particle on field located throughout monodisperse medium at given value volume fraction solids φ, considering many such realizations (random) medium, determined. Comparison this with Brinkman...

Summary The determination of the optimal type, location, and trajectory a nonconventional well is extremely challenging. problem more complicated than other optimization problems because wide variety possible types (i.e., number, orientation laterals) that must be considered. In this paper, general methodology for wells presented. procedure entails Genetic Algorithm (GA) applied in conjunction with several acceleration routines include an artificial neural network, hill climber, near-well...

Summary Drift-flux modeling techniques are commonly used to represent two- and three-phase flow in pipes wellbores. Unlike mechanistic models, drift-flux models continuous, differentiable, relatively fast compute, so they well suited for use wellbore within reservoir simulators. require a number of empirical parameters. Most the parameters current simulators were determined from experiments small-diameter (2 in. or less) pipes. These may not be directly applicable wellbores surface...

▪ Abstract Efficiently and accurately solving the equations governing fluid flow in oil reservoirs is very challenging because of complex geological environment intricate properties crude gas at high pressure. We present these challenges review successful promising solution approaches. discuss detail modeling with strongly varying rock properties. This requires subgrid-scale models that represent physics due to fine-scale fluctuations. A second focus on multiphase, multicomponent systems...

The accuracy of the Darcy velocity, flux, and stream function computed from lowest‐order, triangle‐based, control volume mixed finite element approximations to two‐dimensional pressure equation is considered. method, similar integrated difference methods analogous interpolation Galerkin results over “control volumes,” shown yield a conservative velocity field smooth streamlines. streamlines fluxes through system with approach are compared those which approximates variables separately. It...

Abstract Practical production optimization problems typically involve large, highly complex reservoir models, thousands of unknowns and many nonlinear constraints, which makes the numerical calculation gradients for process impractical. This work explores a new algorithm using optimal control theory. The approach is to use underlying simulator as forward model its adjoint gradients. Direct coding is, however, time consuming, code dependent on in sense that it must be updated whenever...

Abstract The optimization of subsurface flow processes is important for many applications, including oil field operations and the geological storage carbon dioxide. These optimizations are very demanding computationally due to large number simulations that must be performed typically dimension simulation models. In this work, reduced‐order modeling (ROM) techniques applied reduce time complex large‐scale procedures all entail proper orthogonal decomposition (POD), in which a high‐fidelity...

A procedure for developing coarse‐scale continuum models from detailed fracture descriptions is developed and applied. The coarse are in the form of a generalized dual‐porosity representation, which matrix rock fractures exchange fluid locally while large‐scale flow occurs through network. methodology here introduces local subgrids to resolve dynamics within provides appropriate parameters describing fracture‐fracture, matrix‐fracture, matrix‐matrix flow. geometry subgrids, as well required...

Summary Subsurface geology is highly uncertain, and it necessary to account for this uncertainty when optimizing the location of new wells. This can be accomplished by evaluating reservoir performance a particular well configuration over multiple realizations then based, example, on expected net present value (NPV) or cumulative oil production. A direct procedure such an optimization would entail simulation all at each iteration algorithm. could prohibitively expensive use large number...