Perform Flow Simulations Research Articles

HYSTERETIC MODELING ON THE CONVECTIVE TRANSPORT OF ORGANIC SOLVENT IN AN UNSATURATED SOIL ZONE

A mathematical model is described for the prediction of convective upward transport of an organic solvent driven by evaporation at the surface, which is known as the major transport mechanism in the in-situ photolysis of a soil contaminated with 2,3,7,8-tetrachlorodibenzo-p-dioxin(TCDD). A finite-element model was proposed to incorporate the effects of multiphase flow on the distribution of each fluid, gravity as a driving force, and the use of hysteretic models for more accurate description of k-S-p relations. Extensive numerical calculations were performed to study fluid flow through three types of soils under different water table conditions. Predictions of relative permeability-saturation-pressure (k-S-p) relations and fluids distribution for an illustrative soil indicate that hysteresis effects may be quite substantial. This result emphasizes the need to use hysteretic models in performing flow simulations including reversals of flow paths. Results of additional calculations accounting for hysteresis on the one-dimensional unsaturated soil columns show that gravity affects significantly on the flow of each fluid during gravity drainage, solvent injection, and evaporation, especially for highly permeable soils. The rate and duration of solvent injection also have a profound influence on the fluid saturation profile and the amount of evaporated solvent. Key factors influencing water drainage and solvent evaporation in soils also include hydraulic conductivity and water table configuration.

Seismic interpretation with fluid flow simulation

Dave Hale*, John Killough, and Jeff Emanuel, Landmark Graphics, show how performing flow simulation at the same time as seismic interpretation can enable rapid testing of the impact of alternate seismic interpretations on the resulting fluid flow.

A multi‐block lattice Boltzmann method for viscous fluid flows

AbstractCompared to the Navier–Stokes equation‐based approach, the method of lattice Boltzmann Equation (LBE) offers an alternative treatment for fluid dynamics. The LBE method often employs uniform lattices to maintain a compact and efficient computational procedure, which makes it less efficient to perform flow simulations when there is a need for high resolution near the body and/or there is a far‐field boundary. To resolve these difficulties, a multi‐block method is developed. An accurate, conservative interface treatment between neighboring blocks is adopted, and demonstrated that it satisfies the continuity of mass, momentum, and stresses across the interface. Several test cases are employed to assess accuracy improvement with respect to grid refinement, the impact of the corner singularity, and the Reynolds number scaling. The present multi‐block method can substantially improve the accuracy and computational efficiency of the LBE method for viscous flow computations. Copyright © 2002 John Wiley & Sons, Ltd.

A Finite-Volume Method with Hexahedral Multiblock Grids for Modeling Flow in Porous Media

This paper presents a finite-volume method for hexahedral multiblock grids to calculate multiphase flow in geologically complex reservoirs. Accommodating complex geologic and geometric features in a reservoir model (e.g., faults) entails non-orthogonal and/or unstructured grids in place of conventional (globally structured) Cartesian grids. To obtain flexibility in gridding as well as efficient flow computation, we use hexahedral multiblock grids. These grids are locally structured, but globally unstructured. One major advantage of these grids over fully unstructured tetrahedral grids is that most numerical methods developed for structured grids can be directly used for dealing with the local problems. We present several challenging examples, generated via a commercially available tool, that demonstrate the capabilities of hexahedral multiblock gridding. Grid quality is discussed in terms of uniformity and orthogonality. The presence of non-orthogonal grid and full permeability tensors requires the use of multi-point discretization methods. A flux-continuous finite-difference (FCFD) scheme, previously developed for stratigraphic hexahedral grid with full-tensor permeability, is employed for numerical flow computation. We extend the FCFD scheme to handle exceptional configurations (i.e. three- or five-cell connections as opposed to the regular four), which result from employing multiblock gridding of certain complex objects. In order to perform flow simulation efficiently, we employ a two-level preconditioner for solving the linear equations that results from the wide stencil of the FCFD scheme. The individual block, composed of cells that form a structured grid, serves as the local level; the higher level operates on the global block configuration (i.e. unstructured component). The implementation uses an efficient data structure where each block is wrapped with a layer of neighboring cells. We also examine splitting techniques [14] for the linear systems associated with the wide stencils of our FCFD operator. We present three numerical examples that demonstrate the method: (1) a pinchout, (2) a faulted reservoir model with internal surfaces and (3) a real reservoir model with multiple faults and internal surfaces.

The Development of Appropriate Upscaling Procedures

Permeability upscaling should be carried out with careful attention to the nature of rock heterogeneities. While there are many large-scale features which must be taken into account, there are also important heterogeneities at the small-scale. Many sedimentary structures contain laminae at the mm–cm scale, and beds at the m-scale, which give rise to strong contrasts in permeability. We use a 2D model derived from a photo-panel of an aeolian outcrop, along with permeability measurements from a North Sea oil field, to demonstrate the effects of small-scale heterogeneity. This model is similar in size to a typical cell of a reservoir geological model. We take imaginary probe and core plug measurements from the model, average them, and compare these with the effective permeability for the model computed from a finite difference flow calculation. Although this procedure is standard practice, we show that it can lead to biased estimates of the permeabilities used in flow simulation. As an alternative we suggest using models of representative beds, and performing flow simulation to calculate effective permeabilities for both single-phase and two-phase flow.

Testing for Erosion-Corrosion Under Disturbed Flow Conditions Using a Rotating Cylinder with a Stepped Surface

Abstract Erosion-corrosion is most severe in the vicinity of flow disturbances. In the past, erosion-corrosion under disturbed flow conditions has been studied experimentally in flow loops and numerically by performing flow simulations. In this study, a new, compact experimental setup was tested, intended for the study of erosion-corrosion under disturbed flow conditions, involving a rotating cylinder geometry with a sudden step. A thorough characterization of this new setup was initiated, involving wall mass-transfer measurements complemented with direct numerical simulation of the turbulent flow around it. A large variation of the wall mass-transfer rates behind the step was measured, similar in character to the one obtained in flow through a sudden pipe expansion. Flow simulations have confirmed that this flow geometry will create a qualitatively similar mean flow pattern as observed in a sudden pipe expansion flow involving flow separation and reattachment. Simulations also have shown that there is a ...

Flow Simulation of Geologic Models

SummaryWe report upon our experience in performing flow simulation within detailed three dimensional geologic models. Such models have the potential to significantly improve mechanistic understanding of fluid flow through our reservoirs, especially those influenced by strong contrasts in permeability at multiple scales. We have found that utilizing these static models in a dynamic sense places new requirements upon the models, and forces a reevalua-tion of the theoretical foundations behind our flow simulators. We review a range of physical and numerical concepts, and provide the required conceptual extensions and new derivations.