Grid Manipulation Research Articles

Adaptive discontinuous Galerkin methods in multiwavelets bases

We use a multiwavelet basis with the Discontinuous Galerkin (DG) method to produce a multi-scale DG method. We apply this Multiwavelet DG method to convection and convection–diffusion problems in multiple dimensions. Merging the DG method with multiwavelets allows the adaptivity in the DG method to be resolved through manipulation of multiwavelet coefficients rather than grid manipulation. Additionally, the Multiwavelet DG method is tested on non-linear equations in one dimension and on the cubed sphere.

Strategies for Efficient Particle Resolution in the Direct Simulation Monte Carlo Method

The accuracy and computational cost of a direct simulation Monte Carlo simulation are directly related to the number of particles per cell. Optimal computational efficiency is achieved when the minimum number of particles needed for accurate resolution is used in each cell. Particle count is shown to scale proportionally with the inverse of gas density. This indicates that high density regions will tend to have few particles while low density regions are over resolved. Three methods of controlling the distribution of particles are presented—direct variation of particle weights, variation of time steps, and grid manipulation. A combination of time step variation and grid manipulation is indicated to be the most effective strategy. A sample plume expansion problem is used to demonstrate these strategies. Computational savings of up to an order of magnitude are observed.

Reservoir Characterization of the Giant Hugoton Gas Field, Kansas

Hugoton field in Kansas is the largest gas field in North America, with cumulative production over 23 Tcf. Infill and deep drilling activity over the last 10 yr have made it possible to build an extensive database of modern wireline log and core data. Such data formed the basis for a wide-ranging reservoir characterization done to obtain critical information for optimum reservoir management of the field. Reservoir heterogeneity and formation-evaluation problems made it difficult to characterize fluid distribution, estimate gas in place, and determine permeability from wireline log data, but few of the problems in this reservoir characterization study are unique to Hugoton. The techniques described here may be applicable to other reservoirs. Technologies employed to solve the formation-evaluation and lateral-variability problems included artificial neural networks, resistivity modeling, geostatistics, and three-dimensional grid manipulation. ©Copyright 1997. The American Association of Petroleum Geologists. All rights reserved.1Manuscript received April 29, 1996; revised manuscript received October 21, 1996; final acceptance June 10, 1997. 2Amoco Production Co., 1670 Broadway, Denver, Colorado 80202. 3Amoco Production Co., 501 WestLake Park Blvd., Houston, Texas 77253. Current address: Altura Energy Ltd., P.O. Box 4294, Houston, Texas 77210. 4Amoco Production Co., 501 WestLake Park Blvd., Houston, Texas 77253. 5Amoco Production Co., 4502 E. 41st St., Tulsa, Oklahoma 74102. 6Amoco Production Co., 501 WestLake Park Blvd., Houston, Texas 77253. Current address: PGS Reservoir, 10550 Richmond Ave., Houston, Texas 77042. 7Amoco Production Co., 1670 Broadway, Denver, Colorado 80202. Current address: Rocky Mountain Petrophysics, P.O. Box 470337, Aurora, Colorado 80047. We thank the Hugoton JOMT of Amoco Production Company for permission to publish this study. We are grateful to Mobil Exploration and Production, U.S., especially W. H. Jamieson, Jr., for permission to use and publish additional core and log data. We also thank David Reese from Amoco (Denver) for his work on equations relating water saturation to permeability, porosity, and height in the gas column. 3-D seismic interpretation by Mike Bahorich (formerly with Amoco, currently with Apache) is appreciated. Thanks go to Amoco operations and reservoir engineers too numerous to mention for teamwork and testing of the ideas herein. Ann Pettit and Stefan Nowina provided invaluable technical support. This paper benefited from constructive reviews by Robert Raynolds, Joyce Budai, N. C. Wardlaw, Salman Bloch, and Virginia Riggert.*Tcf = trillion cubic feet; Gcf = billion cubic feet.

Rapid evaluation of the hydrochemistry of a sedimentary basin using only ‘standard’ formation water analyses: example from the Canadian portion of the Williston Basin

The Canadian portion of the Williston Basin is used as an example of how > 15,000 ‘standard’ formation water analyses in about 15 aquifers can be evaluated rapidly using easily available culling and data distribution display software. Techniques and software used include a program for culling erroneous and missing data in ‘standard’ formation water analyses, electronic grids of stratigraphic surfaces and unit boundaries from the new Geological Atlas of the Western Canada Sedimentary Basin, grid manipulation software, and a geochemical modelling program (SOLMINEQ.88). Intra- and inter-basinal hydrochemical continuity at the regional scale was matched visually by comparing salinity maps on the Canadian side of the basin with salinity maps from the American side, and with the adjacent Alberta Basin. Inter-aquifer continuity to identify aquifer systems and the relative strength of aquitards was determined using a combination of. (1) salinity distribution maps; (2) maps showing salinity differences between aquifers and across intervening aquitards; and (3) the relation among SO 4 in formation waters, the distribution of anhydrite, and the saturation of the formation waters with respect to anhydrite. Evaporites strongly influence the composition of adjacent formation waters, even to the extent that in one aquifer the normal increase of salinity with depth is reversed. The process of freshwater influx into the western part of the basin is demonstrated by a series of salinity maps; they suggest that the process is current and has included removal of halite from the major basinal aquitard. This regional-scale evaluation required an elapsed time of only about 10 working days, hence a fairly rapid study.

Stochastic Structural Modeling of Troll West with Special Emphasis on the Thin Oil Zone

The Troll field is a giant gas field located in the Norwegian sector of the North Sea. In the Troll West Oil Province (TWOP) and Troll West Gas Province (TWGP), the field also contains a thin oil zone (22-26 m in TWOP, 12-14 m in TWGP) with an estimated STOOIP of approximately 600 10[sup 6]Sm[sup 3]. The Troll reservoir is a coastal deltaic deposition characterized by high-permeable sands alternating with micaceous low-permeable sands. The combination of a near-horizontal layered structure and a thin oil leg makes the predicted target locations very sensitive to small changes in the structural model. Only minor vertical adjustments of the high-permeable sands may lead to significant changes in the lateral position of oil prospects. A stochastic structural model was developed to study the effects of various uncertainties (seismic interpretation, depth conversion, well tie, OWC and GOC, reservoir zonation, etc.) on the location of the oil prospects and related volumes. The model is a multivariable two-dimensional Gaussian model for the different layer thicknesses, conditioned on the interpreted seismic reflectors and observations from about 20 wells. In the modeling, standard software for generating multi-Gaussian stochastic fields is combined with a program system for grid manipulation and mapping.more » We can produce [open quotes]probability maps[close quotes] showing the areal probability of various events. These maps can be used in planning for appraisal and future production well locations. It can be used to give probability distributions for the bulk volume of reservoir sands in the oil zone and as a framework for stochastic three-dimensional petrophysical modeling. We believe this is the first study of its kind where the results have had a direct impact on the further field development strategy. Several elements in our approach should be directly applicable to fields where uncertainty in the structural model is important.« less

A simple method for handling grids.

A simple method for handling electron microscope grids is described here. While assuring their identification and safety, this method provides improved handling, temporary storage, and identification of grids bearing ultra-thin sections, and in addition, provides a novel method for preparing bulk samples. Grids are attached at their edges to the weakly adhesive surface of a "Post-it" note pad which sits in a petri dish. The grids are safely immobilized on the pad, classified based on their location, and identified by convenient pad notation. Grid manipulation and identification are simplified using this device, which is easily assembled from readily available and inexpensive materials.

Control point forms for interactive grid manipulation

Abstract The mathematical structure of the control point forms for algebraic grid generation is presented. A fundamental prerequisite for the effective application of interactive grid manipulation is the simultaneous utilization of the control points with the constraints from the specified boundaries. The structure established is a commutative algebra generated from a collection of basic operators that is isomorphic to a collection of boundary elements that are ordered in terms of set theoretic intersections and unions.