No abstract

Abstract-This is a concise critical survey of the theory and practice relating to the ordered Gaussian elimination on sparse systems. A new method of renumbering by clusters is developed, and its properties described. By establishing a correspondence between matrix pattems and directed graphs, a sequential binary partition is used to decompose the nodes of a graph into clusters. By appropriate ordering of the nodes within each cluster and by selecting clusters, one at a time, both optimal ordering and a useful form of matrix banding are achieved. Some results pertaining to the compatibility between optimal ordering for sparsity and the usual pivoting for numerical accuracy are included.

The paper describes methods of solving several reservoir engineering and data processing problems using slow to medium speed computing machines. The problems handled are:Solution of the Hurst-van Everdingen material balance equation for which at first only water influx terms and y curves for PVT samples were calculated with the IBM 602A and 604 computers, while later the complete solution of the equation was programmed on the IBM 607 computer. The application of this equation requires computing cumulative water influx volumes at successive dates and matching these figures with the difference between the corresponding cumulative reservoir volumes withdrawn, and the corresponding cumulative expansions of the initial volume of reservoir oil and gas.Vapor-liquid equilibrium flash calculations which are solved rapidly with the IBM 602A or 604. Auxiliary calculations were made to convert the results into usable engineering quantities.Statistical analyses, performed on core data for several fields, providing a better understanding of the reservoir characteristics.Preparation of the annual (statistical) reserve report. This report starts with the previous year's figures for the gross and net reserves, cumulative and ultimate production, separated into oil, condensate and total liquid figures by leases. Revisions to reserves, classified according to 10 categories such as discoveries, new zones, extensions, etc. are added to the opening reserves and ultimate production figures, while the yearly production figures are subtracted from the revised figures and added to the cumulative figure. Statistical data concerning leasehold titles and ownership fractions, well counts, etc. are recorded. All figures are summarized according to zones, fields, leases, divisions and areas.Miscellaneous uses of analytical procedures for production accounting figures, such as oil pipe line runs, etc. provided better control of production operations. Introduction The annual reserve report is a statistical statement of gross and net reserves, including revisions of reserve estimates and production during the year. The responsibility for preparing this report was assigned to reservoir engineers and by 1952 the report required considerable engineering, clerical and stenographic time.

The Hierarchical Dependence Graph (HDG) described in this paper extends the theory of directed acyclic graph (DAG) [1,21 by allowing hierarchical representation of workflows. It can be used to explicitly express the dependences across JDF [31 (process) nodes and resources derived from any JDF job description. It defines a flexible and semantic-rich model to represent JDF workflow as a set of DAGs at different abstractions: intent level, process group levels and process execution level. By explicitly representing JDF workflows in the HDG, not only it enables the separation of the workflow itself from MIS/or Controller implementations to support fully dynamic JDF workflows, but also it provides a theoretic basis for formal analysis of JDF workflows. Furthermore, we introduce the concept of Connectivity Matrix and its transformations to allow two views derived from a single model: process-centric view and resource-centric view. By exploiting the fact that each of these views is a DAG with a hierarchical structure, we then show how various analytical properties defined for DAG can be recursively applied to analyze JDF workflows, particularly in the following perspectives: (1) validating JDF workflows in terms of cyclic dependence, missing resources and dangling resources; (2) identifying the impacted JDF nodes or resources due to the resource availability and workflow status changes; (3) intelligently handling failures or exceptions by considering causal relations between resources and processes.