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Scientific Visualization in Oil and Gas Exploration Leon Fedencznk University of Calgary Brian Wyvill University of Calgary Kristina Hoffmann Gambit Consulting Ltd. analyses are means of analyzing data to extract and summarize information. Through statistical analysis, one can develop a meaningful information summary in order to understand historical data, develop predictive models, and have the ability to quantifY the results. Statistical techniques enable patterns and trends to be extracted from the data, and to establish relations between the different data sets. In brief, statistical techniques compress and organize large amounts of data into a small set of information. They aid in the identification of any valid relationships and patterns hidden in exploration databases. This can be useful in directing exploration and development efforts in areas with the highest possible potential. ABSTRACT In this paper we present a method for interpretation of statistical results from discriminant analysis. The specific attention has been given to the application of Scientific Visualization to the presentation of results from statistical analysis. Techniques are presented to aUow a geologist in oil and gas exploration, to make a visual analysis of the statistical results. In particular, we explain how to convert multidimensional geological data into a single parameter, which is later presented in 2D and 3D space. A discriminant criterion is developed and then used to classifY each of the multivariate observations into one of two groups: producers and nonproducers. The posterior probability of membership in each group for the test data is presented as the production probability. Furthermore, this probability governs the colour and density during the rendering process. Statistical modelling can be used to: locate areas favourable for exploration; to determine the "when" and "where" for the treatment, in order to optimize the exploitation programs of the reservoirs; INTRODUCTION implement quality programs and the identification of potential bypasses. Successful exploration in the oil and gas industry is the result of careful data acquisition and creative data analysis techniques. Geological data is multidimensional, often noisy, nonreproducible and worst of all, the majority of geological samples are mixtures of simpler components. Statistical methods help earth scientists to take a closer look at some of the geological hypothesis and find hidden patterns, variance, and original compositions of sample data. Unfortunately, it is often difficult to translate statistical results into geologically meaningful statements. Statistical and numerical In addition, we show how scientific visualization helps in the statistical data interpretation. Scientific visualization of geological data [Sabella88] [Connolly86] and the results of the statistical studies in [Fedenczuk9l] has taken on an increasingly important role in exploration. This is due to the quantitative nature of the geological and geophysical data and the increasing amounts and availability of that data. We feel that statistical techniques could be applied more successfully in predicting oil and gas discoveries 675 if advanced visualization tools were used to improve the interpretation. example, the production capacity as a function of the subset of parameters; DATA ANALYSIS AND MODELLING discrimination functions to distinguish between on/off-field anomalies; contour maps probability; Statistics in Oil and Gas Exploration Finding oil or gas is inherently probabilistic, which is supported by the rather limited success of drilling programs. The entire process of oiUgas exploration is made up of a large component of chance factors. Therefore, it is highly probable that oil and gas reservoirs of appreciable size still remain undetected. So far, discovered reserves are a reflection of currently applied technology (including technology used in data analysis) and current economic realities. New innovative data interpretation techniques will help in locating yet undiscovered reserves. Improved data analysis can be achieved by the use of advanced visualization techniques to interpret results from multivariate statistical procedures (e.g. factor analysis) [Fedenczuk92]. Statistical processing can establish the degree of uncertainty surrounding exploration events while visualization techniques provide a presentation and interpretation tool. of the production a list of possible bypasses (abandoned wells which could be producers, but were probably damaged during the completion). The Scope of Statistical Analysis The following is a list of tasks in geostatistical analysis: perform necessary data checks, develop frequency distributions, check correlations, find relevant differences between group of objects, and establish level of confidence for obtained results; develop mathematical models to predict production rates; develop models allowing a discrimination between several groups of objects; Objectives The primary objective of data analysis and modelling is to estimate the production capacity or production probability, based on available geological, petrophysical, and engineering data. Statistical models allow for the selection of regions of interest or specific sites (wells) which represent higher potential than the surrounding locations. The possible deliverables of statistical models are: find similarity between individual wells; apply advanced graphical tools to display multidimensional data. Multivariate Statistical Procedures One of the most useful statistical procedures is the Linear Discriminant Function. It can provide a numerical criterion or set of criteria for help in assigning an individual observation or object to one of several populations (e.g. good or bad performers). In addition, Factor Analysis and specially Q-mode Factor, Analysis have been successful in investigations of patterns, order and similarity in data. These methods yield new numerical values corresponding to a smaller number of factors that are useful in reproducing an optimal set of geological, log, hydrodynamic, geochemical, and completion parameters necessary to represent a statistical model and to support geological interpretations; mathematical models describing, for 676 the original data matrix. Often, this approach is described as the unmixing technique intended to find similarity between observations [Ehrlich87]. This contrasts with techniques dealing with similarity between variables. This is a very useful tool to trace the well connectivity and response. The interpretation of statistical results can be facilitated by advanced visualization tools which are capable of presenting close data sets of more than three dimensions [Fedenczuk92]. diagnostics indicate when more terms should be added to the model, and how to identifY outliers. Application of the Discriminant Function Discriminant analysis results in a function, which is a linear combination of variables and provides the best discrimination between the classes in the data set. In the initial stage Univariate analysis should be performed for each variable. Tables with Min,_Max, Average, and Std. values are very useful for cleaning data In addition, the correlations between all of the variables should be tested. In the next step the smallest subset of significant variables should be selected using stepwise procedures. This subset of variables should predict the dependent variable, the perfonnance class, or the response variable used to describe a phenomenon. Regression techniques are used for quantitative variables (continuous scale), such as production rates. However, in additi on to the quantitative variables, predictive models must often incorporate qualitative variables, such as the response group or formation. Typically, the dependent variable is associated with the oil/gas production rate, the weIl quality, or the weIl response to a specific treatment. Discriminant Analysis can act as a tool to overlay multidimensional infonnation. The discriminant criterion is developed and then used to classifY each ofthe multivariate observations into one of the groups. In the simplest case the classifications can be based on: Diagnostics and parameter selection The selection and diagnostics help to identifY the independent variables which significantly influence the outcome of the dependent variable. Typically, the data contains more information than is required for the model. The procedures used to identifY the significant parameters required to describe the phenomenon are: the initial production (pr<x,!ucers and nonproducers); c-, response to a treatment (yes/no). Stepwise Regression; The discriminant function should be built on a base of the preselected set of variables from stepwise discriminant analysis. The verification of the function should be done on a test set. In general, a proper application of the discriminant analysis is done on two data sets: learning and testing set. They can be created by random selection of the observations from the total data into these sets. For more information please refer to SAS/STA1"'" manual. The fmal result of such analysis is mappable information, the posterior probability of membership in each group for the test data can be presented as the production probability. Backward Regression Analysis; Rsquare Regression; Stepwise Discriminant Analysis. Through these procedures one can identifY a suitable and optimal subset of variables. All possible subsets of variables can be tested by adding and deleting variables one at a time until, by some criteria, a reasonable stopping point has been reached. The diagnostics are used to determine whether models adequately represent the data upon which they are based The 677 can be derived from simulations, statistics, etc. The modelling leads to a series of numbers representing data in the experimental space, with additional time dependence (ifrequired). VISUALIZATION Components of visualization The scientific visualization process can be viewed as a sequence of transformations that convert a data set into a displayable form which leads to an enhanced capability for prediction and discovery. There are typically three stages in this process: Multidimensional View of 3D Information The visualization of a scalar function of three variables, in a form p=p(x,y,z) can be regarded as a function which maps the fourth dimension (P) into a 3D space. In some cases we can map information into 2D space in the form of the contour map (equivalent to the elevation map as p=p(x,y). For volume data we can use the 3D analog of 2D contour plots and pseudo-colour maps in the form of isosurfaces [Wyvi1l86], 3D points [Cline88], 3D self-emitting voxels [Sabella88], translucent voxels [Levoy90], viewing colour-roded density data [Nielson91], or opaque voxels [Chen85]. data manipulation, must identifY the dimensionality and features in data sequences, determine how they change relative to time and position, and how they interact; modelling, maps the previously processed data into data structures and a set of visualization primitives, with positional parameters, colour, texture, reflection and so on; Data Presentation The probability obtained from Discriminant Analysis can be presented as a contour map. This is equivalent to a simultaneous analysis of several contour maps on the light table. Furthermore, for more advanced users of the visualization tools this probability can govern the colour and density during the rendering process. For the purpose of visualization, one needs to apply a threshold or cut-{)ffvalue as a criterium for the selection of the area of the interest For example, an 80% probability of the well to be a producer can serve as a criterion. Similarly, the discriminant score can be applied with a value that corresponds to the same success probability. A choice of the high value of the probability as a cut-off will cause that some of the potentially producing areas will not be included in the area of the interest. On the opposite side, shifting the cut-off value below 80% will increase a risk of drilling dry wells. In the second case we will not overlook too many potential producers. rendering, produces an image of the data, as defmed in the visualization modelling, using such operations as projection, shading, and hidden surface removal. Data Manipulation Any data associated with the petroleum exploration is transformed into a form that is suitable for subsequent visualization operations and may include such operations as griding, interpolation, and smoothing. For example, real data is often provided on a sparse grid. IdentifYing which characteristics of data are relevant for modelling, is the first important step in designing effective data visualization techniques. Each 3D point acquires data for: colour, density, opacity, surface properties (reflection. rock, water, etc.), volume properties (refraction, density, viscosity, sonic velocity, strength, elasticity, etc.) Optionally, this stage involves the construction of a mathematical model, to be used as a data source for the visualization. In many cases, the model that is used to describe a particular phenomena The best approach is a creation of two areas of interest which are based on two tails. One of the areas corresponds to the highest values of 678 production probability, and the second corresponds to a very low probability of the producer membership. The gray area between these two borders (contour lines) often represents the opportunity area, where the advanced technology can improve the odds of the correct prognosis. Special attention in the higher end of the gray area should be placed to all abandoned wells. This is especially true in the case of fonnations which are prone to the damage during the drilling process and where wells could be abandoned due to the misinterpretation of the DST tests. In the case of the old fields for which there is available information in the public data bases, the analysis can produce a simple list of the abandoned wells, which were misclassified by the discriminant function. union PuQ=PnQ These operations allow us to construct expressions to add and extract regions of interest from the statistical solutions and enhance their graphical representations. Thus, interactions between different data sets and their responses can be extracted for the purpose of the interpretation and visualization. However, these operations do not form a complete boolean algebra due to the fact that P n P " P and P n Ap "tP. Boolean Operations We applied the boolean operations (union, complement, intersection, and difference) to posterior probabilities. If two sets P and Q represent posterior probabilities, spatially defined as P(X,Y;I.) and q(x,y,z), which have been derived from two discriminant functions, then the operations can be defined as: SUMMARY The volume of information available to industry has increased several fold in the past decade. Nowhere is this more evident than in the data related to oil and gas exploration. Statistical techniques and advanced graphics can help us to gain a better understanding of this information by providing insight into the meaning of variations in specific parameters and by providing meaningful summaries of specific information. In general, statistical and numerical techniques were developed to deal with large quantities of data and are therefore efficient and effective means of processing large volumes of data. Statistical techniques provide methods of summarizing large quantities of data into manageable and usable estimates, while Scientific Visualization provides better tools to interpret the results of the statistical modelling. The final 2D or 3D image allows geologists to identifY the most probable areas, which are potentially productive with respect to hydrocarbon exploration. Furthermore, these techniques enable the risk factor to be qualified and confidence limits to be determined. Informed decisions regarding large capital intersection complement difference P-Q=PnQ 679 expenditures can only be made when the risk factor is properly understood. Fedenczuk91 1.1. Fedenczuk, M. Bercov, TERNPLOT - SAS Creation of Ternary Plots, SAS Users Group International Sixteenth Annual Conference, New Orleans, Louisiana, February 1991, pp. 771-778.. REFERENCES Chen85 L.S. Chen, G.T. Herman, RA. Reynolds, J.K. Udupa, Surface Shading in the Cuberille Envirornnent, IEEE Computer Graphics and Applications, 5(12), 1985. Levoy90 M Levoy, Efficient Ray Tracing of Volume Data., ACM Transactions on Graphics, Vo1.9, No.3, July 1990, pp.245-261. Cline88 H.E. Cline, W.E. Lorensen, S. Ludke, C.R Crawford, and B.c. Teeter, Two Algorithms for the Three-Dimensiona I Reconstruction of Tomograrns, Medical Physics, Vol. 15, No.3, May/June 1988, pp. 320-327. Nielson91 G.M. Nielson, TA Foley, B. Hamll11l1, and D. Lane, Visualizing and Modeling Scattered Data., IEEE Multivariate Computer Graphics and Applications, Vol. 11, No.3, pp. 47-55, May 1991. Connolly86 E.T. Connolly, L.1. Fedenczuk, Chemical Water Analysis of Formation Methods Recognition, Use and Quality Control by Computer Manipulation and Mapping, Canadian Well Logging Society Journal, Vo1.l5, Number I, December 1986, pp.21-80. Sabella88 P. Sabella, A Rendering Algorithm for Visualizing 3D Scalar Fields, Computer Graphics, Vol. 22, No.4, 1988. Wyvi1l86 G. Wyvill, C. McPheeters, B. Wyvill, Data Structures for soft Objects. The Visual Computer, Vol. 2, No.4, 1986. R. Ehrlich and W.E. Full, Sorting If you have any questions or comments, or desire further information, the authors may be contacted at: Department of Computer Science The University of Calgary 2500 University Drive NW. Calgary, Alberta T2N IN4 Canada [email protected] Ehrlich87 Out Geology-Unrnixing Mixtures, in Use and Abuse of Statistical Methods in Earth Sciences, Edited by W. B. Size, Oxford University Press, New York, 1987, pp.33-46. Fedenczuk92 L.L. Fedenczuk, M. Bercov, TETRAPWT - Four Vertices Are Better Than Three, SAS Users Group International Seventeenth Annual Conference, Honolulu, Hawaii, April 1992, pp.534-538. SAS, SAS/STAT are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. 680