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In this paper we introduce Ji-Fi, a new Joint Impedance & Facies Inversion system, which gives a significant increase in quality over model-based Simultaneous Inversion, because it incorporates the correct physics! We first review Simultaneous Inversion, then introduce Ji-Fi and compare one against the other, first with a wedge model and then using a case study.
Abstract Bayesian decision theory is a statistically based theory that is used to assess the degree of certainty and the potential costs when making decisions. This paper presents a methodology, based on the Bayesian decision theory, used to infer subsurface lithofacies and saturation fluid by integrating different data sources, such as well logs data and seismic attributes, which are derived from an elastic seismic inversion. This methodology was applied on a data volume from an offshore Brazilian field to generate, as a final product, a lithofacies model and a fluid indicator for this field. Uncertainty quantification of the models was also analyzed at this work. To infer the subsurface lithofacies, the existing facies were identified from well logs data, using the expectation maximization (EM) algorithm. This step defines the lithofacies behavior in seismic attributes domains through the use of probability density functions (PDF). Next, the subsurface lithofacies were classified by applying the maximum posterior probability (MAP) classification, using the seismic attributes as input and the PDFs computed previously. The environment was divided into cells, then the probability and uncertainty was assessed to infer the lithofacie for each cell. After inferring the subsurface lithofacies, the fluid was inferred for the cells identified as reservoir lithofacies. Assuming an oil-water system, the fluid substitution theory and the Bayes theorem were applied to the well log data to determine the PDFs for each scenario. Following the Bayesian decision theory, the most likely fluid and the associated error was determined for each cell identified as reservoir. Introduction Since the first petroleum exploration studies of seismic reflexion, the seismic sensibility to lithological parameters, such as porosity, lithofacies, fluid properties, and pore pressure is notorious. However, in the 1990s, it became possible to extract these lithological parameters from seismic information. This development occurred as a result of technological progress in seismic processing and rock physics. Since then, the new challenge has been to estimate the uncertainties inherent at the quantitative seismic interpretation process in an attempt to reduce the risk linked to petroleum exploration (Avseth et al., 2001). The methodology of reservoir properties inference, suggested in this work, is presented as a flow of processes that infers lithofacies and reservoir rock saturation fluid from the integration of pre -stack seismic data, petrophysics data, and rock physics relations. The migrated seismic data have been previously processed in an attempt to preserve or restore the relative amplitudes. The petrophysics data are in-situ observations along the wells (log data) and the rock physics models correlate the seismic attributes with the media properties. The central idea of this work is to integrate information from different sources, each one with its own resolution and uncertainty. This work analyzes these uncertainties and its propagation for the final reservoir characterization model. The uncertainty analysis is useful for making decisions that quantify the contribution of each data source (Takahashi, 2000). One successful solution for this kind of problem (reservoir characterization with uncertainties analysis) is the statistical probability theory application. Using the Bayesian methodology, through the Bayes theorem, is possible to develop this kind of model with a proven practical effect (Loures and Moraes, 2002). In this context, the rock physics is used as theoretical base to characterize the seismic signature arising from variations in lithological parameters. Commonly, well log data (and core sample data), are punctual information with good resolution that serve as an information source for the necessary rock physics studies. Conversely, the seismic data represents low resolution information that covers the whole extension of the subsurface volume in study. Figure 1 represents the workflow based on AVO inversion concepts, rock physics, and statistical methods. This work consists of two stages:Lithofacies Inference-This is developed from well data, seismic attributes, and pattern recognition techniques. With the application of the Bayesian decision theory, probability density functions (PDF) are obtained from each facies along the seismic cube. The lithofacies inferences are made from those PDFs. One example of the application of this technique can be found in the work of Braga and Loures (2005).
Reliable facies prediction is a key problem in reservoir characterization. Facies classification using an arbitrary selected zone is the simplest method. However, the problem is that the interpretation result strongly depends on the size of the selected zone. Using an RPT (rock physics template), we can define an accurate zone instead of defining an arbitrarily sharp cutoff for the zone. The next level of sophistication is using a statistical technique, whereby we can calculate not only the best zone, but also the probability of occurrence of that zone. Baye’s theory is normally used for probabilistic facies classification. However, the prior belief is a fundamental part of Bayesian statistics. The posterior probabilities are heavily influenced by the prior probabilities, so any error caused by the interpretation of the prior probability will be amplified in the posterior probability. The objective of this study is to improve the prior probability predictions using rock physics analysis for quantitative facies classification. We use an RPT as a guidance to define these prior probabilities. For seismic reservoir characterization, well data along with rock physics theory via RPT are used to define the prior probability. We found that Baye’s prediction increases as we define the prior probabilities from the RPT.
Reliable facies prediction is a key problem in reservoir characterization. For reservoir facies characterization, three different methods are normally used (Figure 1a, 1b, 1c). We combined method 2 (Figure 1b) and Method 3 (Figure 1c) to improve facies classification for quantitative seismic interpretation (Figure 1d). Facies classification using an arbitrarily selected zone is the simplest method (Figure 1a). However, the problem is that interpretation results strongly depend on the size of the selected zone. Using an RPT, we can define an accurate zone instead of defining an arbitrary sharp cutoff for the zone (Figure 1b). Using a statistical technique (Figure 1b), we can calculate not only the best zone, but also the probability of occurrence of that zone. Bayes’ theory is normally used for probabilistic facies classification. This theory primarily involves a prior to posterior updating technique. Mathematically Bayes’ theory is given by (Stigler, 1983):
Multi-point geostatistical inversion can easily integrate different types of geophysical data. This paper presents a novel inversion method that combines facies classification and multi-point geostatistics. Bayesian classification is developed for facies classification. And then the probability map of each facies derived from classification can be integrated in multi-point geostatistics inversion as soft information to reduce the number of iterations. Snesim algorithm is selected as multi-point geostatistical component in the inversion method. The geostatistics result is used to update the prior model in facies classification, and so forth. This inversion method can reduce the number of iterations and increase the accuracy of facies identification. The method was tested on a synthetic model and the results demonstrated the validity of the proposed inversion technique.
Facies classification at the well location is generally based on sedimentological models, however, the extension of the classification of an individual well into the entire reservoir model is contingent on the calibration of a rock physics model that links rock and fluid properties with geophysical measurements such as seismic velocities and/or electromagnetic-derived resistivities. The goal of this work is to present a workflow to define a geologically consistent facies classification at the well location, to accurately reconstruct this classification using elastic and electrical properties, and to extend the classification to the 3D reservoir model. The initial classification at the well location is obtained using traditional statistical methods applied to computed rock properties such as mineralogical volumes, porosity, density and permeability. The facies reconstruction based on elastic/electrical properties is obtained using a Bayesian approach that combines rock physics with statistical models. The workflow is illustrated through the application to the Rock Springs Uplift field, Wyoming, which hosts several potential CO2 storage reservoirs.
Facies classification aims to assign a rock type or class to each location of a 3D reservoir model, based on the available rock and fluid properties. At the well location, the classification can be based on measured well log data, formation-evaluation computed curves, and core samples. However, far away from the well, most of these properties are not available and the classification must be derived from geophysical properties estimated from surface measurements, such as seismic and electromagnetic properties. Several methods for facies classification have been presented in literature (Doyen, 2007; Avseth et al., 2005; MacGregor, 2012). These methods generally differ from the mathematical approach (deterministic or statistical methods) and for the input data (core samples, well logs, or geophysical inverted attributes). The scale of core samples allows petrophysicists to generate a very detailed facies description; however, the extension of this classification to well log and to 3D reservoir models is difficult to achieve due to the lower resolution and data noise of well logs and surface geophysical measurements respectively. The aim of this work is to show that the integration of a rock physics model in the classification and the use of statistical methods for uncertainty quantification can overcome this limitation.