A model for real -time control of a multipurpose reservoir under the conditions of uncertainty is developed. The control model is formulated as a multistage decision process. It is conceptualized in the form of two sub -processes. The first level process is a Forecast - Strategy Process which performs as an open-loop feedback controller. It is defined by a sequence of forecasts and optimal release strategies against these forecasts. At each forecast time (time of issuing the forecast), the optimal release strategy is computed for the time period equal to the lead time of the forecast, and it remains in execution until the next forecast time. The second level process, defined for each forecast time, is a Control Process which for the given forecast generates the release strategy satisfying the preference criterion (minimization of expected disutility). This process is formulated as a truncated Markovian adaptive controller performing on a finite set of discrete times --the same set which indexes the forecast inflow process. To evaluate the past performance of the control, a set of measures of effectiveness is proposed. Computational aspects of the control model are analyzed. Structural properties of the reservoir control process are explored in the main theorem which assures the monotonicity of the optimal strategy with respect to one of the state variables. Also, the properties of the optimal strategy for the case of a categorical forecast are proven. Next, two suboptimal strategies are derived: (1) partial open -loop strategy and (2) naive /partial open-loop strategy. Finally, a'discretization procedure which guarantees convergence of the numerical solution is discussed, and the computational requirements of the optimal and two suboptimal strategies are compared.

From the standpoint of real -time reservoir operation, the multipurpose control problem may be reduced to a dual purpose problem of (1) flood control under uncertain inflow and (2) conservation control (water supply, power generation, low flow augmentation, recreation, etc.) after the flood has receded. A preference criterion for real -time flood control under the conditions of uncertainty is developed in accordance with three postulates: (1) The input to the control process is a probabilistic forecast of the inflow hydrograph, (2) The control decisions are based upon the decision maker's value judgments concerning preferences over operating attributes, trade -offs between reservóir purposes, and attitude toward risk. (3) The conservation control is imbedded into the flood control through the attribute space of the preference criterion allowing thus for explicit consideration of the trade -offs between reservoir purposes. The preference criterion is developed within the framework of utility theory. The value judgments of the decision maker are quantified in terms of a two -attribute disutility function. It is argued that minimization of expected disutility is a plausible and well motivated criterion for multipurpose real -time reservoir control under uncertainty. A suitable disutility model is developed. The case of a group decision maker is analyzed in depth. Common group utility models based on aggregation of individual utility functions and interpersonal utility comparisons are critically reviewed. An alternative approach based on direct group value judgments is suggested, and a general group utility model for decision -making in engineering systems is developed. The disutility assessment procedures are analysed, and response biases that may be introduced into the decision maker's preference structure by the use of an inappropriate assessment scheme are identified. Some principles and novel techniques for assessing disutility functions are advocated; they are motivated by results of psychological research in human decision behavior, and are further supported by experimental evidence. Results of assessment of the reservoir control disutility function for several single and group decision makers are presented.

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Digitized by Kansas Correctional Industries

Key petrophysical properties of reservoir sequences are determined by their individual mineral compositions, and are routinely evaluated through the analysis of cores and geophysical well logs. However, mineralogical studies are seldom incorporated in reservoir assessment. The objectives of the study were to investigate the influence of mineralogy on petrophysical properties of petroleum reservoir beds and the application of mineralogical studies in reservoir evaluation. Mineralogical analyses were performed on core samples from the Plover Formation, the principal reservoir sequence in the Northwest Shelf area of Australia, intersected in two separate wells in the Laminaria petroleum field. The techniques used included X-ray powder and oriented-aggregate analysis, optical microscopy and whole rock geochemistry. Quantification of each mineral phase based on whole-rock powder data was performed using the Rietveld-based Siroquant technique. Results from the Siroquant assay were used as an indicator of mineralogy for the individual samples and were compared with core plug and geophysical log data. X-ray micro-tomography analysis of selected samples was also performed. The reservoir sequences in both wells were sand-dominated, consisted mostly of quartz, clay mineral matrix and cement of silica, pyrite or calcite. The abundance of clay minerals increased in the shale and shaly sandstone intervals. Comparison of mineralogical and core plug analyses of samples from the same depths showed that the down-hole variations in porosity, permeability, grain density and radioactivity were accompanied by changes in mineralogy. Higher proportion of clay minerals in shales was indicated by higher gamma log signals. The gamma log may be taken as an indicator of shaliness only in intervals where kaolinite is proportional to the quantity of illitic clays. Sonic log and neutron log porosity values are comparable with core plug porosity data in sandstone intervals. However, clay minerals increase the sonic log response, thereby increasing porosity in shaly intervals. Clay minerals tend to decrease the neutron log response causing higher porosity indication in shales, similar to that expected in sandstones. Routine density log analysis underestimated porosity values because of the contribution of dense minerals to the bulk density of the formation. Use of laboratory determined grain and fluid densities resulted in improved density log porosity compared to core porosity. X-ray tomography analysis revealed an overall positive correlation between mineralogy and porosity data. Routine geophysical log evaluation revealed inconsistent results when compared to core analysis data because of the influence of minerals on various logs. It is essential that mineralogical studies be included in reservoir assessment. X-ray tomography may provide an alternative approach in evaluating porosity and mineralogy.

The petroleum industry commonly uses single-layer models to characterize and forecast long-term production in tight gas reservoir systems. However, most tight gas reservoirs are layered systems where the permeability and porosity of each layer can vary significantly, often over several orders of magnitude. In addition, the drainage areas of each of the layers can be substantially different. Due to the complexity of such reservoirs, the analysis of pressure and production history using single-layer analyses techniques provide incorrect estimates of permeability, fracture conductivity, drainage area, and fracture half-length. These erroneous values of reservoir properties also provide the reservoir engineer with misleading values of forecasted gas recovery. The main objectives of this research project are: (1) to demonstrate the typical errors that can occur in reservoir properties when single-layer modeling methods are used to history match production data from typical layered tight gas reservoirs, and (2) to use the single-layer match to demonstrate the error that can occur when forecasting long-term gas production for such complex gas reservoirs. A finite-difference reservoir simulator was used to simulate gas production from various layered tight gas reservoirs. These synthetic production data were analyzed using single-layer models to determine reservoir properties. The estimated reservoir properties obtained from the history matches were then used to forecast ten years of cumulative gas production and to find the accuracy of gas reserves estimated for tight gas reservoirs when a single-layer model is used for the analysis. Based on the results obtained in this work, I conclude that the accuracy in reservoir properties and future gas flow rates in layered tight gas reservoirs when analyzed using a single-layer model is a function of the degree of variability in permeability within the layers and the availability of production data to be analyzed. In cases where there is an idea that the reservoir presents a large variability in ‘’k”, using a multi-layer model to analyze the production data will provide the reservoir engineer with more accurate estimates of long-term production recovery and reservoir properties.