The Quality Map: A Tool for Reservoir Uncertainty Quantification and Decision Making
- Paulo S. da Cruz (Petrobras) | Roland N. Horne (Stanford U.) | Clayton V. Deutsch (U. of Alberta)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2004
- Document Type
- Journal Paper
- 6 - 14
- 2004. Society of Petroleum Engineers
- 4.3.4 Scale, 5.6.4 Drillstem/Well Testing, 5.1.1 Exploration, Development, Structural Geology, 5.8.4 Shale Oil, 5.5 Reservoir Simulation, 5.3 Reservoir Fluid Dynamics, 5.1.5 Geologic Modeling, 5.1 Reservoir Characterisation, 2 Well Completion, 5.7.2 Recovery Factors, 5.6.3 Deterministic Methods
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The parameters that govern fluid flow through heterogeneous reservoirs are numerous and uncertain. Even when it is possible to visualize all the parameters together, the complex and nonlinear interaction between them makes it difficult to predict the dynamic reservoir responses to production. A flow simulator may be used to evaluate the responses and make reservoir management decisions, but normally only one deterministic set of parameters is considered, and no uncertainty is associated with the responses or taken into account for the decisions.
This paper introduces the concept of a "quality map," which is a 2D representation of the reservoir responses and their uncertainties. The quality concept may be applied to compare reservoirs, to rank stochastic realizations, and to incorporate reservoir characterization uncertainty into decision making (such as choosing well locations) with fewer full-field simulation runs.
The data points necessary to generate the quality map are obtained by running a flow simulator with a single vertical well completed in all the layers and varying the location of the well in each run to have good coverage of the entire horizontal grid. The quality of the horizontal cell in which the well is located is the cumulative oil production after a long production time.
The geological model uncertainty is captured by generating multiple stochastic realizations and building a quality map for each realization. The quality maps of all the realizations provide a distribution of quality values for each cell of the map grid. A mean quality map can be obtained by taking the expected value for each cell, and a map of quality uncertainty can be obtained by taking the standard deviation of the distribution for each cell.
If a loss function is specified, an L-optimal quality map can be generated by retaining, for each cell, the quality value that minimizes the expected loss. This map allows us to locate wells accounting for the geological uncertainty as well as for the risk profile of the decision maker.
The methodology for building the quality map is presented in detail, and the applications of the map are demonstrated with 50 realistic reservoir models.
The uncertainty in any geological model is unavoidable given the sparse well data and the difficulty in accurately relating geophysical measurements to reservoir-scale heterogeneities. The two largest static uncertainties - the reservoir geometry as defined by surfaces and the petrophysical property distributions - may be quantified by geostatistical methods.
When no uncertainty is considered, reservoir decisions may be made using a deterministic geological model and some optimization algorithm.1,2 Once a decision is made, such as the number, type, and location of the wells, there are techniques to transfer the uncertainty in the static parameters to the flow responses through flow simulations.3,4
However, uncertainty ought to be taken into account for decision making. Stochastic models of the static parameters may be used directly for decisions that do not require flow simulations.5,6 However, for most of the reservoir decisions, the value of each option needs to be estimated using a flow simulator.
For a limited number of production scenarios and geological models, the "full approach" of obtaining one flow response for each reservoir model and each production scenario and then choosing the scenario that is the best on average over all the models may be applied.7-9 Decisions with more complex problems and with a larger number of models may be made based on response surfaces generated with experimental design techniques.10,11
Multiple geostatistical realizations can be ranked to decrease the number of models to process through a flow simulator for decision making. Deutsch and Srinivasan12 present several ranking techniques, showing that there are limitations in all of them, but that the best results are obtained with some flow-simulation- based technique.
Vasantharajan and Cullick13 present the concept of a quality measure of the reservoir for locating wells. The quality measure of a grid cell is the sum of the oil volume around that cell, adjusted by connectivity and tortuosity. Important parameters, such as horizontal and vertical permeabilities, distance to water/oil and gas/oil contacts, and presence of faults are not considered in this measure.
Even if all the static parameters were considered, it would be very difficult to integrate all of them into a measure of quality for well locations. The interactions between the parameters are nonlinear. How can we weight permeabilities and volumes in the same formula to evaluate a quality measure for well locations? Also, the production responses to the static parameters are dynamic. A high vertical permeability, for example, has a positive contribution in the beginning of the oil production, but after some time, the good communication with the bottom layers may increase the water production, adding a negative contribution to the quality of that region.
The quality map, introduced in this paper, uses a flow simulator to integrate all the parameters that affect the flow of fluids through heterogeneous reservoirs and to ensure that the proper nonlinear and dynamic interactions between them are taken into account.
The geological uncertainty is accounted for by generating multiple geostatistical realizations and by building one quality map for each of the realizations. A summary map over all the real- ization maps is obtained using the concept of loss function,14,15 which also allows the incorporation of the profit-seeking and risk-aversion profile of the company into the process of selecting well locations.
The methodology for generating the quality value of each cell of the map for a specific realization is presented. Then it is shown that a few data points are sufficient to interpolate by kriging a map for each realization. A method for generating the mean quality map, the map of the quality uncertainty, and the L-optimal quality map using the local quality distribution over the quality maps of all the realizations is also presented.
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