Developing New Fields Using Probabilistic Reservoir Forecasting
- C.S. Kabir (ChevronTexaco) | A. Chawathe (ChevronTexaco) | S.D. Jenkins (Chevron Nigeria Ltd.) | A.J. Olayomi (Chevron Nigeria Ltd.) | C. Aigbe (Chevron Nigeria Ltd.) | D.B. Faparusi (Chevron Nigeria Ltd.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- February 2004
- Document Type
- Journal Paper
- 15 - 23
- 2004. Society of Petroleum Engineers
- 5.7.2 Recovery Factors, 5.1 Reservoir Characterisation, 2.3.4 Real-time Optimization, 5.7.5 Economic Evaluations, 4.3.4 Scale, 5.6.1 Open hole/cased hole log analysis, 2.4.3 Sand/Solids Control, 5.2 Reservoir Fluid Dynamics, 3.3.6 Integrated Modeling, 5.6.4 Drillstem/Well Testing, 5.4.1 Waterflooding, 5.5 Reservoir Simulation, 4.6 Natural Gas, 5.1.1 Exploration, Development, Structural Geology, 5.3.4 Reduction of Residual Oil Saturation, 4.1.5 Processing Equipment, 1.2.3 Rock properties, 5.1.2 Faults and Fracture Characterisation, 5.8.8 Gas-condensate reservoirs, 5.5.8 History Matching, 5.5.3 Scaling Methods, 5.2.1 Phase Behavior and PVT Measurements, 5.1.5 Geologic Modeling
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Limited and uncertain geologic and engineering data at the onset of any new field development are the bane of reservoir characterization and simulation. The problem stems from the uncertainty in various model-input variables, such as reservoir connectivity, fluid viscosity, and endpoint saturations, to name a few. Given this scenario, an ad hoc, one-factor-at-a-time approach to earth and flow-simulation modeling cannot possibly yield unbiased information for making objective business decisions.
This study presents three field cases in which both engineering and earth-model variables were varied in a systematic way to assess reservoir performance by use of the experimental design (ED) approach.
Results of the field cases show that well requirements (both producers and injectors) turned out to be fewer than anticipated. Equally important, one case study showed that laboratory measurements could minimize uncertainty surrounding oil viscosity and endpoint saturations. At the same time, we learned that the preferred horizontal-well orientation was marginally superior to vertical wells in light of high reservoir anisotropy. In another case, stratigraphy, gas/oil contact (GOC), and aquifer strength became the primary variables for the full-factorial design after the initial screening. Here, we proved that the project could proceed because it met the minimum reserves criterion. Perhaps most importantly, all studies showed how to obtain unbiased information in far fewer flow-simulation runs than one would do using an ad hoc approach.
The availability of very limited data with large uncertainty presents significant challenges to any new field development. Stakes are high when deepwater prospects are evaluated. With advances in 3D seismic, the reservoir surface may be mapped with a certain degree of confidence. However, a few exploratory wells cannot provide detailed information about the reservoir's internal architecture, particularly with respect to flow barriers or baffles. In short, we are confronted with large uncertainty in the reservoir's flow and, sometimes, fluid properties.
Given limited and uncertain data, questions arise about how to proceed with a field-development plan. Historically, we have used reservoir simulation and sensitivity analyses as tools for predicting various scenarios, followed by economic analysis. But the approach has been less than satisfactory because of the ad hoc nature of the exercise, meaning the need to change one variable at a time. In essence, this approach relies on setting one variable at the p-10 or p-90 level while keeping others at the p -50 level in a simulation run. Subsequent ranking of the independent variables can conceivably be biased. Potentially, this bias stems from two sources. First, simulations may not contain independent information in the resultant 2n+1 simulations, where n represents the number of variables. Second, the method relies on comparing solutions in which all but one variable are set at the p-50 level. Finally, when one uses p-50 values in the conventional analysis, the p-50 outcome may be an unrealistic expectation owing to nonlinear fluid-flow behavior in the reservoir. In addition, the traditional tornado chart, used for ranking the variables, does not provide any information pertaining to "statistical significance" of the independent-variable effects on the dependent variable.
However, systematic approaches1-9 have emerged to account for uncertainty associated with various input variables, on the basis of ED. For instance, Chewaroungroaj et al.5 demonstrated the use of ED with a series of dimensionless variables to allow extension of the results to similar systems. On the other hand, Corre et al.7 used ED to integrate data from diverse sources, including seismic, in their effort to quantify uncertainty. Application of ED also has been extended to history-matched reservoirs.8
In ED, geologic (e.g., fluid contacts, net-to-gross pay thickness) and engineering (e.g., anisotropy, well count) variables are varied simultaneously, unlike the ad hoc, one-variable-at-a-time approach. The advantage of the ED approach is that it generates relatively unbiased p -10, p-50, and p-90 probabilistic estimates by capturing nonlinear interactions of variables. Full-factorial three-level designs, which account for nonlinearities, are currently reasonable with analytic simulations10 or when only a few (n<4) variables are involved. Realistically, with finite-difference simulations, one can afford to do only a subset of the simulations at a cost of some higher-order interactions between the variables. Here, we chose to rely on the statistical principle of sparsity; that is, the main effects of a few variables cause most primary influences.
In this paper, we used a three-step procedure that involves variable screening using a simple, linear design, followed by a nonlinear analysis and the response surface approach. This methodology is outlined in detail in Friedmann et al.2 and is similar to the one originally presented by Damsleth et al.1
This paper demonstrates the use of ED for making rapid and unbiased business decisions and, therefore, differs from those available in the literature. In particular, the paper stresses an operating-company approach, vis-a-vis developing new data-gathering strategies and the like. We also discuss the limitations of ED, especially in an earth-science context, wherein variable screening tends to be more qualitative than quantitative in nature.
In essence, the proposed approach entails a three-step procedure using ED. First, we screen a large number of variables by using the two-level (low and high) design of Plackett and Burman (PB).11 This step is designed to identify the major variables, or "heavy hitters," influencing the dependent variable (recovery, for instance) by capturing only the linear effects. Rapid screening with a minimum number of flow simulations is the focal point here.
Second, the time-lapse recovery (or any other dependent variable) is used to rank the sensitivity of the major variables, identified in Step 1. The variables belonging to the 95% confidence interval are selected for the three-level (low, mid, and high) D-optimal or full-factorial design. Thereafter, flow simulations are run on the basis of this design. This step is designed to capture both linear and nonlinear effects in addition to interactions between the variables.
Third, we generate a response surface with multivariate analysis by fitting a polynomial, which then serves as a proxy to the flow simulator. To fill in the information void generated by the few flow-simulation runs, Monte Carlo simulations are done with the response surface to generate the cumulative distribution function (CDF). Recovery factors corresponding to different probabilities are then derived from the CDF.
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