Uncertainty Analysis in Predictive Reservoir Simulation Using Gradient Information
- O.J. Lepine (Elf Exploration U.K.) | R.C. Bissell (Elf Exploration U.K.) | S.I. Aanonsen (Norsk Hydro A/S) | I.C. Pallister (GeoQuest RT) | J.W. Barker (Elf Exploration U.K.)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 1999
- Document Type
- Journal Paper
- 251 - 259
- 1999. Society of Petroleum Engineers
- 5.1 Reservoir Characterisation, 5.6.5 Tracers, 5.5 Reservoir Simulation, 5.1.5 Geologic Modeling, 5.6.9 Production Forecasting, 5.5.11 Formation Testing (e.g., Wireline, LWD), 1.2.3 Rock properties, 5.3.2 Multiphase Flow, 4.1.2 Separation and Treating, 5.2.1 Phase Behavior and PVT Measurements, 5.6.4 Drillstem/Well Testing, 4.1.5 Processing Equipment, 5.5.8 History Matching, 1.6.9 Coring, Fishing
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We demonstrate how gradient-based techniques can be used to estimate uncertainty in predictive reservoir simulations made following history matching. We discuss how the gradient calculations can help in finding the parameters that make the largest contributions to the uncertainty, estimating the uncertainty on these parameters, and estimating the uncertainty in predicted quantities by use of a linear analysis. The methodology is illustrated on two field examples, and compared with other methods of uncertainty quantification.
Reservoir simulation is used to forecast oil and gas production profiles under selected development scenarios. Almost all the data used in reservoir simulation are subject to uncertainty. This uncertainty may be quite large, as is usually the case for the distribution of rock properties (porosity and permeability) away from the wells. Consequently, the production profile associated with any development scheme cannot be predicted exactly; the best that can be done is to calculate a range of possible profiles.
Of course, this is well recognized within the industry.1 When new field developments are being considered, it is standard practice to consider a range of possible reservoir models and to run reservoir simulations for each one to produce a range of production profiles. Each of these models would respect the data available for the reservoir under consideration, which would generally include seismic data, log, core and well-test data from exploration and appraisal wells, and geological knowledge of the region or from analog reservoirs. The number of such models varies from case to case, but sufficient computing power is generally available that it is perfectly feasible to construct several different models and to run the corresponding reservoir simulations within a reasonable time frame.
When it comes to assessing incremental developments of fields already in production, however, the situation is more complicated. In addition to the sources of data mentioned above, there will be "historical" production data available, i.e., measurements of pressure and of oil, gas and water rates throughout the time that the reservoir has been in production. To forecast future production profiles in such cases, the standard procedure consists of three steps:
- construct an initial reservoir model;
- adjust this model until the simulated production data matches the historical production data;
- use this adjusted model to simulate the future production.
This standard procedure leads only to a single production forecast for each development scenario. It does not permit any assessment of uncertainty. Although the historical production data should contain information on the reservoir that will reduce the uncertainty in future performance,3,4 substantial uncertainty usually remains even after long periods of production.
An obvious method of estimating the uncertainty would be to generate multiple initial reservoir models, history match each one of them and simulate future production on all of them.5-7 A refinement of this approach has been presented by Oliver et al.8 who estimate the probability density of the parameters by using a combination of stochastic reservoir realizations and automatic history matching with uncertainty on the data. However, we are not aware of any company that has adopted an approach of this type. The reason it has not caught on is undoubtedly that it is so expensive. In the near future, we may expect that it will be possible to consider a small number of different models built in this way. But even this requires a decision to use additional resources to match multiple models rather than to fine-tune the match of a single model (or simply to use more grid blocks in the model).
In this paper, we consider an alternative way of estimating uncertainty in the future performance of reservoirs already in production.9 It is based on the recognition that, once the values of the parameters of the reservoir model have been adjusted to obtain an acceptable history match, it will probably be possible to perturb these values slightly and still have a match that would be considered acceptable. If the same perturbations are applied during the predictive simulations, a range of possible future production profiles will be obtained. Further, provided that the perturbations are sufficiently small, a linear perturbation analysis can be used to derive confidence intervals for the future production performance. All that is required to do this is a single reservoir simulation of the historical and predictive periods, provided that the derivatives (gradients) of the production variables with respect to the parameter values are known. If the calculation of these gradients has been coded in the simulation model, they may also be obtained from the same simulation run at the cost of a relatively small increase in computing time.10
It should be noted that none of the ideas behind this approach are new. The theoretical basis is described in standard textbooks;11,12 its application in the context of reservoir simulation has been described by Dogru et al.13 for single phase flow and by Kalogerakis9 for multiphase flow, although he applied it only to a simple single-well coning problem. The gradient calculation was first published in the SPE literature over a decade ago.10 However, it is only recently that software tools have become available that enable this approach to be used in practice.
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