Uncertainty Quantification in Reservoir Performance Using Distances and Kernel Methods--Application to a West Africa Deepwater Turbidite Reservoir
- Céline Scheidt (Stanford University) | Jef Caers (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2009
- Document Type
- Journal Paper
- 680 - 692
- 2009. Society of Petroleum Engineers
- 5.5.7 Streamline Simulation, 5.1 Reservoir Characterisation, 5.5 Reservoir Simulation, 7.6.2 Data Integration, 5.5.8 History Matching, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 5.6.5 Tracers, 5.1.5 Geologic Modeling, 4.1.5 Processing Equipment, 5.1.8 Seismic Modelling, 5.6.9 Production Forecasting, 2.4.3 Sand/Solids Control, 6.1.5 Human Resources, Competence and Training, 4.3.4 Scale
- geostatistics, ranking, uncertainty quantification, distance, kernel methods
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Stochastic simulation allows generating multiple reservoir models that can be used to characterize reservoir uncertainty. In many practical situations, the large computation time needed for flow simulation does not allow an evaluation of flow on all reservoir models. In this paper, we propose a method to select a subset of reservoir models reflecting the same uncertainty in flow response as the full set. Using the concept of distance, we map the reservoir models to a low-dimensional space where kernel clustering is applied to identify a subset of representative reservoir models of the entire set. Flow simulation and subsequently uncertainty quantification are performed on this subset. A case study is presented of an architecturally complex deepwater turbidite offshore reservoir with large uncertainty in the type of depositional system present.
Petroleum reservoirs are often modeled using well-established structural, geostatistical, or other property modeling methods. With these methods, it is well known that a large number of reservoir models (termed "realizations") can be rapidly generated, each of which will respect the data (wells, seismic, production) and geological constraints (e.g., channeling) input into the algorithms. Uncertainty quantification in reservoir performance aims at defining the P10, P50, and P90 statistics of the flow response of interest, which can be quantified by evaluating a large number of reservoir models through a flow simulator. However, because flow simulation can be extremely time consuming, it is often not practical to run flow simulation on each model. The engineer must then select a subset of realizations to quantify uncertainty. The traditional way to select a subset of realizations is to rank them using static or dynamic properties [e.g., original oil in place (OOIP), streamlines]. Ranking techniques are used to select reservoir models that represent the P10, P50, and P90 quantiles of the response (Ballin et al. 1992; Caers 2005). This approach has been proven efficient when the ranking measure is highly correlated to the response of interest. However, ranking is often based on rather simple statistics extracted from the realization (e.g., OOIP), which may not correctly capture simulation behavior. These statistical measures often have a poor correlation with the response measured by the flow simulator. Moreover, the level of correlation is not known in practical studies, or can only be guessed.
In this paper, we employ a different technique to identify a subset of reservoir models that will be evaluated by flow simulation to compute the statistics (P10, P50, P90) of the response of interest. This method, called the distance kernel method (DKM), was proposed by Scheidt and Caers (2007, 2008). It is based on the definition of a dissimilarity distance between reservoir models, which indicates how similar any two reservoir models are in terms of their associated response of interest. In other words, the distance is defined such that it has a good correlation with the flow response of interest. The principle idea is to rely on the distance to identify a few typical realizations (in terms of flow behavior) and, thus, cover the spread of uncertainty accurately by only performing a small number of simulations. The small subset of realizations, therefore, is selected to have statistics similar to those of the entire set.
|File Size||1 MB||Number of Pages||13|
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