Uncertainty is not an inherent feature of our reservoirs; it is due to our lack of knowledge and understanding about the reservoir. Uncertainty can only be modeled, but there is no objective measure of uncertainty. The uncertainty will be as large as the modeler decides to make it. Therefore, one must be open-minded - very open-minded. This introduces us to a new modeling paradigm: It is necessary to think in terms of what we don't know, rather than in terms of what we know. This paradigm shift associated with the right tools provides for better decisions, faster.

Managing uncertainty

We believe that in order to appropriately manage uncertainty linked to various aspects of reservoir management, we need a method and a tool that satisfies the following requirements:

• To be able to evaluate the complete range of uncertainties. It is then necessary to be able to capture them, i.e., to quantify and store different structural scenarios and/or geological models. Last, all of it must be integrated in a consistent framework to automatically quantify their cumulative impact.
• One must be able to identify the relevant elements of uncertainty and filter out those that don't matter.
• Finally, once key uncertainty elements have been identified, it is necessary to rapidly know what actions are required to reduce their uncertainty to an acceptable level. For a reservoir modeling point of view, that would mean: 1) refining the interpretation, 2) refining the model, or 3) gathering more data because interpretation and modeling uncertainty cannot be refined any further with existing information.

Uncertainty and 3-D reservoir modeling

Understanding 3-D uncertainties. With today's software, constructing a 3-D geological model of the reservoir is relatively simple. Once a model is constructed, it should be easy and automatic to construct multiple versions (either by simply changing a parameter and/or performing stochastic simulation, etc.). We will postulate that constructing multiple 3-D models is the only way to assess the cumulative impact of data, interpretation and modeling uncertainties on reservoir management decisions.

3-D uncertainty analysis. A typical 3-D uncertainty analysis workflow is as follows:

1) evaluate the uncertainties - taking each step of the workflow along with all the parameters involved, one must quantify how much is unknown about each one of them;
2) integrate the uncertainties - through the construction of a complete reservoir model;
3) analyze the impact of constructing multiple models on the metrics used to make a decision; and
4) iterate to reduce the uncertainties until the risks are minimized sufficiently to allow decision making.
3-D modeling workflow. A 3-D reservoir model consists of the following elements:
• a structural model consisting of horizons and faults;
• fluid contacts - gas-oil (GOC) and oil-water (OWC);
• a sedimentological model (optional);
• a net-to-gross (NTG) model (which may or may not be related to the sedimentology);
• a porosity model;
• a permeability model;
• a water saturation model (highly dependent on everything listed above);
• a pressure-volume-temperature (PVT) model describing formation volume factors and solution gas ratios, etc.; and
• a reservoir simulation model.

Each of these elements has its own way of being quantitatively described, and uncertainty measures may also be different for each. However, it is important to think of them as interconnected members of a single entity. They are highly dependent on one another (e.g. water saturation can be a function of height above contact, which is itself dependent on the position of the reservoir structure and the contacts). Furthermore, there exists a hierarchy in the way they fit together to form a 3-D reservoir model, giving rise to the concept of "nesting," which we will come back to later.

Model uncertainty. Typically, model uncertainty is seen as multiple realizations of a geostatistic-based process. Stochastic simulations will reproduce input parameters "on average," and that is done by construction. Variability in responses from geostatistical simulation is simply due to what is known as Ergodicity: stochastic fluctuations around the input parameters.

The uncertainty related to model parameters is one that is very rarely dealt with in practice, yet it may be one of paramount influence on the global uncertainty. What is essential is to model "what we do not know," i.e., what are the exact values of the modeling parameters.

Multiple realizations. The only way to assess the cumulative impact of all uncertainties is to construct multiple realizations through a combination of scenario-based and stochastic simulations. As mentioned above, once a model is constructed, i.e. a workflow is put in place that fits all the pieces together, changing a piece or part of a piece should be automatic and require no extra effort from the modeler. With today's computer architecture and processing power, this is quickly becoming a non-issue. It is relatively fast to generate a static model, even if it contains millions of cells; to generate a hundred can be done over lunch and a thousand overnight.

Summarizing multiple realizations. For volumetric computations, different types of volumes that can be computed are the gross rock volume (GRV), the net rock volume (NRV), the net porous volume (NPV), the different fluid volumes (OIP and GIP), and the connected volumes using various connectivity criteria. These volumes should be reported not only for the whole model but also for any regions defined on the model, i.e. concessions or lease boundaries, fault-blocks, reservoirs, zones, facies and the intersections of the lot. When a model includes reserves estimations and fluid flow simulation, one should also consider looking at produced volumes, water-cuts and gas/oil ratios (GORs) per well, per platform, per field...These are the "metrics" of the model allowing its classification.

The kind of display one should look at includes three important panels: (a) a summary volume for each model realization - this is referred to as a History Plot; (b) the global histogram of that same information along with the appropriate summary statistics; and (c) the cumulative distribution (CDF). This gives us our first decision-support tool. This tool:

• yields a list of realistic outcomes that can be used as input distributions for Monte-Carlo based economics analysis;
• clearly summarizes the uncertainty in reserve estimates and shows if a sufficient number of models have been generated; and
• allows users to understand the spread in outcomes and the values of important percentiles.
As a result, an economic risk analysis may require that the global spread of the assessed uncertainty is reduced, and it is necessary to identify which factors would benefit from a more rigorous attention.

Identifying key uncertainties

One must be able to identify quickly the key uncertainties, i.e. not necessarily the ones that have the largest spread but the ones whose uncertainty have the biggest impact on the reservoir management decision at hand. The metrics defined above are the link between the estimates and the decision. From them, the impact of each element is deduced.

As a simple illustrating example, let's consider the equation for oil in place (OIP) at reservoir conditions (no gas), where the OIP is equal to the GRV times the NTG times the net porosity (f) times the value of 1 minus the water saturation (Sw).

The GRV consists of a structural piece: horizons and faults, properly connected together, and fluid contacts (NTG, f and Sw).

Identifying which of these elements is more important than the others will help focus resources on relevant issues, stay at the right level of technical detail, and in turn save time and money.

Nested simulations. In terms of 3-D modeling, GRV, NTG, f and Sw have a natural "nesting" or hierarchical ordering: The GRV represents the envelope of the reservoir; only part of it defined by the NTG represents an acceptable type of rock; f is the void space in which if there is no Sw, there is hydrocarbon. The same order is followed when creating a 3-D reservoir model, and a hierarchical dependency is therefore created.

There are two types of approaches when running multiple realizations, which we will refer to as independent simulations and nested simulations.

Independent simulations correspond to drawing one outcome of each element, reporting the volumes (or any summary metrics), and starting again at the very top of the hierarchy and taking a new reservoir structure as to represent the GRV, then a new NTG realization, then a new f realization and finally a new Sw realization.

Performing nested simulations implies drawing multiple sub-elements for each major element and so on. For example, for each reservoir structure, one can consider, say, 5 NTG; for each NTG 5 fs; and for each f 5 Sw. The total number of complete 3-D models for each sample structure in this particular example is 125 (5 by 5 by 5). The total number of realizations becomes very large, but it very quickly shows also which element has the largest impact. This is very important at an early investigation stage when the 3-D model does not need and should not be unnecessarily fine, and it is therefore possible to generate quickly a large number of realizations as shown in Figure 1.

Tornado charts. Tornado charts are great to visually summarize information and more precisely the impact of various plotted parameters. They are excellent decision-support tools for that reason.
If we consider the equation for OIP and multiple "independent" realizations, it is possible to simply de-couple the influence of each element on the total variability of the system by fitting a parametric (say lognormal) distribution to the resulting mean and variances of the different metrics and computing P10 and P90 values that give us a measure of the influence of each parameters on the global variance. The previous example would yield the tornado chart of Figure 2, where it is confirmed that structural uncertainty has the largest impact on OIP.

If a sufficient number of realizations is computed, taking the actual P10 and P90 values for GRV, NTG, f and Sw is a better approach in the sense that it is distribution-free.

Decision making in the face of uncertainty

Now that we have generated hundreds or even thousands of models, how do we make a decision?
There are three major aspects to decision-making in 3-D modeling uncertainty. The first one is to rank the alternative reservoir models and perform more in-depth analysis of extreme and "average" models. The second is to be able to optimize the decision (such as the positioning of a development well) given all the possible representations of the reservoir. The last is to use the resulting distributions as input to a more complete chain of Monte-Carlo simulations which captures elements beyond earth sciences (facilities, transports, oil price, etc.).

Ranking

Generating many models is one thing, but analyzing each one of them is another that is quasi-impossible. It is therefore necessary to be able to select representative models for a more in-depth analysis and understanding of the possible dynamic responses of the reservoirs. However, the rank of a particular model is of course dependent on the criteria or metric chosen to perform the ranking. This means that a model is representative to serve as a basis of a given decision only if the ranking criterion is representative of the decision that needs to be made.

Conclusions

• Modeling uncertainty is a complex issue that can not be solved using simplistic scripts of algorithms that use a subset of the data available. Instead, tools that can integrate all data and test their effect (or lack of effect) on the model must be used.
• Uncertainty is the concern of an integrated asset team. Its integrated 3-D model is the repository of all of the team members' knowledge but also their lack of it-the uncertainties. It also shows the imbrications and interdependencies of all modeling stages. Software tools exist that enable this to happen and can seamlessly capture and integrate structural, reservoir and flow uncertainty.
• Uncertainty evaluation, capture, and integration must be done throughout the life of the reservoir. The tool must be flexible enough to allow scalable, fit-for purpose analysis. There must be a consistency between quick Monte Carlo-based volumetric estimates and 3-D geological models, which do not need to have millions of cells.
• Input parameters have a high degree of uncertainty because they are inferred from sparse, unreliable and biased interpreted data. It is fundamental to be able to capture and use all of it.
• Geological modeling software must be tightly be integrated with dynamic flow simulators to allow a more reliable ranking of the multiple realizations of the reservoir. It is also an ideal way to investigate and optimize alternative field development strategies.
• Geological modeling software needs to be tightly integrated with economic evaluation tools to directly measure the impact of various uncertainties associated with the different elements of the subsurface model.
• Uncertainty is a constitutive part of the Shared Earth Model; every element has an uncertainty associated to it.

For more information, visit www.earthdecision.com.

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