ENABLE Technical Description

ENABLE provides mathematical support to reservoir engineers in their use of reservoir simulation software. This support allows engineers to complete tasks like history matching much more quickly than using the simulator on its own and also provides a more rigorous approach to predicting future reservoir performance or optimising field development.

Input

The engineer defines a set of parameters (called modifiers) that are used to modify the simulation model. The range and initial probability distribution can also be set for each modifier. All the workflows are based on approximating the simulator with a simple mathematical model called an Estimator.

The Estimator

The Estimator is a set of proxy models. Each proxy model fits the behaviour of a simulator output defined by the user; this is called an estimator point. Estimator points are selected on simulator results (e.g. BHP, oil production, water cut) for wells and well groups at selected times. There are three types of estimator points:

1. History match points are attached to selected history data2. Prediction points are chosen on results where an uncertainty calculation is required3. Optimisation points are chosen on results to define an objective function for optimisation.

The Estimator has two parts: (i) a trend surface model which is a polynomial function of the modifiers (up to 3rd order terms are included) with first order interaction between modifiers, and (ii) an additional term based on kriging that ensures the proxy model agrees exactly with results obtained by simulation runs.

Creating the Estimator

The Estimator is calculated by fitting the results of simulation runs launched by ENABLE. The initial estimator is calculated from a set of scoping runs (typically 25). The modifier values for these scoping runs are calculated by an experimental design based on Latin hypercube sampling.

ENABLE fits the proxy models to the simulator results using a genetic algorithm approach that attempts to find a good fit with the minimum number of terms. The Estimator is updated as the results from further runs become available. Proxy model coefficients are updated using a linear Bayes update formula. At regular intervals the genetic algorithm calculation is used to re-optimise the fit.

Selecting the Next Run

Once the initial Estimator has been created, the modifier values for new runs (refinement runs) are calculated by using the Estimator. This calculation is an optimisation which uses a combination of genetic algorithms for global optimisation and gradient- based methods for local optimisation. The objective function for this optimisation depends on the workflow:

• forhistorymatchingandpredictionwithhistorydata, the objective function is a modified likelihood function. The likelihood is a measure of the probability that the run is a match to the history data. The likelihood is modified to include a measure of the uncertainty of the proxy – this is designed to improve the estimator at the same time as searching for good history matches throughout the available modifier space• forthepredictionworkflowwithouthistorydata,the objective function is simply a measure of the uncertainty of the proxy model – as above, designed to improve the estimator• fortheoptimisationworkflowtheobjectivefunctionis defined by the user.

Figure 1. Graph showing Estimator uncertainty reducing as a result of refinement

runs and re-initialisations, until the user is confident that the proxy models are

good approximations to the simulator response.

Calculating Prediction Uncertainty

The prediction uncertainty is the probability distribution of the simulator result at a prediction point selected by the user. This distribution is based on sampling the probability distributions of the modifi ers. If there is no history data these are the (a priori) distributions defi ned by the user. If there is history data then these are the a posteriori modifi er distributions which include the effect of matching the history data. The a priori modifi er distributions are known distributions that can be easily sampled using the inverse method. The a posteriori distributions are sampled using the Markov Chain Monte Carlo method. Prediction uncertainty can then be calculated using two different methods. The fi rst is to take a moderately small sample (say 100) of parameter combinations to create a posterior ensemble of simulation runs. The runs are equi-probable, so the prediction percentiles can be calculated for any result variable at any time by applying order statistics to the run results. The second method for quantifying the uncertainty in prediction is to sample the modifi er space and use the proxy model to calculate the simulator result at a particular time. A combination of the two techniques can also be used.

The ENABLE Technical Advantage

The proxy technique used by ENABLE has several advantages compared with other assisted simulation techniques:

o The proxy model is built automatically as part of the workfl ow and is technically superior to other commercially available algorithmso History match is achieved with fewer runs than other automation methodso The workfl ow is continuous and allows all input to be taken into the prediction phase without re-defi nitiono Prediction confi dence intervals take into account the whole uncertainty (see Figures 2 to 5) and can be quantifi ed easily for all variables at all times using the ensembles approach. It is then possible to add a prediction point and use the proxy to do quick ‘what-if’ analysiso The fl exible approach calculates reservoir performance predictions for fi elds both with and without history in exactly the same manner. There is no need to learn different workfl ows

Figure 3. ENABLE samples the whole space and is able to capture the full range of

likely matches. Sampling bias is avoided.

Figure 4. Two ‘good’ match areas are highlighted from the data in Figure 3.

Figure 5. The blue and red areas from Figure 4 are used to predict well behaviour.

The ENABLE technique is able to give the full range of uncertainty, whereas the

standard sampling approach can only give a narrow vision of future behaviour.

*** Figures 2 to 5 courtesy of Dr Ian Vernon, University of DurhamFigure 2. A standard (non-ENABLE) sampling approach starts at a random point.

The next point is chosen and a calculation made on whether this is a better, or

worse match. Subsequent points are chosen to improve the match, until a ‘most

likely’ point is sampled.

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