Abstract

An approach is investigated, to reduce the amount of CPU time needed to execute a numerical full field model in an optimization loop.

To demonstrate the power of this approach, a real life example is presented. Data from a gas storage reservoir have been used to setup a single tank material balance program. Then, a limited number of simulation runs is carried out. These simulation runs are intended to span over the whole range of input parameter variation (app. 25 runs).

In a next step, a Neural Network (NN) model is setup. By training a Neural Network on the so gained simulation outputs, a model, which is able to interpolate between the individual simulation scenarios is created. In this way, a large variety of different scenarios can be represented with a limited amount of model runs.

The trained Neural Network model is used as a proxy function for an optimization routine. The trained Neural Network has been used as fitness function for the Genetic Algorithm to minimize the output parameter, which is in this example the RMS-error of measured and calculated tank pressure. Due to the very low CPU consumption of the Neural Network, a large number of realisations can be calculated in a short amount of time. By this, the absolute minimum of the desired output parameter (in this case the RMS-error) can be evaluated in a few seconds.

The Genetic Algorithm has succeeded to find a minimum, which is located very close to the absolute minimum of all possible solutions.

Introduction

Numerical models are detailed and powerful predictive tools in reservoir management. While not perfect, they are often the best representation of the subsurface available. Optimization methodologies run these numerical models perhaps thousands of times searching for the most likely or most profitable solution to reservoir management questions. Because of the computational time involved, these methodologies are not used as much as they could be.

An approach is investigated, to reduce the amount of CPU time needed to execute a large number of runs of any CPU intensive numerical model. It can be used to perform a full sensitivity analysis using the uncertainty of the most sensitive input parameter to investigate the uncertainty of important reservoir information, like original hydrocarbon in place, recovery factor or abandonment pressure. This technology can also be used to run thousands of optimization runs in a couple of minutes.

It is proposed to use an artificial neural network (ANN) [1–7] to mimic the behavior of the numerical model. To be able to do that, several runs of the numerical model with a variation of relevant input parameters have to be performed. If all input parameters would have to be modified, the final number of runs would be very large, decreasing the value of this approach to zero.

Experimental Design [8–10]is used to create a set of input parameter variations to reduce the number of sensitivity runs to an affordable minimum. As soon as these runs have been calculated, the variation of the output is correlated to the input variations using an ANN. The neural network learns to behave like the numerical model; it can be described as proxy function of the numerical model. At the same time, the neural network acts as response surface for the Experimental Design. Normally, a polynomial function is used to span a surface over the simulation runs, which have been created using the Experimental Design method. The disadvantage of polynomial functions is their limited capability to represent non-linear dependencies. But exactly the handling of non-linearities is a strong point of neural networks. Therefore, neural networks have been used for the modeling of response surfaces.

Once, the neural network is trained, it needs only a fraction of a second to calculate the result for one set of input parameters. In that way, many thousand runs can be performed in a very short time. If the neural network is used as fitness function for an optimization program (e.g. genetic algorithm) an optimum solution can be found very fast (on a standard PC in less than a minute).

This workflow [11] can be used to either investigate uncertainties of designated input parameters, to optimize operational settings, or shorten the time to history match the numerical model.

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