Schedule Optimisation to Complement Assisted History Matching And Prediction Under Uncertainty
- Heikki Armas Jutila (Heikki Jutila & Associates) | Nigel H. Goodwin (Energy Scitech Ltd)
- Document ID
- Society of Petroleum Engineers
- SPE Europec/EAGE Annual Conference and Exhibition, 12-15 June, Vienna, Austria
- Publication Date
- Document Type
- Conference Paper
- 2006. Society of Petroleum Engineers
- 5.4.3 Gas Cycling, 5.1 Reservoir Characterisation, 4.1.5 Processing Equipment, 4.1.2 Separation and Treating, 5.4.2 Gas Injection Methods, 3 Production and Well Operations, 2.2.2 Perforating, 5.5.8 History Matching, 1.6 Drilling Operations, 4.3.4 Scale, 5.5 Reservoir Simulation
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Recently our business has had great success in developing tools for using full physics simulators in Assisted History Matching (AHM) and prediction of future performance. However, the end user is often left wondering what to do with the large number of forecasts from these studies; any optimisation of the remaining potential has to be done manually.
This paper discusses a method in which the principles of AHM are used to optimise the development. In AHM the practitioner attempts to minimise the error between the observed and simulated data; the ‘objective function'. A large number of ‘geological' variables to the simulator are sensitised. ‘Control' variables are used in the predictive work. These are only limited by the scheduling features of the reservoir simulator and would normally be the number and location of development wells; change in facilities constraints; re-completion; workovers etc. The objective function for development optimisation tends to be an economic one, i.e. Net Present Value (NPV) or some other profitability indicator. The method described in this paper has an advanced feature for generating additional results based on the simulator output time series.
Schedule optimisation is known to be a very difficult problem, not amenable to standard mathematical programming algorithms, and we describe how, in conjunction with the use of a proxy model, we have successfully applied genetic algorithm optimization techniques, to solve the scheduling problem with minimal CPU processing.
The method has been used a number of times and its application is described by some case studies; optimising the number and location of development wells and timing of scheduling events. As a very large number of possible combinations of variables are used the optimisation tends to be less subjective than a manual giving generally better results.
The first part of the paper will describe the theoretical background of the method and in the second part some examples will be described in some detail. Two examples are described; the first one is a scheduling optimization of a hypothetical development the second one is a well location optimization. In the scheduling example a field has ten well locations chosen, 8 producers and one gas injector and one water injector. The problem is to optimize using an economic objective function when to complete, if at all, and which well. The second problem has the same wells but they are all switched on at the same time the objective is to find the optimal locations for these wells.
The application of optimisation techniques to problems in reservoir engineering has a long and distinguished history. This is natural, given the direct relevance to problems of business and engineering interest, and given the many and varied algorithmic techniques which have emerged in the last thirty years. Another aspect of the interest shown in this area is the innovative ways in which the optimisation tools and methods have to be adapted to solve specific engineering problems.
The period around 1980 saw major algorithmic progress on the general problem of non-linear optimisation . The emergence of Sequential Augmented Lagrangian methods, and quasi-Newton (otherwise referred to as variable metric or BFGS) methods was a major step in solving a certain type of problem in realistic time frames. These were generally non-linear small scale problems with a single local optimum and non-linear constraints, with conditions on the convexity of the objective function. Quasi-Newton methods, in particular, improved performance by maintaining a local quadratic approximation to the objective, which was adapted as the optimisation progressed. Only derivatives of the objective function were required. This local approximation may be considered the first adaptive proxy model. The non-linear optimisation algorithm was based on solving a sequence of quadratic programming problems. These ideas found rapid application to a wide range of problems during the 1980's, with a particular challenge to apply them to large scale systems .
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