Abstract
Abstract
Proxy models are becoming more widely used as they can simplify highly complex processes with reasonable accuracy. Especially in risk analysis, where complex relationships between the uncertainty parameters exist, proxy models are used in form of response surfaces to accelerate interpretation and optimization methods. However, the use of proxy models is rarely seen in production optimization.
When the data gathering from wells and surface equipment is fully automated, production optimization can be performed almost in real-time. The bottleneck in this workflow is the high computational effort of simulation models and the large number of input variables to optimize. This disadvantage can be overcome by mimicking the behavior of the system, such as the coupling of a simulation model and the surface network model, by using a computational efficient method. The requirements for such proxy models are high, since they have to capture highly non-linear trends hidden in a small number of representative samples.
This paper presents the usage of neural networks as proxy models. For the production optimization process, genetic algorithms are used. Their advantage lies in the ability to handle a large number of input variables. The neural network operates as fitness function for the genetic algorithm. The optimization result can be achieved extremely fast (within seconds), allowing optimization in near real time. A real life example is also presented in this work.
Introduction
Simulation models are usually used to asses the value and the opportunities in a field. Those models are derived from complex studies involving a high degree of uncertainty and a large amount of parameters that could be either independent or dependent on each other. The relation between the computed simulation results and the input data is generally highly nonlinear. The optimization of such Petroleum Production System, PPS, is therefore an extremely complex task that has many degrees of freedom requiring also many different numerical simulation models or realizations. Furthermore, the calculations from the reservoir to the surface installations involve a series of variable parameters additional to the reservoir parameters. Especially in large fields, the computation becomes either very time consuming or practically impossible to derive all possible solutions. Moreover, when regarding the uncertainty of the input parameters it is completely impractical to address each possible combination of all factors of influence.
Proxy models, which are a simplified representation of the response surface of the numerical models, have been introduced to overcome this problem. This paper describes the possibility to create a proxy model with the help of Neural Networks. By using a limited number of simulation runs, Neural Networks are able to mimic the strongly non-linear behavior of a complex PPS constructing a proxy model that can be used for further investigations such as production optimization.
Experimental Design
It is imperative for sensitivity studies to consider as many influencing uncertainty parameter as possible but minimizing the need for simulation runs at the same time on the other hand. A series of strategies (Design of Experiment) has been proposed, which aim at maximizing the amount of information from a minimum number of runs. Reference 1 proposes a step-like strategy for such a sensitivity study (Figure 1): The first step involves a screening of the sensitivities of the parameters using the full factorial analysis in two levels. All possible combinations of the minimum and maximum occurring values of all parameters are used in the simulation and the most influencing parameters are identified. The full factorial analysis leads to 2n simulation runs, where n is the amount of uncertainty parameters that are investigated. However, to account for very often occurring nonlinearities, Reference 2 suggests to use a three level full factorial analysis (minimum, best estimate, maximum), which extends the number of simulation to 3n. By using the output of this analysis, a tornado chart is generated, from which the influence of the respective parameter on the overall result can be derived. The most influencing parameters, about three,[1] are used to continue the analysis in more detail. The simulation results are then regarded as the space of possible outcomes, which the response surface is constructed on.