Modelling and Optimization of Real-Time Petroleum Production - Using robust regression, bootstrapping, moment matching, and two-stage stochastic optimization
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This work is concerned with the upstream sector of the petroleum industry and seeks todevelop methods for real-time optimization of petroleum production under uncertainty.The real-time production optimization problem deals with planning over a short timehorizon, where the objective is to maximize oil production. The output from the optimizationis a well defined plan of how the choke valves of the wells at the petroleumfield should be adjusted. In order to formulate an optimization model, models describingthe relationship between decision variables and production must be determined.We call these models well models and evaluate different ways of constructing them.The well models are then used to generate input for several optimization models. Inorder to capture different aspects in the production optimization process and handlethe uncertainty in the input parameters, we apply stochastic programming techniques. Three well models for modelling the relationship between production system settingsand production from the wells are presented. The first model, the export well model,is built on the measurements of total exported production, while the second model,the multiphase meter well model, applies the measurements from the individual wells.The third model, the combined well model, uses all of these measurements, aiming toreduce the uncertainty related to the individual well measurements by including the accumulated export production. Several different linear regression techniques are testedfor each model, and bootstrapping is used on the best model to find the probabilitydistributions for the well model parameters. Moment matching is thereafter applied togenerate a representative set of discrete scenarios. We handle the non-linear relationshipbetween the settings of the production system and production from the wells byintroducing a mode formulation. Instead of modelling the relationship for all possiblesettings of the system, we only allow for settings within certain intervals, or operatingmodes. The allowed modes are determined by the available historical data as acombination of previously seen modes and modes that can be estimated based on theavailable data. In a case study of the petroleum field Gjøa in the North Sea, we show that the combinedmodel is preferred for modelling both oil and gas production. The robust linearregression method Huber s T is found to be the best regression technique. Throughbootstrapping, we find that all the parameters for all wells have probability distributionsclose to the normal distribution. In order to include uncertainty in a proper way, two stochastic models which we namethe penalty model and the strategy model are developed. The assumptions behindeach of these models rely on insights from the company Solution Seeker AS on theproduction optimization process. In the penalty model, a constraint can be violatedat a cost of lower oil production. The decision variables suggest how much each chokevalve should be adjusted to optimize production. In the strategy model, it is assumedthat changes to the production system are implemented slowly, so that it is observedwhen the constraint is met. The decision variables suggest both how much each chokeshould be adjusted and a sequence for the adjustments. For the case study at Gjøa, we show that the stochastic models yield a small extraimprovement over the deterministic models. However, a potential for significant improvementof oil production is found by applying either model. The solutions foundhave very good in-sample and out-of-sample stability, especially when moment matchingis applied to create the scenario sets. From four synthetic cases, we find that the sizeof the benefit of incorporating uncertainty in the models depend on the input parameters.Uncertain oil prediction parameters give no additional benefit, while uncertaingas prediction parameters give a small extra benefit using the stochastic models. Thepenalty model and the strategy model usually return the same objective value, butboth models should be tested as variations can occur.