Automated History-Matching of Radial Models Using Self Organizing Classification Method for Underground Gas Storage Reservoirs Characterization
Authors: Huguet Frédéric , Lange Arnaud , Egermann Patrick , Schaaf Thomas 
Published: April 2016

Abstract
Reliable forecasts of pressure, gas saturation and water production are of primary importance for the performance optimization of underground gas storages (UGS). This paper presents the development of a new methodology to achieve the history matching of radial reservoir models taking into account subsurface uncertainties.
Radial models are a simple but consistent way to modelize an aquifer underground gas reservoir, assumed single layered, with about few tens of cells in general to model explicitly the storage and the aquifer. Each reservoir cell holds porosity, permeability, thickness and depth properties. STORENGY has developed a specific radial reservoir simulator called PREPRE dedicated to pressure, gas column thickness and water predictions. Water coning options and Turner parameters (well water loading) have been accounted for semi-analtically, in order to make more reliable water predictions. A major advantage of such models is to run in a few seconds which fits with optimization process requirements when performing the history matching. In the standard workflow, we need to optimize hundreds of reservoir parameters in addition to the dynamics parameters like relative permeability / capillary pressure curves, residual saturation, etc.. This large number of parameters usually results in a very challenging and time-consuming optimization process.
We developed a methodology based on multi-parameters organized classification, based on the Kohonen method (Self Organizing Map algorithm). Models are built using maps of geological property classified in a matrix of about a hundred of classes. Using this approach, it is only needed to optimize the position of the model into the matrix with two parameters in addition to the dynamic parameters. This method then reduces the number of optimized parameters from a hundred to ten.
The objective function to be optimized contains two or three sub-objective functions like well pressure, gas column thickness and water production history-matching errors. We can combine all objectives into one in order to perform mono-objective optimization, but the best approach is to perform multi-objective optimization for uncertainty management purposes. The result is a population of models lying on the pareto front, thus providing information on the models uncertainty.
The topology of the objective functions is very complex, irregular and contains a lot of local minima. An efficient optimizer capable of reaching the global minimum with a good probability is needed. For that purpose, genetic-based CMA-ES optimizer was chosen. Although it converges slowly and needs a lot of function evaluations, usually it always finds a better minimum, compared with other standard optimizers. A new multi-objective CMA-ES version has also been developed, combining elitist and non-elitist methods to get the best compromise between speed and performance, in order to better describe the global pareto front.
These workflows are tested through several optimization processes conducted on various natural gas storage assets. The results illustrate the added value of such approach, particularly the quality of the history matching and the possibility to assess the uncertainties using several matched models for more reliable exploitation forecasts.