Investigation of a new multiphase flow choke correlation by linear and non-linear optimization methods and Monte Carlo sampling

Abstract

In the production engineering point of view, the multiphase flow predictions from producing wells becomes important for an adept production design and management. As the associated costs of direct flow metering are considerable, the empirical and semi-empirical correlations are roughly efficient for this aim. Lack of sufficient data and their inherent epistemic and aleatory uncertainty due to human and equipment errors are, however, major limitations for these correlations. Following our previous article, in this paper, two optimization methods one linear and other non-linear are proposed. As it is shown, the linear regression is not dimensionally suitable to predict flow rate. It seems that due to the complexity of the objective function and also uncertain parameters, the linear regression is not the best algorithm for optimization. However, the non-linear method of Nelder-Mead (by means of MATLAB function Fminsearch) perfectly optimized the fitness function with a negligible average error. Due to the uncertain nature of main parameters in the correlation (such as P wh, BS&W, T, etc.), a Monte Carlo sampling is used replacing these parameters with their PDFs (probability density function) to see if the proposed correlation works well or not. On this base, wellhead pressure (P wh), choke size (S), basic sediment and water term (1 - BS/W/100), temperature (T/Tsc) and gas/liquid ratio (GLR) are considered as random variables. The best probability distribution function (PDF) for each variable is then obtained which most closely reproduce flow through the choke. Monte Carlo sampling which deals with uncertain variables is used to predict the flow rates based on the proposed method and to show the level of uncertainty within the developed correlation results. © 2013 The Author(s).