Abstract

An algorithm was developed for determining the implications of multiphase flow uncertainties. The specific method employed combines the classical uncertainty analysis of Kline and McClintock with multiple random variable probability theory. The initial results indicate that in addition to uncertainty prediction, the algorithm can also be used to statistically reduce the sharp discontinuities common in multiphase flow modeling, thus leading to improved simulation convergeance.

Introduction

Flow assurance and risk assessment are major issues in the offshore petroleum industry today. While there is a push for increasingly more complex flow models it is important not to lose the understanding of the accuracy of such models and their sensitivity to input parameters. Error bars for flow assurance simulations can greatly affect field planning, equipment sizing, and risk assessment.

At present, uncertainty calculations for multiphase flow conditions are not well understood and are rarely reported. Over short distances, uncertainties in prediction of pressure drop in the design stage can be large without causing significant production problems. However as multiphase transport in pipelines extends into tens of miles, a significant error can occur in predicting capacity. The method described can also be extended to the prediction of such values as corrosion rate, arrival temperature, and wax deposition rate.

In developing a method for determining uncertainty, it is desired that re-coding of the model not be necessary, implementation be simple, practical computational constraints be considered (e.g., no Monte Carlo approach). This led to an approach that was discrete and also was able to lessen the effects of sharp discontinuities. Specifically, existing model functions can be evaluated at selected intervals with the results being probability-weighted to arrive at a solution.

Statement of Theory and Definintions

Error bars represent the confidence interval for a given confidence level. When engineering results are specified, error bars are attached to the data to give the reader an idea of the level of uncertainty associated with the results. A list of values for common confidence intervals is given in Table 1. It is important to note that when the confidence level does not accompany the error bars, it is common to assume 2.15 - 1 odds. The values in Table 1 were generated using Eq. 1 in conjuntion with the Gaussian distribution.

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