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Mathematical model for leak location in natural gas pipeline has been developed in this paper. The model employs an isothermal steady state approach. Leak occurrence in the pipeline divides the pipeline into two sections-the upstream and downstream sections respectively. Analyses of leak incidences were carried out in the two pipeline sections giving rise to two equations being developed to address the leak localization. The first leak equation was developed by considering the upstream section of the pipeline while the second leak equation was developed by considering the downstream section of the pipeline. The two equations were analytically developed by slight modification of the Weymouth's equation for gas flow in horizontal pipeline. Matlab software was used in the model simulation. Seven field data were used in the model simulation. The results from the Matlab simulation of the mathematical models developed gave the leak locations for each of the field cases. Comparison of the simulated results with actual results of leak locations determined experimentally revealed high level of accuracy with an average error of only 0.377% which is below the minimum acceptable limit. Furthermore analyses of results show that the two leak equations yield same results when used in the Matlab simulator. The model is highly suitable for accurate detection of leak in natural gas pipeline especially where economics and reliability is of essence.

The ability to detect leak is crucial in pipeline fluid transport operations. Leaks will inevitably occur in pipelines due to wide range of uncertainties. A good leak detection system should not only be able to detect leak but also accurately estimate the actual time of leak occurrence. This will enable proper estimation of the fluid loss, from the pipeline before shut-in of the pipeline or before remedial actions were carried out on the pipeline which ultimately will help quantified the degree of financial or environmental implications resulting from the leak incidence. This paper gives a new model for the estimation of the time of leak in natural gas pipeline. The idea for the model hinges on the notion that the time of response of most pipeline alarm are not necessarily the time actual time the leak occurred. Period of lapse depends on the accuracy, sophistication of the alarm system and volume of leak it is capable of detecting. Most alarm systems respond at later times than the time the leak occurred. Quantification of fluid loss volume demands that the actual time of leak occurrence be determined, this means that the time the leak occurred must be calculated accurately. The model was simulated using the Matlab software. The results show that the model is highly accurate when tested with field data.

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