Modelling of linebreak in high-pressure gas pipes
Although there are many computer codes available for analysis of fluid transients, only. a few are known to be applicable to line break situations and their scope is limited. There is therefore,s till a big potential for development work in the subject. Discrepancies between different models which have been developed have mainly centred on the assumptions used in developing the basic partial differential equations of flow, and subsequent simplifications; the thermophysical model used; representation of various terms in the equations such as the friction term; and the numerical method of solution of the basic partial differential equations. A previous model developed by Tiley (1989), overestimated the actual wave speeds and had problems of instability of the solution. A new approach, in which the three basic partial differential equation of flow are derived, based on the assumption of an unsteady quasi-one-dimensional flow of a real gas through a rigid constant cross-section area pipe, and using the Gamma Delta method is used. No further simplification is made on the basic equations. Significant improvements have been made on the type of equation of state, thermodynamic model, heat transfer approximation and friction factor representation. The QUANT software for thermodynamic and transport properties of real gases is used. A flow dependent explicit equation of Chen (1979) is used to calculate the frictional force and heat transfer is calculated using the concept of recovery factor and adiabatic wall temperature. Numerical solution of the basic equations is performed using the third-order Warming- Kutler-Lomax method, the second-order MacCormack method and the method of characteristics. A pc based computer coding with the C language is used. The QUANT software has successfully been incorporated with the programme. The full benefits of the software could not be realised with linebreak problems due to limitation of the range within which it gives output at present, but satisfactory results have nevertheless been attained. An improved and more accurate way of calculating the break boundary condition has been used. A non-uniform grid spacing has been used, which allow fine grid spacing in the vicinity of the break in order to enable accurate modelling of the rapid transients occurring in that part. Two different models for calculating the heat transfer i. e. one for the case of pipes exposed to the atmosphere and buried pipes have been incorporated with the model. Experimental data from full-scale pipeline tests is used to validate the computer models. Results from the computer model simulations show good agreement with the experimental data. The MacCormack method has been found to be unsuitable for modelling transient flow following linebreak in high-pressure gas pipelines. The method of characteristics has proved to be the method of solution for such applications. A better understanding of the flow following a break in high-pressure gas pipes is achieved, especially the decompression behaviour at the break boundary. Data gathered from feasibility studies conducted in the late 1980's for a pipeline in Tanzania is used to validate the steady state analysis model and to simulate a linebreak in the pipeline. Results of the computer simulation are discussed and recommendations made on the suitability the pipeline design. Additional work is recommended on refining and further testing of the computer programmes and using the Gamdeleps method which covers all the three phases region i.e. gas, liquid and gas/liquid.