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# A New Hydraulic and Thermal Steady-State Calculation Program for Multiphase Pipe Network

[+] Author Affiliations
Di Fan, Qi Kang, Ruochen Zhang, Jing Gong, Changchun Wu

China University of Petroleum-Beijing, Beijing, China

Paper No. IPC2018-78279, pp. V003T04A011; 11 pages
doi:10.1115/IPC2018-78279
From:
• 2018 12th International Pipeline Conference
• Volume 3: Operations, Monitoring, and Maintenance; Materials and Joining
• Calgary, Alberta, Canada, September 24–28, 2018
• ISBN: 978-0-7918-5188-3

## abstract

With the continuous development of offshore oil and gas resources, calculation software for multiphase flowing pipe network has become an important tool for the design and daily operation of multiphase flowing pipe network. Improved accuracy of hydraulic and thermal calculation is an engineering requirement for economic and efficient production. Therefore, a new program is developed for multiphase pipe network in this paper. This program contains a general data structure to describe the complex connection of a pipe network. The structure is based on the conception of the incidence matrix and the adjacency matrix in graph theory. Two processes, hydraulic equilibrium calculation and thermodynamic equilibrium calculation are successively taken in this program to gain the steady-state for a multiphase pipe network. For the hydraulic equilibrium calculation, applying flow equation to each pipe in the network gains a pipe flow vector. A nonlinear system of equations, which represent flow balance of each node, is obtained by multiplying the incidence matrix and the pipe flow vector. To solve these equations, the Newton-Raphson iterative algorithm is used and afterwards, the hydraulic parameters of the pipe network are obtained. For thermal equilibrium calculation, since all the temperature of source nodes is known, the key step is to find the solution order of other node temperature. The program obtains the order by transforming the adjacency matrix. Deng temperature drop formula is used to calculate the end temperature of each pipe. When a node has more than one inflow, an average temperature based on the heat capacity and mass flow is adopted after gaining each pipe’s outlet temperature. Combining hydraulic and thermal algorithms, a complete set of solution program for steady-state of multiphase pipe network is compiled. In the end, two cases are performed to check the accuracy of the program. In the first case, a pipe network is created by using the data collected from a condensate gas gathering network in the South China Sea. The result indicates that the program has a good agreement with the actual data. In the second case, the program is applied in a single-phase network and gains almost the same result calculated by PipePhase and PipeSim.

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