Development of a New Fast Algorithm for Analysis of Unsteady Compressible Flow in Gas Networks

Resumo

The main motivation of this thesis is finding a fast way to simulate a gas network. In order to achieve this purpose, a new formulation for isothermal gas flow in a single pipeline including gravity and friction effects has been introduced and solved by finite element methods. The proposed formulation can be easily adapted to simulate different types of real boundary conditions and involves only one scalar unknown instead of two ones. This kind of formulation condenses unknowns (typically mass flux and pressure or density) and consequently reduces the computational cost and time. Also, it can be extended to gas network easily. In the first part of thesis, in order to solve this compact formulation, the FEniCS open-source computing platform have been used which is able to be solved with a high order accuracy scheme just by changing the type of elements. Then, in order to check the performance of the numerical method, it has been applied to several test problems. In the Second part, the idea has been extended to model gas flow in a transportation network. The network only includes pipes connected at nodes which can be emission or consumption points, or simply structural connections between pipes. In addition to the mass and momentum conservation equations inside the pipes, the mass conservation equations at the nodes should be written. The latter appears to be a set of constraints (one per node) whose respective Lagrange multipliers are the (continuous) pressures at the nodes. Thus, the whole model is a Partial Differential-Algebraic Equation (PDAE). For numerical solution, the finite element method with an implicit time discretization is proposed. The problem leds to solve a nonlinear system of numerical equations per time step what is done by Newton's method. The main advantage of the present methodology is that the algorithm can be parallelized in such a way that, at each time step, every pipe can be solved separately in one processor (or core). The consequences of the parallelization will be reducing extra computing time, especially in large gas network. The introduced methodology is verified and validated by applying the implemented FORTRAN computer code in a triangular network and a part of the real Spanish gas network. Also, in order to show the ability of methodology, the mentioned typical triangular network is solved for sudden changes at consumption nodes. Moreover, it has been shown that the proposed scheme exactly conserves the mass at the nodes and in the whole network, and a new simple and compact way of computing the network line-pack over time is given. This kind of line pack formulation gives a straight forward way to calculating consuming and lost gases in a network. In the end, the numerical results and calculation times showed that used methodology, even with large time-step and coarse mesh, are in good agreement with experimental and in a very short time.