天然气管网在瞬变流条件下的储气运行
Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions
摘要：
我们制定了一个非线性最优控制问题的天然气管道网络，其中包括存储库的日内运行。考虑了可压缩气体通过管道、压缩机、储层和井的流动动力学。特别地，储层被建模为在等温条件和均匀密度下存储气体的刚性中空容器，并且井被建模为垂直管。对于每个管道，流动动力学描述的密度和质量通量变量的耦合偏微分方程（PDE）系统，与使用Darcy-Wiesbach摩擦近似建模的动量耗散。压缩机被建模为按比例增加入口和出口之间的气体压力。所有网络组件的控制方程在空间上离散化，并组装成一个非线性微分-代数方程（DAE）系统，该系统将地上管道和地下油藏动态合成为一个单一的降阶模型。我们寻求最大化的目标函数，量化的经济利润和网络效率的流量方程和不等式，代表操作限制。使用原始-对偶内点求解器解决了该问题，并在几个管道测试网络上的计算实验和仿真中验证了所提出方法的有效性。
英文摘要：
We formulate a nonlinear optimal control problem for intra-day operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are considered. In particular, a reservoir is modeled as a rigid, hollow container that stores gas under isothermal conditions and uniform density, and a well is modeled as a vertical pipe. For each pipe, flow dynamics are described by a coupled partial differential equation (PDE) system in density and mass flux variables, with momentum dissipation modeled using the Darcy-Wiesbach friction approximation. Compressors are modeled as scaling up the pressure of gas between inlet and outlet. The governing equations for all network components are spatially discretized and assembled into a nonlinear differential-algebraic equation (DAE) system, which synthesizes above-ground pipeline and subsurface reservoir dynamics into a single reduced-order model. We seek to maximize an objective function that quantifies economic profit and network efficiency subject to the flow equations and inequalities that represent operating limitations. The problem is solved using a primal-dual interior point solver and the solutions are validated in computational experiments and simulations on several pipeline test networks to demonstrate the effectiveness of the proposed methodology.
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