Optimal Control of Transient Flow in Natural Gas Networks

We outline a new control system model for the distributed dynamics of compressible gas flow through large-scale pipeline networks with time-varying injections, withdrawals, and control actions of compressors and regulators. The gas dynamics PDE equations over the pipelines, together with boundary conditions at junctions, are reduced using lumped elements to a sparse nonlinear ODE system expressed in vector-matrix form using graph theoretic notation. This system, which we call the reduced network flow (RNF) model, is a consistent discretization of the PDE equations for gas flow. The RNF forms the dynamic constraints for optimal control problems for pipeline systems with known time-varying withdrawals and injections and gas pressure limits throughout the network. The objectives include economic transient compression (ETC) and minimum load shedding (MLS), which involve minimizing compression costs or, if that is infeasible, minimizing the unfulfilled deliveries, respectively. These continuous functional optimization problems are approximated using the Legendre-Gauss-Lobatto (LGL) pseudospectral collocation scheme to yield a family of nonlinear programs, whose solutions approach the optima with finer discretization. Simulation and optimization of time-varying scenarios on an example natural gas transmission network demonstrate the gains in security and efficiency over methods that assume steady-state behavior

Robust Kalman filter-based dynamic state estimation of natural gas pipeline networks

To obtain the accurate transient states of the big scale natural gas pipeline networks under the bad data and non-zero mean noises conditions, a robust Kalman filter-based dynamic state estimation method is proposed using the linearized gas pipeline transient flow equations in this paper. Firstly, the dynamic state estimation model is built. Since the gas pipeline transient flow equations are less than the states, the boundary conditions are used as supplementary constraints to predict the transient states. To increase the measurement redundancy, the zero mass flow rate constraints at the sink nodes are taken as virtual measurements. Secondly, to ensure the stability under bad data condition, the robust Kalman filter algorithm is proposed by introducing a time-varying scalar matrix to regulate the measurement error variances correctly according to the innovation vector at every time step. At last, the proposed method is applied to a 30-node gas pipeline networks in several kinds of measurement conditions. The simulation shows that the proposed robust dynamic state estimation can decrease the effects of bad data and achieve better estimating results.Comment: Accepted by Mathematical Problems in Engineerin

Розрахунок газових мереж низького тиску з урахуванням зосередженого відбору газу по довжині ділянок

Проведено аналітичні розрахунки, які засвідчили, що нормативні методи прогнозування розподілу газу в системах газопостачання низького тиску з сталевих та поліетиленових труб не достовірно описують наявні газодинамічні процеси. Доведено, що похибка обчислення перепаду тиску газу за умови використання моделі рівномірного розподілу газу по довжині газопроводу складає до 70 % і залежить від технологічних параметрів роботи ділянки. Запропоновано уточнений метод розрахунку проектних та експлуатаційних параметрів роботи ділянок з урахуванням моделі зосередженого відбору газу по довжині газопроводів. Для всього діапазону співвідношень шляхової та транзитної витрати газу на ділянках газових мереж низького тиску населених пунктів отримано уточнені залежності перепаду тиску та величини розрахункової витрати газу. Шляхом комп’ютерного моделювання досліджено вплив даних моделей на значення проектних та експлуатаційних параметрів роботи газопроводів систем газопостачання населених пунктів. Доведено необхідність зміни діаметрів деяких ділянок газових мереж з метою попередження аварійних режимів їх роботи.In this paper the analytical calculations were performed demonstrating that normative forecasting methods of gas distribution in the low-pressure gas supply networks, made of steel and polyethylene pipes, do not describe existent gas-dynamic processes correctly. It was proved that the error of gas pressure drop calculations using model of even gas distribution along the pipeline is up to 70% depending on the pipeline operational parameters. Therefore, a revised method for calculating the design and operating parameters of the pipeline sections was presented taking into account a model of the concentrated gas extraction along the pipeline. The refined dependencies oj pressure drop and gas design flow rate were obtained for the full range of relations between route and transit gas flow in the pipeline sections of the low-pressure gas networks of localities. The effects of these models on the values of the design and operational parameters of the gas network pipelines were studied by means of computer simulation. The necessity of changing the diameter ofsome pipeline sections of the gas networks in order to prevent their emergency operation was proved

Relaxations of the Steady Optimal Gas Flow Problem for a Non-Ideal Gas

Natural gas ranks second in consumption among primary energy sources in the United States. The majority of production sites are in remote locations, hence natural gas needs to be transported through a pipeline network equipped with a variety of physical components such as compressors, valves, etc. Thus, from the point of view of both economics and reliability, it is desirable to achieve optimal transportation of natural gas using these pipeline networks. The physics that governs the flow of natural gas through various components in a pipeline network is governed by nonlinear and non-convex equality and inequality constraints and the most general steady-flow operations problem takes the form of a Mixed Integer Nonlinear Program. In this paper, we consider one example of steady-flow operations -- the Optimal Gas Flow (OGF) problem for a natural gas pipeline network that minimizes the production cost subject to the physics of steady-flow of natural gas. The ability to quickly determine global optimal solution and a lower bound to the objective value of the OGF for different demand profiles plays a key role in efficient day-to-day operations. One strategy to accomplish this relies on tight relaxations to the nonlinear constraints of the OGF. Currently, many nonlinear constraints that arise due to modeling the non-ideal equation of state either do not have relaxations or have relaxations that scale poorly for realistic network sizes. In this work, we combine recent advancements in the development of polyhedral relaxations for univariate functions to obtain tight relaxations that can be solved within a few seconds on a standard laptop. We demonstrate the quality of these relaxations through extensive numerical experiments on very large scale test networks available in the literature and find that the proposed relaxation is able to prove optimality in 92% of the instances.Comment: 28 page

Simulation of transient flow in gas pipelines using the finite volume method

The transient flow analysis is fundamental to the simulation of natural gas process, in order to adjust the system to real operative conditions and to obtain the highest level of efficiency, compliance and reliability. The simulation of natural gas pipelines and networks requires mathematical models that describe flow properties. Some models that have been developed year after year based on the laws of fluid mechanics that govern this process, interpreted as a system of equations difficult to solve. This investigation describes the fully implicit finite volume method for natural gas pipeline flow calculation under isothermal conditions and transient regime. The simplification, discretization scheme and implementation equations are approached throughout this paper. The model was subjected to two evaluations: sinusoidal variation of the mass flow and opening-closing valve at the outlet of the pipeline, it is compared with two models: fully implicit finite difference method and method of characteristics. This method proved to be efficient in the simulations of slow and fast transients, coinciding the flow oscillations with the natural frequency of natural gas pipeline

Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline

Pressure Fluctuations in Natural Gas Networks caused by Gas-Electric Coupling

The development of hydraulic fracturing technology has dramatically increased the supply and lowered the cost of natural gas in the United States, driving an expansion of natural gas-fired generation capacity in several electrical inter-connections. Gas-fired generators have the capability to ramp quickly and are often utilized by grid operators to balance intermittency caused by wind generation. The time-varying output of these generators results in time-varying natural gas consumption rates that impact the pressure and line-pack of the gas network. As gas system operators assume nearly constant gas consumption when estimating pipeline transfer capacity and for planning operations, such fluctuations are a source of risk to their system. Here, we develop a new method to assess this risk. We consider a model of gas networks with consumption modeled through two components: forecasted consumption and small spatio-temporarily varying consumption due to the gas-fired generators being used to balance wind. While the forecasted consumption is globally balanced over longer time scales, the fluctuating consumption causes pressure fluctuations in the gas system to grow diffusively in time with a diffusion rate sensitive to the steady but spatially-inhomogeneous forecasted distribution of mass flow. To motivate our approach, we analyze the effect of fluctuating gas consumption on a model of the Transco gas pipeline that extends from the Gulf of Mexico to the Northeast of the United States.Comment: 10 pages, 7 figure

Determination of Gas Pressure Distribution in a Pipeline Network using the Broyden Method

A potential problem in natural gas pipeline networks is bottlenecks occurring in the flow system due to unexpected high pressure at the pipeline network junctions resulting in inaccurate quantity and quality (pressure) at the end user outlets. The gas operator should be able to measure the pressure distribution in its network so the consumers can expect adequate gas quality and quantity obtained at their outlets. In this paper, a new approach to determine the gas pressure distribution in a pipeline network is proposed. A practical and user-friendly software application was developed. The network was modeled as a collection of node pressures and edge flows. The steady state gas flow equations Panhandle A, Panhandle B and Weymouth to represent flow in pipes of different sizes and a valve and regulator equation were considered. The obtained system consists of a set of nonlinear equations of node pressures and edge flowrates. Application in a network in the field involving a large number of outlets will result in a large system of nonlinear equations to be solved. In this study, the Broyden method was used for solving the system of equations. It showed satisfactory performance when implemented with field data

Numerical Simulation of Two-phase Separation in T-junction

T-junctions are commonly used in distributing two-phase flow by piping networks especially in oil and gas industries. However, the nature splitting of liquid-gas phases is a major challenge and is complicated due to the large number of variables that influence it. Understanding the behavior of two-phase flow through a T-junction is very essential as it has significant impact on oil and gas transportation pipeline networks, operation and control of process and power industries and lastly the maintenance efficiency of all the components downstream from the junction. This paper provides a detailed analysis on the effect of associated variables on phase separation efficiency in T-junction. Hence, the analysis uses and develops a numerical model for simulation of two-phase flow distribution in T-junction to elucidate an in depth understanding on two-phase separation at different operating conditions and parameters. In order to achieve the objective, the developed model consists of horizontal main arm and vertical side arm while CFD method is employed to simulate the fluid flow. The present study identifies that the overall mass split ratio, the initial gas saturation and gas density are the most influential factors on fraction of gas taken off in T-junction. Subsequently, the effect of inclination angle of gravity on flow split is investigated and it does not play a significant role on phase separation. At the end of this project, the phenomenon of phase maldistribution when a two-phase mixture passes through a T-junctions is well understood and hence the underlying potential as a simple, cost saving, passive partial separator is able to be included in the design of pipeline networks in the petroleum industry