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Keywords: mathematical model

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Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 14–17, 2019

Paper Number: PSIG-1910

... the column separation by exhibiting identical hydraulic footprints. ghasvari jahromi

**mathematical****model**upstream oil & gas liquid fraction artificial intelligence evolution spatial prediction fatemeh ekram scenario logic & formal reasoning prediction novel model psig 1910 column...
Abstract

ABSTRACT A novel model is used to predict the inception moment and location of a phenomenon known as the column separation or slack line. The existing models for prediction of the cavitation phenomenon in internal flow systems in general are primarily formulated for the capture of the inception moment and initial location of the event only. Hence questions such as where the incepted cavities and bubbles tend to go, or the detailed state of a slack line in time should be addressed using a different approach. The model presented in this paper is validated and verified against experimental data available in the literature before being applied to a 53 Km (33 miles) industrial pipeline. Imposing conditions at the injection and delivery ends of the line tests various scenarios causing column separation. Hydraulic parameters such as pressure head and flowrate as well as interfacial mass transfer rate of the incepting and collapsing bubbles and cavity zones are predicted in real time over the entire domain of space and time. The results predicted the fate of the separated column of the fluid, whether they rejoin or continue to change the size with different rates or even if they become stabilized stationary cavity pockets after passage of minutes or hours. Results are also compared based on the initial cause of the column separation such as huge transients. Also, accurate prediction of the whole column separation event, distinguishes it from other events, which would commonly mimic or mask the column separation by exhibiting identical hydraulic footprints.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 12–15, 2015

Paper Number: PSIG-1508

... the leak location problem into an optimization problem under certain conditions. Then we develop a derivative-based search algorithm to solve that optimization problem. The derivative will be calculated from an approximate of the underlying

**mathematical****model**that describes the dynamics of pipeline systems...
Abstract

Abstract This paper proposes a novel model-based leak location method for pipelines. We first formulate the leak location problem into an optimization problem under certain conditions. Then we develop a derivative-based search algorithm to solve that optimization problem. The derivative will be calculated from an approximate of the underlying mathematical model that describes the dynamics of pipeline systems, by means of discretization and linearization. Results of simulation and tests using real pipeline data show that this proposed method is accurate, timely, and computationally effective. Introduction Pipelines are one of the major transportation means in oil and gas industry. Leakage remains one of the concerns for pipeline operators. Once a leak occurs, it is important to detect and locate it quickly and accurately in order to minimize potential economic loss and/or environmental damage. Thus leak detection and location is an indispensable technology for managing pipelines smoothly and safely. In this note we are only concerned about leak location, assuming that an existing leak has been detected. Despite the fact that many techniques have been developed in order to address this issue, locating a leak timely and accurately remains a challenging problem both in industry and in academia, see and references therein. One of the conventional methods for leak location is the pressure-gradient method which utilizes the fact that the leak outflow changes the steady pressure-gradients for the sections before and after the leak, respectively. Thus the intersection of those two gradient lines represents the true leak location. This method assumes that the pipeline system is in steady state, which however is a quite stringent condition since in practice most pipelines contain rich transients all the time.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, May 11–14, 2010

Paper Number: PSIG-1013

... these accidents one should have clear understanding about what is going on inside the pipeline. That is why

**mathematical****models**are attracted. They are generally accepted as the cheapest way of the investigation using**mathematical****modeling**once can model almost all dangerous situation that take place in the real...
Abstract

ABSTRACT The pipeline state estimation problem is posed to considered by the example of the simplest pipeline is formulated. It contains the simplified Navie-Stokes equations for the interior points of the pipe, and two boundary conditions for the fluid flow through the pump and valve. The main principles of the difference scheme for solving these model equations are described. The iterative quasi-linearization is proposed. The state estimation procedure is build on the basis of quasi-linearized model. Some results of numerical experiments are given. INTRODUCTION In the past few years the state estimation problem for pipeline systems has become one of current importance. These are different approaches to this problem, using the online models. Most of them are built on the correct statement of boundary conditions [6]. This paper represents a new technique for online state estimation based on the pipeline model and a latesh history of date, obtained from pressure sensors and flowmeters installed on the pipeline. The point is that in spite of the fact the modern oil pipelines are equipped with high tech equipments the accidents and oil spills keep happen, damaging the environment. To prevent these accidents one should have clear understanding about what is going on inside the pipeline. That is why mathematical models are attracted. They are generally accepted as the cheapest way of the investigation using mathematical modeling once can model almost all dangerous situation that take place in the real pipeline. But this is not enough. The pipeline when is use is the complex dynamical system, with many input and output signals. The input signals are the operator's commands, such as valve shutting, pump start, tank changeover, etc. output signals are the measurements of pressure and flow in situ, using special pressure sensors and flowmeters. As the case may be the pipeline can reach different states, depending on what command the operator has input. The wrong command can entail serious consequences. For example, the wrong stop of the pump can entail pipeline breakdown and therefore oil spill. But if it was possible for operator to control the flow process in the pipeline using its' online model one would avoid the accident. Mathematical model of a pipeline as a system with distributed parameters is represented with the hyperbolic system of partial equations and boundary conditions. To solve this system means to obtain the system state in the future time moments. But solving the hyperbolic system of partial equations is impossible without known initial state and boundary conditions at the next time moments. To know the state of the pipeline means to know the flow velocity and pressure distributions along the pipe. Despite the boundary conditions the initial state cannot be measured directly. Hence, one has to use identification methods to obtain the current state and to make a prediction on the basis of one. Identification of the current state can be carried out on the basis of some measurements from the past, i.e. using the latest history of date, obtained from pressure sensors.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 20–22, 1999

Paper Number: PSIG-9910

.... The proposed decentralized

**mathematical****model**, which will conduct to the distributed design, has been proven correct on an abstract algebraic model, with the same structure as the real problem. This modular approach is well suited to the high and ever increasing dimension of gas networks, and to the nature...
Abstract

Abstract As natural gas is becoming increasingly important in modern life, its distribution through ever expanding pipeline networks is dependent on optimized control and management. The problem of dynamic optimization is difficult to resolve due to its inherent characteristics. We propose a two-stage approach, where both space and time decomposition are applied, and as a result the problem can be formulated as one of dynamic optimization. The objective is a deadlock-free distributed model, where the computation order is assured correct, and the communication time is minimized. The proposed decentralized mathematical model, which will conduct to the distributed design, has been proven correct on an abstract algebraic model, with the same structure as the real problem. This modular approach is well suited to the high and ever increasing dimension of gas networks, and to the nature of the problem, as well as to the tendency to decentralize services - e.g. BG plc. A decentralized approach also makes the network less dependent on communication hazards and diminishes communication delays and lags, contributing in this manner to a more accurate approach. Solution efficiency is also expected since smaller problems are solved simultaneously with the communication overhead being minimized. 1 Introduction Gas networks are composed of geographically dispersed controllable elements communicating between themselves. Their large extent, high complexity, inherent nonlinearities, and transient nature make the optimisation of their operation and management a difficult computational task. Long computational times, as well as communication unreliability caused by their decentralised nature, result into a loss of solution accuracy. One of the ways to improve computational efficiency is system decomposition and subsequent use of parallelism. A temporal decomposition is suitable to the problem's mathematical structure, whereas a spatial decomposition suits its decentralised nature. Our works fits in a broader line of research, which consists on an examination of the possibility that present global optimisation methods used in gas networks could be replaced by a decentralised approach. This could significantly reduce the computation time, as well as being more closely related to the organisational realities of modern life. Since we work from a theoretical and abstract point of view, we are not concerned with network subtleties which we view as physical details. Our aim is to capture main features of the network organisation that determine the basic network structure and operation. It is our main objective to examine the overall structure of an iterative formulation of the problem of transient optimisation of networks, and then decide on its partition whether it be according to time or space. However, owing to the complexity of the problem studied, its decomposition and the basic structure of the proposed approach to optimisation will be described on an abstract algebraic setting of the kind of the transient optimisation problem.

Proceedings Papers

Publisher: Pipeline Simulation Interest Group

Paper presented at the PSIG Annual Meeting, October 23–25, 1996

Paper Number: PSIG-9606

..., ADVANTAGES AND DISADVANTAGES Abstract

**Mathematical****models**for transient gas flow are described by partial differ- ential equations or a system of such equations. Depending on the degree of simplification with respect to the set of basic equations, the equations may be linear or quite generally non-linear...
Abstract

ABSTRACT Mathematical models for transient gas flow are described by partial differential equations or a system of such equations. Depending on the degree of simplification with respect to the set of basic equations, the equations may be linear or quite generally non-linear. They may be parabolic or hyperbolic of the 1st or 2nd order. With respect to the transport of gas in pipelines, there are two technically relevant special cases of pipe flow: – flow without heat exchange with the ground outside; adiabatic and, more especially, isentropic flow; – flow with complete heat exchange with the ground outside, which is regarded as being a heat storage unit of infinite capacity with constant temperature; isotermal flow. Numerical solution of the partial differential equations which characterize a dynamic model of network takes much computation time. The problem is to find for given mathematical model of a pipeline a numerical method which meets the criteria of accuracy and relatively small computation time. The main goal of this paper is to characterized different transient models and existing numerical techniques to solve the transient equations. 1. Introduction It is a well established fact that flow in gas pipelines is unsteady. Conditions are always changing with time, no matter how small some of the changes may be. When modelling systems, however, it is sometimes convenient to make the simplifying assumption that flow is steady. Under many conditions, this assumption produces adequate engineering results. On the other hand, there are many situations where an assumption of steady flow and its attendant ramifications produce unacceptable results. The steady state in a gas network is described by system of algebraic nonlinear equations. In steady-state problems, loads and supplies are not functions of time; the system variables nodal pressures and branches flows) do not change with time. The steady-state model is widely used as the basis of many traditional design methods because it is usually relatively simple to solve and is conceptually easier to understand. However, in some systems the dynamics cannot be neglected without gross error and we must use a dynamic model. Dynamic models are just a particular class of differential equation model in which time derivatives are present. A good example of the use of steady-state and dynamic models is found in gas networks: in low pressure networks the dynamics are very rapid and can be ignored for most practical purpose and steady-state models are used. In high pressure networks the dynamics are much slower because of the large amount of gas stored in the pipes and cannot be neglected. Transients are initiated in gas systems by the time variant nature of the load at distribution points and from adjustments made by the system operator in reacting to the demands of the system. As larger loads are placed on existing systems, the ability to supply gas at contract pressures during periods of peak customer demand is decreased. To cope with this situation a larger variation of the supply system input capacity must be provided.