Pia Bales’s research while affiliated with Technische Universität Darmstadt and other places

Hierarchical Modelling and Model Adaptivity for Gas Flow on Networks

We investigate the stability and convergence of an implicit box scheme for subsonic flows modelled by scalar conservation laws with dissipative and possibly stiff source terms. The scheme is proposed for solving transient gas flow problems in pipeline networks. Such networks are operated in the subsonic flow region and are characterized by pressure losses due to dissipative friction terms. We verify the properties stated by Kružkov’s theorem (Kružkov, Math. USSR-Sb. 10:217–243, 1970) for the approximate solution and prove its convergence to the entropy solution.

Conference Paper

May 2009

47 Reads

21 Citations

Adaptive linearized models for optimization of gas networks

Abstract We are interested in simulation,and optimization,of gas transport in networks. Different regions of the network,may,be modelled,by different equations: There are three models,based on the Euler equations that describe the gas flow in pipelines qualitatively different: a nonlinear model, a semilinear model and a stationary also called algebraic model. For the whole network, adequate initial and boundary values as well as coupling,conditions at the junctions are needed.,Using adjoint techniques,one can specify model,error estimators for the simplified models. A strategy to adaptively apply the different models,in different regions of the network,while maintaining,the accuracy,of the solution is presented.

Article

December 2007

26 Reads

5 Citations

PAMM

Adaptive linearization for the optimal control problem of gas flow in pipeline networks

We are interested in simulation and optimization of gas networks. Usually, a gas network consists of various components like compressors and valves connected by pipes. The aim is to run the network cost efficiently whereas demands of consumers have to be satisfied. This results in a complex nonlinear mixed integer problem. We address this task with methods provided by discrete optimization. Therefore, the gas dynamics in all pipes and at compressors must be described by piecewise linear constraints. We introduce an adaptive approach for the linearization process to handle the complexity on the one hand and the aimed accuracy on the other and present numerical simulation and optimization results based on our model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Article

6 Reads

3 Citations

Adaptive linearization for the optimal control problem of gas flow in pipeline networks

... The scheme is symmetric in space and first order. For scalar conservation laws, it is stable for τ n ≥ kh, where the constant k > 0 depends on the flux function and h is the uniform box length, and converges to the entropy solution [5]. Finally, to built up the fully coupled grid equations, the coupling conditions (2.8) and (2.9) are discretized at t = t n+1 . ...
Reference:
Combination of Nonlinear and Linear Optimization of Transient Gas Networks

Citing Article

Adaptive linearized models for optimization of gas networks

... For example, Martin et al. [19] formulates a large MILP problem to solve the optimisation of natural gas networks using piece-wise linear approximations of nonlinear constraints at steady state. While Kolb et al. [20] describe how gas network optimisation can be better achieved by developing piece-wise linear approximations of network components. In Camponogara et al. [21] and Aguiar et al. [22] gas-lifted oil field production costs are optimised by combining convex nonlinear regression curves with piece-wise linear approximations of these curves at given pressure and routing constraints. ...
Reference:
Steady-state optimisation of a multiple cryogenic air separation unit and compressor plant

Citing Article
December 2007

PAMM

Hierarchical Modelling and Model Adaptivity for Gas Flow on Networks

... One may use the LP for other applications as well. For example, if the error is too large for certain flow variations near highly transient electric generators, the control engineer may design adaptive switching between the LP and NLP to reduce complexity and improve convergence of optimizing gas dynamics for large network systems [35]. The results presented in this work could open new capabilities to analyze very large pipeline network systems that transport natural gas, or more generally, infrastructure networks involving natural gas, water distribution, carbon capture and storage, hydrogen blending, or traffic flow. ...
Reference:
Linear System Analysis and Optimal Control of Natural Gas Dynamics in Pipeline Networks

Citing Conference Paper
May 2009

An implicit box scheme for subsonic compressible flow with dissipative source term

... However, since there are usually only a few different constant temperature levels and the corresponding network areas are often linked by active elements, the vast majority of connected pipes have the same mutual constant temperature level. The usage of the implicit box scheme of [8,28] as a discretization yields the model for a pipe a = (ℓ, r) ∈ A pi and two adjacent time points t 1 ∈ T and t 0 := t 1 − 1 given as ...
Reference:
Optimizing transient gas network control for challenging real-world instances using MIP-based heuristics

Citing Article
March 2010

Numerical Algorithms