Tobias Kasper Skovborg Ritschel

A Thermodynamic Library for Simulation and Optimization of Dynamic Processes * *This project is funded partly by: 1) Innovation Fund Denmark in the CITIES project (1305-00027B) and in the OPTION project (63-2013-3), 2) the interreg project Smart Cities Accelerator (10606 SCA), and 3) EUDP 64013-0558 in the IEA Annex for energy efficient process control.

Abstract Process system tools, such as simulation and optimization of dynamic systems, are widely used in the process industries for development of operational strategies and control for process systems. These tools rely on thermodynamic models and many thermodynamic models have been developed for different compounds and mixtures. However, rigorous thermodynamic models are generally computationally intensive and not available as open-source libraries for process simulation and optimization. In this paper, we describe the application of a novel open-source rigorous thermodynamic library, ThermoLib, which is designed for dynamic simulation and optimization of vapor-liquid processes. ThermoLib is implemented in Matlab and C and uses cubic equations of state to compute vapor and liquid phase thermodynamic properties. The novelty of ThermoLib is that it provides analytical first and second order derivatives. These derivatives are needed for efficient dynamic simulation and optimization. The analytical derivatives improve the computational performance by a factor between 12 and 35 as compared to finite difference approximations. We present two examples that use ThermoLib routines in their implementations: (1) simulation of a vapor-compression cycle, and (2) optimal control of an isoenergetic-isochoric flash separation process. The ThermoLib software used in this paper is distributed as open-source software at www.psetools.org.

Production Optimization Of Thermodynamically Rigorous Isothermal And Compositional Models

Summary In this work, we consider algorithms for solving production optimization problems that involve isothermal (constant temperature) and compositional oil production processes. The purpose of production optimization is to compute a long-term production strategy that is economically optimal. We present a thermodynamically rigorous model of isothermal oil production processes. We derive the model from first principles by applying a number of assumptions including the assumption of constant temperature. The model is based on two key principles, namely phase equilibrium and conservation of mass and energy. The conservation equations are expressed as partial differential equations, and we model the phase equilibrium as a VT flash process. It is common to formulate the phase equilibrium conditions in oil reservoir flow models as the fugacities being equal. We describe how to derive that condition from the phase equilibrium conditions from the VT flash problem. The VT flash is an adaption of the second law of thermodynamics, i.e. the entropy of a closed system in equilibrium is maximal, to isothermal systems. The VT flash can therefore be formulated as an inner optimization problem that needs to be solved for each grid cell in the discretized reservoir in the forward simulation of the oil production process. We demonstrate that it is natural to model such isothermal production processes with differential-algebraic equations in a semi-explicit index-1 form. We describe a single-shooting algorithm for solving the production optimization problem efficiently. It is key to the efficiency of such algorithms to compute gradients. For that purpose, we use an adjoint algorithm. We implement the singleshooting algorithm in C/C++ using the open-source software DUNE, the open-source thermodynamic software ThermoLib, and the numerical optimization software KNITRO. Finally, we present a numerical example that involves optimal waterflooding.

An algorithm for gradient-based dynamic optimization of UV flash processes

Abstract This paper presents a novel single-shooting algorithm for gradient-based solution of optimal control problems with vapor–liquid equilibrium constraints. Such optimal control problems are important in several engineering applications, for instance in control of distillation columns, in certain two-phase flow problems, and in operation of oil reservoirs. The single-shooting algorithm uses an adjoint method for the computation of gradients. Furthermore, the algorithm uses either a simultaneous or a nested approach for the numerical solution of the dynamic vapor–liquid equilibrium model equations. Two numerical examples illustrate that the simultaneous approach is faster than the nested approach and that the efficiency of the underlying thermodynamic computations is important for the overall performance of the single-shooting algorithm. We compare the performance of different optimization software as well as the performance of different compilers in a Linux operating system. These tests indicate that real-time nonlinear model predictive control of UV flash processes is computationally feasible.

The Adjoint Method for Gradient-based Dynamic Optimization of UV Flash Processes

Abstract This paper presents a novel single-shooting algorithm for gradient-based solution of optimal control problems with vapor-liquid equilibrium constraints. Dynamic optimization of UV flash processes is relevant in nonlinear model predictive control of distillation columns, certain two-phase flow problems, and oil reservoir production with significant compositional and thermal effects. Gradients are computed with the adjoint method and we use various optimization software (fmincon, IPOPT, KNITRO, and NPSOL) for the numerical optimization. We present computational results for a non-ideal five-component flash process which demonstrate the importance of the optimization solver, the compiler, and the linear algebra software for the efficiency of dynamic optimization of UV flash processes.

Economic Optimizing Control for Single-Cell Protein Production in a U-Loop Reactor

Abstract The production of single-cell protein (SCP) in a U-loop reactor by a methanotroph is a cost efficient sustainable alternative to protein from fish meal obtained by over-fishing the oceans. SCP serves as animal feed. In this paper, we present a mathematical model that describes the dynamics of SCP production in a U-loop reactor. We use this model to compute an optimal start-up trajectory by solution of an economic optimizing optimal control problem. The optimal start-up trajectory is an unstable attractor. The practical implementation of this optimal start-up trajectory can be conducted by a proportional controller for the substrate concentration in the top tank of the U-loop reactor.

An efficient and rigorous thermodynamic library and optimal-control of a cryogenic air separation unit

Abstract Cryogenic air separation (CAS) is the leading technology for large scale production of pure N2, O2 and Ar. This process is very electric-energy intensive; thus it is a likely candidate for load balancing of power stations in a smart grid. This type of intermittent operation of CAS, requires a non-linear model based control to achieve optimal techno-economic performance. Accordingly, this work presents a computationally efficient and novel approach for solving a tray-by-tray equilibrium model and its implementation for open-loop optimal-control of a cryogenic distillation column. Here, the optimisation objective is to reduce the cost of compression in a volatile electricity market while meeting the production requirements, i.e. product flow rate and purity. This model is implemented in Matlab and uses the ThermoLib rigorous thermodynamic library. The present work represents a first step towards plant-wide dynamic modelling and smart control of a cryogenic distillation plant.