Matthias Lampe

Simultaneous process and working fluid optimisation for Organic Rankine Cycles (ORC) using PC-SAFT

Abstract Organic Rankine Cycles (ORC) have a broad economically attractive application range since they can be tailored to fit specific conditions. The tailor-made design of ORC involves the selection of a suitable working fluid and the optimisation of the process itself. Today, these design steps are usually performed separately. In this paper, the holistic design of ORC processes is rigorously approached employing computer-aided molecular design (CAMD) to select a working fluid and to simultaneously optimise the corresponding process within a single mathematical problem. Herein, the strong molecular picture underlying the PC-SAFT equation of state is exploited using the recently developed continuous-molecular targeting (CoMT) approach. The effectiveness of the CoMT-CAMD approach is demonstrated for the optimisation of both working fluid and process parameters in a waste-heat ORC application.

Robust multi-objective optimization for sustainable design of distributed energy supply systems

Abstract Sustainable design of distributed energy supply systems involves multiple aims. Therefore, multi-objective optimization is the appropriate concept for sustainable design. However, input parameters are in general uncertain. If uncertainties are disregarded in the optimization, solutions usually become infeasible in practice. To incorporate uncertain parameters, we apply the concept of minmax robust multi-objective optimization for designing sustainable energy supply systems. We propose a mixed-integer linear problem formulation. The proposed formulation allows to identify robust sustainable designs easily guaranteeing security of energy supply. Energy systems are shown to typically exhibit objective-wise uncertainties. Thus, a Pareto front can still be derived. In a real-world case study, robust designs are identified with a good trade-off between economic and ecologic criteria. The robust designs perform remarkably well in the nominal scenario. The presented problem formulation transfers the important theoretical concept of minmax robust multi-objective optimization into engineering practice for the design of sustainable energy systems.

Computer-aided Molecular Design of ORC Working Fluids using PC-SAFT

Abstract Organic Rankine Cycles (ORCs) are used for the transformation of low-temperature heat to power. The key design variables are the process settings and the working fluid. This paper presents a holistic method for the computer-aided molecular design (CAMD) of ORC working fluids. The basis for the design is a novel approach allowing for the simultaneous optimization of the working fluid and the process by exploiting the molecular picture underlying PC-SAFT. The simultaneous design yields a target for a hypothetical working fluid and optimal process settings from one optimization problem. The hypothetical target fluid forms the basis for the CAMD method. For this purpose, a group contribution (GC) method is developed for the prediction of PC-SAFT pure component parameters. Thereby, a holistic design of novel working fluids and optimal processes is achieved.

Multi-objective synthesis of energy systems: Efficient identification of design trade-offs

Abstract The synthesis of energy systems usually has to consider several conflicting objectives leading to a large set of Pareto-optimal solutions with multiple trade-offs. From this large set of solutions, good compromise solutions have to be identified which is a complex and computationally demanding task. We therefore propose a method to reduce both the set of objectives and the solution space: First, the set of objectives is reduced by employing a method from the literature to determine the objectives best representing the design trade-offs. However, in practice, aggregated costs are the decisive criterion. Thus, in a second step, the solution space of the synthesis problem is restricted to an acceptable deviation from minimal aggregated costs. Thereby, only relevant solutions are obtained. The two steps significantly reduce the effort for multi-objective optimization focusing on the most relevant part of the solutions. The proposed method is applied to a real-world case study.

From molecules to dollars: integrating molecular design into thermo-economic process design using consistent thermodynamic modeling

The right molecules are often the key to overall process performance and economics of many energy and chemical conversion processes, such as, e.g., solvents for CO2 capture or working fluids for organic Rankine cycles. However, the process settings also impact the choices at the molecular level. Thus, ultimately, the process and the molecules have to be optimized simultaneously to obtain a thermo-economically optimal process. For a detailed design of the process and also the equipment, a thermodynamic model is required for both equilibrium and transport properties. We present an approach for the integrated thermo-economic design of the process, equipment and molecule on the basis of a comprehensive, thermodynamically consistent model of the molecule. For this purpose, we developed models for transport properties based on entropy-scaling of the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Thereby, a single model predicts both equilibrium and transport properties in our optimization-based approach for the integrated design of the process, equipment and molecule, the so-called 1-stage CoMT–CAMD approach. The predicted transport properties allow for the design and sizing of unit operations as degrees of freedom during the optimization. Computer-aided molecular design allows the design of novel molecules tailored to the specific process while considering safety and environmental issues. The presented approach is exemplified for the design of an organic Rankine cycle showing the merits of detailed sizing of heat exchangers with different heat transfer types and the rotating equipment as part of the optimization. Single-objective optimization is used to obtain a ranking of potential working fluids. The detailed trade-off between the total capital investment and the net power output of the ORC is studied using multi-objective optimization. Thus, the 1-stage CoMT–CAMD approach allows for efficient and holistic designs linking the molecular scale to economics.

Time-series aggregation for synthesis of distributed energy supply systems by bounding error in operational expenditure

Abstract For synthesis of distributed energy supply systems, the complexity of the mathematical optimization problem is commonly reduced by time-series aggregation. Today, the accuracy of the aggregation is measured in the time-series domain, i.e., by the capability of the aggregated time-series to represent the original time-series. In this paper, we propose a method for time-series aggregation measuring the accuracy of the aggregation in the domain of the objective function: The error is evaluated between the operational expenditure resulting from calculations using the aggregated time-series and the original time-series. An adaptive procedure selects representative time-steps for the aggregated time-series. It is shown that aggregation to few time-steps is sufficient to represent the original time-series with excellent accuracy in operational expenditure.

SPREAD - Exploring the decision space in energy systems synthesis

Abstract A method is presented to systematically analyze the decision space in the synthesis of energy supply systems. Commonly, synthesis problems are solved by mathematical optimization yielding a single optimal design. However, optimization is based on a model which never represents reality to perfection. Thus, the designer will be forced to revise parts of the optimal solution. We therefore support the design process by automatically identifying important features of good solutions. For this purpose, we analyze near-optimal solutions. To explore the decision space, we minimize and maximize both the number and the capacity of units while keeping the costs within a specified range. From this analysis, we derive insight into correlations between decisions. To support the decision maker, we represent the range of good design decisions and their correlations in the flowsheet of the energy system. The method is illustrated for the synthesis of an energy system in the pharmaceutical industry.

Rigorous synthesis of energy systems by decomposition via time-series aggregation

Abstract The synthesis of complex energy systems usually involves large time series such that a direct optimization is computationally prohibitive. In this paper, we propose a decomposition method for synthesis problems using time-series aggregation. To initialize the method, the time series is aggregated to one time step. A lower bound is obtained by relaxing the energy balances and underestimating the energy demands leading to a relaxed synthesis problem, which is efficiently solvable. An upper bound is obtained by restricting the original problem with the full time series to an operation problem with a fixed structure obtained from the lower bound solution. If the bounds do not satisfy the specified optimality gap, the resolution of the time-series aggregation is iteratively increased. The decomposition method is applied to two real-world synthesis problems. The results show the fast convergence of the decomposition method outperforming commercial state-of-the-art optimization software.

Rigorous synthesis of energy supply systems by time-series aggregation

Abstract A rigorous solution method is proposed for complex synthesis problems of energy supply systems with large time series. Time-series aggregation is used to iteratively tighten feasible solutions as upper bounds and best possible solutions as lower bounds. To initialize the method, the time series is aggregated to one time step. The lower bound is obtained by relaxing and underestimating the energy demands of all time steps which makes the corresponding equations redundant allowing for an efficient solution of the relaxed synthesis problem. The upper bound results from a restriction to an operation problem for the structure obtained from the lower bound solution. If the bounds do not satisfy the specified optimality gap, the resolution of the time series aggregation is increased and the solution process is restarted. The solution method is applied to an industrial real-world synthesis problem. The results show the fast convergence of the solution method outperforming a commercial state-of-the-art solver.

One-stage approach for the integrated design of ORC processes and working fluid using PC-SAFT

Abstract Organic Rankine Cycles (ORC) can transform low-temperature heat into electrical power. To ensure optimal use of a heat source, process and working fluid need to be tailored to the specific application. We present a one-stage approach for the integrated design of ORC process and working fluid, which identifies the optimal working fluid and the corresponding optimal process in a single optimization problem. For this purpose, a process model is combined with a modern thermodynamic model of the working fluid. The process model is based on equilibrium thermodynamics. The perturbed-chain statistical associating fluid theory (PC-SAFT) is used as physically-based thermodynamic model of the working fluid. The fluid model is extended by a group-contribution method based on PC-SAFT to enable Computer-aided molecular design (CAMD) of novel working fluids within the optimization. The full model enables the integrated design of process and working fluid. The optimization is an MINLP problem depending on two kinds of design variables: continuous process variables and integer variables representing the molecular structure of the working fluid. The one-stage approach is exemplified in a case study for a subcritical ORC process. The approach is shown to efficiently identify the optimal working fluid and the corresponding optimal process parameters. Integer cuts are employed to generate a ranked list of candidates.