Optimization of an Absorption-Based Biogas Upgrading and Liquefaction Process

The first attempt to improve battery performance through model-based design optimization was made by W. Tiedemann and J. Newman in 19751. They varied the electrode thickness and porosity and then observed the effects on the effective capacity. Newman later applied the reaction-zone model to maximize the specific energy of the system using the same varying and observing method2. V. Ramadesigan et al.3developed optimal spatially varying porosity for porous electrodes by considering ohmic resistance model in the electrode. They minimized the ohmic resistance in the positive electrode by varying porosity using control vector parameterization (CVP) method. They also introduced the idea of using graded electrode to further improve the performace. Since the introduction of the pseudo-2D (P2D) model by the Newman group, many efforts have been made in utilizing the P2D model in battery design. W. Du et al. applied an optimization framework based on surrogate method4. S. Golmon et al. performed the multi-objective and multi-design-parameter optimization problem with adjoint sensitivity analysis5 incorporating mechanical stress-strain relationship. S. De and his coworkers6 used a reformulated model, to perform simultaneous optimization of multiple design parameters. N. Xue et al. 7 applied the gradient-based algorithm framework to optimize the cell design. More recently, Y. Dai and V. Srinivasan8used a gradient-free direct search method to maximize the specific energy. Z. Du et al. studies the effects of various design parameters on thick electrode performance9. Most of the aforementioned optimization research, used the sequential optimization approach, also known as CVP. CVP takes the differential algebraic equation (DAE) system describing the battery physics, applies a certain nonlinear programming (NLP) solver to them, discretizes only the control variables, and solves the model. The only exception being the effort by Golmon et al which used an indirect approach. Note that as of today, global optimization cannot be guaranteed when CVP type approaches are used with P2D type models. In general optimization approaches can be classified as indirect and direct approach. In the direct approach there are two main categories – sequential and simultaneous approach. The simultaneous approach10, on the other hand, discretizes both the control variables and the design variables before solving the problem. When used for optimization, the DAE system will only be solved once at the optimal point, compared to the repeated numerical integration needed for sequential optimization. By using high order discretization scheme on both the state and the design variables, simultaneous optimization approach results in faster determination of the optimum with fewer time steps. Furthermore, this approach offers more flexibility over constraints on the state variables. Since the state variables are also discretized, it is possible to apply equality/inequality constraints on their internal values. In this work, we will first apply the simultaneous optimization approach to a resistance model similar to the one mentioned earlier3, and compare its performance with the sequential approach. We will also explore the application of the same optimization approach to the P2D model, and identify the challenges. It is viewed as a controversial topic in the literature wherein different authors disagree on the relevance of graded porosity for improved performance8. By using a simultaneous optimization approach and guaranteeing global optimization for convex problem statements, we hope to provide additional insights. Acknowledgements The authors are thankful for the financial support by the Clean Energy Institute at the University of Washington and the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy through the Advanced Battery Materials Research (BMR) Program (Battery500 Consortium).

This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.

Multidisciplinary design optimization (MDO) was performed on a helicopter rotor blade. The blade was modeled as a rigid flapping blade for dynamics; Blade Element Theory (BET) was the analysis approach to model the aerodynamic loading, and a simple linearly elastic hollowed rectangular section was the main structural component. MATLAB was used to solve the flapping differential equations and its Sequential Quadratic Programming (SQP) and Genetic Algorithm (GA) were used for the optimization. A Particle Swarm Optimization (PSO) routine was also tested. The optimization process consisted of three cases. The first case was a simple cantilever beam under centrifugal and an assumed bending loads. The optimization was performed using the SQP, GA, and PSO algorithms. The SQP resulted in the superior design with 75.45 compared to the GA's 87.1 and the PSO's 79.2, but a local minimum was present. The second case was an expansion of the first case by turning it into multidisciplinary problem. Aerodynamics was included in the design variables and objective function. Only the SQP algorithm was used and there was a reduction in hub vertical shear by 33.6%. The blade mass increased by 36.84%. The last case was an improvement to the second by creating a multiobjective problem by including the hub radial shear and the results were improved significantly by reducing the hub vertical shear by 34.06% and radial shear by 17.87% with a reduction of blade mass by 23.86%.

Performance analysis of support vector machine, Gaussian Process Regression, sequential quadratic programming algorithms in modeling hydrogen-rich syngas production from catalyzed co-gasification of biomass wastes from oil palm

For most engineering optimization problems, it is difficult to find the global optimum due to the unaffordable computational cost. To overcome this difficulty, a new sequential approximate optimization approach using radial basis functions is proposed to find the global optimum for engineering optimization. In the approach, the metamodel is constructed repeatedly to replace the expensive simulation analysis through the addition of sampling points, namely, extrema points of response surface and minimum point of density function. Optimization algorithms simulated annealing and sequential quadratic programming are employed to obtain the final optimal solution. The validity and efficiency of the proposed approach are tested by studying several mathematic examples and one engineering optimization problem.

Optimal Design of Heat Exchanger Networks by Using SQP Algorithm Based on GPU Acceleration

Recently, with the wide adoption of electric vehicles, transportation network has shown different characteristics and been further developed. In this paper, we present a new time-flow impedance function, which may be more realistic than the existing time-flow impedance functions. Based on this new impedance function, we present an optimization model for a mixed-mode traffic network in which battery electric vehicles (BEVs) and gasoline vehicles (GVs) are chosen. We suggest two approaches to handle the model: One is to use the interior point (IP) algorithm and the other is to employ the sequential quadratic programming (SQP) algorithm. Three numerical examples are presented to illustrate the efficiency of these approaches. In particular, our numerical results show that more travelers prefer to choosing BEVs when the distance limit of BEVs is long enough and the unit operating cost of GVs is higher than that of BEVs, and the SQP algorithm is faster than the IP algorithm.

Hydrogen has recently come into focus as potential future energy carrier. Distributing the required hydrogen in liquefied state offers several advantages and the demand for liquid hydrogen (LH2) will increase in the near future. The relatively low efficiency and high specific costs of today’s small hydrogen liquefaction plants is a drawback. The capacity of new liquefiers is therefore expected to increase considerably. The implementation of such large-scale hydrogen liquefaction plants requires highly efficient process designs with low technological risk and optimized total cost of ownership. For large-scale liquefaction processes, a specific energy consumption SEC close to 6 kWh per kg LH2 with a significant reduction in specific liquefaction costs were achieved with the recent process development and optimization carried out by Linde Kryotechnik AG in cooperation with the Institute of Plant and Process Technology of the TU Munchen [1, 2, 3]. The focus of this paper is set on the main aspects of equipment and process integration to be considered in the development of cost-optimized liquefaction processes. With regard to the optimal balance between technical readiness, efficiency and costs, the challenges as well as the opportunities in the upscaling of process equipment are discussed for a 100 metric tons per day (tpd) liquefier developed within this work. A special consideration is given to the design of cycle compressors, cryogenic expanders and plate-fin heat exchangers with catalytic ortho-to para-hydrogen conversion.

Liquid hydrogen will likely play a significant role in the future of energy as its applications are growing fast. Due to the low efficiency of the existing liquefaction plants, many studies are dedicated to the liquefaction processes. The accuracy of the simulations crucially depends on the fluid package and prediction of thermodynamic properties. Four common equations of state implemented in Aspen HYSYS used for hydrogen liquefaction, including PR, MBWR, SRK, and BWRS, are investigated to find their accuracy for estimating volumetric and calorimetric properties, that are essential for precise simulation of hydrogen liquefaction processes. Results show that MBWR is the best choice for hydrogen liquefaction processes, which are simulated by Aspen HYSYS. MBWR predicts thermodynamic properties of hydrogen and parahydrogen very well, in the whole range of temperature and pressure typically met in the liquefaction processes. The MBWR performs well in predicting enthalpy of ortho-para conversion too. Although PR performs better than SRK and BWRS, none of them yields reliable data in low temperatures, so they could not be applied for liquefaction processes. However, they may lead to desirable results for processes that experience higher temperatures range. An innovative, simplified hydrogen liquefaction cycle is developed to be able to capture the mere effect of EOS on essential performance parameters of the liquefaction cycles such as SEC and COP. Applying PR and MBWR to the developed cycle shows that PR compared to MBWR leads to 10% and 4% deviation in SEC and COP, respectively.

Comparison of SQP and AL algorithms for deterministic constrained production optimization of hydrocarbon reservoirs

Although Heat Exchanger Network (HEN) synthesis methods have been in existence for forty years, several issues still need to be resolved in order to obtain more realistic networks. Moreover, the complexity of the problem further increases when Heat Integration is performed at the Total Site level rather than at the process level. The usual approach is first to perform Heat Integration within the processes, and later to consider the non-integrated parts for Total Site Heat Integration. This sequential approach can omit some promising solutions and thus generally leads to worse results compared to the approach where the entire Total Site is synthesized simultaneously (Nemet et al., 2014). In order to obtain more realistic results, several practical constraints should be accounted for, such as transport between processes, optimal intermediate utility temperature level(s), pipeline design, heat losses and pressure drop (Nemet et al., 2015).In this work a synthesis of the Total Site is performed, which simultaneously considers integration within and between plants (at the plant and at the Total Site levels). For this purpose, the superstructure optimization approach is used. The superstructure contains all the possible matches for heat exchange within and between processes. Heat exchange between processes can be performed in the following ways: i) directly, by exchanging heat between the hot stream of one process and the cold stream of another process, or ii) indirectly, by utilizing an intermediate utility at optimal temperature levels (these are optimization variables). In both cases the transport of the heat carrier, either the process stream or the intermediate utility stream, is considered. Because there are severe nonlinearities and numerous options for heat recovery, the model is difficult to implement even for small-scale problems. However, when evaluating potential matches, it usually happens that most matches are either infeasible given heat transfer limitations, or unviable for economic reasons. A two-step approach is therefore proposed, where in the first step match alternatives are pre- screened with respect to infeasibility and unviability, and in the second step, a more detailed design is synthesized, taking into consideration the reduced superstructure obtained in the first step. The proposed two- step procedure yields results simultaneously at both the process and the Total Site levels, while also accounting for important properties such as heat losses, pipeline design and cost, temperature/pressure drop during transport between processes, and different types of heat exchangers.

Conventional liquefied biomethane (LBM) production plants consist of upgrading and liquefaction processes. Commonly, the captured CO2 during biogas upgrading is emitted into the atmosphere. One alternative, to produce more LBM, is to combine the conventional LBM production plant with the Power-to-Gas concept. Within this context, green H2 produced from renewable electricity can react with the CO2 in the biogas mixture, producing additional CH4. The present study evaluated the feasibility of integrating methanation with conventional LBM production plants. The performance of the proposed process designs was assessed through exergy and cost analysis considering detailed models. The results illustrated that integrated direct biogas methanation was superior to methanation of captured CO2. The integrated scheme with direct biogas methanation increased the LBM production by 52.2 % compared to the conventional LBM production plant but with lower exergy efficiency. It was indicated the feasibility of the integrated scheme through direct biogas methanation was highly dependent on the price of H2. A H2 price of 1.27 USD/kg H2 was required to produce LBM at a similar price as the conventional LBM production plant.

For current sequential quadratic programming (SQP) type algorithms, there exist two problems: (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using e-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented. This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.

Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow

Thermal placement optimization of multichip modules using a sequential metamodeling-based optimization approach