عدم قطعیت و تجزیه و تحلیل حساسیت جهانی در طراحی نیروگاه های تولید بخار مستقیم سهموی برای کاربردهای دماهای فرآیندی

A non-deterministic uncertainty and global sensitivity analysis, based on the Sobol’s method, is developed for a parabolic-trough direct steam generation plant for process heat applications. The objective of this work is to evaluate the robustness of the simulation-based design stage, identifying major modelling sources of uncertainty, as well as quantifying and ranking the relevance of its contribution to the system performance output uncertainty. An important finding obtained from the case considered in this work is that, although the complex characteristics of the direct steam generation two-phase regime introduces additional sources of uncertainty into the low-level modelling stage, the propagation and impact of this uncertainty to system level energy and economic-based design indicators is largely mitigated by higher-level input factors uncertainty. The economic design indicator uncertainty and global sensitivity analysis shows that the lowest relative output uncertainty is obtained by the levelized cost of energy with a coefficient of variation of 4.3%; followed by payback time with 12.1%. The largest contributors of input factors uncertainty to the levelized cost of energy uncertainty are the market discount rate and boiler efficiency, showing total sensitivity indices of 0.67 and 0.23, respectively.

The increasing interest in solar industrial process heat is demonstrated by the growing number of recent studies in market potential [1], [2], [3], [4], [5] and [6], as well as by ongoing efforts to develop suitable collector technology to efficiently address that potential [7], [8], [9], [10] and [11]. In the industrial sector, the most commonly used heat distribution medium is steam, due to its high energy density, simplicity to control and distribute, and the already extensive experience gained in its handling [12]. There are, at present, several available solar system configurations that can generate saturated steam at low pressure – the unfired boiler, indirect steam generation and direct steam generation systems [12]. These configurations have various relative advantages and drawbacks depending on the perspectives of the particular criteria, such as energy efficiency, integration simplicity, dispatchability, environmental issues, safety, and economic performance. Nonetheless, out of the options available, direct steam generation (DSG) is considered to be one of the most promising possibilities for lowering steam generation costs using solar systems. Previous scientific studies report that direct steam generation has the potential of lowering energy costs by up to 25% when compared to the more extended unfired boiler configuration [13]. These improvements are achieved by simplifying integration, an increase in solar field efficiency, fluid cost reductions and others – which translate into greater plant efficiency and lower capital costs. From a strictly thermodynamic point a view, integration with direct steam generation has the benefit of not requiring any additional temperature differential in the solar field outlet in order to overcome the unfired boiler pinch point, and hence has a lower outlet temperature and higher solar field efficiency. Moreover, its return piping can be directly connected to the pipe with lower condensate return temperatures, thus providing a lower return temperature than the unfired boiler configuration (which is restricted due to the heat exchanger thermodynamic integration between the solar and industrial plant). Another advantage is that the higher convection coefficient in the two-phase regime provides better heat transfer conditions between the fluid and the absorber tube, thus improving the collector’s thermal efficiency. Several solar collectors are currently capable of generating steam. However, according to the studies performed by [5], [13] and [14], parabolic-trough collectors obtain the lowest energy costs for the medium temperature levels required by industrial processes. Recent studies of direct steam generation with small parabolic-trough collectors conducted by [15], [16] and [17] assessed the influence of the main operational variables, identifying important design restrictions, as well as demonstrating the suitability of small parabolic-trough collectors for direct steam generation from a thermo-hydraulic perspective. At the experimental level, the works by [18] and [19] confirmed the technical feasibility of small parabolic troughs for integration to a steam consumption process. These recent milestones show that research in DSG is providing important contributions towards commercial introduction and a wider degree of industrial acceptance. Nevertheless, the physical mechanism behind direct steam generation still places special challenges on solar energy engineers when compared to simpler one-phase systems; this is because of the more complex characteristics of two-phase flow regime modelling. For example, during the phase-change transition in the solar field, there is a pronounced thermo-hydraulic coupling between temperature and pressure. For this reason, the correct assessment of pressure losses becomes a more determinant factor in performance assessment – given that they not only affect hydraulic performance but indirectly affect thermal performance, as well. Added to this, there is a more prominent heat transfer coefficient difference from off-test conditions than in the liquid phase, leading to increasing relevance of the local flow regime and phase change conditions. Furthermore, in the two-phase regime, there is a strong coupling between pressure loss and local steam quality. Finally, correlations available in the scientific literature for two-phase regime modelling usually carry more uncertainty due to the higher complexity and multitude of physical phenomena involved. In summary, all these factors may (or may not) induce relevant uncertainty in the model output since the impact of a specific input factors uncertainty is controlled not only by its deviation but also by the sensitivity of the model for that particular variable or parameter. Consequently, in order to explicitly assess and evaluate the relative importance of each input factor, a probabilistic non-deterministic approach along with a global sensitivity analysis is proposed in this work. The main objective is to provide additional information for the preliminary design stage of a solar industrial solar plant, as well as to help strengthen the validity and robustness of deterministic studies. A review of the existing literature shows that the vast majority of solar thermal energy modelling and analysis still addresses the problem using local one-factor-at-a-time (OAT) approaches; very few use non-deterministic global methods. There are a few examples of non-deterministic approaches applied to other research areas – the recent works by [20], [21] and [22] identifying and outlining possible methods to incorporate uncertainty into solar thermal electricity performance analysis. Another example is the work by [23] who studied the influence of solar irradiance uncertainty on the economic performance of a solar thermal electricity plant in Chile. Other examples are the works of [24] and [25], which performed uncertainty analyses on solar domestic hot water cases. Nevertheless, despite the proven capabilities of non-deterministic modelling and global sensitivity analysis methods, there are to date, and to our knowledge, no known global sensitivity, or uncertainty, analyses performed on DSG solar systems for industrial process heat. In particular, no works were found in scientific literature addressing the problem of the specific uncertainty originating from the particular characteristics of two-phase regime modelling. In the present work, a global sensitivity and uncertainty analysis is developed for the thermo-economic performance prediction of a DSG parabolic trough solar plant in an industrial process heat application scenario. The quantification of the uncertainty of input factors is built on recommended methodologies [26], and realistic probabilistic functions are derived from data available in the scientific literature, reported experimental data, and economic prediction studies. A reference boundary scenario with representative demand, climate, and economic boundary conditions is considered. Special care is devoted to analysing the uncertainty impact of specific thermodynamic factors closely related to the physics of DSG on the technical and economic performance of the solar plant. The main goals and findings of the present work are quantifying the robustness and reliability of the simulation-based design of DSG process heat solar plants, identifying major modelling bottlenecks, and rank the relevance of input factors uncertainty contributions to the overall system performance uncertainty. Section 2 presents the methodology and algorithms. In Section 3, a description of the model and scenario conditions is developed. In Section 4, the input factor probability distributions are developed. In Section 5, the results of the sampling process and model evaluations are shown. In Section 6, the uncertainty and sensitivity analyses are developed and, in Section 7, certain final conclusions are summarized.

A variance-based uncertainty and global sensitivity analysis has been developed for a parabolic-trough direct steam generation plant for industrial process heat, based on the Sobol’s method. Uncertainty measures and total sensitivity indices of major energy- and economic-based solar plant design indicator sources of uncertainty were identified, quantified and ranked. The results show that although several low-level modelling factors of parabolic-trough DSG solar plants carry relatively large magnitudes of uncertainty, most of them show a negligible influence on integrated higher-level output design indicators after being propagated throughout the model. This is a favourable result from a robustness point of view. In particular, it has been verified that, in the case analysed, the additional uncertainty introduced by two-phase regime modelling is mitigated by larger sources of uncertainty when propagated to output variables at higher data analysis levels. These results are closely associated with the design characteristics and operating conditions of the considered collector, which, because of its large diameter and low specific pressure losses, minimizes the effect of the thermo-hydraulic coupling, thus reducing sensitivity to the uncertainty of several input factors. Nevertheless, a higher degree of sensitivity to DSG factors is expected for parabolic-trough collectors with smaller absorber diameters, especially at lower-level modelling level outputs such as in operational variables - given that, in these cases, thermo-hydraulic coupling is stronger, hence hydraulic uncertainty has a more pronounced impact on the thermal level. Furthermore, at this data flow level, two-phase input factors uncertainty is not being mitigated by higher-level sources, thus its impact is expected to be larger. For this reason, additional studies in these particular areas are advisable and recommended. The results obtained show that, for energy-based design indicators such as solar fraction and plant efficiency, the largest uncertainty contributors are the collector characterization and the climate data; whilst for economic-based indicators, the ranking of uncertainty contribution shows a strong dependency on the scope and time horizon of the particular output variable. Therefore, a key finding in this work is that the selection of a particular design indicator has a very significant influence on the relative importance distribution of the sources of uncertainty in the design stage, leading to different combinations of complexity, completeness, and robustness. Consequently, the ranking of input factors proposed in this work provides an added measure for a more judicious selection of design indicators by including robustness to different sources of uncertainty as an additional criterion. The present work shows that non-deterministic approaches provide a valuable additional source of information for the simulation-based design stage of industrial process heat solar plants, which can be used to help strengthen and reinforce the validity and robustness of deterministic-based studies.