**1. Introduction**

Cogeneration and polygeneration systems are an essential part of industrial production of materials and energies, consuming or generating heat, electricity, mechanical, and chemical energy [1,2]. Ambitious efforts of national and European institutions to reduce greenhouse gases emissions and to ensure sustainable industrial production [3–9] at the same time cannot be successfully met without increasing material and energy efficiency of the industry [10–13] by simultaneous energy, economic, environmental, and risk and safety optimization [14–16] of existing industrial cogeneration and polygeneration systems [17,18].

Efficient steam production, and its transport and use for both process heating and polygeneration purposes, has been targeted on various complexity levels in numerous recent studies [19–38]. Starting with techno-economic studies optimizing the efficiency of a single equipment unit [24,27,30,34,35], through steam consumption optimization in a single production unit [25,32,38,39], and cogeneration potential exploitation [19,33,36,40,41] to total site heat and power integration [20–23,28,33,37,42], the goal is always to reduce operational expenses, improve steam system stability, and decrease fuel

consumption in industrial plants. Steam system topology and the impact of pressure and heat losses from steam pipelines on optimal cogeneration system sizing and operation has been addressed in several papers [22,37,43–45], but most studies consider neither o ff-design operation of steam turbines nor variable steam pressure levels as important aspects in the optimization procedure. A systematic method comprising characteristics of a real steam system operation [35,46] (variable pipeline loads, steam pressures, and temperatures) as well as real process steam/work demands has the potential to fill the knowledge and experience the gap between the modeling approach in utility systems' optimization and real steam system operation.

Process steam drives are important steam consumers in heavy industry [20,31,34] and play a significant role in the design and operation of complex steam networks. The most common driven equipment includes compressors, pumps, and fans (blowers) [34,38,47]. The steam turbines used can be of simple condensing, backpressure, or of a combined extraction condensing type [36]. Steam consumption is influenced by several factors that include the actual steam inlet parameters, steam discharge pressure, actual turbine revolutions, as well as the shaft work needed, which varies according to the process requirements. Process compressors driven by steam turbines are standard equipment of ethylene production and gas processing and fractionation plants [38,47], and they are also frequently used in compression heat pump-assisted distillations [48–51]. Thus, they are deeply integrated in the process. The shaft work needed depends on several process parameters, including (but not limited to) the distillation feed amount and composition, desired product quality, and column and compressor design parameters. This highlights the pressing need to develop a robust method for process steam drive sizing which would incorporate not only the real steam-side condition variations but also the process-side shaft work variations. Improper sizing results either in limited shaft work delivery (undersizing), causing possible process throughput limitations, or ine fficient steam use (oversizing). Moreover, the steam drive design and operation have to be optimized with respect to the whole steam system, always taking into account the marginal steam source, its seasonal operation variations [52], and the possible steam pipeline capacity constraints [26,43].

Given all the prerequisites, it is only natural that examination and precise evaluation of such complex process parameters poses a challenge which can hardly be faced successfully without employing robust simulation environment. For almost two decades, researchers have strived to combine the colossal computing capacity of the Aspen Plus ® simulation engine with the exceptional data-processing capabilities of the MATLAB ® software [53,54]. Several papers have been published, mostly focusing on multi-objective optimization [55–59] or automation problems solution [60,61]. Unfortunately, only scarce details regarding the chosen approach can be found. Hence, the perspective to close this gap in knowledge remains particularly attractive.

The contribution of this paper to the field of knowledge is twofold:


Table 1 provides a comparison of the key parameters and characteristics of relevant recently published methods with the proposed method, all of them aiming at: 1. Maximization of the cogeneration potential exploitation; 2. optimal process steam drive sizing; and 3. optimal steam vs. electrodrive use. As is seen in Table 1, the relevant methods are focused mostly on steam-side modeling and optimization, while the proposed method presents a coupled steam- and process-side modeling approach. Moreover, several of the relevant methods do not incorporate such important aspects as the varying inlet steam parameters or shaft work requirements and implement fix turbine and driven equipment e fficiencies instead of considering their variations in the real operation. As documented

on an industrial case study, failure to implement the real operational parameters of a system leads to steam drive undersizing and, consequently, to limited process throughput.

The e ffect is that the more pronounced, the farther the process drive is located from the main steam pipeline. Further findings from the industrial case study include the fact that the incorporation of a steam drive into an existing steam network can significantly a ffect its balance (and, thus, its operation) and thus create a new operation bottleneck, or remedy its existing ones. Furthermore, the marginal steam source operation mode is also a ffected, which has to be considered when evaluating the economic feasibility of such an investment proposal.

Paper organization is as follows: Part 2 presents the proposed complex steam drive sizing method and is subdivided into process-side and steam-side model subparts. Following that, part 3 introduces an industrial case study with the description of the existing system layout, proposed change, available process data, and their processing, including initial analyses and their results serving as additional model input parameters. Part 4 presents the calculation results, including a comparison of the presented steam drive sizing method with several others (included in Table 1), and evaluating the economic feasibility of the proposed system change. Discussion is followed by a concise conclusion part summing up the novelty and significance of the presented method and the key findings extracted from the industrial case study results.


**Table 1.** Comparison of key parameters of the proposed method with recently published papers. Legend: BE = balance equations, Calc. = calculated, N/A = not

## **2. Process Drive Sizing Method**

#### *2.1. Equipment Operation Assessment and Modeling*

#### 2.1.1. Heat Pump-Assisted C3 Fraction Splitting

Heat pump-assisted distillation is a good example of incorporating a steam drive into an industrial process; thus, it was chosen for illustration. In such systems, overhead distillate vapors from a separation column are compressed and subsequently condensed in the column reboiler [51,62]. For this type of heat pump to be applicable, the separated components have to be of similar boiling points [63]. However, this leads to a relatively low driving force in the reboiler; thus, to deliver the required power input, the vapor throughput needs to be su fficiently high. Hence, stable operation of the heat pump compressor is of the uttermost importance. Amongst the compressor drives, steam drives (turbines) are the most usual. These are normally shaft-bound with the compressor and, therefore, their correct sizing is just as important as that of the compressor itself. In the case of steam turbines, however, the whole sizing process is more complicated as steam quality fluctuations and overall steam network properties have to be considered.

A typical arrangemen<sup>t</sup> of a heat pump-assisted distillation is provided in Figure 1. Here, a propane– propylene mixture is split into separate components of high purity (>99.6% vol.). The energy necessary for the separation is provided by a condensing steam turbine.

**Figure 1.** Process scheme. Legend: BL = battery limit, cond. = condenser, CW = cooling water, C3A = propane, C3E = propylene, frac. = fraction, HPS = high-pressure steam, PP = polypropylene, prod. = production.

To design (size) a process drive correctly, the process itself must be understood thoroughly. This encompasses not only the physical structure of the system but also the physicochemical and mechanical non-idealities and, most importantly, over-time variations in feedstock quality and mass flow [64]. To provide the most authentic results, the model was constructed as follows:


The model briefly described above was, due to its complexity, constructed in the simulation environment of the Aspen Plus® software which provided fast-to-obtain and reliable results. Yadav et al. [67] provided a comprehensive tutorial on utilizing Aspen Plus® potential in distillation column operation simulation. For the separation column, the RadFrac model was chosen, which stands as a universal rigorous model for multi-stage component separation. Each of the three heat exchangers was modeled using a short-cut method (HeatX model) which proved satisfactory for the cause. Both the compressor and the turbine were modeled using the Compr model [68,69], though individual approaches differed significantly.
