**1. Introduction**

The sustainable development of modern society requires the efficient energy usage to limit the depletion of fossil fuels resources and minimise the environmental hazard of their combustion, which is leading to the generation of harmful emissions and, especially, CO2 and greenhouse gases. It is the most important for industries with high levels of energy involved in production processes. One of such processes is the synthesis of such valuable product as ammonia, which is widely used in different industrial applications, such as the production of fertilisers, fibres, polymers and plastics, papers, acids and explosive materials [1]. It is also can be used as a carbon emission-free carrier of hydrogen, offering a high energy density that could be used in a system for energy transport, storage and power generation [2].

Up to 72% of industrial ammonia production worldwide is based on the steam reforming of methane from natural gas [3]. It is mainly performed using the Haber–Bosch process, requiring gaseous nitrogen from air and hydrogen. Their mixture is forming syngas that is moving through the catalyst at temperatures up to 600 ◦C and pressures up to 32 MPa. The synthesis reaction is exothermic, with the generation of large amounts of heat energy that have to be removed with a good cooling system. This industrial process is responsible for consumption up to 5% of natural gas global production, accounting for nearly 2% of the world's energy generation and emitting about 1% of greenhouse gases [4].

The practical industrial realisation of this process is performed mostly with reactors of three different types: reactors with direct internal cooling, reactors of adiabatic quench cooling and indirect adiabatic cooling. [5] reports a comparison of these reactor cooling systems, showing the advantage in the efficiency of the internal direct cooling system. An exergy approach for modelling and optimisation of an industrial ammonia synthesis unit was presented in [6]. It was concluded that the biggest part of exergy destruction is happening in the ammonia reactor. The exergy study of two concepts in ammonia synthesis loop configurations is presented in [7]. It includes an adiabatic reactor with three stages including intermediate quench cooling and indirect-cooled reactor. It is concluded that the major equipment (reactor, heat exchangers) must be accounted for first for improvement of the overall design with consideration for the implementation of heat integration.

In recent years, to reduce fossil fuel usage and the impacts on the environment of conventional ammonia production, green processes of ammonia production with the use of green hydrogen have been investigated. The comparative study of such production schemes, presented in [8], has shown the importance of maximising the heat recovery of the overall system that requires efficient heat exchangers. The use of ammonia synthesis combined with nitrogen production and power generation is discussed in [9]. The uses of solar energy in ammonia production and optimisation for energy, cost and carbon emission are studied in [10]. The thermochemical storage systems of solar energy based on ammonia are investigated in [11]. The efficient and compact recuperative heat exchangers are needed to increase heat recuperation and save energy in all these processes involving ammonia synthesis. The principles of heat transfer intensification are the major tool in developing the construction of such heat exchangers [12].

Plate Heat Exchangers (PHEs) are one of the high-efficiency types of compact heat exchangers with intensified heat transfer. The main construction features and principles of operation and design for PHE have been well discussed in publications (see, e.g., [13]). The most known is plate-and-frame PHE, which was initially developed and used in food production and later confirmed its efficiency in many different applications. It is proved in many research results; for example, in [14] it was shown that, for water to water heat transfer, plate-and-frame PHE has about a 13% lower cost than a tubular heat exchanger at the same position. The high efficiency of PHE is confirmed at the chemical industry [15], in the process of the CO2 capture [16], for waste heat utilisation from exhaust gas [17]. However, the range of operating conditions for plate-and-frame PHE is limited by pressure below 25 bar and a temperature not more than 180 ◦C, mostly by the presence of elastomeric gaskets. For severe working conditions with aggressive fluids, the cost of gaskets from sophisticated elastomers can substantially increase the cost of the whole PHE.

To increase the field of PHE applications in different industries by limiting the use of elastomeric gaskets, constructions of the brazed (BPHE) and welded (WPHE) types of PHE were developed. In WPHE, the sealing of passages between plates is made by welding, allowing an increase of the working temperatures and pressures significantly. Currently, different types of WPHE are developed and fabricated by PHE producers. The most frequently used are Plate-and-Block (Compabloc) PHE and Plate-and-Shell HE (PSHE), compared in [18]. Now, WPHEs finding their way in many applications, e.g., more than 750 Compabloc heat exchangers were installed at different positions in the oil refining industry [19]. The welded construction allows an increase in working temperatures below 400 ◦C and pressure up to 42 bar.

The main feature of Compabloc WPHE is the use of crossflow of streams in one pass and the overall counter-flow arrangement in a whole heat exchanger. Such a construction feature is also used in WPHE, specially developed for operation inside the shell of the column for ammonia synthesis at temperatures up to 525 ◦C and pressures about 320 bar [13] (pp. 79–80). It consists of round, corrugated plates, like the one shown in Figure 1. The plates are produced with different diameters to fit the columns, with inside diameters from 600 to 1200 mm. In the manufacturing process, plates are collected and welded together to form criss-cross flow channels with multiple contact points at the edges of corrugations. It makes a robust construction capable of withstanding high-pressure difference between heat-exchanging streams. The created round block of welded plates is equipped with welded collectors and baffles that are organising the multi-pass flow of heat exchanging streams through the channels systems. There is a crossflow of streams in an individual pass with globally countercurrent flow arrangement in WPHE as a whole. From the point of flow distribution in a channel and the pressure drop in it, such an arrangement has an advantage compared to plate-and-frame PHE where the flow is distributed from a relatively small port to the full width of the channel. It involves additional pressure loss in that distribution zone that can be avoided with crossflow of streams in one pass of considered WPHE. However, the crossflow can involve a considerable reduction in the effective mean temperature difference between streams, and the deterioration of heat transfer effectiveness, the overall countercurrent flow in multi-pass WPHE is organised to limit this effect. However, the influence of crossflow in individual passes has to be considered accurate enough for an engineering applications design of WPHE.

**Figure 1.** The plate of WPHE for an ammonia synthesis column.

The convenient way to account for crossflow in a heat exchanger is the use of the relationship between effectiveness, ε, of heat transfer and the number NTU of heat transfer units. Equations of such a relationship for idealised flow models of both fluids—mixed and unmixed—and one fluid mixed, and another unmixed, are presented in the book [20]. But in real heat exchangers, such a relationship can differ significantly, depending on the heat exchanger type and the level of flows mixing in its channels. This phenomenon was investigated by a number of researchers. The case of two unmixed fluids with the development of approximate equation for it was studied by Triboix [21]. For compact heat exchangers with different and complex finned surfaces, a hybrid method was proposed in [22]. The survey of recent developments on heat transfer in crossflow tubular and tubes-and-fins heat exchangers is presented in [23]. For crossflow tubular heat exchangers with different tube passes, closed-form relationships of temperature effectiveness are proposed by Magazoni et al. [24]. The results of the study of multi-row cross flow tubes-and-fins heat exchangers are reported in [25] and approach to calculate overall heat transfer coefficient for water–air tubes-and-fins heat exchanger in [26]. The results of the parametric study of cross flow heat exchangers with heat transfer enhancement by external and internal recycles were reported by Luo [27]. For compact diffusion-bonded crossflow heat exchangers, the results of theoretical and experimental study of heat transfer were reported in [28], with further

development in [29]. In their study of the cabinet cooling system, Borjigin et al. [30] have found that, at certain conditions with crossflow PHE, the system has lower thermal resistance and better cooling performance with counter-flow PHE.

Presently, there are very few published data accurate enough to perform design and optimisation of the considered WPHE type for the engineering applications. The correlations obtained for counter-flow PHEs need to be validated and adopted for the considered type of channels with the crossflow and variable angle of corrugations on the surface of forming round channel plates. There are no data allowing adequate estimations of the level of fluid mixing in PHE channels for the use of published relations for the crossflow correction factor, depending on the level of fluids mixing in channels.

The aim of the present paper is to develop a method of modelling and optimisation, which considers WPHE for an ammonia synthesis column with round plates that is accurate enough for engineering applications. It is based on mathematical modelling and experimental data on heat transfer and pressure drop in WPHE channels. Reported here are the results of an experimental study, in laboratory conditions, of the thermal and hydraulic performance of a one-pass crossflow model of WPHE for ammonia synthesis column. On that basis, the mathematical model of multi-pass WPHE is developed, and its validation in industry performed. After that, the use of the model for optimisation of WPHE for specific conditions of its operation is described.
