Optimizing Large-Scale Inorganic Processes: Model-Based Digital Design of RH-DS Apparatus

Abstract

The design of industrial installations using digital design techniques (digital twin), aligned with the concept of Industry 4.0, provides a tool to optimize maintenance costs, process gas emissions, energy consumption and to reduce the risks associated with production testing. Modern manufacturing plants conduct chemical processes by combining production experience with model-based research. Analyzing processes using advanced digital techniques can replace traditional methods of technological process balancing. The methodology based on the digital twin already serves as a holistic system of process connections, supporting production, research and development, production planning, and quality control. This paper presents the digital design, optimization, and comparison of process data obtained through simulations for two different types of ammonia recovery units in soda ash production using the ammonia–soda process. Using specialized modeling software and relying on historical data, engineering assumptions, and new concepts, virtual models were created in which the material and thermal balances of the process were simulated. This research is divided into two stages. In the first stage, a model-based approach and model optimization techniques are presented, while in the second stage, the preparation of models of the distillation installation is presented, and the influence of various structural parameters of the equipment on the temperature profile and gas flow rate in the ammonia recovery section is discussed. The process of the research method, based on simulations in a virtual environment, allows for evaluating the implementation potential of the proposed concepts, optimizing process parameters, and redefining the approach to conducting chemical processes. A series of simulations conducted in studies on ammonia recovery indicated a potential increase in gaseous ammonia recovery by up to 14.09%, taking into account the type of distillation apparatus or the height of the packing section.

1. Introduction

Redefining the conduct of chemical processes with the use of digital twins is one of the key elements of Industry 4.0. The two most advanced concepts in Industry 4.0 are the Industrial Internet of Things (IIoT) and the digital twin. The digital twin technology enables Industry 4.0 to replicate or represent physical devices, processes, or individuals in cyberspace with exceptional precision [1,2,3,4,5,6]. The term “Digital Twin” first appeared in the preliminary version of NASA’s technology roadmap in 2010 [7]. In NASA’s plans, the digital twin was also referred to as the “leader of the virtual digital fleet”. NASA was the first organization to create a definition for the digital twin, describing it as an integrated, multi-physics, large-scale, probabilistic simulation of a vehicle or system that uses the best available physical models, sensor updates, and fleet history to reflect the life of its “flying twin” [8,9,10]. The definition that connects most descriptions of the digital twin (DT), aside from being a virtual representation of a physical object, is the bidirectional transfer or sharing of data between the physical counterpart and the digital model. This data exchange includes quantitative and qualitative information (related to material, production, process, etc.), historical data, environmental data, and, most importantly, real-time data [11,12,13]. While definitions of the DT typically do not specify its lifespan, some authors consider the digital twin a “cradle-to-grave” model, meaning it can be applied throughout the entire lifecycle, from the creation of a product to its disposal. This holistic approach emphasizes the continuous interaction between the physical and digital realms, allowing for real-time updates, monitoring, and optimization across the product’s lifecycle [14,15]. The use of digital twins offers several benefits, including the following:

• The more accurate determination of the product lifecycle;
• A reduction in costs associated with building prototype installations (or multiple prototype installations), which can also be time-consuming;
• The ability to simulate experiments that, due to safety concerns or practical limitations, cannot be conducted at the laboratory or industrial scale;
• The real-time monitoring, analysis, and forecasting of potential issues, which supports critical decision-making during emergencies and helps to reduce the risk of failures and losses;
• The optimization of various components within industrial plants, including process parameters and raw material consumption indicators, across the entire process scale, which may consist of multiple interconnected units.

Digital twins assist in the analysis and optimization of processes. To fully leverage their potential, it is necessary to input essential data into the models, which can be challenging in the initial stages of digital design. The required data must be collected and maintained throughout the entire product lifecycle and can also be shared for other tasks. Data are typically available in various formats and across different endpoints. The process of collecting and integrating these data with existing information systems can be complex due to the large volume of data involved. Moreover, the structures and frameworks for Digital twins are not yet standardized, which adds to the challenge of implementing this technology effectively [16,17]. An additional concern related to digital twin technology involves products with long lifecycles, such as buildings, aircraft, ships, machinery, and even entire cities. The lifecycles of these products are significantly longer than the validity of the software used for designing or simulating digital twins, as well as for storing and analyzing data for a digital twin [18]. This creates a substantial risk that, in the future, the formats used in the software may become obsolete or locked in with the same vendor due to new software versions or proprietary tools [19,20]. Process modeling techniques using equation-oriented modeling platforms are gradually replacing traditional methods of evaluating new process concepts at the laboratory scale or by building pilot plants. Digital process design enables the creation of sophisticated, efficient mathematical optimizations for individual processes or entire process schemes, leading to economically viable process models. Modern industry is redefining chemical process concepts by optimizing the use of raw materials or even adopting new, less environmentally harmful materials at lower costs. A digitally designed factory serves as a tool for safely testing even the most innovative assumptions through an unlimited number of simulations. Several industries, including manufacturing, have embraced this concept in their digital production efforts, creating opportunities to integrate the physical and digital worlds fitting the concept of the “digital counterpart of a physical product” introduced by Michael Grieves at the University of Michigan in 2003 [21,22]. Chemical process modeling is a modern technique for data analysis, experiment design, parameter estimation, and the validation of new (or modified) processes, along with new equipment concepts, within virtual production units or even full-scale virtual production lines. This approach allows for effective experimentation in a predictive digital environment with high accuracy. Specifically, the modeling of RH-DS apparatuses—where the RH section functions as a preheater for the distiller, and the DS section serves as the distiller—used in distillation installations can be highly beneficial. The RH section can be modeled as a scrubber unit with packing or as a bubble-cap tray apparatus, enabling accurate and predictive experiments. Minimizing losses and increasing ammonia recovery in the distillation section using digital twin technology represents a novel approach to analyzing soda production via the Solvay process. The research described in this publication focused on the preheater section of the distiller, known as the RH. Numerous modifications of this apparatus in a digital environment allowed for a broader assessment of the impact of equipment design and packing size on increasing the load of post-filtration liquid, thus boosting daily soda production while simultaneously enhancing ammonia recovery. The simulation results presented in the digital environment also enabled the evaluation of the maximum packing level in the RH section, beyond which ammonia recovery ceased to be efficient. Distillation is one of the most commonly used unit operations in industry. It is a complex, multivariable, nonlinear dynamic system, with the degree of nonlinearity determined by the range of operations within the distillation process. The complexity of distillation columns can vary from simple binary separations with a constant molar excess to more challenging multi-component, non-ideal separations involving chemical reactions and multiple feed and side streams. For a column to operate efficiently, it must not only be well-designed but also be supported by effective process control strategies. Maintaining the required controlled variables is essential in the face of various disturbances that commonly occur in industrial settings [23,24]. As industrial processes, such as those occurring in packed distillation columns, have become more integrated and flexible, the performance requirements have increased, leading to more complex operational and control challenges. The difficulty in adequately controlling a distillation column arises from its nonlinear dynamic behavior, which exhibits an asymmetrical nature. As a result, controllers may require frequent tuning to compensate for changes in the column’s dynamics as operating conditions fluctuate. Considerable effort is therefore directed toward finding control strategies that offer better performance than conventional control methods [25].

Conventional methods for controlling technological processes, based on proportional–integral–derivative (PID) controllers, are inadequate for more complex systems. Modern approaches to process control emphasize the integration of advanced technologies such as artificial intelligence (AI), the Internet of Things (IoT), model predictive control (MPC), big data integration, and digital twins.

In this study, the digital twin modeling software gProms Process 2023.2.0 was used to develop models as a set of equation-oriented stages for simulating the ammonia recovery process in the RH-DS apparatus, allowing for the determination of equipment and process parameters that could be implemented in a production facility. The use of chemical process modeling within the gProms software environment has been discussed in numerous publications [26,27,28,29,30,31,32,33]. However, to the best of our knowledge, studies using gProms Process 2023.2.0 for modeling distillation columns in the ammonia soda production process have not yet been conducted. This article presents a case study on modeling two types of RH-DS apparatuses (with the RH section as a packed scrubber and as a bubble-cap tray apparatus), along with a comparison of preliminary simulation results aimed at determining the optimal parameters for ammonia (NH₃) recovery. A typical scrubber apparatus (heat and mass exchanger) consists of a column of a specific height corresponding to the given capacity of the apparatus, containing scrubber packing (in the analyzed production cases, the packing consisted of Pall rings with a diameter of 80 mm). The packing is placed on supporting grids in layers of 3 m and 12 m. To separate the liquid phases, a distribution tray is placed above the upper scrubber layer, where the liquid is introduced into the desorption process. In some devices, additional distribution trays are placed between the scrubber layers to improve the scrubber’s performance. The main difference between a scrubber apparatus and a bubble-cap tray apparatus is the replacement of the Pall ring packing with sieve trays (non-weir trays with holes and trays with holes and weirs). Key parameters analyzed include temperature, pressure, post-filtration liquid flow, and heat and mass transfer characteristics, which are influenced by the apparatus design. The RH-DS distillation column is divided into two gas-coupled sections (with liquid connection occurring only indirectly through the lime mixer—the prelajmer, PLM—where slaked lime decomposes NH₄Cl present in the post-filtration liquid):

(a)

Upper section (RH): This section, known as the preheater of the distiller (reschofer), is where volatile ammonium salts (such as ammonium carbonates) decompose. It is typically configured as a packed scrubber divided into segments or as a bubble-cap tray apparatus. The design choice influences the efficiency of heat and mass transfer within the section.

(b)

Lower section (DS): This section, referred to as the distiller, is where the recovery of ammonia from the remaining salts occurs. It is usually designed as a bubble-cap tray apparatus to facilitate the separation process.

Digitally prepared models of real apparatuses enable unrestricted modifications to existing production systems and an infinite number of simulations for new concepts. This approach provides data essential for evaluating the feasibility of implementing new solutions. Each time, the data obtained from digital process simulations are correlated with process data collected in archiving programs, which allows for the analysis of both current and historical data (data from automatic analyzers and data from laboratory analyses). The main parameters analyzed in the industrial installation include the flows, temperatures, and concentrations of process gasses (gas concentrations measured using Orsat apparatus or online methods) and analyses of fluids involved in the process (direct alkalinity determination in ammonia solutions, ammonia determination using the distillation method (total titration), the determination of chloride content in ammonia solutions using Mohr’s method, CO₂ determination, the performance assessment of column filters, the determination of soda content in ammonia condensates, the determination of iron compounds expressed as Fe₂O₃ using the thiocyanate method, and the determination of HCO₃⁻ and CO₃²⁻ in filter wash water). By precisely defining process changes within the digital twin environment, the risks associated with conducting technological tests are minimized. This reduces process-related losses to zero by eliminating the need for shutting down production lines during tests and facilitates the introduction of innovative solutions that can enhance production levels while simultaneously reducing emissions from the production process. The information obtained from the DT enables time and cost savings by eliminating the need for conducting tests.

2. Raw Materials and Modeling Approach

2.1. Post-Filtration Liquid

The raw material for the RH section was post-filtration liquid. The ammonia present in this liquid existed in the form of ammonium carbonates and bicarbonates as “free” ammonia ((NH₄)₂CO₃, NH₄HCO₃). The concentration of free ammonia in the post-filtration liquid ranged from 18.7 to 22.1 g/dm³, while “bound” ammonia, found as ammonium chloride (NH₄Cl) and, to a small extent, ammonium sulfate ((NH₄)₂SO₄), ranged from 55.25 to 62.9 g/dm³. The temperature of the liquid entering the column was 75 °C [34,35,36].

2.2. Lime Milk

Lime milk (a suspension of calcium hydroxide in water) was required for the decomposition of bound ammonia, with a concentration of 238–280 g/dm³ CaO and a temperature of 95–100 °C. The temperature of the slaked lime is a crucial parameter for the ammonia regeneration process, as it directly affectes the steam consumption in the distillation column [34,35,36].

2.3. Steam

Superheated steam was introduced into the system as a heat carrier, with a pressure of 3 bars and a temperature of 170 °C. Steam with these parameters provides the required amount of energy without the need for a heat exchanger, while simultaneously lowering the partial pressure of ammonia, which facilitates its desorption [34,35,36].

2.4. Modeling Approach

2.4.1. Chemical Reactions

A thermodynamic formulation of reaction kinetics based on reaction rate was implemented to rigorously predict the correct equilibrium constant and allow for a dynamic approach to the equilibria of individual reactions [37,38].

The general reaction i can be defined as

$$aB+bB \leftrightarrow cC+dD$$

(1)

The following reaction can be expressed as

$$R^{i/f}=k^{i/f} \left({\left[A\right]}^a{\left[B\right]}^b\right)$$

(2)

The reverse reaction can be expressed as

$$R^{i/b}=k^{i/b} \left({\left[C\right]}^c{\left[D\right]}^d\right)$$

(3)

The equilibrium can be expressed as

$$R^{i/f}=k^{i/f} \left({\left[A\right]}^a{\left[B\right]}^b\right)=R^{i/b }{=k}^{i/b} \left({\left[C\right]}^c{\left[D\right]}^d\right)$$

(4)

The thermodynamic equilibrium constant $K_{eq}^i$ is expressed as

$$K_{eq}^i={\displaystyle \frac{\left({\left[C\right]}^c{\left[D\right]}^d\right)}{\left({\left[A\right]}^a{\left[B\right]}^b\right)}}={\displaystyle \frac{k^{i/f}}{k^{i/b}}}$$

(5)

The net reaction rate Rⁱ for the reaction i can be expressed as

$$R^{i }=R^{i/f}-R^{i/b}=k^{i/f}({\left[A\right]}^a{\left[B\right]}^b-{\displaystyle \frac{1}{K_{eq}^i}}{\left[C\right]}^c{\left[D\right]}^d),$$

(6)

where

k^i/f is the rate constant for the following reaction I;

[A], [B], [C], and [D] are the activity of components A, B, C, and D that take into account the non-ideality of the solution;

a, b, c, and d are the stoichiometric coefficients of the components A, B, C, and D;

Kⁱ_eq is the thermodynamic equilibrium constant of the reaction.

Kⁱ_eq is calculated from the free energy of the reaction ${∆G}_R^i$ as follows:

$$\mathrm{l}\mathrm{n}\left(K_{eq}\right)=-{\displaystyle \frac{{∆G}_R^0}{RT}},$$

(7)

where

$${∆G}_R^0={\sum }_i{V}_j{G}_j^0$$

(8)

All unit operation models in which chemical reactions occurred were equipped with a Kinetics dialog box tab (Figure 1), which could be used to define the reaction rate constant for each reaction. Higher values of the rate constants will drive the system closer to thermodynamic equilibrium.

2.4.2. Mass and Heat Transfer Between Gas and Liquid Phases

Transport between the liquid and gas phases was modeled using a multi-component mass and heat transfer approach based on rates. In the modeling environment used for this study, we could observe various layers applied in the modeling of liquid–vapor transport in the form of a rate-based formulation. The project required a rate-based formulation due to certain reactions (particularly those involving solid phases) where the rate was limited and applying equilibrium assumptions would lead to an overestimation of sodium bicarbonate formation. The software used in the project enabled us to specify the mass and heat transfer coefficients for each phase by physically entering parameters into the model or by applying a model that automatically calculated the necessary parameters by enforcing the specifications (“target”) of a particular model variable while simultaneously removing the specifications of a variable (“corrected variable”) from another model, which enabled the conduction of highly predictive process simulations and, consequently, the achievement of the objective of studying ammonia recovery.

2.4.3. Ammonia Regeneration Process in RH-DS Units

The ammonia regeneration process in RH-DS units involved recovering NH₃ from the post-filtration liquid. In the filtrate liquid, ammonia existed in the form of “free” ammonia (NH₄OH–NH₃(aq)), carbonate and bicarbonate salts (NH₄HCO₃, (NH₄)₂CO₃), and stable salts ((NH₄Cl with a small amount of (NH₄)₂SO₄)).

The recovery of ammonia from the “free” form occurred in the RH section with the involvement of steam, which constituted the main source of process heat (9)–(11), while the regeneration of ammonia from the “bound” form took place in the PLM and DS section (12) and (13) with the assistance of steam and lime milk:

$${{(\mathrm{N}\mathrm{H}}_4)}_2{\mathrm{C}\mathrm{O}}_3+\mathrm{Q}\to 2{\mathrm{N}\mathrm{H}}_{3\left(\mathrm{g}\right)}\uparrow +{\mathrm{C}\mathrm{O}}_{2\left(\mathrm{g}\right)}\uparrow +{{\mathrm{H}}_2\mathrm{O}}_{\left(\mathrm{c}\right)}\hspace{1em}∆\mathrm{H}>0$$

(9)

$${\mathrm{N}\mathrm{H}}_4\mathrm{H}{\mathrm{C}\mathrm{O}}_3+\mathrm{Q}\to {\mathrm{N}\mathrm{H}}_{3\left(\mathrm{g}\right)}\uparrow +{\mathrm{C}\mathrm{O}}_{2\left(\mathrm{g}\right)}\uparrow +{{\mathrm{H}}_2\mathrm{O}}_{\left(\mathrm{c}\right)}\hspace{1em}∆\mathrm{H}>0$$

(10)

$${\mathrm{N}\mathrm{H}}_4\mathrm{O}\mathrm{H}+\mathrm{Q}\to {\mathrm{N}\mathrm{H}}_{3\left(\mathrm{g}\right)}\uparrow +{{\mathrm{H}}_2\mathrm{O}}_{\left(\mathrm{c}\right)}\hspace{1em}∆\mathrm{H}>0$$

(11)

$$2{\mathrm{N}\mathrm{H}}_4\mathrm{C}\mathrm{l}+\mathrm{C}\mathrm{a}{\left(\mathrm{O}\mathrm{H}\right)}_2+\mathrm{Q}\to {2\mathrm{N}\mathrm{H}}_{3\left(\mathrm{g}\right)}\uparrow +\mathrm{C}\mathrm{a}{\mathrm{C}\mathrm{l}}_2+2{{\mathrm{H}}_2\mathrm{O}}_{\left(\mathrm{c}\right)}\hspace{1em}∆\mathrm{H}>0$$

(12)

$${{(\mathrm{N}\mathrm{H}}_4)}_2{\mathrm{S}\mathrm{O}}_4+\mathrm{C}\mathrm{a}{\left(\mathrm{O}\mathrm{H}\right)}_2+\mathrm{Q}\to {2\mathrm{N}\mathrm{H}}_{3\left(\mathrm{g}\right)}\uparrow +\mathrm{C}\mathrm{a}{\mathrm{S}\mathrm{O}}_4+2{{\mathrm{H}}_2\mathrm{O}}_{\left(\mathrm{c}\right)}\hspace{1em}∆\mathrm{H}>0$$

(13)

3. Development of RH-DS Models in gProms Process 2023.2.0 Software Environment

gProms Process is a process modeling environment specifically designed to support a digital approach to design [39,40,41,42], from early research and development stages to the commissioning of installations. Cutting-edge tools in the most powerful modeling and optimization environment for the processing industry provide a 21st-century experience that offers value far beyond that achievable with traditional flow sheet simulators.

gProms Process is the first widely used modeling environment that supports all key stages and activities of digital process design:

• The construction of digital twins of processes using industry-leading, high-accuracy models;
• Calibration based on experimental or industrial data using state-of-the-art parameter estimation and model validation tools;
• Global system analysis for the rapid exploration of the decision space and quantification of risk;
• Multidimensional optimization to determine an optimal solution.

The gPROMS software is applied in various process environments, such as the thermal simulation of planar SOFCs (solid oxide fuel cells), hydrogen production via low-temperature water–gas shift reactions, multi-stage flash (MSF) desalination plants, or the digital design and optimization of fixed-bed catalytic reactors [43,44,45,46]. The design of digital models for the RH-DS apparatus begins with the collection of comprehensive technical documentation related to the modeled unit, including the effective contact area along with the volume parameters of the packing, calculations of the pressure drop described by the pressure drop coefficients for both liquid and vapor, and daily process data from the production plant. The fundamental modeling approach involves defining an appropriate model and implementing the materials used in the process, along with a package of physical properties for each raw material. Additionally, it requires identifying all relevant data for the unit model (separately for the RH and DS sections) and defining all supplementary equations in “first-principles modeling” (custom modeling), such as vapor–liquid equilibrium, reactions in the liquid phase, liquid–solid equilibrium, volatility coefficients, and activity.

This well-prepared digital process environment allows for the modification of raw material and apparatus parameters, enabling the acquisition of results from a series of simulations necessary for assessing model parameters such as heat transfer, reaction kinetics parameters, and the collection of archived variables (saved variable set) as preliminary data for simulations in block flow sheets. The results of simulations in the digital twin serve as a basis for developing concepts for new solutions to be implemented in the production plant, as well as verifying the correctness of unit operations within the existing system.

Following the procedure outlined above, models of the RH-DS apparatus were prepared, with the RH section modeled as a packed scrubber (Figure 1) and the RH-DS apparatus with the RH section modeled as a bubble-cap column with trays (Figure 2).

4. Model Optimization Techniques

Once a fully validated model is available, it can be utilized for various activities, including steady-state simulations and dynamic simulations to determine performance under different equipment parameter values or operating conditions. However, two advanced analytical and design techniques are particularly important, extending far beyond standard simulation and providing truly digital design capabilities:

(1)

Large-scale mathematical optimization (including mixed-integer nonlinear programming, MINLP), where multiple decision variables are altered simultaneously to maximize or minimize (typically economic) objective functions while ensuring that constraints regarding equipment, process, and product quality are considered. This enables the simultaneous determination of optimal values for numerous design and operational variables, taking into account all relevant factors. The use of MINLP primarily occurs during the process design phase (both at the level of the entire process in a production plant and for individual installations or single reactors) by determining the optimal combination of discrete decisions (e.g., equipment selection, operating modes) and continuous variables (e.g., flow rates, temperatures). In the subsequent stage, digital modeling programs use MINLP for operational control to define optimal control strategies for operational systems in real time. For example, it can optimize parameters such as production rates or energy consumption, taking into account constraints imposed by the physical system or external factors. In addition, MINLP is used to model complex behaviors in production systems, such as nonlinear relationships between variables or decisions that involve multiple relationships continuously, and it can be applied to optimize maintenance schedules and predict equipment failures. MINLP algorithms can be used for real-time decision-making or can be used in digital twin simulations to optimize energy use and resource allocation.

(2)

Global system analysis (GSA) to systematically explore the decision space of the process by calculating the impact of variability in model input data (e.g., values of key design parameters) or uncertainty in model parameters (e.g., experimentally determined kinetic parameters) that affect process KPIs. GSA activities include conducting sensitivity and uncertainty analyses to minimize technological risks [46,47].

Examples of types of studies supported by GSA [48,49]:

-

Parametric studies involve conducting a large number of simulations to analyze the impact of various factors. GSA examines systems holistically, without focusing on individual components, correlating interrelationships, feedback loops, and dynamic interactions among elements (Figure 3).

-

Uncertainty analysis considering uncertainties in factors such as parametric, structural, input, or scenario uncertainties to determine the probability of responses using Monte Carlo simulations, sensitivity analyses, probabilistic methods, or scenario analyses (Figure 4).

5. Results

During this research work, the RH section of the distillation column, where the decomposition of ammonium carbonates and bicarbonates occurred, was analyzed as a packed scrubber with two packing height variants—3 m and 12 m (Figure 5)—as well as a bubble-cap column with trays (Figure 6). The research focused on the fill heights of 3 m and 12 m, as these are the most commonly used filling levels in the RH tower for soda production. The researchers focused on the processes occurring in the scrubber and bubble-cap columns, which are currently present in the analyzed industrial plant, and for these types of apparatus, assessments of optimization potential are being prepared. The conducted studies in the digital environment show significant differences in the performance of the packed scrubbers compared to the bubble-cup columns with trays concerning the analyzed ammonia recovery amounts and temperature profiles within the volume of the apparatus. Below (Figure 5), the temperature profiles for the 3 and 12 m packed scrubber are presented. (1) is the intersection point of the curve at the filtrate lye inlet to the apparatus and point (2) is the increase in the temperature in the lower part of the RH due to the entry of steam–gas mixtures from the DS section. An increase in temperature was also observed in the upper part of the RH apparatus due to the condensation of ammonia and water vapor.

For the assumed atmospheric pressure in the model of 0.0 bars of relative pressure (1 bar of absolute pressure), the decomposition temperature of NH₄HCO₃ was 58 °C, while the decomposition temperature of (NH₄)₂CO₃ was 60 °C. The distillation process was endothermic (ΔH > 0) and required the input of large amounts of heat. The amount of heat necessary for the distillation process exceeded the amount derived from the theoretical values for the reaction. Specifically, to decompose volatile ammonia compounds, in addition to supplying heat to raise the solution to the decomposition temperature of ammonium carbonate salts, additional heat must be supplied to drive off dissolved NH₃ and CO₂ from the solution into the gas phase, considering the solubility of ammonia in water and the fact that carbon dioxide decreases the partial pressure of NH₃ due to its high chemical affinity. Considering the solubility of NH₃ in water, it was observed that the gas solubility behaved differently than what is predicted by Henry’s law. The deviation from Henry’s law was caused by the ease with which NH₃ molecules form chemical bonds with water. This study also took into account the fact that as temperature increases, the bond between NH₃ and water dissociates, resulting in ammonia behaving according to Henry’s law at a temperature of 100 °C. Analyzing the above temperature distribution data in the RH apparatus (Figure 5), higher temperatures were observed in the packed scrubber with a packing height of 3 m, oscillating between 97 °C and 100.5 °C, and in the bubble-cap column (Figure 6), where the temperature distribution ranged from 92 °C to 101 °C. This significantly facilitated the decomposition of both “free” ammonia compounds and the breakdown of chemical bonds between ammonia and water compared to the apparatus with a packing height of 12 m, where the temperature range was from 90 °C to 100.6 °C.

The temperature changes observed in the lower part of the RH apparatus (2) in Figure 5 and Figure 6 resulted from the flow of the gas phase from the distiller containing NH₃ and H₂O. In the upper part of the apparatus, they are a consequence of the flow of the post-filtration liquid (1). In the case of the packed scrubber with a height of 3 m, a sharp temperature jump from 99 °C to 100.5 °C was observed at 10% of the height of the lower part of the apparatus.

In the analyzed distillation system, the condition was met where the partial vapor pressure of ammonia in equilibrium with the liquid phase was greater than the partial pressure of ammonia in the gas phase, except at point (2) where vapors from distillation—the NH₃ and H₂O gas phase—entered the RH section and at the inlet of the filtrate (1) into the RH section.

In the analysis of recovered NH₃ in the scrubber apparatus with a 3 m packing height (Figure 7) with molar flow of NH₃ at the outlet: 831.063 kmol/h, a 14.09% lower recovery of gaseous ammonia was observed compared to the apparatus with a 12 m packing height (molar flow of NH₃ at the outlet: 948.217 kmol/h), corresponding to a difference of 117.154 kmol/h of recovered NH₃. Analyzing the results obtained from the simulations conducted in a digital environment clearly shows the correlation between the type of apparatus used (scrubber with 3 m and 12 m packing heights or aeration apparatus) and the potential for ammonia recovery from free forms (ammonium carbonates and bicarbonates). Increasing the ammonia recovery by 14.09% when using the scrubber apparatus with 12 m packing had a significant impact on the entire soda production process via the ammonia method. The recovered ammonia gasses from the distillation process, after cooling, were directed to the absorption unit, where the purified brine was saturated with gaseous ammonia. Increasing the amount of recovered ammonia gasses by 14.09% directly translated to an increase in the concentration of ammonia brine after the absorption process, thus enhancing the efficiency of the absorption process and, in the next step, the carbonation process. Additionally, this reduced the need to replenish ammonia losses in the industrial installation. The impact of increasing the amount of recovered ammonia will be further analyzed in subsequent stages of this research. In the apparatus with a 3 m packing height, the highest amount of recovered ammonia was achieved at 90% of the apparatus height. In contrast, in the tray bubble column, the maximum flow was observed at 77% of the apparatus height (Figure 8).

When comparing the recovered ammonia flow rates in the 12 m scrubber apparatus and the bubble column with trays, the molar flow rate of ammonia at the outlet of the tray column was 8.68% lower than the flow rate in the scrubber apparatus with a 12 m packing height, corresponding to a difference of 75.716 kmol/h of recovered NH₃.

Additional GSA for 100 samples (Figure 9) allowed for the assessment of ammonia gas recovery along with the filling height and process steam consumption in the analyzed case of using the RH apparatus with a filling height of 2–20 m.

In the course of this research, using a digital twin, uncertainty analyses were also conducted with the use of the global system analysis function, based on the Monte Carlo method, to determine the point at which the curve flattened as the packing level in the scrubber apparatus increased. Figure 10 presents the results of pseudo-random sampling analyses in the packing height range from 0 to 100 m. The analyzed graph shows the point of curve flattening, beyond which further increases in packing height became ineffective (from 40 m to 100 m, the increase in recovered ammonia was 1 mol/mol).

Based on the obtained results, the potential for implementing the use of the scrubber apparatus with a 12 m packing height and the tray bubble column with trays will be evaluated in further studies, along with referencing the process of digital simulations together with data from an industrial facility.

6. Conclusions and Summary

The use of digital twin concepts in the production of soda ash by the ammonia–soda process represents a novel approach in the field of chemical process modeling. Digital twins are rapidly entering the realm of processes, and from their inception to the present day, digital twins have been a concept shaped by their users. It is anticipated that their evolution will transform them into an intelligent platform [50]. Therefore, it is crucial to expand the possibilities of using digital twins and to specialize their capabilities in various industrial sectors through teams of experts from specific fields.

In traditional prototyping, product redesign is time-consuming and costly due to the use of physical materials and labor. Moreover, destructive testing results in the end of an expensive prototype. In contrast, with the use of the DT, products can be recreated and subjected to destructive testing without additional material costs. Thus, even assuming that the costs (of traditional prototyping methods and virtual methods) are similar in the initial stage, the costs of traditional testing increase with rising inflation, whereas the cost of virtual testing significantly decreases over time [51,52,53].

Simulations of temperature distribution in the apparatus and simulations of ammonia recovery in a digital environment demonstrated numerous benefits for the balancing of industrial installations and the assessment of the implementation potential of the proposed solutions. The data obtained from these simulations allow for an efficient evaluation of the impact of digital twin-derived data on other process installations, such as the absorption unit.

The main objective of this research is to assess the potential for reducing the use of process steam and increasing the amount of recovered ammonia, which will consequently lead to a reduction in process costs and a decrease in emissions of process gasses. This is particularly relevant as companies are changing their approach not only due to national and international legal requirements or consumer pressure but also because adopting environmental management strategies creates opportunities for business organizations [54,55,56,57]. Understanding the holistic view of DTs across many relevant domains will allow for a better evaluation of the state of the art and where the technology is going. It is essential to address the proposed research efforts to unleash the potential of DTs for the future [58].

The optimization method for chemical processes in soda production by the ammonia–soda process presented in this publication was implemented. This, in turn, allowed for a positive evaluation of the data obtained from digital simulations, the correlation between simulation-derived data and process data, and the implementation potential of the proposed digitally modeled solutions.

Work is ongoing on further implementations of the digital twin for carbonation and absorption installations. In summary, the digital twin is a suitable tool for simulating process parameters, new technological solutions, and minimizing the safety risks associated with conducting process tests. Such prepared digital analyses expand their applications to other industries as well, including the refinery industry, fuel cell design and optimization, hydrogen production, and even medicine (DTs enable the creation of accurate virtual models of human organs, tissues, and even entire bodies, allowing for real-time simulation of various health scenarios).