CET vol 99


 
 
 
 
 
 
 
 
 
 
                                                                                                                                                                 DOI: 10.3303/CET2399102 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 8 January 2023; Revised: 26 March 2023; Accepted: 5 May 2023 
Please cite this article as: Bacci Di Capaci R., Oliverio S., Brunazzi E., Galletti C., Pannocchia G., 2023, Digital Twin of a Tubular Flow Reactor 
Oriented to the Development of the Control System, Chemical Engineering Transactions, 99, 607-612  DOI:10.3303/CET2399102 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL.  99, 2023 

A publication of 

 

The Italian Association 

of Chemical Engineering 

Online at www.cetjournal.it 

Guest Editors: Sauro Pierucci, Flavio Manenti 

Copyright © 2023, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-98-3; ISSN 2283-9216 

Digital Twin of a Tubular Flow Reactor Oriented to the 

Development Of The Control System 

Riccardo Bacci di Capaci*, Simona Oliverio, Elisabetta Brunazzi, Chiara Galletti, 

Gabriele Pannocchia 

Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 2, 56122, Pisa, Italy 

 riccardo.bacci@ing.unipi.it 

This work is aimed at developing the first version of a digital twin of a plant prototype for the flexible production 

of different chemical formulates, to be used in various industrial fields, from the medical health to the tanning 

sector. The analyzed system is a tubular flow reactor characterized by multiple additions of components and by 

a series of static mixing elements. Firstly, the 1D dynamic modeling of the reactor is addressed, by defining the 

geometry, parameters, and operating conditions to reasonably describe the process evolution over time. Then, 

the corresponding feedback control system is designed to obtain the desired final products, by respecting the 

required specifications, in terms of mean concentration, degree of mixing, and flow rates. Different types of 

control architectures are derived and compared. The results show that not only SISO control schemes, but also 

multivariable solutions are possible, which effectively guarantee set-point tracking and disturbance rejection. 

1. Introduction 

The concept of Industry 4.0 is a core topic of global interest and is now leading to a major economic 

transformation; this technological paradigm pushes toward a totally automated production, and a digital and fully 

interconnected industry. Digital twin, that is, a highly complex virtual model, which intends to be the exact replica 

of its physical counterpart, as a machine, a plant, or a process, is one of the so-called Key Enabling 

Technologies (Wan et al., 2015). 

The project Turboflux lays within the Industry 4.0 paradigms and aims at creating a highly flexible plant, to 

produce different chemical formulates, from the health sector, such as detergents, disinfectants, bactericides, 

but also substances typical of the tanning and paint industries. The desired formulations are produced from a 

limited number of basic components in liquid state, fed directly inline, and mixed by means of a series of static 

mixing devices installed within the pipeline (Thakur et al., 2003). 

The Turboflux plant consists of two main sections: i) holds the static mixing system and the pneumatic pumps 

for the components and the formulate, and a buffer tank for temporary storing; ii) hosts the kegging machine for 

the final products and the control panels with external access in a safe area. The static mixing zone is comprised 

of a series of five parallel pipes connected by 180 ° curves (for around 20 m length in total): the main fluid is fed 

into the primary pipe; a series of smaller pipes is used for the additives. The main pipe is the mixing and reaction 

environment, and the final sector is a calm zone for stabilization, quality monitoring, and properties control. 

Components are fed with a dedicated pump, a control valve and two splitting valves, so they can be added in 

two different sectors of the pipe; mass flow meters are installed to guarantee a high precision in dosages. The 

recipes are developed for each final product; the relative quantitative and the procedure of injection are 

established in advance. 

In this work, a first version of the digital twin of the Turboflux system is presented. The final version of this model 

will be then used for monitoring, diagnosis and controlling purposes, as well as to ensure safety and predictive 

analysis to counteract possible process perturbations (Bacci di Capaci et. al, 2017). The outline of the paper is 

as follows: Section 2 analyzes the system dynamics through mathematical models and numerical methods; in 

Section 3 open-loop analysis is performed, while in Section 4 different control system architectures are 

illustrated. Finally, conclusions are drawn in Section 5. 

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2. Methodology 

The dynamics of a selected section of the Turboflux plant is investigated in this work and described by a 

simplified axial dispersion model. In reactors or mixers with tubular geometry, the axial dispersion is indeed a 

key phenomenon, which significantly influences the process dynamics and the main performance parameters, 

as yield and selectivity (Bahadori, 2012). In scenarios with a minimal geometric complexity, Computational Fluid 

Dynamics (CFD) offers various tools for an accurate investigation of the dispersion. To this aim, suitable CFD 

simulations, previously used for the computation of velocity and concentration fields of the system (Bacci di 

Capaci et al., 2022), are here exploited to estimate an average coefficient of axial dispersion, and thus to define 

the corresponding dynamic model. 

Axial dispersion is a widely recognized approach for describing real flow conditions within a simplified model of 

a tubular reactor, that is, of plug flow (PF) type. As well-known, the PF model assumes that, for each axial 

coordinate, the fluid has a perfectly flat profile of any variables, as velocity and concentration. This means that 

no element of fluid overtakes or mixes up with any others, placed downstream or upstream the main flow 

direction. The axial dispersion model instead considers dispersive effects, such as slips and/or vortex 

formations; these stochastic phenomena are due to the local diffusion of components/reagents, which alters the 

perfect system segregation. 

As basic relation, the following system of partial differential equations (PDE) is here adopted: 

𝜕 < 𝐶𝑖 >

𝜕𝑡
= −

𝜕 < 𝑢𝑧𝐶𝑖 >

𝜕𝑧
+

𝜕𝐷𝑎𝑥

𝜕𝑧 

< 𝜕𝐶𝑖 >

𝜕𝑧
+ 𝑟𝑖 (1) 

where <uz> is the average axial velocity through a general cross-section of the tubular reactor; <Ci> is the 

average concentration of the i-th species on the same cross-section; Dax is the axial dispersion coefficient; ri is 

the reaction rate of the i-th species; z is the axial coordinate. Both concentration and axial velocity are functions 

of two independent variables, i.e., of space z and time t. With suitable assumptions (Moreau et al., 2017), Eq(1) 

can be reformulated as: 

𝜕 < 𝐶𝑖 >

𝜕𝑡
+< 𝑢𝑧 >

𝜕 < 𝐶𝑖 >

𝜕𝑧
− 𝐷𝑎𝑥

𝜕2 < 𝐶𝑖 >

𝜕𝑧2 − 𝑟𝑖 = 0 (2) 

Note that the axial dispersion coefficient (Dax) includes different contributions: molecular dispersion Dm, turbulent 

dispersion Dt, numerical dispersion Dn, and spatial dispersion Ds. This last contribution is at least one order of 

magnitude larger (10-2 m2/s) than the others. Therefore, Ds can reasonably approximate the whole axial 

dispersion, both in laminar (Moreau et al., 2017) and turbulent regime (Talvy et al., 2007). 

The main formulation produced within Turboflux plant is the well-known sanitizing gel, an alcohol-based mixture 

in aqueous solution. The World Health Organization provides the following composition: i) ethanol 80% v/v; ii) 

glycerol 1.45% v/v; iii) hydrogen peroxide 0.125% v/v; iv) distilled water to complement. For the sake of 

simplicity, the CFD simulations and the dynamic simulation of the preliminary digital twin assumed that the main 

(that is, vector) fluid flow rate is pure ethanol, and the additive fluid flow rate is single, comprised of pure distilled 

water. Therefore, in Eq(1) only one additive component is considered (i.e., i = A) and no reaction occurs (rA = 

0); that is, the tubular reactor reduces to an inline mixer. The profile of spatial dispersion coefficient 𝐷𝑠(𝑧) was 

obtained from the results of suitable preliminary CFD simulations performed in transient conditions, as 

suggested by Moreau et al. (2017). The following equation was thus adopted: 

𝐷𝑠(𝑧) =
< (𝑢𝑧−< 𝑢𝑧(𝑧) >)(𝐶𝐴−< 𝐶𝐴 >) >

𝑑 < 𝐶𝐴 >
𝑑𝑧

≈ 𝐷𝑎𝑥(𝑧) (3) 

where <uz> and <CA> are the mean velocity and concentration averaged over a selected cross-section; uz and 

CA are the local axial velocity and concentration, for each cell of the CFD discretization domain within the 

corresponding cross-section. Further details of the derivation of 𝐷𝑠(𝑧) are here avoided for the sake of brevity. 

As a preliminary digital twin, the developed model refers to a limited subsection of the real plant. In particular, 

the simulation involves an initial empty pipe of 0.6 m length and a 2 m-length pipe equipped with static mixing 

devices of Ross LPD type (Ross, 2023). The following material and molar steady-state balances are considered: 

𝑄𝑜
𝑣𝜌0 + 𝑄𝐴

𝑣𝜌𝐴 = �̇�𝑚𝑖𝑥

𝑄𝐴
𝑣

𝑀𝑊𝐴
𝜌𝐴 = (

𝑄𝐴
𝑣

𝑀𝑊𝐴
𝜌𝐴 +

𝑄0
𝑣

𝑀𝑊0
𝜌𝐴) 𝑦𝐴,𝑖𝑛

 (4) 

where 𝑄0
𝑣 and 𝑄𝐴

𝑣 are the inlet volumetric flow rate of vector and additive fluid, respectively; �̇�𝑚𝑖𝑥 is the total 

mass flow rate after mixing; MW and 𝜌 are molecular weight and density; 𝑦𝐴,𝑖𝑛 is the molar fraction of additive 

fluid after mixing. The overall model consists of: i) a static summation node which represents a site of perfect 

608



instant mixing, corresponding to the location of the additive fluid inlet; ii) a dynamic block, e.g., the value of inlet 

molar fraction (𝑦𝐴,𝑖𝑛) can be measured at the outlet (𝑦𝐴,𝑜𝑢𝑡) only after the block’s dynamics. At each time instant, 

a mean axial fluid velocity is calculated, as �̅�𝑧 = �̇�𝑚𝑖𝑥/(𝑆𝜌𝑚𝑖𝑥), where 𝑆 =
𝜋

4
𝐷2 is the constant cross-section of 

the pipeline, being D the diameter. The density (𝜌𝑚𝑖𝑥) of the considered ethanol-water mixture is evaluated by 

using a suitable correlation obtained in a previous study (Orsi et al., 2013), based on water mass fraction values. 

Note that the proposed approach can be easily extended to other sections of the real tubular mixer in future 

versions of the digital twin. 

As known, an appropriate discretization method allows one to turn the initial PDEs problem into a system of 

ordinary differential equations (ODEs). Different algorithms have been developed within MATLAB for numerical 

integration of PDEs. The Method of Lines (MOL) is here adopted, as suggested by Pellegrino (2019). As ODE 

discretization method, the finite difference approach is here adopted. Eq(1) is thus reformulated in terms of 𝑦𝐴, 

i.e., the mole fraction of additive fluid: 

𝜕 < 𝑦𝐴 >

𝜕𝑡
= −< 𝑢𝑧 >

𝜕 < 𝑦𝐴 >

𝜕𝑧
+

𝜕𝐷𝑎𝑥

𝜕𝑧 

𝜕 < 𝑦𝐴 >

𝜕𝑧
 (5) 

where 𝐶𝐴 = 𝐶𝑇𝑦𝐴, being 𝐶𝑇 the total molar concentration, which is constant. The first and second derivatives are 

respectively approximated by the first-order and second-order finite differences, both centered in zk. 

Reformulating Eq(5), we get a set of N ODEs in the independent variable t, which can be easily integrated once 

defined the initial condition. 

𝑑𝑦𝐴(𝑧𝑘)

𝑑𝑡
= −�̅�𝑧

𝑦𝐴(𝑧𝑘+1) − 𝑦𝐴(𝑧𝑘−1)

2𝛥𝑧
+ �̅�𝑎𝑥

𝑦𝐴(𝑧𝑘−1) − 2𝑦𝐴(𝑧𝑘) + 𝑦𝐴(𝑧𝑘+1)

𝛥𝑧2
 (6) 

with k = 1, … N-1. Note that, for the sake of simplicity, from the profile of 𝐷𝑠(𝑧) obtained with Eq(3), a mean 

axial dispersion coefficient is considered: �̅�𝑎𝑥 = 0.04 m2/s. Given Eq(5), an initial condition (IC) with respect to 

time and two boundary conditions (BC) for the axial coordinate are to be imposed; in particular, as IC at t = 0, 

𝑦𝐴(0, 𝑧) = 0 ∀ z > 0; as BCs, at z = 0 𝑦𝐴 = 𝑦𝐴,𝑖𝑛 ∀ t > 0, and at z = L (= 2.6 m) 
𝑑𝑦𝐴

𝑑𝑡
= 0 ∀ t > 0. Ode45 function of 

MATLAB was finally used as numerical integration solver. 

3. Open-loop Analysis 

As first, a detailed analysis of the open-loop dynamics of the system modeled by Eq(6) is carried out. In 

particular, the effect of a generic variation of the mean input concentration is evaluated; afterwards, the system 

response to its actual inputs, i.e., the flow rate of two manipulated fluids (additive and vector), is investigated. 

The propagation of the concentration of additive fluid is first evaluated by imposing an instantaneous variation 

of the mean input additive molar fraction (𝑦𝐴,𝑖𝑛); in particular, a step equal to 0.1. A constant axial velocity is 

imposed �̅�𝑧 = 6.89 m/s, for a total mass flow rate �̇�𝑚𝑖𝑥 = 167.8 kg/min. Figure 1a shows the corresponding time 

response. Note that the system does not respond significantly for around 0.3 s; then, before reaching the new 

stationary value (𝑦𝐴,𝑜𝑢𝑡 = 𝑦𝐴,𝑖𝑛), it presents some oscillations which decay in about 0.2 s. A brief parametric 

sensitivity analysis is also reported, by only varying the mean axial dispersion coefficient �̅�𝑎𝑥; three other values 

are tested: 0.01, 0.05, and 0.08 m2/s. Figure 1b shows the corresponding responses. As the �̅�𝑎𝑥 increases, 

overshoot and settling time decreases; that is, the input molar fraction of additive fluid (i.e., its concentration) 

appears at the outlet section more quickly and steadily; a higher coefficient indeed implies better diffusion of 

additive in the vector fluid, and then a more stable dynamic. 

 

Figure 1: Propagation of additive concentration in the inline mixer: a) for nominal and b) different values of �̅�𝑎𝑥 

609



The trend of the mean molar fraction of additive in response to a step on the volumetric flow rate of additive fluid 

itself (𝑄𝐴
𝑣) is then analyzed. As initial condition, a constant flow rate is assumed, 100% composed by vector fluid, 

that is, 𝑦𝐴(0) = 0; a step of 10 L/min on 𝑄𝐴
𝑣 is imposed. The specific flow rate values are then 𝑄𝑜

𝑣 = 200 L/min 

and 𝑄𝐴
𝑣 = 10 L/min. From molar balance on the additive fluid, the new stationary value of the mean molar fraction 

of additive is equal to 𝑦𝐴,𝑜𝑢𝑡 =

𝑄𝐴
𝑣

𝑀𝑊𝐴
𝜌𝐴

(
𝑄𝐴

𝑣

𝑀𝑊𝐴
𝜌𝐴+

𝑄0
𝑣

𝑀𝑊0
𝜌𝐴)

 = 0.14. Figure 2a shows the corresponding system response. 

Again, the system does not respond for about 0.3 s; then, before reaching the stationary value, it presents 

oscillations decaying in about 0.2 s. This behavior recalls the underdamped dynamics of a linear system of the 

second order plus time delay (SOPTD), whose transfer function in Laplace domain is 𝑃(𝑠) =
𝐾𝑝

𝜏2𝑠2+2𝜉𝜏𝑠+1
𝑒−𝜃𝑠. 

 

Figure 2: Propagation of additive molar fraction in response to step on: a) additive; b) vector fluid flow rate 

To perform tuning of proportional-integral (PI) controllers for the digital twin, it was indeed decided to 

approximate the dynamics of the inline mixer with a SOPTD model. Hence, the four characteristic parameters 

are required: i) a time constant 𝜏; ii) a time-delay 𝜃; iii) a damping factor 𝜉. The fourth parameter, i.e., the gain 

𝐾𝑝, can be easily obtained from the input(u)-output(y) stationary variations, i.e.: 𝐾𝑝 =  
∆𝑦

∆𝑢
=

𝑦∞−𝑦0

𝑢∞−𝑢0
=

𝑦𝐴,𝑜𝑢𝑡

𝑄𝐴
𝑣  = 0.014 

min/L = 0.84 s/L. The three dynamic parameters are obtained by minimizing the error e between the response 

of the nonlinear system of Eq(6) and of the SOPTD model, in terms of IAE and ISE indices, defined as: 

𝐼𝐴𝐸 = ∑|𝑒𝑗|𝑑𝑡

𝑁𝑡

𝑗=0

;         𝐼𝑆𝐸 = ∑ 𝑒𝑗
2𝑑𝑡

𝑁𝑡

𝑗=0

 (7) 

where j is the time index and 𝑁𝑓 is the final time sample. To this aim, a standard 3D grid-search method and an 

unconstrained optimization problem were performed; the optimal solution was indeed found by using fminsearch 

MATLAB function with the default options. Further details are here avoided for the sake of brevity; only final 

mean parameters are reported: 𝜏 = 0.037 s; 𝜃 = 0.33 s; 𝜉 = 0.629. 

Note that the controller tuning is done on the overall model V·P, comprised of two elements in series: the mixing 

system dynamics, i.e., the linear process model (P) just identified, and the control valve (V) dynamics, assumed 

as a first-order linear system: 𝑉(𝑠) =
𝐾𝑣

𝜏𝑣𝑠+1
. Two valves are considered: i) the additive fluid valve VA; ii) the vector 

fluid valve V0. A constant time (𝜏𝑣) equal to 1 second is imposed for both valves. As for the gains, a linear 

relationship between the flow rate range and the percentage valve stroke is considered. The obtained values 

are 0.0033 L/s for VA and 0.066 L/s for V0. The root locus of model V·P is then investigated, and the basic 

technique of Ziegler-Nichols is adopted for tuning; obtained parameters are 𝐾𝑐 = 768; 𝜏𝐼 = 3.86 s. 

The same approach was followed for the relation between the vector fluid volumetric flow rate (𝑄o
𝑣) and the 

mean molar fraction of the additive fluid. Open-loop dynamics was studied (see Figure 2b), another SOPTD 

linear model was obtained (a negative gain 𝐾𝑝 is now observed), and the corresponding PI controller tuning was 

performed. Details are here omitted for the sake of brevity. 

4. Control systems 

The different control architectures developed are here briefly illustrated. Basic controllers of traditional type are 

considered, i.e., with feedback structure and PI algorithm. In detail, 3 output variables are assumed measurable: 

1) the mean outlet molar fraction of additive fluid (𝑦𝐴), obtained by Eq(6); 2) the mixing degree (MD) at the axial 

coordinate z = 0.8 m; 3) the outlet total mass flow rate (𝑀𝑡𝑜𝑡). The output variables are assumed affected by 

white noise, a zero-mean signal with a fixed variance. Controlled variables are compared with the reference 

values (SP, Set-Point) and control errors are calculated, which then represent input variables to the control 

system. Once computed, control actions are then translated into the two manipulated variables, i.e., vector fluid 

(𝑄0
𝑣) and additive (𝑄𝐴

𝑣) flow rates, whose ranges are 0-400 and 0-20 L/min, respectively. Note that MD was 

610



previously evaluated from the results of extensive CFD simulations, as a function of z, for a volumetric flow rate 

of vector fluid equal to 200 L/min and for three different values of additive fluid flow rate, i.e., 1, 10 and 20 L/min.  

Figure 3 shows the profiles of the mixing degree obtained from postprocessing of CFD results. MD proves close 

to unitary for z > 1.6 m, that is, higher than the reference industrial value of 0.95, the so-called "perfect mixing", 

regardless the flow rate of additive fluid. As said, MD is controlled at z = 0.8 m, i.e., in a region of significant 

variability with respect to the volumetric flow rates ratio. To obtain a broader domain of solution for MD, a fitting 

surface was evaluated, that is, a non-linear static function of the type 𝑀𝐷 = 𝑓(𝑧, 𝑅𝑣), where 𝑅𝑣 = 𝑄𝐴
𝑣 𝑄0

𝑣⁄ . In 

particular, the polynomial function poly42 of MATLAB was employed, with a fitting coefficient R2 = 97%. 

 

Figure 3: Postprocessing of CFD results: profile of the mixing degree for three levels of additive fluid flow rate 

Several control architectures were then tested. As single SISO controllers, Type 1 controls the outlet mean mole 

fraction of additive (𝑦𝐴), in case A) where the vector fluid flow rate (𝑄0
𝑣) is the only manipulated variable (MV), 

and in case B) where the additive fluid flow rate (𝑄𝐴
𝑣) is the only MV; SISO Type 2 controls the mixing degree, 

in case A) with 𝑄0
𝑣

 as single MV and B) with 𝑄𝐴
𝑣

 as MV. As decentralized MIMO architecture, in Pairing 1 𝑦𝐴 is 

matched with 𝑄𝐴
𝑣 and 𝑀𝑡𝑜𝑡 is controlled with 𝑄0

𝑣; Pairing 2 performs the opposite: 𝑦𝐴 is matched with 𝑄0
𝑣 and 𝑀𝑡𝑜𝑡 

is controlled with 𝑄𝐴
𝑣. As ratio controllers, Type1 is based on the set-point of mole fraction of additive (𝑦𝐴

𝑆𝑃); Type 

2, on the set-point of total mass flow rate (𝑀𝑡𝑜𝑡
𝑆𝑃 ). Only some architectures are briefly illustrated below. 

In the SISO control scheme Type 1–B), the vector flow rate is fixed at its mean value of 200 L/min; the two 

parameters of the PI controller are suitably modified from the values shown in Section 3 to obtain improved 

responses. Proportional gain Kc must be positive to guarantee closed-loop stability, since the process has 

evident positive gain: when the flow rate of additive fluid increases, its mole fraction increases. Some step 

variations on the set-point, between 0.14 and 0.15, are imposed. The corresponding time trends of the mole 

fraction, mixing degree, and total mass flow rate are shown in Figure 4a. Figure 4b shows the time trend of 

additive flow rate, that is, the manipulated variable. 

 

Figure 4: SISO control Type 1–B). Time trends of a) outputs and b) manipulated variable 

Since the vector fluid flow rate is much greater than additive fluid flow rate, it is reasonable to manipulate 𝑄0
𝑣 to 

control the total mass flow rate. This happens in decentralized MIMO control Pairing 1, where parameters of 

two PI controllers are suitably retuned with respect to the corresponding SISO controllers to obtain improved 

responses by limiting loop interactions. Variations are imposed on two set-points at different times, to clearly 

observe the system behavior in terms of reference tracking and disturbance rejection. It is indeed possible to 

simultaneously guarantee the desired composition (𝑦𝐴) and total mass flow rate (𝑀𝑡𝑜𝑡). Figure 5 shows the time 

611



trends of the two controlled and manipulated variables. To move controlled variables to set-point, the vector 

fluid flow rate varies between 190 and 215 L/min; the additive flow rate, between 9.5 and 11.5 L/min. 

 

Figure 5: Decentralized MIMO control Pairing 1. Time trends of a) controlled and b) manipulated variables 

Finally, in ratio control Type 2, the mean molar fraction of additive (𝑦𝐴) is manipulated by the additive flow rate 

(𝑄𝐴
𝑣) and, simultaneously, a desired flow rate of vector fluid (𝑄𝑜

𝑣,𝑆𝑃) is imposed based on the set-point of total 

mass flow rate (𝑀𝑡𝑜𝑡
𝑆𝑃 ). In particular, the vector fluid flow rate is evaluated as 𝑄𝑜

𝑣,𝑆𝑃 = (𝑀𝑡𝑜𝑡
𝑆𝑃 − 𝑄𝐴

𝑣𝜌𝐴) 𝜌0⁄ . Note that 

in this architecture, to ensure the appropriate flow rate ratio, it is also necessary to measure the volumetric flow 

rate of additive fluid 𝑄𝐴
𝑣. Results are here omitted for space limits. 

5. Conclusions 

In this paper, a first version of the digital twin of a tubular flow reactor was developed. The analyzed system is 

an inline mixer to produce the sanitizing gel, i.e., an ethanol-water mixture is considered. Firstly, the 1D dynamic 

modeling of the mixer is addressed; geometry, parameters, and operating conditions are defined to reasonably 

describe the process evolution over time. Among others, axial dispersion coefficient and mixing degree are 

evaluated from the post-processing of suitable CFD analysis. Then, different types of control architectures are 

designed to obtain the desired final products, by respecting the required specifications, in terms of mean molar 

fraction of additive fluid, mixing degree, and total mass flow rate. The results show that not only SISO control 

schemes, but also multivariable solutions are possible to guarantee set-point tracking and disturbance rejection. 

Acknowledgments 

This research was funded by the POR FESR project 2014–2020 ‘TURBOFLUX’ promoted by the Tuscany 

region. 

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	Digital Twin of a Tubular Flow Reactor Oriented to the Development Of The Control System