Evaluating the Performance of Yarrowia lipolytica 2.2ab in Solid-State Fermentation under Bench-Scale Conditions in a Packed-Tray Bioreactor

Abstract

Solid-State Fermentation (SSF) offers a valuable process for converting agri-food by-products (AFBP) into high-value metabolites, with Yarrowia lipolytica 2.2ab (Yl2.2ab) showing significant potential under laboratory-scale controlled conditions; however, its assessment in larger-scale bioreactor scenarios is needed. This work evaluates Yl2.2ab’s performance in a bench-scale custom-designed packed-tray bioreactor. Key features of this bioreactor design include a short packing length, a wall-cooling system, and forced aeration, enhancing hydrodynamics and heat and mass transfer within the tray. Preliminary studies under both abiotic and biotic conditions assessed Yl2.2ab’s adaptability to extreme temperature variations. The results indicated effective oxygen transport but poor heat transfer within the tray bed, with Yl2.2ab leading to a maximum growth rate of 28.15 m_gx g_ssdb⁻¹ h⁻¹ and maximum production of proteases of 40.10 U g_ssdb⁻¹ h⁻¹, even when temperatures at the packed-tray outlet were around 49 °C. Hybrid-based modeling, incorporating Computational Fluid Dynamics (CFD) and Pseudo-Continuous Simulations (PCSs), elucidated that the forced-aeration system successfully maintained necessary oxygen levels in the bed. However, the low thermal conductivity of AFBP posed challenges for heat transfer. The bioreactor design presents promising avenues for scaling up SSF to valorize AFBP using Yl2.2ab’s extremophilic capabilities.

1. Introduction

Among non-conventional yeasts of industrial interest, Yarrowia lipolytica (Yl) is a dimorphic microorganism with a unique trait known as metabolic flexibility [1,2,3,4]. This flexibility enables Yl to utilize various carbon-based sources for its metabolism, including hydrophobic and agri-food waste-based substrates [1,2,3,4]. Its metabolic adaptability to these substrates, producing high-value metabolites such as proteases, biofuels, food additives, and therapeutic compounds, makes Yl a promising yeast for diverse industrial applications [1,2,3,4,5,6,7]. Among the possibilities for increasing the metabolic potential of Yl, Solid-State Fermentation (SSF) presents several technical advantages [1,2,3,4,5,6,7,8,9,10] due to its potential to produce high yields of metabolites, and the risk of contamination is lower compared to other biotechnological processes such as Liquid-Based Fermentation (LBF). Additionally, SSF downstream processing is economically more attractive than LBF [4,8].

When agri-food by-products (AFBP) are used as a substrate for Solid State Fermentation (SSF) altogether with Yl, a properly designed bioreactor to ensure efficient metabolic production is required. Factors such as temperature, oxygen, and substrate moisture can significantly impact its metabolic activity [1,2,3,4,5,6,7,8,9,10,11,12,13]. Because of this, most experimental studies assessing the impact of Yl have been carried out under laboratory-scale controlled conditions where the effects of heat and mass transport on its metabolic activity present a minor impact [1,2,3,4]. Among these SSF laboratory-scale studies, Yarrowia lipolytica 2.2ab (Yl2.2ab) has shown significant potential for valorizing AFBP-based substrates to produce metabolites such as proteases, having optimal performance at temperatures around 45 °C [2,14]. This laboratory result makes Yl2.2ab a promising microorganism for study under larger-scale bioreactor conditions, where variations in temperature, oxygen concentration, and substrate moisture can drastically impact its metabolic performance.

Four types of bioreactor designs have been implemented for carrying out conventional or unconventional SSF using synthetic culture media or AFBP as substrate-based, respectively [8,14]. These designs can be classified as (i) reactors without both mixing and forced aeration, (ii) reactors without mixing and with forced aeration, (iii) reactors with mixing and without forced aeration, and (iv) reactors with both mixing and forced aeration. Among the promising conventional bioreactors, packed-bed and packed-tray bioreactors have shown to be effective technologies for scaling up SSF under conventional scenarios [10,11,12,14,15]. However, heat and mass transfer resistances have significantly impacted the performance of the microorganism, an aspect that is exacerbated when AFBP-based substrates are used [10,11,12,13,14,15,16,17]. To this end, studies of Yl under larger-scale scenarios in bioreactors based on packed-bed and packed-tray technologies are limited and need to be analyzed to assess its potential for larger-scale bioreactors. In particular, for Yl2.2ab, these studies need to be initiated to assess its performance under conditions that can elucidate its potential for industrial applications.

This work evaluates the performance of Yl2.2ab in a bench-scale custom-designed packed-tray bioreactor. The bioreactor design, A new system concept for the assessment of SSF, incorporates features of both tray and packed-bed bioreactors, including a low packing height, a wall-cooling system, and forced aeration, using an in-house oxygen dispersion system to enhance hydrodynamics and heat and mass transfer within the bioreaction zone [14,15]. Preliminary experimental and modeling studies under both abiotic and biotic conditions were carried out to shed light on the adaptability and effectiveness of Yl2.2ab in the growth and production of proteases under extreme temperature and moisture variations within the bioreaction zone. Hybrid modeling, which combined Computational Fluid Dynamics (CFD) and Pseudo-Continuous Simulations (PCSs), along with experimentation, elucidated the bioreactor’s performance regarding fluid dynamics and heat and mass transport and their impact on Yl2.2ab growth and protease production. It is worth mentioning that this work, based on a novel bioreactor design, aims to guide future efforts associated with the scaling-up of SSF to valorize AFBP-based substrates using Yl2.2ab, which presents metabolic flexibility and extremophilic character, as elucidated throughout this research.

2. Materials and Methods

2.1. Microorganism

Lyophilized Yl2.2ab, from the collection of the solid-fermentation pilot plant of the Metropolitan Autonomous University [18], was suspended with 10 mL of a sterile 0.01% (v/v) Tween-80 solution. Then, 1 mL of the cell suspension was inoculated in an Erlenmeyer flask containing 30 mL of potato dextrose agar (PDA) and incubated at 45 °C for eight days. The cells were collected by adding 30 mL of a sterile 0.01% (v/v) Tween-80 solution and shaking them at medium speed with a magnetic stirrer on a shaking rack to detach the cells from the agar surface. Finally, 500 μL of the cell solution was mixed in vials with 500 μL of a 30% (v/v) glycerol solution and sterilized glass beads to preserve the microorganism. The preserved strain was kept refrigerated at 4 °C until use.

2.2. Inoculum Preparation

Three to four glass beads were taken from the vials and placed in flasks with PDA. The flasks were incubated at 45 °C for 8 days. The cell culture medium was collected by adding 3 mL of a sterile 0.01% (v/v) Tween-80 solution and shaking it with a sterile magnetic bar. Then, a 100-μL suspension aliquot was taken and diluted to a ratio of 1:100 with sterile 0.01% (v/v) Tween-80 solution, and finally, the cells were counted in a Neubauer^® (Marienfeld, Germany) chamber, with 1 × 10⁹ cells per gram of solid support on a dry basis (cell g_ssdb⁻¹).

2.3. Solid Culture Medium (Fermentable Solid Mass)

The tray was packed with pellets of a solid culture-based medium previously treated and containing 46.7% of fruit and vegetable by-products and 53.3% of soybean paste. The fruit and vegetable by-products were dehydrated before their use and, along with the soybean paste, were ground to homogenize the pellet size (1.41–1.68 mm). The tray was packed with 400 g of the moisturized fermentable solid mass (fruit and vegetable by-products, also referred to as AFBP throughout the document, and soybean paste). The fermentable solid mass, before being packed in the bioreactor, was moisturized with 240 mL of the mineral salt solution containing ions and micronutrients (as described below) required for the growth and metabolism of Yl2.2ab and then inoculated with a solution of 1 × 10⁹ cells g_ssdb⁻¹, with an initial moisture of 60% in the solid mass [2,14,18]. The tray (300 cm²; 15 × 20 cm), packed with 400 g of the moisturized solid culture medium, was adjusted to have a packing height of 2 cm. SSF in the bench-scale packed-tray bioreactor was carried out with a cooling temperature of 45 °C for 72 h, supplying saturated air at a constant inlet flow rate of 300 mL min⁻¹. Note that the moisture, nutrients, and micronutrients contained in the fermentable solid mass, as well as the initial operational temperatures set in the bioreactor, were conditions determined in laboratory-based experimentation to optimize the performance of Yl2.2ab in terms of growth and production of proteases.

Mineral Salt Solution (Micronutrients)

The mineral salt solution was prepared with the following composition (g L⁻¹): 0.02 (NH₄)₂SO₄; 1.0 KH₂PO₄; 0.5 MgSO₄7H₂O; 0.5 KCl; and 30 C₆H₁₂O₆. The salts were dissolved in a 0.2 M NaOH-NaH₂PO₄ buffer solution (pH of 12 and 5 mM CaCl₂) [2,14,19].

2.4. Chemical and Elemental Composition of the Solid Culture-Based Medium

Nitrogen content was determined by the Micro–Kjeldahl method [20], and total sugars were measured by the phenol-sulfuric method [21]. Water activity (a_w) was assessed with an AQUA Lab^® CX2 system (Decagon, Pullman, WA, USA), and moisture content was measured with a Thermobalance (OHAUS^®, Heuwinkelstrasse, Switzerland). Elemental analysis of total carbon (C), hydrogen (H), nitrogen (N), and oxygen (O) contents was performed using an Elemental Analyzer^® (Perkin Elmer Series II CHNS/O Analyzer 2400, Waltham, MA, USA). The chemical and carbon-based elemental composition for protein (CH₁.₉₄O_0.56N_0.27), fat (CH_1.84O_0.114), carbohydrate (CH₂O), and fiber (CH_1.67O_0.83) were determined for the fruits and vegetables (CH_2.08O_0.82N_0.035) and soybean paste (CH_1.85O_0.75N_0.144) packed in the bioreactor tray.

Table 1. Chemical and elemental composition of the components of the solid culture-based medium (AFBP).

Component (%)	Fruits and Vegetables	Soy Paste
Moisture	5.09	6.91
Protein	7.43	34.56
Carbohydrates	73.04	52.01
Fat	2.02	1.36
Fiber	11.13	5.30
Ash	6.38	6.77
Element (%)
C	66.72	44.20
H	11.58	6.83
N	2.80	7.43

presents the chemical and elemental composition of the components of the solid culture-based medium.

2.5. Enzyme Extraction and Proteolytic Activity

To obtain the enzymatic extract, 20 mL of distilled water was used for every 6 g of fermented dough. The fermented material was shaken for 10 min and then centrifuged at 7000 rpm for 10 min. The precipitate was discarded, and the remaining liquid (supernatant) was used to determine the proteolytic activity.

Proteolytic activity in the extracts was determined using a modified version of the method reported in the literature [22]. A 1% casein solution was prepared in a 50 mM phosphate buffer solution (pH of 7) containing 50 mM CaClCO₂. For each assay, 100 μL of the enzyme extract was mixed with 900 μL of the casein solution. The reaction was carried out at 40 °C for 10 min, and then 1 mL of 5% trichloroacetic acid (TCA) at 4 °C was added to stop the reaction. The samples were centrifuged at 10,000 rpm for 10 min, and the precipitate was discarded. The supernatant was recovered and filtered through fine-pore filter paper (Per-Filter Grade 615, pore opening of 8 μm). Finally, the filtrate was read using a spectrophotometer at 280 nm. A control was prepared with 100 μL of enzyme extract and 900 μL of buffer solution, treated the same way as the samples. A tyrosine calibration curve (1 mg mL⁻¹) was used. One unit of protease activity was defined as the amount of enzyme necessary to release 1 μg of tyrosine per minute under the assay conditions.

2.6. Physical and Thermodynamic Properties of the Solid Culture-Based Medium

Some physical properties of the solid culture medium were determined using well-established correlations. The individual density (ρ_i) of each component and the compositional density of pellets packed in the bioreactor tray were determined using the following equations [14,23,24]:

$${\rho }_w=997.18+0.0031439 T-0.0037574 T^2$$

(1)

$${\rho }_p=1329.9-0.51814 T$$

(2)

$${\rho }_f=925.59-0.41757 T$$

(3)

$${\rho }_c=1599.1-0.31046 T$$

(4)

$${\rho }_{fi}=1311.5-0.36589 T$$

(5)

$${\rho }_a=2423.8-0.28063 T$$

(6)

where ${\rho }_w, {\rho }_p, {\rho }_f, {\rho }_c, {\rho }_{fi}, \mathrm{and} {\rho }_a$ are the individual densities for water (w), protein (p), fat (f), carbohydrate (c), fiber (fi), and ash ($a$), respectively, and T is the temperature, in °C. The density of solids was calculated using the following equation:

$${\rho }_b=\frac{1}{\sum X_i/{\rho }_i}$$

(7)

where ${\rho }_b$ is the density of solids, $X_i$ is the mass fraction of each component, and ${\rho }_i$ is the individual density of each component.

The procedure proposed by Choi et al. [25] was applied to determine the thermal conductivity of the solid culture-based media. This method calculates thermal conductivity ($k$) based on the conductivities ($k_i$) and the volumetric fractions of each component ($X_{vi}$):

$$k_b=\sum \left(k_i{X}_{vi}\right)$$

(8)

Conductivity values in W·(m·K)⁻¹ were calculated at the required temperature (T, in °C) using the following equations:

$$k_w=0.57109+0.0017625 T-6.7306\times {10}^{-6} T^2$$

(9)

$$k_p=2.2196+0.0062489 T+1.0154\times {10}^{-4} T^2$$

(10)

$$k_f=0.1807+0.0027604 T-1.7749\times {10}^{-7} T^2$$

(11)

$$k_c=0.2014+0.0013874 T-4.3312\times {10}^{-6} T^2$$

(12)

$$k_{fi}=0.18331+0.0012497 T-63.1683\times {10}^{-6} T^2$$

(13)

$$k_a=0.3296+0.001401 T-2.9039\times {10}^{-6} T^2$$

(14)

where $k_w, k_p, k_f, k_c, {\mathrm{a}\mathrm{n}\mathrm{d} k}_{fi}$ are the conductivities for water, protein, fat, carbohydrates, fiber, and ash, respectively. The volumetric fraction of each component was determined using the following equation:

$$X_{vi}=\frac{X_i{\rho }_b}{{\rho }_i}$$

(15)

The conductivity of the solid culture medium packed in the bioreactor tray was calculated using the value of the fraction occupied by the solid culture medium ($X_{vb}$) and the void fraction ($X_{va}$). The solid-based fraction was calculated with the following equation, considering that the mass fraction of the solid culture medium is equal to 1:

$$X_{vb}=\frac{X_b{\rho }_{ap}}{{\rho }_b}$$

(16)

where $X_b$ is the mass fraction of the solid culture-based medium and ${\rho }_{ap}$ and ${\rho }_{bs}$ are the apparent and real densities, respectively. The void fraction ($X_{va}$) was calculated by using the following equation:

$$X_{va}=1-X_{vb}$$

(17)

Thus, using $X_{va},\mathrm{the}$apparent density of the packed tray can be determined as ${\rho }_{ap}{=\rho }_b\left(1-X_{va}\right),$and the apparent conductivity of the packed tray ($k_{ap}$) was calculated with the following equation:

$$k_{ap}=k_a{X}_{va}+k_b{X}_{vb}$$

(18)

The heat capacity of the solid-based medium was determined as a function of its components [26,27] using the following equation:

$$C{p}_b=1.42mc+1.549mp+1.675mf+0.837ma+4.187mw$$

(19)

where mc, mp, mf, ma, and mw are the individual mass fractions of carbohydrates (c), proteins (p), fats (f), ash (a), and water (w), respectively.

Table 2. Physical and thermodynamic properties of solid packed in the bioreactor tray.

Property		Value
Apparent density, ${\mathit{\rho }}_{\mathit{a}\mathit{p}}$	$\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$	828.6
Solid density, ${\mathit{\rho }}_{\mathit{b}}$	$\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$	1381.2
Thermic conductivity, ${\mathit{k}}_{\mathit{a}\mathit{p}}$	${\mathrm{W}\left(\mathrm{m}\mathrm{K}\right)}^{-1}$	0.158
Heat capacity, $\mathit{C}{\mathit{p}}_{\mathit{b}}$	$\left(\mathrm{J}\right) {\left(\mathrm{g}\mathrm{K}\right)}^{-1}$	1.840

shows the calculated values for the thermal conductivity of the solid culture-based medium.

2.7. Bench-Scale Packed-Tray Bioreactor

The concept of a wall-cooled packed-tray bioreactor emerged from the integration of the low-packing-height characteristic of tray bioreactors with the wall-cooled system and forced-aeration features of packed-column bioreactors. This design combines the benefits of both types, enhancing hydrodynamics and heat and mass transfer mechanisms essential for hosting SSF-valorizing AFBP-based substrates. The rectangular aspects of the tray were maintained to achieve a lower packing height; the challenge was designing the air diffuser to feed air (oxygen) by convection through the length packed with AFBP-based pellets and improve convective mass and heat transfer in the bioreaction zone.

Experimentation was carried out in this bench-scale packed-bed bioreactor to mimic the performance of Yl2.2ab under industrial scenarios. These scenarios include determining how fluid dynamics and mass transport impact the transport of oxygen to the solid-based phase inoculated with Yl2.2ab and how fluid dynamics and heat transport resistances, due to the poor conductivity of the solid-based medium (based on AFBP), affect the growth and metabolic activity of Yl2.2ab.

Figure 1 shows the bioreactor design, which, as mentioned earlier, was constructed as a rectangular vessel with a total volume of 4.5 L. It consists of two modules coupled together by stainless steel screws, and the top cover is integrated in the same way. The bioreactor was designed to include various sensors (instrumentation) to monitor in-line temperature, pressure drop, and species such as water, oxygen, and carbon dioxide [14].

Thus, the hypothesis behind the bioreactor design posited that the air diffuser would improve oxygen distribution along the packing length. Additionally, we hypothesized that the short packing length, convection, and cooling from the walls would regulate the temperature to levels favorable for Yl2.2ab growth and metabolic reactions based on laboratory results. Our third hypothesis was that this design would also reduce the drying of the solid-based medium. To assess these hypotheses, three different types of experiments were considered in the designed bioreactor:

(i)

An abiotic heat transfer experiment was carried out to determine if the temperature could be homogeneous before starting the bioreaction at inlet volumetric flow rates of air of interest for SSF. It was essential to ensure that the temperature was conducive to optimal Yl2.2ab growth and protease production, as identified at the laboratory scale.

(ii)

An abiotic mass transfer experiment was conducted to assess how oxygen is properly transported along the packing length at different volumetric flow rates.

(iii)

A biotic experiment was carried out to elucidate how Yl2.2ab behaves under scenarios where fluid dynamics, mass transport, and heat transport mechanisms impact its growth and the production of proteases.

It is worth mentioning that these experiments, although preliminary, were essential for future experimental work associated with SSF-valorizing AFBP using Yl2.2ab.

Table 3. Bioreactor operating conditions in the abiotic studies.

Parameter	Magnitude
Fermentable solid mass	53.3% soybean paste and 43.7% fruit and vegetable by-products
Heating (cooling) system temperature	45 °C
Inlet flow rate (saturated air)	200, 300, and 400 mL min−1
Packed-tray height	2 cm
Packed-try density	0.66 g cm−3
Packed-tray mass (moistened)	400 g
Initial moisture of the bed	60%
Particle size of packing	1.41–1.68 mm
Void fraction of the packed bed	0.4

shows the operating conditions and bed properties used during the abiotic experiments. Note that under the biotic experiment, the inlet flow rate of the air was 200 mL min⁻¹. Aside from this, the other operating conditions and bioreactor parameters were similar to the abiotic experiments.

2.7.1. Airtightness Test

The bioreactor’s airtightness was determined by testing two different types of neoprene O-ring gaskets, i.e., rectangular and round, as follows: first, aeration flow was supplied to the bioreactor. Then, the aeration flow was stopped, and the inlet and outlet valves were closed. Afterward, the pressure inside the system was recorded every 10 min for 1 h. This test was carried out before starting every experiment to ensure that the system was not leaking.

Table 4. Physical properties of neoprene O-ring gaskets.

	Neoprene Gaskets
Geometry	Rectangular	Circular
Operating temperature	−40 to 93 °C	−20 to105 °C
Density	0.9 g cm−3	1.45 g cm−3
Thickness	6.35 mm	4.7 mm

presents the properties of the gaskets, elucidating how the round gasket has a larger density than the rectangular one.

Figure 2 displays the bioreactor system during the airtightness test, evaluating the round and rectangular gaskets. The rectangular gasket did not provide a hermetic seal, causing significant pressure drops. In contrast, the round gasket offered a tight seal of the system with no observed pressure drops. This was attributed to the larger density of the round gasket, leading to less deformation and a more robust seal between the modules that comprise the bioreactor body. Thus, during abiotic and biotic experiments, the round gasket was used to ensure a proper seal of the bioreactor.

2.7.2. Monitoring of Temperature

The temperature was measured in the packed tray using several thermocouples positioned in different zones. The temperature data were recorded online every 5 min using a data acquisition interface. During abiotic and biotic experiments, temperature was monitored at different positions of the packed region. Figure 3 shows the zones where the temperature was monitored to quantify temperature gradients from the inlet to the outlet and from the cooling system to the center of the packed region.

2.7.3. Respirometry

The macroscopic performance of Yl2.2ab was tracked by monitoring the consumption of O₂ and the production of CO₂ by the microorganism. The bioreactor was supplied with saturated air to ensure the microorganism’s respiration (O₂) and remove the CO₂ and metabolic heat. The air effluent was dehydrated using a silica gel column. The air effluent was then directed to the gas chamber, where Vernier^® CO₂/O₂ gas sensors measured the CO₂ and O₂ concentrations. The LabPro^® interface and LoggerPro^® software (https://www.vernier.com/downloads/logger-pro-demo/, accessed on 22 March 2024) of the Vernier^® sensors performed the online data acquisition. Concentrations of CO₂ and O₂ were obtained as percentage values (mL gas per 100 mL of air).

2.8. Modeling and Simulations

The modeling of the packed-tray bioreactor was conducted using a hybrid framework. Before and after the bioreaction zone, Computational Fluid Dynamics (CFD)-based simulations were implemented to describe transport phenomena at the local level considering the system in 2 dimensions (2D). To model the packed tray (also referred to as the packed bed). When the microorganism was inoculated over the APBP-based pellets, biological reactions following a macroscopic approach were considered. The specifics of the two types of modeling, i.e., CFD and PCSs, can be reviewed in the literature [28,29]. Before and after the packed tray, the following governing equations ex-pressed in vectorial form were applied to simulate the performance of the bioreactor using CFD:

Hydrodynamics, considering that the fluid is incompressible and Newtonian, with values of ${\mu }_f$ and ${\rho }_f$ associated with air supplied in the bioreactor:

$$\nabla ·{\mathsf{u}}_{\mathsf{f}}=0$$

(20)

$${\rho }_f\frac{{\partial \mathsf{u}}_{\mathsf{f}}}{\partial t}=-\nabla p+{\mu }_f{\nabla }^2{\mathsf{u}}_{\mathsf{f}}$$

(21)

Mass transfer, considering the molecular diffusion of different species (CO₂, O₂, and H₂O) in nitrogen under diluted conditions. Fick’s constitutive equation was used to describe diffusion mechanisms:

$$\frac{\partial c_{i_f}}{\partial t}=-{\mathsf{u}}_{\mathsf{f}}·\nabla c_{i_f}+\nabla ·\left(D_{i_f}\nabla c_{i_f}\right)$$

(22)

Heat transfer, considering Fourier’s constitutive equation and the conductivity of air:

$${\rho }_f{C}_{pf}\frac{\partial T_f}{\partial t}=-{\rho }_f{C}_{pf}{\mathsf{u}}_{\mathsf{f}}·\nabla T_f+\nabla ·\left(k_f\nabla T_f\right)$$

(23)

Initial and boundary conditions were assigned according to the physics associated with the bioreactor operation, which also depended on the operational conditions set for each experiment, under biotic or abiotic conditions.

The following heat and mass transfer governing equations based on PCSs using a 2D pseudo-homogeneous model, were used to describe transport phenomena and bioreactions in the packed zone, in which the AFBP-based support was inoculated with Yl2.2ab.

$$\frac{\partial c_{i_p}}{\partial t}=-{\mathsf{u}}_{\mathsf{p}}·\nabla c_{i_p}+\nabla ·\left(D_{i_p}\nabla c_{ip}\right)\pm {{{\mathit{\rho }}_{\mathit{a}\mathit{p}}Y}_{i/{CO}_2}R}_{{CO}_2}$$

(24)

$$\begin{gathered} {\rho }_{pb}{C}_{pb}\frac{\partial T_p}{\partial t}=-{\rho }_f{C}_{pf}{\mathit{u}}_{\mathit{p}}·\nabla T_p+\nabla ·\left(k_{eff}\nabla T_p\right)+\underset{evaporation}{\underbrace{q_{evap}}} \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\underset{reaction}{\underbrace{{\mathit{\rho }}_{\mathit{a}\mathit{p}}\left(-∆H_{rc}\right){Y_{c/{CO}_2}R}_{{CO}_2}}} \end{gathered}$$

(25)

Hydrodynamics was simulated using the model developed for the studied reaction system in our previous contribution [15]. It is worth noting that when the packing (AFBP-based pellets) in the tray was not inoculated with Yl2.2ab, reaction terms were not included in the heat and mass transfer governing equations. The initial and boundary conditions were as stated in the literature for the same reactor conception, i.e., the wall-cooled packed-bed reactor, and are given as follows considering a 2D pseudo-homogenous model [26,27,28,29,30]:

Initial conditions:

$$t=0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{u}_z=u_{zss}$$

(26)

$$C_{ip}=C_{i0}$$

(27)

$$T_p=T_{p0}$$

(28)

Boundary conditions:

$$z=0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{u}_{pz}=u_{z0}$$

(29)

$$u_{z0}{c}_{i0}=c_{ip}{u}_{pz}-D_{ip}\frac{\partial c_{ip}}{\partial z}$$

(30)

$$u_{z0}{\rho }_{f}C{p}_f{T}_0=u_{pz}{\rho }_{f}C{p}_f{T}_p-k_{eff}\frac{\partial T_p}{\partial z}$$

(31)

$$z=L\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\frac{\partial {\mathrm{u}}_{\mathrm{p}\mathrm{z}}}{\partial \mathrm{z}}=\frac{\partial {\mathrm{c}}_{\mathrm{i}\mathrm{p}}}{\partial \mathrm{z}}=\frac{\partial {\mathrm{T}}_{\mathrm{p}}}{\partial \mathrm{z}}=0$$

(32)

$$\begin{gathered} \begin{array}{cc}\hfill x=0 \\ x=R_{Wall}& \frac{\partial u_{pz}}{\partial x}=\frac{\partial c_{ip}}{\partial x}=\frac{\partial T_p}{\partial x}=0\hfill \end{array} \end{gathered}$$

(33)

$$u_{pz}=0 \mathrm{and} \frac{\partial c_{ip}}{\partial x}=\frac{\partial T_p}{\partial x}=0$$

(34)

$$-k_{\mathrm{e}\mathrm{f}\mathrm{f}}\frac{\partial T_{\mathrm{p}}}{\partial \mathrm{x}}=h_w\left(T_{\mathrm{p}}-T_{\mathrm{c}}\right) \mathrm{o}\mathrm{r} \frac{ \partial T_{\mathrm{p}}}{\partial \mathrm{x}}=0$$

(35)

Although it is a simplified model to describe such a complex SSF process in a bench-scale bioreactor, it captures the main mechanisms involved in the catalytic bed, such as mass and heat transfer, convection, dispersion, conduction, evaporation, as well as the impact of the reaction. Hence, the 2D pseudo-homogeneous model worked for the present research, but it needs to be improved in future research for larger-scale applications. Complementing the experimental design behind the research hypotheses associated with the bioreactor design, the aim of the modeling was to conduct a preliminary study to shed light on the following:

(i)

Determine how the forced-aeration dispersion system works, evaluating if its design properly impacts hydrodynamics, and how air is distributed along the packed tray.

(ii)

Assess how oxygen is distributed in the packed tray since its presence is essential for different biological reactions.

(iii)

Provide insights into the complex performance of the SSF and elucidate challenges in describing the performance of Yl2.2ab when using AFBP as a substrate source.

Numerical solutions of the governing equations describing the performance of the wall-cooled packed-tray bioreactor were carried out using the numerical framework of COMSOL Multiphysics 4.4^®. To discretize and solve the parabolic partial differential equation, the finite element method (FEM) was used for the discretization of spatial terms, while the Backward Differentiation Formula (BDF) was used as the default time-stepping algorithm.

2.8.1. Bioreaction: Kinetics and Heat of Reaction

The global bioreaction based on empirical formulas for the studied system is presented in Equation (36) [26].

Table 5. Yield coefficients associated with Equation (36).

Yield Coefficient	Value	Units
$\mathit{S}\mathit{u}\mathit{b}\mathit{s}\mathit{t}\mathit{r}\mathit{a}\mathit{t}\mathit{e},{\mathit{Y}}_{\mathit{S}/{\mathit{C}\mathit{O}}_{\mathbf{2}}}$	3.38	[mol S ∙mol CO2−1]
$\mathit{O}\mathit{x}\mathit{y}\mathit{g}\mathit{e}\mathit{n},{\mathit{Y}}_{{\mathit{O}}_{\mathbf{2}}/{\mathit{C}\mathit{O}}_{\mathbf{2}}}$	0.89	[mol O2 ∙mol CO2−1]
$\mathit{B}\mathit{i}\mathit{o}\mathit{m}\mathit{a}\mathit{s}\mathit{s},{\mathit{Y}}_{\mathit{X}/{\mathit{C}\mathit{O}}_{\mathbf{2}}}$	2.38	[mol X∙ mol CO2−1]
$\mathit{W}\mathit{a}\mathit{t}\mathit{e}\mathit{r},{\mathit{Y}}_{\mathit{W}/{\mathit{C}\mathit{O}}_{\mathbf{2}}}$	1.08	[mol W∙ mol CO2−1]

presents yield coefficients obtained from elemental balances (C, H, O, and N) carried out for AFBP, Yl2.2ab, oxygen consumed, and COCO₂ and water produced from the metabolic activity of Yl2.2ab. In Equation (36), the stoichiometric balance is stated as a function of the production of CO₂, as can be identified from the yield coefficients.

$$\begin{gathered} Y_{S/{CO}_2}{CH}_{1.87}{O}_{0.71}{N}_{0.0913}+Y_{O_2/{CO}_2}{O}_2\to Y_{X/{CO}_2}{CH}_{1.74}{O}_{0.45}{N}_{0.132}+{CO}_2+ \\ {Y}_{W/{CO}_2}{H}_{2}O \end{gathered}$$

(36)

The macroscopic kinetic model coupled to the reactor model is given by the following equation:

$$\underset{Reaction rate}{{R=R}_{{co}_2}\underbrace{=\frac{{d{Y}_{{co}_2}}_p}{dt}={\mu }_x{X_{{co}_2}}_p\left(1-\frac{{X_{{co}_2}}_p}{{X_{{co}_2}}_{max,}}\right)}}$$

(37)

$$R_i={\mathit{Y}}_{\mathit{i}/{\mathit{C}\mathit{O}}_{\mathbf{2}}}{R}_{{\mathit{C}\mathit{O}}_{\mathbf{2}}} ; i: X,S,W, or C$$

(38)

This unstructured model is well-known in the literature as the logistic kinetic model [7], commonly used to analyze microbial growth kinetics from a macroscopic perspective. Kinetic parameters such as ${\mu }_x \mathrm{a}\mathrm{n}\mathrm{d} {c_{{co}_2}}_{max}$ were varied to elucidate their influence on the performance of the bioreactor design around the apparent ones.

The enthalpy of the bioreaction in Equation (25) must be calculated, using the carbon involved in species reacting and being formed during the biological reaction as the reference; its calculation is based on the following thermodynamic-based equation:

$${∆H}_{rc}=\sum n_p{∆H}_{C_{Products}}-\sum n_r∆H_{C_{Reacteants}}$$

(39)

where ${∆H}_{C_{Products}} \mathrm{a}\mathrm{n}\mathrm{d} ∆H_{C_{Reacteants}}$ are the combustion enthalpies of products and reactants associated with the carbon present in their structures, respectively, while $n_i$ is the number of moles of species i. Note that the enthalpy of the reaction was calculated using stoichiometric coefficients based on biomass such that Equation (36) becomes Equation (40).

$${1.42 CH}_{1.87}{O}_{0.71}{N}_{0.0913}+0.37 O_2\to {CH}_{1.74}{O}_{0.45}{N}_{0.132}+0.42 {CO}_2+0.45 H_{2}O$$

(40)

To calculate combustion-based enthalpies, Tillman’s correlation (Equation (41)) was applied to the substrate and biomass [31].

$${∆H}_C=188 C-718 \frac{Btu}{lb}$$

(41)

where C is the percentage of carbon involved in the empirical formula stated in Equation (40), as follows:

$${∆H}_C(Substatre-based source)=9434 \frac{Btu}{lb}=582 \frac{kJ}{mol }$$

(42)

$${∆H}_C (Biomass)=9095.6 \frac{Btu}{lb}=482.76 \frac{\mathrm{k}\mathrm{J}}{\mathrm{m}\mathrm{o}\mathrm{l}}$$

(43)

$${∆H}_{rc}=482.76 \mathrm{k}\mathrm{J} {\left(\mathrm{m}\mathrm{o}\mathrm{l}\right)}^{-1}-1.42\left(582 \mathrm{k}\mathrm{J} {\left(\mathrm{m}\mathrm{o}\mathrm{l}\right)}^{-1}\right)=-343 \mathrm{k}\mathrm{J} {\left(\mathrm{m}\mathrm{o}\mathrm{l}\right)}^{-1}$$

(44)

2.8.2. Model Parameters

Table 6. Model parameters used during simulations of the performance of the bioreactor design under abiotic and biotic conditions.

Parameter	Description	Units	Value	Status
${\mathit{k}}_{\mathit{f}}$	Thermal conductivity of air	W ${\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$	0.027	-
${\mathit{C}}_{\mathit{p}\mathit{f}}$	Specific heat capacity of air	kJ kg−1 K−1	1.005	-
${\mathit{\mu }}_{\mathit{f}}$	Dynamic viscosity of air	$\mathrm{P}\mathrm{a}\mathrm{s}$	0.01907	-
${\mathit{\rho }}_{\mathit{f}}$	Density of air	$\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$	1.13	-
${\mathit{\rho }}_{\mathit{b}}$	Solid-based density	$\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$	1381.2	Calculated
${\mathit{\rho }}_{\mathit{a}\mathit{p}}$	Packed-tray density	$\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$	828.6	Calculated
${\mathit{Q}}_{\mathit{i}\mathit{n}}$	Inlet flow rate	$\mathrm{c}{\mathrm{m}}^3{\mathrm{m}\mathrm{i}\mathrm{n}}^{-1}$	200–400	Operation variable
$\mathit{ϵ}$	Void fraction in the tray	Dimensionless	0.4	Calculated
${\mathit{d}}_{\mathit{p}}$	Pellet diameter	$\mathrm{m}\mathrm{m}$	1.41–1.68	Calculated
${\mathit{D}}_{\mathit{i}\mathit{p}}$	Effective dispersion coefficient	${\mathrm{m}}^2{\mathrm{s}}^{-1}$	1.67 × 10−11	Calculated
${\mathit{k}}_{\mathit{e}\mathit{f}\mathit{f}}$	Effective thermal conductivity	W ${\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$	0.1048	[32]
${\mathit{k}}_{\mathit{a}\mathit{p}}$	Thermal conductivity of the solid	W ${\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$	0.158	Calculated
${\mathit{\mu }}_{{\mathit{C}\mathit{O}}_2}$	Apparent specific rate coefficient based on the production of CO2	${\mathrm{h}}^{-1}$	0.64	Calculated
${\mathit{X}}_{{{\mathit{C}\mathit{O}}_{\mathbf{2}}}_{\mathit{m}\mathit{a}\mathit{x}}}\left({\mathit{c}}_{{{\mathit{C}\mathit{O}}_{\mathbf{2}}}_{\mathit{m}\mathit{a}\mathit{x}}/}{\mathit{\rho }}_{\mathit{s}\mathit{s}\mathit{d}\mathit{b}}\right)$	Apparent coefficient of the maximum amount of CO2	mgCO2 gssdb−1	153.48	Calculated
${\mathit{h}}_{\mathit{w}}$	Wall heat transfer coefficient	W ${\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$	0.0511	[29]
	Bed height	$\mathrm{m}$	0.02	Calculated
${\mathit{T}}_{\mathit{c}}$	Coolant temperature	$\mathrm{K}$	313	Operation variable
${\mathit{T}}_{\mathbf{0}}$	Inlet temperature in the packed tray	$\mathrm{K}$	313	Operation variable
${\mathit{T}}_{\mathit{r}}$	Inlet temperature in the system	$\mathrm{K}$	298	Operation variable
$\mathit{M}$	Moisture content	%	60	Operation variable

presents the model parameters used in the solution of the bioreactor model. Most parameters were determined from correlations, while others were calculated in this work.

3. Results and Discussion

This section is divided into three subsections to emphasize the main results of this contribution. Section 3.1 presents results associated with hydrodynamics, with the aim of assessing how the in-house air distributor works and analyzing the flow patterns before and after the packed zone as well as within it. Section 3.2 shows the results associated with mass transfer under abiotic conditions, providing inferences on how oxygen present in the fed air is transported and distributed in the bioreaction region. Section 3.3 analyzes heat transfer under abiotic conditions to evaluate how the cooling system works and to elucidate the magnitude of the temperature gradient in the bioreactor design, especially in the bioreaction region, which is packed with the AFBP-based substrate and has lower conductivity compared to synthetic-based supports. To this end, the experimental results are presented, followed by modeling results. Finally, Section 3.4 presents the experimental results of the performance of Yl2.2ab in the bench-scale bioreactor. Due to the heat released by the reaction and the low conductivity of the AFBP-based substrate, temperature gradients are expected. Thus, by analyzing macroscopic respirometry data, monitoring the in situ bed temperature, and measuring protease activity over time, Thus, by analyzing macroscopic respirometry data, monitoring the in situ bed temper-ature, and measuring protease activity over time, the extremophilic properties of Yl2.2ab, identified under laboratory-controlled conditions, are now being assessed in a bench-scale bioreactor. Additionally, the simulation results obtained with the hybrid-based model are pre-sented to evaluate how transport phenomena impact macroscopic kinetics. Additionally, the simulation results obtained with the hybrid-based model are presented to evaluate how transport phenomena impact macroscopic kinetics.

3.1. Hydrodynamics

Figure 4a–c displays the velocity field at steady state in the bench-scale bioreactor when the inlet flow rate was varied at three levels: 200 mL min⁻¹, 300 mL min⁻¹, and 400 mL min⁻¹. Figure 4d shows the streamlines in the bioreactor, elucidating how the fluid flow patterns were distributed throughout the different regions of the system. Figure 5 displays how the average velocity profile performs along the x-axis, where molecular momentum mechanisms are dominant. The bioreactor can be analyzed in three regions: the first region, i.e., the air distributor, where the in-house designed system feeds the air; the second region, i.e., the packed bed, where the biological reactions take place; and the third region, associated with the head of the reactor, where gases exit the reactor.

Based on these hydrodynamic results, streamlines were obtained (Figure 4d), and the flow patterns corroborate what was elucidated from the velocity fields. When the average velocity magnitude along the x-axis was plotted (Figure 4e), it was inferred that the main shear stresses over the fluid were at the wall, while a pseudo-hydrodynamic plug flow was observed at the core of the bed. Note that based on our hydrodynamic results for the bench-scale packed-tray bioreactor, published in 2019 [15], due to the tube-to-particle diameter ratio, the void fraction was considered constant in the packed region since most of the x-axis and z-axis lead to a pseudo-constant void fraction, while the main fluctuations in void fractions were associated with the wall zone. The inlet flow rate used to obtain Figure 4d,e was 300 mL min⁻¹, which was the flow rate applied during experimentation under biotic conditions, as discussed in Section 3.4.

The distributor worked in a promising way, feeding air through the whole packed region. This is essential for two aspects: moving metabolic heat once the biological reaction starts and feeding oxygen to Yl2.2ab for its metabolic-based oxidation reactions. Nevertheless, at this time, a warning must be given regarding the pressure drop, as identified in 2019 [15], since the accessories, including the air distributor and the outlet flow design, and pellet diameters used to pack the bioreaction region led to high pressure drops (the pressure drop increases from 0.1 to 30,000 Pa m⁻¹), which can have a negative impact on cost when scaling up the bioreactor.

3.2. Oxygen Mass Transport

3.2.1. Experimentation

To analyze how the mass transfer dispersion of oxygen impacts bioreactor performance, particularly in the packed region, residence time distribution (RTD) curves were first obtained experimentally for oxygen at different inlet flow rates: 200 mL min⁻¹, 300 mL min⁻¹, and 400 mL min⁻¹. Figure 5 displays RTD curves for oxygen under different scenarios at the mentioned inlet flow rates, comparing experimental observations, model predictions when determining the dispersion coefficient for oxygen, and the ideal RTD curve for oxygen when there is no dispersion phenomenon involved in the bioreactor. Taking the ideal RTD curve as a reference, it was identified that significant dispersion mechanisms are involved in the studied bioreactor at the inlet flow rates studied. Three regions in the bed can contribute to these dispersion mechanisms, making it difficult to elucidate the dispersion mechanisms for the packed region. Therefore, dispersion analysis was carried out following Levenspiel’s approach [33], in which RTD curves were obtained by introducing a tracer pulse of oxygen at the inlet and measuring its concentration at the outlet over time. This method determined the dispersion coefficient for the entire reactor rather than just the packed region.

The procedure for the determination of the dispersion coefficient is described below:

(i)

Tracer experiment: a known amount of oxygen-based tracer was injected into the bioreactor, and the outlet concentration was monitored as a function of time (see Figure 5).

(ii)

Normalizing the RTD curve: oxygen concentration-based data were normalized to obtain the exit age distribution function:

$$E(t)=\frac{C_{O_2}\left(t\right) }{{\int }_0^{\infty }{C}_{O_2}\left(t\right) dt}=\frac{C_{O_2}\left(t_i\right)}{\sum C_{O_2}\left(t_i\right){∆t}_i}$$

(45)

(iii)

Calculating moments: the mean residence time and variance were computed:

$$\overline{t}={\int }_0^{\infty }tE\left(t\right)dt=\frac{\sum t_i{C}_{O_2}\left(t_i\right){∆t}_i}{\sum C_{O_2}\left(t_i\right){∆t}_i}=\frac{\sum t_i{C}_{O_2}\left(t_i\right)}{\sum C_{O_2}\left(t_i\right)}$$

(46)

$${\sigma }^2={\int }_0^{\infty }{(t-\overline{t})}^{2}E\left(t\right)dt$$

(47)

(iv)

Determining the dispersion coefficient (D_i): the relationship between the variance and the dispersion coefficient was applied to calculate D_i:

$${\sigma }^2=\frac{2D_{i}L}{{u_o}^2}+\frac{L^2}{{u_o}^2}$$

(48)

$$D_i={u_o}^2\left(\frac{{\sigma }^2-{\left\{\overline{ t}\right\}}^2}{2L}\right)$$

(49)

The dispersion coefficients were determined and then used to predict RTD curves, as presented in Figure 5. Observations were predicted properly considering experimental deviations. As the inlet flow rate increased, deviations were higher but acceptable, providing a clear idea of the effect of dispersion mechanisms in the transport of oxygen species in the bioreactor.

Table 7. Parameters determined from RTD curves.

Flow (mL min−1)	Experimental
	$\overline{t}$	${\sigma }^2$	$D_i/u_{o}L$
200	18.78	89.15	0.125
300	11.89	33.75	0.117
400	10.52	19.92	0.102

presents the values for the module $\raisebox{1ex}{$D_i$}\!\left/ \!\raisebox{-1ex}{$u_{o}L$}\right.$ for each inlet flow rate, considering that $u_o$ was taken as the inlet velocity calculated from the inlet flow rate and L is the length of the packed region. Note that D_i is an apparent parameter that contains dispersion mechanisms involved in the three regions of the bioreactor: distributor-based, packed, and head regions. To this end, these results suggest that diffusion, back-mixing, and even dead zones play significant roles in the overall dispersion observed in the bioreactor. The value of the module decreases as the inlet flow rate increases, indicating that at larger inlet flow rates, back-mixing mechanisms become dominant. As a reference. [34] reported that $\raisebox{1ex}{$D_i$}\!\left/ \!\raisebox{-1ex}{$u_{o}L $}\right.$= 0.141 for a tubular-based reactor, using bromocresol green as a tracer and a bed with a void fraction of 0.4, while Rojas et al. [35] reported that $\raisebox{1ex}{$D_i$}\!\left/ \!\raisebox{-1ex}{$u_{o}L$}\right.$= 0.145 for an industrial leaching system, adjusting the experimental values to the serial tank dispersion model.

3.2.2. Simulations

Once the dispersion coefficient was determined via RTD curves, this parameter, although apparent, was used to predict oxygen concentration profiles in the bioreactor, considering it isothermal at 40 °C. Figure 6a depicts the bioreactor’s oxygen concentration via a surface predicted at three different operational times (0, 1, and 6 h) and different inlet flow rates (200 mL min⁻¹; 300 mL min⁻¹; and 400 mL min⁻¹). Figure 6b shows the average oxygen concentration obtained from the surface prediction in the packed region of the bioreactor as a function of time at the three inlet flow rates. Note that in these simulations, hydrodynamics was coupled to the mass transport equation under abiotic conditions. At any inlet flow rate, oxygen reached all zones within the packed region at the desired concentration, demonstrating that the oxygen distributor design worked as expected. Regarding the time for the oxygen concentration to reach a pseudo-steady state in the packed region, it took 2 h for the lowest inlet flow rate, while it took 4 h at the highest inlet flow rate due to the effect of the residence time, which is lower for the highest inlet flow rate. Although these simulations were obtained under abiotic conditions, as hypothesized, oxygen would be present before 4 h in the packed region at the studied inlet flow rates. This suggests that once the biological reactions initiate, there would be sufficient oxygen for their metabolic activity, appropriately accomplishing one of the challenges during SSF.

3.3. Heat Transfer

3.3.1. Experimentation

Considering that one of the challenges of using AFBP-based substrate during SSF is designing a reactor that can overcome its low thermal conductivity, the following discussion presents heat transfer under abiotic conditions to elucidate whether conductive and convective heat transfer mechanisms can homogenize the temperature in the packed region before the bioreaction initiates. Figure 7 displays the temperature profiles along the z-axis at different inlet flow rates: 200 mL min⁻¹, 300 mL min⁻¹, and 400 mL min⁻¹. Considering that temperature monitoring was carried out at the center of the bed, a packed-bed depth of 0 mm is located at the exit of the packed region (z = 20 mm), and a packed-bed depth of 20 mm is located at the start of the bed (z = 0 mm), while the coolant temperature was fixed at 45 °C and the inlet temperature of the bioreactor was fixed at 20 °C, the following can be identified:

The temperature gradient along the z-axis of the packed bed varies with the inlet flow rate. As the inlet volumetric flow increased, cooling by convection also increased such that at z = 0 mm, the inlet temperature in the packed region was 39 °C at 400 mL min⁻¹, while it was 41 °C at 200 mL/min. Considering that the whole bioreactor was submerged in a water-based coolant system with a temperature of 45 °C, it is clear that the residence time in the distributor zone was insufficient to heat the fluid to the desired temperature of 45 °C. In fact, the fluid being transported through the packed region at any inlet flow rate did not reach the coolant temperature, elucidating heat transfer resistances by conduction along the x and y axes, with temperature gradients ranging from 2 to 6 °C at an inlet volumetric flow rate of 400 mL min⁻¹ and from 1 to 4 °C at an inlet volumetric flow rate of 200 mL min⁻¹.

Due to the residence time of fluid in the bioreactor, at higher inlet flow rates, the temperature reaches higher values, approaching the coolant temperature. Since at time zero, the entire packed region was at 45 °C, it can be inferred that, on the one hand, the air being supplied to the reactor must be fed at temperatures closer to the coolant temperature since convective heat transfer is dominant in the bed. To this end, feeding the fluid at larger inlet temperatures in the distributor zone will help achieve the desired metabolic temperature in the packed zone once biological reactions begin. On the other hand, once the reaction initiates in the packed region, the low conduction of the AFBP-based substrate will cause metabolic heat to accumulate in the bioreactor, making convection rather than radial cooling the main mechanism for cooling the bioreaction zone. This suggests that the reactor design must be improved to enhance heat transfer mechanisms.

As a reference, Ashley et al. [36] reported a 5 °C difference between the outlet (40 °C) and inlet (35 °C) temperatures when feeding air in a tubular bioreactor in the absence of microbial growth. During fermentation, temperature gradients caused increments in temperature in the packed-bed bioreactor, with lower temperatures at the bioreactor inlet. The lower part of the bed presented lower temperatures due to the convective mechanism and the lower temperature of the fed air, while at higher parts of the bed, convection was insufficient to remove metabolic heat.

3.3.2. Simulations

To carry out heat transfer simulations, essential parameters such as effective thermal conductivity (k_eff) and wall heat transfer coefficient (h_w) are necessary to accurately describe temperatures in the packed region. These parameters were determined from correlations and need to be properly verified in future studies for the system under investigation. The aim of the heat transfer simulations in this section was to demonstrate how convective and conductive mechanisms interact to cool the bioreactor.

Figure 8 displays temperature surface plots obtained at different times (0–8 h) for the bioreactor when operated under various inlet flow rates (200–400 mL min⁻¹). The aeration flow temperature in the bioreactor inlet was maintained at 20 °C, while it is assumed that the initial temperature for starting up the experiments was 45 °C throughout the bioreactor. Once the air is fed, the bioreactor operates in adiabatic mode. As the inlet volumetric flow rate increases, convective heat transfer becomes more effective in removing heat from the bioreactor. Nevertheless, due to the low conductivity of the AFBY-based packing, cooling the bioreactor from 45 to 20 °C requires more than 8 h at inlet flow rates of 200 mL min⁻¹ and 300 mL min⁻¹, while it takes 8 h at 400 mL min⁻¹. Although preliminary, these abiotic simulations suggest that convective heat transfer alone might not be sufficient to cool the bioreactor, agreeing with the literature when using AFBY as a substrate-based source during SSF [36].

3.4. Solid-State Fermentation

3.4.1. Experimentation

Figure 9 displays transient profiles associated with the production rate of carbon dioxide, the consumption rate of oxygen, the temperature at the outlet of the packed region, and the proteolytic activity of Yl2.2ab. These transient profiles were obtained in the bench-scale bioreactor, which operated with an inlet volumetric flow rate of 300 mL min⁻¹ of saturated air, an inlet temperature of 20 °C, an initial moisture content of 60% in the solid mass, and a coolant temperature of 45 °C. Based on the observed CO₂ production rate, Yl2.2ab experienced an adaptation period (lag phase) of approximately 8 h. Following this phase, the microorganisms began to actively metabolize the substrate, entering an exponential growth phase that spanned from 8 to 12 h, with a peak production rate occurring at 12 h. After this peak, there was a significant and constant decline in CO₂ production between 12 and 20 h. Following this decline, the CO₂ production rate exhibited a more gradual decrease, observed from 20 to 40 h.

When relating the CO₂ production rate to the oxygen consumption rate (Figure 9a), temperature (Figure 9b), and proteolytic activity (Figure 9c), the following three aspects can be inferred:

(i)

Oxygen was consumed throughout the entire experiment by Yl2.2ab, with higher consumption observed in the range of 6 to 16 h (from 10 to 12 mg g_ssdb⁻¹ h⁻¹). The minimum consumption rate was observed before 6 h (from 2 to 10 mg g_ssdb⁻¹ h⁻¹). It is worth noting that appreciable consumption of oxygen was identified from 16 to 45 h (from 6 to 10 mg g_ssdb⁻¹ h⁻¹), even when the microorganisms had already entered the stationary phase. This trend in oxygen consumption during the biological process can be explained by the distinct phases of microbial growth and metabolism. Initially, in the lag phase, microorganisms adapt to their new environment, resulting in low oxygen consumption. As they transition to the exponential growth phase, their metabolic activity surges, leading to a significant increase in oxygen consumption. During the subsequent phase, as the microorganisms approach the stationary phase, nutrient decrement, associated with mass transport resistances or depletion, and product accumulation slow their growth or production rate of COCO₂. Despite this, oxygen consumption remains considerable because the microorganisms continue to need oxygen for essential maintenance and cellular functions.

(ii)

Regarding temperature, when the flow of air was supplied, the temperature decreased to 41 °C at the outlet of the packed region due to convective cooling, as demonstrated in our abiotic heat transfer experiment. However, during the lag and exponential phases, the metabolic activity of the microorganisms increased, causing the temperature to rise to 49 °C, with the peak recorded at 18 h . This rise in temperature is due to the exothermic nature of microbial metabolism, along with the low thermal conductivity of the substrate-based packing or significant heat transfer resistances in the core and wall of the packed region. Once the microorganisms entered the stationary phase and the COCO₂ production rates decreased significantly, the metabolic heat generation diminished, causing the temperature to decrease to 45 °C at 36 h , where it then stabilized.

(iii)

Concerning proteolytic activity, it reached a maximum at 36 h of fermentation. This peak occurred when the temperature was close to the optimal level of 45 °C, as determined in laboratory-scale controlled conditions [2]. At this point in the fermentation, Yl2.2ab had entered the stationary phase, characterized by a low production rate of COCO₂ and a significant consumption rate of OCO₂. The optimal temperature likely enhanced enzyme activity, contributing to the observed peak in proteolytic activity. Consequently, after 36 h , as the metabolic processes stabilized and nutrient availability decreased, the proteolytic activity subsequently declined.

As a reference, most yeasts have an exponential growth time ranging from 1 to 2 h, corresponding to an apparent growth rate of 0.7 to 0.35 h⁻¹ [37,38]. The apparent rate of CO₂ production obtained in this study was 0.53 h⁻¹. The maximum COCO₂ production rate obtained in this study was approximately 12 mg g_ssdb⁻¹ h⁻¹, which is much higher than the value reported for M. anisopliae (0.37 mg g_ssdb⁻¹ h⁻¹) [37,38].

3.4.2. Simulations

Figure 10 displays a sensitivity study of bioreactor performance, varying the maximum specific growth rate (μ_X). Simulations were carried out with the model and parameters presented in Section 2.8 under biotic conditions. Given that many transport phenomena and macroscopic parameters are unknown for the studied bioreactor, transport parameters were obtained from the literature, and macroscopic kinetic parameters were varied around an initial value determined using conventional methodologies that neglect transport phenomena, relying solely on Equation (37).

Figure 10a shows our bioreactor simulations when μ_X was varied from 0.23 to 0.66 h⁻¹, finding that μ_X = 0.53 h⁻¹ is a parameter that closely describes observations related to the production rate of CO₂ (see Figure 9). These simulations elucidate the complex interaction of transport phenomena and kinetics, demonstrating that small variations in μ_X lead to different performance outcomes. Given the uncertainty in characterizing transport phenomena, this parameter for Yl2.2ab can be considered an apparent one. It indicates that it only works for our microorganism and can be influenced by other mechanisms that were not properly characterized, such as convective and dispersive heat and mass transport mechanisms, including fluid dynamics.

Figure 10b presents surface plots of the concentration of CO₂ in the bioreactor. In these simulations, three cases were considered: μ_X (or μ) = 0.32, 0.62, and 0.66 h⁻¹. As illustrated in Figure 10a, the value of μ significantly impacted the phases involved in microorganism growth, such that a higher value accelerates all phases, resulting in higher concentrations of CO₂ at earlier times, and vice versa. These simulations demonstrate the sensitivity of the bioreactor’s performance to variations in the maximum specific growth rate, stressing the need for the accurate characterization of transport phenomena and macroscopic kinetics. This will be essential for future novel designs of bioreactor technology for SSF using AFBP substrate-based packed beds.

4. Conclusions

This work elucidates, through a preliminary experimentation design and a simplified modeling framework, the potential of Yl2.2ab in SSF using AFBP in a bench-scale packed-tray bioreactor. The key findings of our research include the following:

(i)

The custom-designed packed-tray bioreactor, featuring a short packing length, a wall-cooling system, and forced aeration, was effective in maintaining necessary oxygen levels but faced challenges with heat transfer due to the low thermal conductivity of the AFBP-based substrate. The forced-aeration system successfully maintained adequate oxygen transport, which is critical for the metabolic activity of Yl2.2ab. Under the tested conditions, Yl2.2ab exhibited a maximum growth rate of 28.15 m_gx g_ssdb⁻¹ h⁻¹ and achieved a maximum protease production of 40.10 U g_ssdb⁻¹ h⁻¹. The microorganism’s metabolic flexibility and extremophilic characteristics were crucial for its performance in SSF, even under varying temperature conditions (40 to 49 °C) within the bioreactor.

(ii)

The integration of CFD and PCSs provided valuable insights into the hydrodynamics and heat and mass transfer phenomena within the bioreactor. The sensitivity study revealed that variations in the maximum specific growth rate (μ_X) significantly impact bioreactor performance, indicating the importance of accurately characterizing transport phenomena and macroscopic kinetics for scaling-up processes.

Further research is needed to scale up the bioreactor design for industrial applications, ensuring that the transport phenomena and kinetic parameters observed at the bench scale are applicable at larger scales. To this end, mass and heat transport parameters under abiotic conditions must be determined following engineering approaches reported in the literature. In addition, the enhancement of the bioreactor’s heat transfer capabilities through improved design or material selection could mitigate the challenges associated with the low thermal conductivity of the substrate. Exploring the use of Yl2.2ab with different AFBP-based substrates and under various environmental conditions will help to generalize the findings and expand the potential industrial applications. Finally, incorporating more sophisticated models, including real-time monitoring and control systems, could improve the accuracy and efficiency in the design, operation, and scaling-up of SSF.