Pressure drop, mechanic deformation, stabilization and scale-up of wheat straw fixed-beds during hydrothermal pretreatment: Experiments and modeling

Accepted Manuscript Pressure drop, mechanic deformation, stabilization and scale-up of wheat straw fixed-beds during hydrothermal pretreatment: Experiments and modeling Wienke Reynolds, Marc Conrad, Sarah Mbeukem, Rainer Stank, Irina Smirnova PII: DOI: Reference:

S1385-8947(18)32201-0 https://doi.org/10.1016/j.cej.2018.11.001 CEJ 20303

To appear in:

Chemical Engineering Journal

Received Date: Revised Date: Accepted Date:

3 August 2018 23 October 2018 1 November 2018

Please cite this article as: W. Reynolds, M. Conrad, S. Mbeukem, R. Stank, I. Smirnova, Pressure drop, mechanic deformation, stabilization and scale-up of wheat straw fixed-beds during hydrothermal pretreatment: Experiments and modeling, Chemical Engineering Journal (2018), doi: https://doi.org/10.1016/j.cej.2018.11.001

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Pressure drop, mechanic deformation, stabilization and scale-up of wheat straw fixed-beds during hydrothermal pretreatment: Experiments and modeling

Wienke Reynolds1*, Marc Conrad1, Sarah Mbeukem, Rainer Stank2, Irina Smirnova1

1

Hamburg University of Technology, Institute of Thermal Separation Processes, Eissendorfer Strasse 38, D-21073 Hamburg, Germany

2

Hamburg University of Applied Sciences, Fakultät Life Sciences, Department Verfahrenstechnik, Ulmenliet 20, 21033 Hamburg, Germany

*

Corresponding author: M.Sc. Wienke Reynolds Tel.: +49 (40) 42878-2988, Fax: +49 (40) 42878 4072 E-mail address: [email protected]

1

Abstract Fixed-bed reactors for liquid hot water pretreatment (LHW) are a promising approach for profitable lignocellulose pretreatment. The flow-through treatment in a tightly packed biomass bed enables high solids loadings and recovery of a considerable hemicellulose oligomer fraction in the liquid product stream. However, the dense biomass packing, as well as the elevated hydrolysate viscosity, cause a significant pressure drop over the bed length, which is likely to compress the fixed-bed irreversibly. This is expected to lead to fluid maldistribution or in the worst case to complete blocking of the reactor. Fixed-bed scale-up, in this case, is therefore not possible without a detailed understanding of the processes inside the bed. This work investigates the pressure drop, fixed-bed mechanics, scale-up as well as possible stabilization techniques of a perfused wheat straw bed during LHW pretreatment experimentally and based on a comprehensive process model. The results show that it is possible to predict the behavior of a fixed-bed with changing bed and fluid properties with the developed model, including heat and mass transfer, reaction kinetics as well as fluid mechanics and bed compression at 3 L lab and 40 L pilot scale. Further, it could be shown that the pressure drop and bed compressibility strongly limit the scale-up potential of the investigated lignocellulose fixed-bed and elaborate stabilization internals are required.

Keywords Liquid hot water; flow-through fixed-bed; pressure drop; compression; modeling; bed stabilization

2

1

Introduction

For LHW treatment in the present work, a flow-through fixed-bed is applied. Hydrothermal treatment, aquasolv or liquid hot water (LHW) is used to pretreat lignocellulosic biomass for separation of the three main fractions hemicellulose, cellulose and lignin for further processing to platform chemicals. The process takes advantage of the auto-ionization of water at elevated temperatures. The H+ ions from auto-ionization as well as from the organic acids released from the biomass’ hemicellulose itself catalyze the cleavage of inter- and intramolecular bonds. The contained hemicellulose is depolymerized via LHW and solubilized together with a small lignin fraction, called aquasolv liquid (AL) lignin [1]. The digestibility of the cellulose in the remaining lignin-cellulose-complex for enzymatic hydrolysis is increased by hemicellulose solubilization and biomass structure alteration. A subsequent enzymatic treatment can then separate the C6sugar fraction from the insoluble aquasolv solid (AS) lignin [2].

In order to build a tightly packed fixed-bed for LHW pretreatment, almost dry and pelletized wheat straw is inserted into the autoclave in a special cartridge. The pellets swell inside the cartridge when being wetted until they form a dense bed, far above the compaction grade of an unforced packing. Depending on the bed structure, the fluid properties (viscosity, density), as well as the process conditions (temperature, pressure, flow rate, etc.), a more or less severe pressure drop due to fluid flow, can occur which exerts a certain force on the packing [3]. In case of a compressible packing, the porosity of the bed will decrease locally in case the compressive strength is exceeded, depending on the compaction grade of the bed material as well as the resistance of the material itself in the uncompressed state. In case the bed is being compressed, the pressure-drop increases even further, leading in turn again to advancing bed compression [4]. In the worst case, this can cause blocking of the fixed-bed and emergency shut-down of the process due to the self-enhancing pressure drop. Therefore, it is necessary to predict the

3

performance of plant-scale equipment by means of model equations for perfused compressible packed beds with respect to bed depth and column diameter.

The solubilization during LHW treatment leads to a solids mass loss of up to 44 wt%, causing, in turn, a porosity change from initially 0.79 to 0.88 during fixed-bed treatment [5,6]. As stated before in Reynolds et al. (2015) [5], two kinds of porosities need to be considered in the biomass fixed-bed: The actual bed porosity ε (formula 9) represents the total fluid volume fraction. The so-called effective flow porosity εeff is the volume fraction, which is actually available for liquid flow, considering biomass swelling and dead zones as well as stagnant liquid on the particle surface. It was shown that εeff reaches a constant value of 0.41 directly after the biomass is swollen, even though hemicellulose is still being solubilized [5]. However, the bed structure and particle size still change and the increasing actual porosity definitely has an impact on the pressure drop [7,8]. Experimental experience showed that the resisting power of the biomass packing decreases faster than the pressure drop with advancing biomass solubilization. At a certain pretreatment progress, the compressive strength is therefore exceeded by the hydrodynamic force, which irreversibly compresses the material without additional stabilization methods. To solve this problem, a quantitative description of pressure drop and fixed-bed mechanics during hot water treatment of lignocellulose is necessary. Both effects are studied and modeled in this work with the aim to develop suitable stabilization methods for large-scale applications. Based on the results from the present work and two previous publications [7,8], a comprehensive fixed-bed model is developed, which depicts the interacting effects of chemical reactions, heat and mass transfer as well as fluid dynamics and bed mechanics with changing fixed-bed properties. Since fixed-beds are used in multiple fields of high-pressure process engineering, the developed model and analysis techniques are also considered important for other applications like preparative HPLC,

4

high-pressure adsorption, distillation and extraction as well as heterogeneous catalysis and highpressure biomass extraction or processes with fluid flow through foam-like packings [9].

1.1

Pressure drop

Calculation of the pressure in fixed-beds that deform under the stress build up by the pressure drop is a rather new research field, especially in combination with changing bed properties due to chemical reaction [8]. But still, the classic models like Darcy’s law or the Ergun equation have shown to be applicable for deformable beds [3] and will, therefore, be applied in this work. The classical Ergun equation requires the mean equivalent spherical diameter of the particle packing, which would not be meaningful for a fibrous packing. In Darcy’s law, however, all pressure drop dependencies are summarized in a so-called permeability K which can be fitted experimentally for any kind of fixed-bed with fluid-flow in the laminar regime: 𝑑𝑝(𝑧,𝑡) 𝑑𝑧

=−

𝜂(𝑧,𝑡)∙𝑈(𝑧,𝑡) 𝐾(𝑧,𝑡)

(1)

Pressure drop correlations usually work with the superficial velocity, noted here with U, in contrast to the interstitial velocity u. The equation which will be applied in this work is the equivalent of the Ergun equation for turbulent flow derived from Darcy’s law, known as Forchheimer equation [4,9] (see equation 5).

1.2

Fixed-beds with changing properties

Depending on the residence time and operation mode of the fixed-bed, porosity and bed structure can significantly vary with time t and bed position z due to partial solubilization of biomass constituents. The solute concentration influences fluid properties like the viscosity η or the density ρ. Furthermore, bed porosity and fluid properties influence the interstitial velocity u as well as the permeability K. In the LHW fixed-bed treatment, these effects are additionally interfering with heat transfer and the solubilization reaction which in turn influences the solid 5

and fluid properties. This results in a complex system of interacting transport effects, which needs to be displayed in a set of connected balancing equations.

Research on changing bed porosity has been published e. g. for wood chip or pulp fiber packings during pulping or displacement washing [4]. But also biotechnological applications are discussed [10]. Often, the permeability K of a fixed-bed with changing properties is expressed as a function of the porosity. The most common relation for this is the Kozeny-Carman permeability model [4,10–13]:

𝐾(𝑧, 𝑡) =

𝜀(𝑧,𝑡)³ 𝜃∙𝑆V (𝑧,𝑡)²∙(1−𝜀(𝑧,𝑡))²

𝜀(𝑧,𝑡)³∙𝑑 (𝑧,𝑡)2

P 𝐾(𝑧, 𝑡) = 180∙(1−𝜀(𝑧,𝑡))²

(2) [4]

(3) [11]

This approach was further combined with the dispersion model for non-ideal flow [14] and radial velocity distributions [15]. Models for bed permeability and hydrodynamics in packings with changing bed characteristics are in most cases expressed in the following form [16]: 𝐾(𝑧,𝑡) 𝐾0

= 𝑓(

𝜀(𝑧,𝑡) 𝜀0

)

(4)

Exemplary approaches by different research groups are summarized in table A.1 in the appendix.

1.3

Bulk solids mechanics and constitutive models

Solids packings have an exceptional position in continuum mechanics and can be settled between fluids and Hook’s solid body [17]. As mentioned in section 1.2, the stress distribution in bulk solids in a cylindrical vessel can be described with an axial force balance, similar to Janssen’s method for the calculation of the stress distribution in hoppers [18].

6

In the classical Janssen’s theory, the force balance comprises gravitational forces and wall friction, which is incorporated into the equation as a horizontal stress ratio [17]. In a perfused bed, this force balance has to be extended by an additional load in flow direction due to the pressure drop [18]. Such force balances have already been applied by several authors [8–10,19] and will be the basis of the tension model in this work.

1.4

Compressible fixed-beds

The pressure drop across the perfused fixed-bed results in an external force on the packing which can cause deformation [9]. Due to connectivity and therefore friction between the particles, a solid stress is build up [4]. If the frictional forces between the particles and at the wall are sufficiently large, the bed may carry an external load. If the compressive strength of the bed is exceeded, it densifies [4]. The entire compressible bed responds to the compressive force by deformation into a more densely packed arrangement [10]. Depending on the type of material, this compression can be reversible (elastic, see e. g. [9]) or irreversible (plastic, see e. g. [8]). The choice of the flowing medium at the same time influences the compressibility by means of the emerging pressure drop (fluid viscosity and density) but also through lubrication between particles [9].

Biological materials show a complex and time-dependent behavior when being loaded, with an inertial deformation resp. consolidation stage at low compression (particle rearrangement/bed consolidation) [20], a non-linear stress-strain behavior and relaxation (rate of stress decline at a constant deformation) [21]. Consolidation is the irreversible bed compaction due to relative movement of particles being rearranged into a denser configuration [10,19]. Furthermore, the filling of voids with fines produced by particle collapse, fiber slipping and fiber orientation changes need to be considered [13][19]. In contrast to particle deformation, consolidation and

7

relaxation effects are irreversible and likely to depend on the deformation speed [19]. In literature, it is also discussed that fluid flow from the fiber packing might work as a viscous damper. Some researchers tried to link the local bed compressibility σ*(z,t) as a function of local bed porosity ε(z,t) in a function of the form σ*(z,t) = f(ε(z,t)), with z being the axial coordinate of the bed. [4]. Such a mostly empirical equation can be a function of particle geometry, packing or orientation [22]. This applies mostly to the irreversible compression of plastic materials with a yield stress. The compressive strength σ*(z,t) must be distinguished from the local bed tension σS(z,t): The bed may carry an external load with a solid tension σs(z,t) < σ*(z,t) in case the frictional forces are sufficiently large to support the bed. Depending on the type of material, the correlation can also be interpreted the other way round, so that the porosity ε(z,t) = f(σs(z,t)) is a response to the local tension (ideal elastic materials). The tension-porosity-correlations used by different authors are listed in table A.2 in the appendix.

If the bed compressibility under an external load is investigated, e. g. by using a pneumatic piston, it can be observed that the local voidage does not change uniformly throughout the bed as the column is compressed [8]. Depending on the intensity of the friction between the particles and the column wall and how the solid stress is transmitted through the bed, the porosity changes more or less with the local pressure [13].

On the basis of the dewatering of pulp suspensions by material compression during the paper production process, further pressure effects can be named. With advancing dewatering, the voids are reduced and the contact between the fibers increases which furthermore are being bent and compressed [10]. Beyond the compaction grade of an unforced packing, this causes internal tensions in the packing which are related to the compressive strength [22]. Same applies for the biomass packing during LHW treatment in this work. The packing is much denser than an

8

unforced packing and therefore already possesses a basic tension due to compression without flow.

1.5

Objectives of this study

Experimental investigations for our previous publication Reynolds et al. (2016)[2] revealed that the tensions inside the fixed-bed during hot-water extraction of hemicellulose are the major limiting factor for process scale-up. For the design of suitable reactors, a more detailed understanding – and ideally a model – of the pressure drop and the fixed-bed mechanics are needed. In order to determine all dependencies in the complex compression behavior of the perfused straw bed, the pressure drop at a certain pretreatment progress and the bed compressibility and rheological behavior without flow are initially investigated separately at ambient conditions. All parameters of the model equations are estimated. Later, the model equations are combined and fed into the existing process model with heat and mass transfer equations and changing bed properties [6]. Fig. 1 displays how the present work completes the results from previous studies and generates, as well as applies, the complete fixed-bed model. The pressure drop model was validated for hot water pretreatment at process conditions and enables prediction of the bed compression at a certain extraction progress. This approach has already been successfully applied by Beavers et al. (1981) [9], who measured pressure drop vs. compression without flow in order to predict the mass flow at a certain pressure drop in highly deformable porous media. However, in contrast to other works (see table A.2), this work differs between the compressive strength σ*, which is described by an empirical equation, and the bed tension σ, which is modeled using an axial force balance. Based on the derived tension equation, suitable stabilization mechanisms are identified and evaluated using the complete fixed-bed model or tested experimentally at laboratory and pilot scale.

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Model parameterization & validation

Experiments

Modeling

Model application

Process design

Batch LHW

Batch kinetics

Scale up

(kinetics estimation, previous work)

(previous work)

(previous/this work)

3L fixed-bed LHW

Solid, fluid & bed properties

Bed compression & stabilization

(previous work)

(this work)

Heat & mass transfer, dispersion

Optimization & operation modes

- Parameter est. - Bed properties - Filling process - Dispersion - Pressure drop - Model validation - Bed stabilization (previous/this work)

40L fixed-bed LHW - Scale-up - Heat transfer - Pressure drop - Bed stabilization (previous/this work)

(unpublished)

(previous work)

Pressure drop & bed compression

Model limitations, transferrability & limitations

(this work)

(unpublished)

Complete model

Techn. evaluation

(this work)

(partly this work)

Experimental verification & application

Fig. 1: Schematic overview of the interaction of experiments, modeling and process design executed in this work and the combination with previous studies [5,6] to generate and apply the complete fixed-bed model in the present publication.

2

Materials and methods

2.1

Biomass

Wheat straw pellets with a moisture content of approx. 10 wt% were purchased from SpeersHoff, Stelle, Germany. Moist, hydrothermally pretreated wheat straw samples were produced according to Reynolds and Smirnova (2018) [6] at 200 °C, 50 bar and 250 g/min in a 3 L 10

laboratory flow-through reactor. The treatment was stopped after 10, 15, 20 and 30 min. to evaluate the influence of treatment the time on pressure drop and mechanical bed properties. Additionally, untreated moist biomass (0 min. case) was tested. All data for solid skeletal density, actual and effective porosity, as well as hemicellulose content at different pretreatment times that are used in this work, were taken from Reynolds et al. (2015) [5].

2.2

Analytical methods

The solid biomass moisture content has been determined gravimetrically in triplicates according to an NREL laboratory procedure [23]. Hydrolysate properties, as well as data for the changing hydrolysate viscosity with treatment progress at ambient conditions, were taken from Reynolds and Smirnova (2018) [6]. The hydrolysate viscosity at elevated temperatures and pressures was measured using a rotational viscometer Rheostress RS75 with a PZ38 measurement geometry in a Thermo Haake D400/300 high-pressure cell at the Ruhr Univerität Bochum, Lehrstuhl für Feststoffverfahrenstechnik. For the test, a sample volume of 32ml was taken from the accumulated hydrolysate of a 30 min. LHW treatment at 200 °C and measured at 30 bar pressure (Helium) and 30 – 80 °C with 10-600 1/s shear rate in 20 steps.

2.3

Pressure drop measurements

Pressure drop measurements with pretreated biomass were executed directly in the LHW hydrolysis plant introduced by Reynolds and Smirnova (2018) [6] and the associated stainless steel cartridges (L/D = 5.2) sealed with slot screens (see fig. 2). The void volume of the cartridges is 3 L with a length of 0.47 m and an inner diameter of 0.09 m. Initial pressurization of the autoclave to 50 bar process pressure was realized with compressed 99.95 % N2. For hot water extraction, demineralized water was continuously pressurized to 50 bar and heated up at a mass flow of 0.25 kg/min in order to perfuse the wheat straw pellets in the reactor from bottom to top.

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Since the LHW pretreatment itself is a comparatively fast reaction with rapidly changing bed properties, the pressure drop dependency on the superficial velocity and the bed porosity was measured as a kind of snapshot after 0 – 30 min. pretreatment time at 20 °C and 50 bar pressure. Later on, the pressure drop at process conditions can be calculated by extrapolation with the actual fluid properties at process temperature. For this, the LHW treatment was interrupted, the plant was cooled down and the reactor pressurized again with nitrogen. The pressure drop was measured at 100 to 400 g/min. mass flow or 2.62 · 10-4 to 1.05 · 10-3 m/s respectively in 20 g/min. steps. The pressure drop of the empty plant with cartridge and slot screens was subtracted. Furthermore, online pressure drop measurements during the LHW treatment were conducted in order to validate the developed permeability correlation.

2.4

Acrylic glass reactor tests

The initial biomass swelling behavior was examined in an acrylic glass reactor with a L/D of 5.2, similar to the stainless steel cartridge. The reactor was used as a replacement for the LHW autoclave in the 3 L plant setup (see fig. 2). Filling tests were run using 750 g wheat straw pellets with a water flow of 250 g/min at 70 °C water temperature and 1 bar pressure.

2.5

Mechanical material testing

Compression experiments were performed using a Zwick/Roell Z010 material testing machine with test expert II software. The AC-driven traverse with an axial Xforce sensor works position controlled. Biomass compression analysis was executed with a piston (89 mm diameter) directly in the stainless steel cartridge (90 mm inner diameter) which is normally used for the highpressure LHW-extraction and sealed at the bottom with a slot screen, enabling water discharge under compression [6]. In order to investigate the changing bed compressibility with varying porosity and hemicellulose content, LHW biomass samples after 0, 10, 15, 20 and 30 minutes

12

treatment time were mechanically tested at ambient conditions and in triplicates. It is important to always keep the biomass wet and at a similar moisture content, which is close to process conditions since the force needed to compress a water-saturated material is substantially less than that needed to compress the same material in air [11].

F Decompression

Fixed-bed

Water outlet

Compression Δp

N2 Compression Water

Fig. 2: Simplified flowsheet of the 3 L plant with pressure drop measurement and the subsequent compression tests in similar reactor geometry with a vertical piston.

For each compression test, a new batch of biomass was applied, since aging behavior of the biomass cannot be excluded. For analysis, 575 g of the wet, pretreated biomass with an adjusted representative moisture content of 80 wt% were loosely filled into the cartridge and the piston was positioned directly at the filling height. Under compression, the biomass packing was only a few cm thick, so that the assumption of an equally distributed porosity is reasonable. The piston compressed the biomass to 50, 60 and 70 % of the initial filling height with a drive of 50 mm/min. and stopped at each position for 10 min. in order to record the biomass’ relaxation behavior. The applied force was recorded. Under compression, the biomass’ moisture content first decreases, voids are filled with water until excess water is squeezed out of the cartridge. Since the critical tension was recorded after 10 min. biomass relaxation at a certain compression,

13

dynamic pseudo-viscous effects due to water being displaced from the packing are not relevant [19]. At this point, it is expected that biomass temperature does not affect its compressibility.

2.6

Fixed-bed stabilization tests

LHW stabilization tests were executed with several cartridge-stabilizer-designs at 3 L lab scale (200 °C, 50 bar, 1 kg biomass, 250 g/min flow, 30 min. treatment duration, L/D = 5.2) and 40 L pilot scale (200 °C, 50 bar, 2.75 – 11 kg biomass, 3 kg/min flow, 30 min. treatment duration, L/D = 2.6, plant description see [2]). The cartridge designs include the classic stainless steel cartridge without any stabilizer (provoking bed compression) or with stainless steel stabilizers as well as a reduced biomass loading. Furthermore, a cartridge with horizontal stabilizers was constructed. The single experiments and designs are listed in table 1 and exemplarily shown in fig. 3.

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Tab. 1: Fixed-bed stabilization experiments. Cartridge-stabilizer design

Tested scale

Effect

Standard cartridge without stabilizer

3 L lab plant

Provoke bed compression and experiment failure

Standard cartridge with vertical

3 L lab plant

Increase wall friction

3 L lab plant

Decrease bed length

Cartridge with combined vertical-

3 L lab and 40 L

Decrease bed length and wall

horizontal stabilizers

pilot plant

friction

Standard cartridge with only 25 %

3 L lab and 40 L

Increase porosity, expanded bed

biomass loading

pilot plant

Standard cartridge with supportive

3 L lab and 40 L

stabilizer Segmented cartridge with horizontal stabilizers

packing (Raschig Super-Ring type 0,1 pilot plant

Increase critical compression tension σ*

(1.4301 stainless steel), Raschig GmbH)

15

No stabilizer

Vertical stabilizer

3 horizontal stabilizers

Combined stabilizer example

Fig. 3: Schematic drawing of the tested stabilizer designs.

2.7

Modeling

The modeling equations on pressure drop and solids tension proposed in this work represent only a specific detail of the complex fixed-bed LHW model, which was developed from the equations in this work and previous publications [5,6]. The final model considers hemicellulose degradation kinetics, heat and mass transfer, non-ideal flow, as well as changing fixed-bed and material properties, during the filling process and the extraction period. In the present work, the complete model was applied in order to simulate the behavior of the compressible reactive fixedbed and for the model-based evaluation of possible bed stabilization techniques. The presented model for the biomass fixed-bed reactor is one-dimensional with a coordinate z along the reactor length, assuming ideal mixing in radial direction. It is assumed that the biomass bed is fully established at the beginning of the process, neglecting the initial swelling of the biomass pellets. The number (20), as well as the size of the discrete stages, stays constant. Solid and liquid phases are treated as continuous phases. It is assumed that hemicellulose and AL-lignin saturation in the liquid phase is not reached and that any solubility effects on the biomass solubilization reactions are covered by a lumped mass transfer resistance term in the

16

mass transfer equations [6]. The modeled solid phase has a constant bulk volume with variable porosity, even if the bed tension exceeds the compressive strength and bed compression is likely to occur. This means that if the bed tension σS exceeds the compressive strength σ*, a variable length of the biomass packing cannot be depicted by the model. This feature is not important for the present work since bed compression should be avoided during the complete pretreatment process and the main focus lies on the tensions inside a stable bed. Bed compression could e. g. be depicted by setting the porosity of the critical discrete stage of the fixed-bed to ε = 1 and equally redistributing the biomass in the residual part of the bed. An alternative but more complicated approach to this would be a varying layer thickness dz which changes due to compression [19]. The complete fixed-bed system was modeled using AspenTech Aspen Custom Modeler TM V8.0 (ACM). The equation system was solved using a backward finite difference discretization method and the implicit Euler approach as integrator method [24]. Water and nitrogen properties are taken from the International Association for the Properties of Water and Steam [25].

AL-lignin kinetics The AL-lignin release is calculated using first-order reaction kinetics and an Arrhenius temperature approach, which were incorporated into the existing fixed-bed model [6]: 𝑑𝑋AL (𝑧,𝑡) 𝑑𝑡

= −𝑌step (𝑧, 𝑡) ∙ 𝑘AL (𝑧, 𝑡) ∙ 𝑋AL (𝑧, 𝑡)

(10)

𝑑𝑌AL (𝑧, 𝑡) 𝑑𝑌AL (𝑧, 𝑡) 𝑑 2 𝑌AL (𝑧, 𝑡) = 𝑌step (𝑧, 𝑡) ∙ (−𝑢(𝑧, 𝑡) ∙ + 𝐷ax (𝑧, 𝑡) ∙ + 𝑘AL (𝑧, 𝑡) ∙ 𝑋AL (𝑧, 𝑡)) 𝑑𝑡 𝑑𝑧 𝑑𝑧 2 (11) With the reaction constant 𝐸

A,AL 𝑘AL (𝑧, 𝑡) = 𝑘AL,0 ∙ exp (− 𝑅𝑇(𝑧,𝑡) )

(12)

17

And the axial dispersion coefficient [6] Dax (z, 𝑡) = 0.1631 · u(z, 𝑡).

(13)

The filling of the reactor is considered using a step function of an imaginary compound with concentration YStep(z,t) of the following form [6]: 𝜀0 ∙

𝑑𝑌step (𝑧,𝑡) 𝑑𝑡

= −𝜀0 ∙ 𝑢(𝑧, 𝑡) ∙

𝑑𝑌step (𝑧,𝑡)

(14)

𝑑𝑧

The boundary conditions (Dirichlet, Neumann, and Danckwerts) and initial conditions are defined as follows Inlet 𝑌Step (𝑧, 𝑡) = 𝑌Step Inlet 𝑢Inlet ∙ 𝑌AL = 𝑢(𝑧, 𝑡) ∙ 𝑌AL (𝑧, 𝑡)

(15) for z = 0 and t ≥ 0 (16)

𝑑𝑌AL (𝑧, 𝑡) − 𝐷ax (𝑧, 𝑡) ∙ 𝑑𝑧

𝑑𝑌Step (𝑧, 𝑡) =0 𝑑𝑧 𝑑𝑌AL (𝑧, 𝑡) =0 𝑑𝑧

(17) for z = L and t ≥ 0 (18)

𝑋AL (𝑧, 𝑡) = 𝑋AL,0 𝑌Step (𝑧, 𝑡) = 0 𝑌AL (𝑧, 𝑡) = 0

(19) for z ∈ [0, 𝐿] and 𝑡 = 0

(20) (21)

18

Pressure drop The pressure drop in the changing fixed-bed was modeled using the Forchheimer equation 𝑑𝑝(𝑧,𝑡) 𝑑𝑧

=𝑘

𝜂f (𝑧,𝑡)

1 (𝜀act (𝑧,𝑡))

∙ 𝑈(𝑧, 𝑡) + 𝑘

𝜌f(𝑧,𝑡)

2 (𝜀act (𝑧,𝑡))

∙ 𝑈(𝑧, 𝑡)2

(5)

with the superficial velocity 𝑚̇

𝑈(𝑧, 𝑡) = 𝜌 (𝑧,𝑡)∙𝐴 = 𝑢(𝑧, 𝑡) ∙ 𝜀 (𝑧, 𝑡)

(6)

f

and the continuity equation in the following form: 𝑑

𝐴 ∙ 𝑑𝑡 (𝜀act (𝑧, 𝑡) ∙ 𝜌f (𝑧, 𝑡)) +

𝑑𝑚̇ (𝑧,𝑡) 𝑑𝑧

=0

(7)

The permeability correlation is empirical and was developed in this work: 𝑘𝑖 (𝜀(𝑧, 𝑡)) = (1−𝜀

𝐴𝑖

𝐵 act (𝑧,𝑡)) 𝑖

− 𝐴𝑖

(8)

The results of this work demonstrated, that the permeabilities k1 and k2 show a very clear dependency on the actual porosity εact. This correlation fulfills the logical boundary conditions of no pressure drop at εact = 1 (no biomass) and infinite pressure drop at εact = 0 (no voids). The porosity is calculated as follows: 𝜀act (𝑧, 𝑡) = 1 −

𝑚bm (𝑧,𝑡) 𝐴∙𝑑𝑧∙𝜌bm (𝑧,𝑡)

(9)

Fixed-bed mechanics For the calculation of a tension profile in the biomass, a differential force balance with z as axial coordinate and z = 0 at the reactor bottom was developed according to fig. 4. The applied force Ff(z,t) due to fluid flow and the resulting pressure drop is directed upwards in flow direction. The wall friction Fw(z,t) is directed in the opposite direction of the flow. The weight Fg(z,t) is also directed downwards. The resulting force F(z,t) as product of the cross-sectional area A and the tension σS(z,t) is expected to be directed upwards.

19

F (z + dz) z + dz Fw (z)

Ff (z)

Fg (z) z

F (z) Fig. 4: Differential force balance for fixed-bed tension profile calculation.

The resulting force balance is 𝑑𝐹(𝑧, 𝑡) = 𝐴 ∙ 𝑑𝜎𝑠 (𝑧, 𝑡) = 𝐹f (𝑧, 𝑡) − 𝐹w (𝑧, 𝑡) − 𝐹g (𝑧, 𝑡)

(22)

with 𝐹f (𝑧, 𝑡) = (𝑘

𝜂f (𝑧,𝑡)

1 (𝜀act (𝑧,𝑡))

∙ 𝑈(𝑧, 𝑡) + 𝑘

𝜌f (𝑧,𝑡)

2 (𝜀act (𝑧,𝑡))

∙ 𝑈(𝑧, 𝑡)2 ) ∙ 𝐴 ∙ 𝑑𝑧

(23)

and 𝐹g (𝑧, 𝑡) = (1 − 𝜀act (𝑧, 𝑡)) ∙ (𝜌S − 𝜌f (𝑧, 𝑡)) ∙ 𝑔 ∙ 𝐴 ∙ 𝑑𝑧

(24)

The wall friction Fw(z,t) is derived as a proportional force from the resulting axial force F(z,t) with the friction coefficient λ and the horizontal load ratio μ. For the modelling, λ = 0.5 and μ = 0.5 were estimated from literature values for cereals given in Stiess (2009) [17]. 𝐹w (𝑧, 𝑡) = 𝜆 ∙ 𝜇 ∙

2∙𝜋∙𝑟 𝐴

∙ 𝐹 (𝑧, 𝑡) ∙ 𝑑𝑧

(25)

This yields the following differential equation for the tension σS(z,t) in the fixed-bed. 𝑑𝜎𝑠 (𝑧, 𝑡) 𝜂f (𝑧, 𝑡) 𝜌f (𝑧, 𝑡) 2𝜆𝜇 = ∙ 𝑈 (𝑧, 𝑡) + ∙ 𝑈 (𝑧, 𝑡)2 − ∙ 𝜎𝑠 (𝑧, 𝑡) 𝑑𝑧 𝑟 𝑘1 (𝜀act (𝑧, 𝑡)) 𝑘2 (𝜀act (𝑧, 𝑡)) −(1 − 𝜀act (𝑧, 𝑡)) ∙ (𝜌s − 𝜌f (𝑧, 𝑡)) ∙ 𝑔

(26)

The tension profile can now be calculated directly for a certain treatment time and a suitable boundary condition. Either way, the differential equation can be introduced into the fixed-bed model by Reynolds and Smirnova (2018)[6] and solved numerically together with the system of partial differential equations for heat and mass transfer. The latter approach would result in a 20

tension profile which dynamically changes with the extraction progress. The choice of an appropriate boundary condition (tension at the reactor inlet at z = 0), however, is a major task for the solution of the tension equation, since the actual tension at position z = 0 is unknown. It seems reasonable to set a Dirichlet boundary condition at z = 0. In a loosely packed bed with fluid flow from the bottom, this condition would be σS(z = 0) = 0, since no pressure drop is built up at this position [9]. In the present case, the bed is pre-compressed due to swelling inside the limited volume of the biomass cartridge. Theoretically, the same state would be reached using an initially loose biomass packing which is compressed to the size of the reactor. The precompression of the biomass results in a basic stress in the biomass packing which is working homogeneously in all directions, except for a small influence of the weight force, which is negligible. Without any external forces, the net tension in a differential element of the fully relaxed and pre-compressed bed can be expected to match σS(z = 0) = 0. In any case, a parameter variation of the equation shows that in a sufficiently long bed, the tension always reaches a constant value at z >> 0, irrespective the chosen σS(z=0). Therefore, the influence of the initial tension is neglected and σS(z = 0) = 0 is chosen as lower boundary condition.

2.8

Error analysis

All LHW treatment experiments were executed in duplicates. Analytical methods, pressure drop tests, and compression experiments were repeated at least three times. Experimental errors are given as standard deviation. Evaluation of the model performance is done using the root mean square error (RMSE): 𝑛exp

exp

2

mod ) ∑k=1 (𝑌H,i,k −𝑌H,i,k

𝑅𝑀𝑆𝐸 = √

𝑛exp

(27)

21

3

Results and discussion

3.1

Pressure drop and AL-lignin release

For the development of a suitable model, which is able to predict the mechanical behavior of the perfused biomass bed, detailed knowledge of the pressure drop during the process is necessary. Fig. 5 shows the measured differential pressure drop dp/dz as a function of the superficial velocity U with varying pretreatment progress. The pressure drop curves were modeled with the Forchheimer equation (formula 5) with R² ranging from 0.6 to 0.99. The modeled pressure drop is given as solid line in fig.5. As expected, the pressure drop rises with increasing velocity and decreases with advancing hemicellulose extraction and thus increasing porosity. During hemicellulose extraction, the porosity changes from initially 0.79 to 0.88 after 30 minutes of treatment time. Based on these data, a permeability correlation as function of the porosity ki(z,t) = f(εact(z,t)) can be developed and parameterized. (see equation 8). Different from the equations by other authors for Darcy’s law given in table A.1, the correlation does not work with a reference permeability K0 at a certain base case porosity ε0. It is further important to satisfy the limiting cases lim

𝜀act (𝑧,𝑡) → 1

lim

𝜀act (𝑧,𝑡) → 0

𝑘𝑖 = 0 and

𝑘𝑖 = ∞.

22

1.6 0 min

dp/dz (bar/m)

1.4

10 min

1.2

15 min

1.0

20 min

30 min

0.8 0.6

0.4 0.2 0.0 0

0.00025

0.0005 0.00075 U (m/s)

0.001

0.00125

Fig. 5: Measured differential pressure drop for water flow in the wheat straw packing at 20 °C and 50 bar with increasing superficial velocity for different pretreatment times. The modeled pressure drop curves (Forchheimer equation) are given as solid lines.

Tab. 2: Permeability correlation parameters. Index i

Permeability ki

Ai

Bi

RMSE

1

k1

9.5 · 10-14

3.4

8.2 · 10-22

2

k2

1 · 10-12

7

5 · 10-12

The permeabilities k1 and k2 are only a function of the bed porosity and bed structure and do not depend on the fluid properties. This allows transferring the Forchheimer equation to process conditions at elevated temperatures and pressures by inserting the viscosity and density of the fluid at process conditions (200 °C and 50 bar). For this, however, detailed knowledge of the

23

viscosity and density of real hydrolysate at elevated temperatures and pressures becomes necessary. Introducing the Forchheimer equation with the determined permeabilities into the existing fixedbed model results in a pressure drop curve with a magnitude which is too low by a factor of roughly 25 when the viscosity of pure water is used (see fig. 6 b)). Additionally, the modeled pressure drop decreases too early, with an overshoot at 10 minutes, when the reactor is completely filled, whereas the experimental curve shows a soft peak which follows more or less the trend of the dissolved components in the hydrolysate (see fig. 6 a)). Obviously, the difference between the modeled and experimental pressure drop occurs mainly due to the influence of the water-soluble lignin fraction (aquasolv liquid, AL-lignin) and partly of dissolved C5-sugars in the hydrolysate on the viscosity (see fig. 6 a)). The viscosity increases until it reaches its maximum after 15 to 20 minutes when the modeled pressure drop curve with the viscosity of pure water decreases. In this context, a linear relationship between the AL-lignin and the fluid viscosity at ambient conditions of the following form is suggested with avisc = 0.223 and ηw = 0.001 Pa·s (R² = 0.95, see fig. 6 a)):

𝜂f (𝑥) = 𝜂w (𝑥) + 𝑎visc ∗ 𝑌AL (𝑥)

(28)

The viscosity of the hydrolysate is calculated based on the viscosity of pure water ηw at ambient or process conditions (taken from the International Association for the Properties of Water and Steam [25]). The AL-lignin concentration is modeled using the AL-lignin kinetics in equation (10) – (21) with EA,AL = 176,175.2 J/mol, kAL,0 = 1,65 · 1017 1/s and an RMSE of 0.0034 kg/kg. A clear effect of the dissolved sugars or any other measurable dissolved compounds on the viscosity could not be seen, neither during permeability estimation nor in the LHW experiments, although sugar oligomers are known to have an impact on viscosity [26]. With reference to

24

literature, this is expected to become of more importance only at higher sugar concentrations [26]. The effect of dissolved components on the fluid density is minor (see [6]) compared to the viscosity. As can be seen from the non-linear pressure drop curves in fig. 5, the influence of turbulent flow in the second (turbulent) term of the Forchheimer equation cannot be neglected. However, in the low velocity range of the LHW extraction, the first (laminar) term of the Forchheimer equation, which contains the viscosity, dominates the calculated pressure drop. An additional effect is the dissolved or dispersed gas and in consequence foaming of the hydrolysate. N2 from the precompression of the autoclave to 50 bar, on the one hand, dissolves into the liquid. Even though the solubility of nitrogen in water at these conditions is quite poor [27], an effect on the viscosity cannot be excluded and has already been shown for other gases like CO 2, which causes a slight rise in viscosity with increasing mole fraction [28]. Dispersed bubbles in a fluid, on the other hand, are also known to have a reinforcing effect on the viscosity [29]. Taylor (1932) [29] suggested a linear relationship for the influence of dispersed gas bubbles on the overall viscosity. This effect, however, is minor compared to the viscosity increase due to AL-lignin. On the other hand, the hydrolysate with solubilized or compressed dispersed nitrogen expands in the pressure regulating valve at the reactor outlet which leads to pressure fluctuations in the experimental data. Also, precipitation of dissolved AL-lignin and humins or lignohumic complexes [30–32] in the cooler tend to block the pressure regulating valve and disturb the pressure control. Pressure drop peaks occur when the pressure regulating valve at the reactor outlet opens slightly to counteract a rising system pressure and thereby causes a higher fluid velocity. This seriously influences the pressure drop measurement (see fig. 6 b)) but cannot be overcome so far with the commercially available high-pressure control valves. Furthermore, the actual swelling behavior of the biomass cannot yet be quantified but definitely has a major impact on the pressure drop – especially during the initial filling process.

25

Concentration (kg/kg)

0.10

AL-lignin viscosity

0.08

0.006

3.0

0.005

2.5

0.004

2.0

Δp (bar)

a)

C5 sugars

ηf (Pa·s)

0.12

1.5

0.06

0.003

0.04

0.002

1.0

0.02

0.001

0.5

0.000

0.0

0.00

0

10

20

Treatment duration (min)

30

b)

0

10 20 Treatment duration (min)

30

Fig. 6: a) Dynamic change of dissolved AL-lignin, C5 sugars concentration in the hydrolysate at the reactor outlet as well as hydrolysate viscosity at 20 °C and 1 bar with the modeled AL-lignin concentration as solid line (data from [6]). b) Modeled pressure drop with pure water viscosity (solid line), viscosity as a function of the AL-lignin (dashed line) and experimental pressure drop of a representative single experiment with 3 horizontal stabilizers (grey area) at process conditions (200 °C, 50 bar).

Fig. 7 shows the decreasing viscosity of an exemplary hydrolysate sample and water with rising temperature. Additionally, the hypothetical viscosity calculated via equation (28) with an average AL-lignin concentration of 0.008 kg/kg and avisc = 0.223 is shown as dashed line. The viscosity of the tested hydrolysate sample shows a very clear linear proportionality to the pure water (R² = 0.97). Unfortunately, measurements were only possible up to 80 °C due to repolymerization reactions and humin formation in the hydrolysate. However, the data already show that the viscosity of the hydrolysate does not drop as sharp as that of the pure water curve. It is rather shifted by a constant value of approx. 2.5 mPa·s. With this information as well as the viscosity data from [6], at least a rough estimation of the viscosity difference between hydrolysate and pure water at process conditions via extrapolation is possible. It was decided to

26

calculate the hydrolysate viscosity at process conditions based on the linear relationship given in equation (28) with avisc being manually adapted to the measured pressure drop data (see fig. 6 b)). This then also includes the unknown effect of dissolved gas and bubble formation. For 200 °C and 50 bar treatment conditions, avisc was set to 2. With this value, the majority of the pressure drop data points is enclosed by the modeled pressure drop curve. On the one hand, the unknown effect of dispersed and dissolved gas is considered within avisc. An explanation for this significantly higher value compared to ambient conditions could be the state of the AL-lignin in the hydrolysate at process conditions. At 200°C, the AL-lignin is solubilized into the hydrolysate and first precipitates in the cooler in the downstream line after the fixed-bed reactor. The viscosity of a polymer solution is assumed to be higher than the viscosity of a suspension of the same polymer. Arguments favoring this assumption are unfolding of the molecule as well as an increased surface area and therefore interaction with the fluid. Especially the changing surface properties of the lignin in line with the interactions between the lignin and the water are expected to have a major impact on the hydrolysate viscosity. The dielectric constant of water, for example, decreases with temperature [25], enforcing interactions with the rather hydrophobic AL-lignin which is soluble at process conditions. Since the pressure drop data are supposed to be used for the design of a fixed-bed where no bed compression due to pressure drop occurs, it is rather advisable to over-predict this property.

27

3.5

3.0 ηf (mPa·s)

2.5 2.0 1.5 1.0 0.5 0.0 0

50

100 150 T (°C)

200

250

Fig. 7: Temperature dependence of the viscosity of water (solid line) (according to [25]) and representative hydrolysate sample (diamonds) as well as the hypothetical viscosity calculated via equation (28) with an average AL-lignin concentration of 0.008 kg/kg and avisc = 0.223 (dashed line).

Using the viscosity correction, the developed pressure drop model allows a qualitative discussion of the effect of reactor scale-up and geometry by means of the L/D ratio. A reactor scale-up drastically increases the pressure drop over the fixed-bed length. The underlying effect is simply the increase in reactor length and superficial velocity in case of a constant residence time τ. Consequently, the pressure drop can be minimized by decreasing the L/D ratio at larger reactor scales. Unfortunately, the solution of the pressure drop problem is not that simple – additional effects like wall friction, bed compressibility as well as bed homogeneity and channeling effects need to be considered for the development of an effective stabilization method. As already shown by Verhoff et al. (1983) [10], a completely different bed behavior can be observed depending on whether the bed compressibility or the wall support dominates the mechanic behavior of the perfused bed. This results in an optimization problem for the reactor geometry.

28

The use of a suitable model is inevitable for reactor design, since the apparent effects are often working in opposite directions: E. g. a large column diameter (small L/D) at a fixed reactor volume and fluid residence time favors a low fluid velocity (~ 1/D²) but makes bed inhomogeneity and channeling more likely, whereas a small column diameter favors high wall friction (~ D) [19]. This is especially critical for reactor scale-up since reactor diameter D (risk of inhomogeneous bed extraction and low wall friction) and bed length L (increase in pressure drop) need to be enlarged.

3.2

Filling process and biomass swelling

The swelling behavior of the biomass definitely has a major impact on the pressure drop, especially during the initial filling process. However, today it is impossible to evaluate this process at process conditions in the stainless steel autoclave with available analytical techniques. Therefore, swelling tests in a substitute reactor made from acrylic glass were executed. Fig. 8 shows the formation of the biomass bed with treatment time in this installation. At the start, the reactor is loosely filled with the dry biomass pellets which are then successively wetted with increasing water level. The reactor is completely filled after approx. 9 min. The experiment shows that the biomass starts to take up the warm water quite fast (swelling begins approx. 3 min. after wetting) but still needs up to 20 min. to fully expand and to fill the reactor with a homogeneous packing. This can nicely be seen in the last and second last picture in fig. 8 by the contrast of the biomass against the fluid, which has been colored by extractives from the biomass. The inhomogeneous packing during the first 15 to 20 min. of the process could be another reason for the underestimation of the pressure drop with the Forchheimer equation (5). Since the permeabilities ki(z,t) do not depend linearly on the porosity εact(z,t) (see equation (8)), a higher packing density at the reactor bottom can severely influence the pressure drop during the bed formation. Additionally, severe entrapment of gas inside the bed and thus maldistribution of

29

the fluid and dispersed bubbles in the outlet flow could be observed, as already expected in section 3.1 as a reason for elevated pressure drop.

Fig. 8: Formation of the swelling biomass bed as a function of treatment time during the initial filling process.

3.3

Fixed-bed mechanics and rheological behavior

During LHW treatment of lignocellulosic biomass, most of the hemicellulose fraction is solubilized into the liquid phase, leading to a decrease of the total solid mass. At the same time, the actual bed porosity increases.

30

F

1. Inertial deformation phase

2. Compression phase 400

1.0

300 σ (kN/m²)

dσ/dt (kN/m²s)

1.5

0.5 0.0

200 100

-0.5

0 0.0

0.1

0.2 ε (-)

0.3

0.57

0.67

0.72

ε (-)

Compression test

400

3. 400

σ*

200

2. 100

1.

σ (kN/m²)

300

σ (kN/m²)

0.62

σ*

3. Relaxation phase

300 200

σ* 0 0

500

1000 Time (s)

1500

2000

100 1200

1400

1600 1800 Time (s)

2000

Fig. 9: Representative stepwise compression test with inertial deformation, the compressive strength σ* and three compression and relaxation phases.

The stepwise measured force-compression curves allow analysis of several different material properties: the inertial deformation, the dynamic compression behavior, the relaxation behavior at constant load as well as the compressive strength σ* at a certain compression at steady state (see fig. 9). As a critical comment at this point, it must be pointed out that the stepwise compression, of course, might result in a different compressive strength than with direct adjustment of a certain compression stage since the biomass obviously shows a time-dependent compression behavior. This indicates that also the starting point of compression is likely to influence the compressive strength at a certain compaction.

31

During the inertial deformation phase, the loose bed still consists of many voids. Particles are rearranging, leading to a sudden compaction of the material. This results in a negative gradient dσS/dt until the bed is compacted enough and the particles are close enough to exhibit elastic or plastic behavior. The subsequent compression is slightly non-linear, indicating strain hardening properties like it was observed by Peleg (1980) [33] as well as Faborode and O'Callaghan (1989) [34]. Strain or work hardening behavior describes the strengthening of the bed during deformation. In contrast to the linear Hooke’s law, the stress-strain relationship, in this case, is e. g. a power law [34]. The following relaxation phase at constant deformation rather points towards behavior similar to a viscoelastic fluid than a solid, with a damped and mostly irreversible deformation. By analyzing the compression and relaxation curves, possible representative rheological material models could be derived. However, already quite simple rheological models lead to differential equations for the stress-strain-relationship which are often not resolvable analytically. Integration of a material model into the LHW fixed-bed model will therefore not be realized in this work. However, detailed quantitative analysis of the compression and relaxation curves can give a quite good idea of the material properties and help to derive σ*, which is essential for the prediction of a potential compression of the perfused fixed-bed due to an occurring pressure drop. Imagining the case of a pre-compressed biomass packing, which is likely to be compressed by the fluid drag, the minimum resistance of the bed with a given porosity is the tension at complete relaxation. Therefore, the compressive strength σ* was read at the end of each relaxation phase in the compression tests as indicated in fig. 9. Fig. 10 shows the compressive strength σ* plotted against the actual bed porosity εact. All data from different treatment durations and compression levels are plotted directly. Hence, no error bars are shown and the correlation accuracy is given as a confidence level of α = 0.95 as dashed

32

lines. It can be seen that the hemicellulose content of the wheat straw did not affect the biomass compressibility and that σ* is only a function of εact.

σ* · 10-5 (N/m²)

6

4

2

0

0.70

0.75

0.80 εact (-)

0.85

0.90

Fig. 10: Critical compression tension σ* as a function of the actual bed porosity εact, for all tested pretreatment times. The solid line represents the model equation (29) with a confidence interval of α = 0.95 as dashed lines.

The literature equations given in table 2 do not allow an accurate fit of the measured data for σ* as a function of the actual bed porosity εact. Instead, the following correlation for σ* as a function of εact for the compaction of wet wheat straw particles is suggested in this work: N

𝜎 ∗ = 4 ∙ 106 ∙ 𝑒 −19.1 ∙ 𝜀act (m2 )

(29)

which can be interpreted as follows: -

𝜎 < 𝜎∗: Bed is stable,

-

𝜎 ≥ 𝜎∗: Bed deformation.

33

This correlation, of course, does not include possible softening of the biomass material at elevated temperatures. Here, further calorimetric experiments or introduction of an additional safety factor into the modeling evaluation would be necessary.

3.4

Compressible fixed-bed model

Applying the differential force balance in equation (26) with the Forchheimer equation and its permeability correlation together with the fixed-bed model allows the spatial and temporal comparison of the actual bed tension and compressive strength during the LHW. Fig. 11 shows the numerical solution of the model equation system for the 3 L laboratory plant and the 40 L pilot plant. The solution of equation (26) shows that the tension accumulates along the z-axis of the reactor with increasing reactor length. Bed compression is, therefore, most likely to happen at the reactor end. However, interpretation of the tension equation in combination with the fixed-bed model is not that simple, since also the hemicellulose solubilization with increasing temperature from the reactor bottom has to be considered. It can be nicely seen, how the increasing porosity at the reactor bottom due to advancing hemicellulose degradation by the inflowing hot water lowers the bed tension on the one hand but also the compressive strength on the other hand. In the 3 L plant, the compressive strength approaches the bed tension line until it crosses it at 11 min. treatment duration. At this point, a beginning compression of the fixed-bed from the reactor bottom is expected. The biomass is being pushed towards the upper end of the cartridge, leading to an empty section at the reactor bottom. In the fixed-bed in the 40 L plant, this critical point is already reached after 7 min. Here, the reduced stabilizing effect of the wall friction at 40 L plant scale and a lower L/D ratio becomes obvious. Since the solids loading of the 40 L plant is slightly lower than the one of the 3 L plant, also the critical tension, as well as the relative actual bed tension, are lower.

34

This mirrors the experiences with the experimental plants. The 40 L fixed-bed needs a far stronger stabilization construction than the 3 L plant. Additionally, the tension adds up over a longer bed and the fluid velocity is faster, leading to a higher tension at the reactor top despite the lower solids loading. Interestingly, the bed is more likely to block at the reactor bottom at the beginning of the extraction whereas the top of the bed is susceptible towards compression at the end of the process. The latter case is expected for a bed with a homogeneous porosity. Here, again, the importance of the dynamics of the process with its changing bed and fluid properties become obvious.

a)

0.00

Reactor length

Reactor length

b)

0.25

0.50 σ·

0.75

10 5 (N/m²)

11 min.

7 min.

30 min.

30 min.

1.00

1.25

0.00

0.25

0.50 σ·

0.75

1.00

1.25

10 5 (N/m²)

Fig. 11: Modeled bed tension σS (solid line) and compressive strength σ* (dashed line) trends along the reactor at 3 L (a) and 40 L (b) reactor scale for the time of bed compression and 30 min. treatment duration.

As mentioned before, in this work the worst case in terms of pressure drop, bed tension and compression is considered. Usually, the bed at 3 L scale tends to block after 15 – 20 minutes of treatment time in a standard LHW experiment (1 kg biomass, 200 °C, 250 g/min flow) and not already after 11 min. as predicted by the model. Obviously, either the compressive strength of

35

the biomass packing is different (e. g. due to the elevated temperatures) or the pressure drop and bed tension are overpredicted. Additionally, a partial self-stabilizing effect of the fixed-bed in critical sections due to radial compression/wall friction or an increase of the critical tension is possible.

Decrease fluid viscosity/density

Decrease velocity: - Low L/D ratio

𝑑𝜎𝑠 (𝑧, 𝑡) 𝜂f (𝑧, 𝑡) 𝜌f (𝑧, 𝑡) 2𝜆𝜇 = ∙ 𝑈(𝑧, 𝑡) + ∙ 𝑈(𝑧, 𝑡)2 − ∙ 𝜎𝑠 (𝑧, 𝑡) − (1 − 𝜀act (𝑧, 𝑡)) ∙ (𝜌s − 𝜌f (𝑧, 𝑡)) ∙ 𝑔 𝑑𝑧 𝑟 𝑘1 (𝜀act (𝑧, 𝑡)) 𝑘2 (𝜀act (𝑧, 𝑡))

Decrease reactor length: - Low L/D ratio - Intermediate bottoms Increase permeability ki: - Increase porosity

Decrease reactor diameter: - Vertical stabilizer - High wall friction

σS < σ*: Bed is stable σS > σ*: Bed deformation

Increase critical tension σ*: - E.g. filling bodies

Fig. 12: Identification of possible stabilization methods from the differential force balance in equation (26).

In addition to the tension modeling, the differential force balance can be used to find suitable reactor designs and fixed-bed stabilization methods (see summary in table 3). In fig. 12, all influencing parameters on the fixed-bed tension identified from the model and the derived stabilization mechanisms are illustrated. In fig. 13, the effect of a vertical stabilizer, filling bodies and a reduced L/D ratio of 2.6 (50 % of original L/D = 5.2) in the 3 L lab plant are further shown graphically. As discussed before, a low L/D ratio favors a small pressure drop. Additionally, it is expected to prevent extensive summation of the fixed-bed tension along the reactor length due to the fluid drag. However, a too short and expanded fixed-bed would necessarily lead to fluid channeling and inhomogeneous biomass wetting/extraction. As can be seen in fig. 13 c), a lowered L/D

36

cannot prevent bed compression, it is rather delayed. Analysis of the modeling data revealed, that this delay occurs mostly due to a poorer heat transfer and therefore retarded solubilization reaction. This means that a decrease in L/D might even be counterproductive for a fast and controllable reaction. More promising is the installation of evenly distributed permeable intermediate bottoms inside the fixed-bed, which are filled separately and absorb a major part of the built up tension. Still, this reaches its limits in reactors at m³ production scale. In the 3 L laboratory fixed-bed, already 3 intermediate bottoms at a L/D ratio of 5.2 and an overall bed length of 0.47 m are necessary to stabilize the fixed-bed throughout the complete extraction duration. The number of intermediate bottoms can be reduced if they are combined with a vertical permeable stabilizing plate (see fig. 13 a)). The additional mode of action here is an increase in wall friction. Certainly, the wall friction stabilizing effect should not be too strong. This would lead to a severe radial compression of pelletized biomasses inside the cartridge during the initial swelling phase. This would have just the contrary effect and produce a high-pressure drop with strong tensions coming along or even complete blocking of the bed. Individually designed stabilizer combinations with vertical and horizontal plates have successfully been tested in 3 and 40 L scale at TUHH. Also possible are internals or cartridge constructions that enable an alternating flow and thereby reduce the number of required stabilizer compartments. Another stabilizing method is the introduction of filling bodies (e. g. Raschig rings made from stainless steel or PTFE) into the biomass bed. This has successfully been applied at 3 and 40 L plant level. It is expected that due to the rigidity of the filling bodies themselves and by the filling bodies and the biomass becoming wedged together, the compressive strength σ* is raised as shown in fig. 13 b). However, recovery of the filling bodies directly after the LHW appears to be elaborate. It is advisable to realize this step as a solid-liquid separation after enzymatic treatment of the LHW pretreated biomass, e. g. by means of a sieve which retains the filling

37

bodies during the draining process. However, the enzymatic treatment requires strong mixing which might in turn damage the filling bodies. An additional adjustable parameter is the porosity. Theory indicates that the lower the porosity, the smaller is the pressure drop. However, in practice, a loosely packed bed favors blocking due to fluid drag even further. For the positive effect of a low porosity, a so-called expanded bed needs to be established, in which the biomass is fluidized and does not encounter the upper slot screen of the reactor in any case. This operation mode has successfully been tested at TUHH in 3 and 40 L scale with no detectable pressure drop in both cases. But of course the solid to liquid ratio is very unfavorable for an economic process. The water consumption, in turn, can be drastically reduced if a mixture of water and gas or steam is used – a process modification that would also reduce the tensions inside the bed via a reduced pressure drop. This, however, would be a totally different process compared to the standard LHW described in this work and requires a completely new plant layout.

38

Tab. 3: Summary of potential fixed-bed stabilization methods including their effects and drawbacks. Stabilization

Validation Effect

Drawback

mechanism

successful High constructive

Horizontal stabilizers

Decrease length

Lab and pilot scale effort

Vertical stabilizers

Increase wall friction

Radial compression

Lab and pilot scale

Fluid bypasses

–

Very high l/s ratio

Lab and pilot scale

Different process

–

Decrease pressure Decrease L/D drop and length Decrease pressure Increase porosity drop Decrease fluid viscosity

Decrease pressure

& density

drop

Supportive

Subsequent separation Increase σ*

packing/filling bodies

Lab and pilot scale necessary

39

a)

b)

Reactor length

Reactor length

Reactor length

c)

standard

standard

11 min.

vertic. stab.

filling bodies

16 min.

0.00 0.25 0.50 0.75 1.00 1.25 1.50

0.00 0.25 0.50 0.75 1.00 1.25 1.50

0.00 0.25 0.50 0.75 1.00 1.25 1.50

σ · 10 5 (N/m²)

σ · 10 5 (N/m²)

σ · 10 5 (N/m²)

Fig. 13: Modeled bed tension σS (solid line) and compressive strength σ* (dashed line) trends at 3 L reactor scale and using different bed stabilization methods. At 11 min. treatment duration: Vertical stabilizer (doubled circumference, a)), filling bodies (b). At 11 and 16 min. treatment duration: Reduced L/D ratio of 2.6 (c).

Taken on its own, none of the stabilization mechanisms mentioned above will find a remedy in terms of fixed-bed blocking at production scale. Therefore, a combination of multiple approaches needs to be found that is strong enough but also technically feasible and easy to handle during plant operation. Furthermore, additional experimental studies for fixed-bed scaleup are necessary in order to asses, up to which reactor size, the fixed-bed is a realistic reactor design for hot water extraction.

4

Conclusions

The comprehensive fixed-bed model established in this work offers a powerful tool for the understanding and design of biomass fixed-bed processes with changing the fluid and solid properties on different scales. It considers the interacting effects of chemical reactions, heat and mass transfer as well as fluid dynamics and bed mechanics with changing fixed-bed properties. Since all transport and mechanical phenomena were investigated separately, the model is predictive, scalable and the approach is further transferrable to other fixed-bed applications. It

40

could be shown, that the developed model is able to predict the pressure drop and compression behavior of a perfused wheat straw bed during liquid hot water pretreatment. The pressure drop was represented using the Forchheimer equation and a biomass specific permeability correlation as a function of the bed porosity suggested in this work. Compression tests of pretreated biomass packings revealed, that the compressibility is independent of the pretreatment progress and thus the hemicellulose content. Experimental and modeling studies further showed that the addressed fixed-bed is not scalable without the installation of sophisticated mechanical stabilizers. Different promising stabilization methods were modeled as well as experimentally tested and evaluated in terms of their mode of action, their performance during the process and their scaleup potential. It could be concluded that not just a single stabilizing technique, but a combination thereof is necessary to enable a steady large-scale biomass bed with a simple and easy-to-handle design under operating conditions.

Acknowledgments The authors are grateful to the German “Bundesministerium für Bildung und Forschung” (BMBF) for the financial support in the context of the German project cluster BIOREFINERY2021 (031A233). The personal commitment to measuring the hydrolysate viscosity at elevated temperatures and pressures by Stefan Pollak and Vincent Bürk from the Ruhr Univerität Bochum, Lehrstuhl für Feststoffverfahrenstechnik is acknowledged. Special thanks also go to Thomas Steinweger from Hamburg University of Technology, Institute for Reliability Engineering, for the provision of the material testing machine and his expertise.

Abbreviations ACM:

Aspen Custom ModelerTM

AL

Aquasolv Liquid

41

AS:

Aquasolv Solid

CFD:

Computational fluid dynamics

LHW:

Liquid Hot Water

RMSE:

Root mean square error

PTFE:

Polytetrafluorethylen (Teflon)

TUHH:

Hamburg University of Technology

42

Latin Symbols a

Constant (–)

avisc

Proportional factor for viscosity calculation from AL-lignin concentration

A

Fixed-bed cross-sectional area (m²)

A

Laminar factor in the Brauer equation (–)

Ai

with i = 1,2; Constant in the Permeability correlation (–)

b

Constant (–)

B

Turbulent factor in the Brauer equation (–)

Bi

with i = 1,2; Constant in the Permeability correlation (–)

c

Constant (–)

d

Constant (–)

dP

Particle diameter (m)

D

Inner reactor diameter (m)

Dax

Axial dispersion coefficient (m²/s)

e

Constant (–)

E

Youngs modulus of elasticity (N/m² or Pa)

EA,AL

Activation energy (J/mol)

f

Function (–)

F

Resulting force (N)

Ff

Force due to liquid flow (N)

Fg

Weight force (N)

Fw

Force due to wall friction (N)

g

Gravity (m/s²)

h

Bed height (m)

h0

Initial bed height (m)

43

kAL

First or second order reaction rate constant (1/s or 1/s²)

kAL,0

Reaction rate pre-exponential factor (1/s or 1/s²)

ki

with i = 1, 2; Permeability as function of ε in the Forchheimer equation (–)

ki

with i = 1, 2, 3; Constant (–) Harkonen

K

Permeability (m²)

K0

Initial permeability (m²)

Kmin

Minimal permeability (m²)

L

Bed length (m)

𝑚̇

Mass flow (kg/s)

m

Mass (kg)

m

Empirical constant of the stiffness of the network (N/m² or Pa)

mS

Solids mass (kg)

mbm

Mass of the dry biomass (kg)

n

Empirical constant (–)

nexp

Number of experiments (–)

p

Pressure (N/m² or Pa)

Δp

Pressure drop (N/m² or Pa)

Δp0

Pressure drop (N/m² or Pa)

r

Bed radius (m)

R

Universal gas constant (J/(mol · K))

R2

Coefficient of determination (–)

SV

Specific surface area of the porous medium (m²/m³)

t

Time (min)

T

Temperature (°C or K)

U

Superficial fluid velocity (m/s)

44

u

Interstitial fluid velocity (m/s)

V

Reactor or bed volume (m³)

V0

Initial bed volume (m³)

x, y

Empirical bed constants in the exponent (–)

XAL

Solid AL-lignin mass fraction in the total reaction system (kg/kg)

XAL,0

Initial solid AL-lignin mass fraction in the total reaction system (kg/kg)

YAL

Soluble AL-lignin mass fraction in the liquid phase (kg/kg)

Ystep

Liquid mass fraction of the imaginary step concentration (kg/kg)

z

Axial coordinate (m)

45

Greek Symbols α

Compressibility (1/Pa)

α

Standard deviation

α0, αt

Adjustable parameter (–)

αm,0

Initial compressible filter cake resistance (m/kg)

𝛼̅m

Average compressible filter cake resitance (m/kg)

ε

Bed porosity (m3void/m3reactor)

ε0

Initial bed porosity (m3 void/m3reactor)

εact

Actual bed porosity (total fluid volume fraction) (m3total void/m3reactor)

εcrit

Critical flow porosity (m3 void/m3reactor)

εeff

Effective flow porosity (m3free liquid/m3reactor)

ηw

Dynamic viscosity of pure water (Pa·s)

ηf

Dynamic viscosity of the hydrolysate (Pa·s)

θ

shape factor constant (–)

κ

Kappa number (–)

λ

Friction coefficient (–)

μ

Horizontal load ratio (–)

ρ

Density (kg/m³)

ρbm

Skeletal density of the dry biomass (kg/m³)

ρf

Fluid density (kg/m³)

ρS

Solids density (kg/m³)

σS

Solid tension (N/m²)

σ*

Critical solid tension (N/m²)

τ

Residence time (s or min.)

46

47

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51

Model parameterization & validation

Model application

Experiments

Modeling

Process design

Batch LHW

Batch kinetics

Scale up

(kinetics estimation, previous work)

(previous work)

(previous/this work)

3L fixed-bed LHW

Solid, fluid & bed properties

Bed compression & stabilization

(previous work)

(this work)

Heat & mass transfer, dispersion

Optimization & operation modes

- Parameter est. - Bed properties - Filling process - Dispersion - Pressure drop - Model validation - Bed stabilization (previous/this work)

40L fixed-bed LHW - Scale-up - Heat transfer - Pressure drop - Bed stabilization (previous/this work)

(unpublished)

(previous work)

Pressure drop & bed compression

Model limitations, transferrability & limitations

(this work)

(unpublished)

Complete model

Techn. evaluation

(this work)

(partly this work)

Experimental verification & application

F Decompression

Fixed-bed

Water outlet

N2 Compression Water

Compression Δp

No stabilizer

Vertical stabilizer

3 horizontal stabilizers

Combined stabilizer example

F (z + dz) z + dz Fw (z)

Ff (z)

Fg (z) z

F (z)

1.6 0 min

dp/dx (bar/m)

1.4

10 min

1.2

15 min

1.0

20 min

30 min

0.8 0.6

0.4 0.2 0.0 0

0.00025

0.0005 0.00075 U (m/s)

0.001

0.00125

0.12

0.005

2.5

0.004

2.0

Δp (bar)

viscosity

ηf (mPa·s)

Concentration (kg/kg)

AL-lignin

0.08

3.0

a)

C5 sugars 0.10

0.006

1.5

0.06

0.003

0.04

0.002

0.02

0.001

0.5

0.00

0.000

0.0

0

10

20

Treatment duration (min)

30

b)

1.0

0

10 20 Treatment duration (min)

30

3.5

3.0 ηf (mPa·s)

2.5 2.0 1.5 1.0 0.5 0.0 0

50

100 150 T (°C)

200

250

0

1

3

7

11

20

t (min)

F

1. Inertial deformation phase

2. Compression phase 400

1.0

300 σ (kN/m²)

dσ/dt (kN/m²s)

1.5

0.5 0.0 -0.5

200 100

0 0.0

0.1

0.2 ε (-)

0.3

0.57

0.67

0.72

ε (-)

Compression test

400

3. 400

σ*

200

2. 100

1.

σ*

σ (kN/m²)

300

σ (kN/m²)

0.62

3. Relaxation phase

300 200

σ* 0 0

500

1000 Time (s)

1500

2000

100 1200

1400

1600 1800 Time (s)

2000

σ* · 10-5 (N/m²)

6

4

2

0 0.70

0.75

0.80 ε (-)

0.85

0.90

a)

b) 1

Reactor length (z/L)

Reactor length (z/L)

1

11 min.

7 min.

30 min.

0 0.00

0.25

0.50 σ·

0.75

10 5 (N/m²)

1.00

1.25

30 min.

0 0.00

0.25

0.50 σ·

0.75

10 5 (N/m²)

1.00

1.25

Decrease fluid viscosity/density

𝑑𝜎𝑠 𝑧, 𝑡 𝜂f 𝑧, 𝑡 = 𝑑𝑧 𝑘1 𝜀act 𝑧, 𝑡

∙ 𝑈 𝑧, 𝑡 +

Decrease velocity: - Low L/D ratio

𝜌f 𝑧, 𝑡 𝑘2 𝜀act 𝑧, 𝑡

Decrease reactor length: - Low L/D ratio - Intermediate bottoms Increase permeability ki: - Increase porosity

∙ 𝑈 𝑧, 𝑡

2

−

2𝜆𝜇 ∙ 𝜎𝑠 𝑧, 𝑡 − 1 − 𝜀act (𝑧, 𝑡) ∙ 𝜌s − 𝜌f (𝑧, 𝑡) ∙ 𝑔 𝑟

Decrease reactor diameter: - Vertical stabilizer - High wall friction

σS < σ*: Bed is stable σS > σ*: Bed deformation

Increase critical tension σ*: - E.g. filling bodies

b)

c)

Reactor length

Reactor length

Reactor length

a)

standard

standard

11 min.

vertic. stab.

filling bodies

16 min.

0.00 0.25 0.50 0.75 1.00 1.25 1.50

0.00 0.25 0.50 0.75 1.00 1.25 1.50

0.00 0.25 0.50 0.75 1.00 1.25 1.50

σ (N)

σ (N)

σ (N)

Highlights 

Pressure drop in hydrothermal wheat straw fixed-beds leads to bed compression.



Pressure drop, bed compressibility and axial tension were analyzed and modeled.



A complete model with reaction, heat & mass transfer and mechanics was derived.



The model considers dynamic bed properties due to biomass solubilization.



Reactor scale-up and stabilization were evaluated theoretically and experimentally.

52

F (z + dz) z + dz Δp

Fw (z)

LHW fixed-bed pretreatment Water

Ff (z)

Fg (z) z

Compression

F (z)