Establishment and verification of a shrinking core model for dilute acid hydrolysis of lignocellulose

Abstract

The kinetics of lignocellulose hydrolysis under the conditions of high temperature and dilute acid (mass fraction 0.05%) was investigated in this paper. By studying the reducing sugar concentration versus reaction temperature (170°C–220°C) and reaction time (150–1800 s) during the hydrolysis process of five kinds of crop straw (rice, wheat, cotton, rape and corn), the shrinking core model was established, and the differential equation of the model and its analytical solution were obtained. With a numerical calculation method, the kinetic equation was estimated, and the degradation of reducing sugar obeyed first-order kinetics was obtained. The calculated results from the equations agreed well with the original experimental data. The calculation by the model showed that the reducing sugar concentration increases as the size of the particles decrease, and the uniform particles increase.

Keywords

lignocellulose / dilute acid hydrolysis / shrinking core model

Introduction

Considering the environmental and economic benefits, the utilization of biomass to manufacture fuel ethanol has received worldwide attention [1]. Lignocellulose, especially agricultural wastes, is the most potential resource to develop biomass energy [2]. During the manufacturing process of ethanol, lignocellulose was first hydrolysed into reducing sugars, and then the reducing sugars were fermented into ethanol. The most critical step is the lignocellulose hydrolysis [3–5]. During the process of hydrolysis, reaction temperature and reaction time were the main factors affecting not only the formation of reducing sugar, but also the degradation of reducing sugar [6]. There has been a considerable amount of research on the mechanism of dilute acid hydrolysis, but lignocellulose structures are relatively stable and complex, and different types of biomass have different structures and show different reaction behaviors. The establishment of kinetics model of hydrolysis can provide a theoretical reference for studying lignocellulose hydrolysis behaviors and has a great significance. A variety of kinetic models for acidic hydrolysis of cellulose and hemicellulose have been reported. The origin of the organized kinetic study of cellulose and hemicellulose hydrolysis dated back to the work of Saeman [7] who defined the dilute acid hydrolysis of lignocellulose as two pseudo-homogeneous consecutive first-order reactions. Sasaki et al. [8], Rogalinski et al. [9], Schacht et al. [10], Young and Rowell [11] and Mok et al. [12] also believed that the hydrolysis of cellulose obeyed first-order kinetics; Qian et al. [13] proposed a comprehensive kinetic model which agreed well with experimental data obtained under a broad range of reaction conditions.

Most of the studies mentioned above had to be built on a homogeneous first-order irreversible kinetic model. However, there existed liquid phase and solid phase in the reaction. Few studies have so far investigated the hydrolysis kinetics on liquid phase and solid phase. In this study, five dominant agricultural wastes, namely, rice, wheat, cotton, rape and corn straw, in Hubei province of China were chosen as typical lignocellulosic biomasses. The kinetics of these five kinds of materials was examined during dilute acid hydrolysis at 170°C–220°C. The phenomenon of experiment certainly contradicted the homogeneous first-order irreversible kinetic model. An experimental investigation was conducted in the laboratory to formulate a plausible model. In this work, a shrinking core model has been proposed which can better describe the practical process of lignocellulose hydrolysis and can provide the referential basis for the lignocellulose hydrolysis at dilute-acid conditions.

Experiment

Materials

Wheat, cotton, rape, rice, and corn straws from Hubei province were used as raw materials. Those air-dried straws were sieved to fine particles with sizes less than 180 mesh and then dried in a hot air oven at 80°C until constant weight before being used in the experiments. The contents of cellulose, hemicellulose, lignin and ash were analyzed, using the van Soest method [14,15]. The results are listed in Table 1.

Experimental setup and operations

One main component of the experimental setup was the batch reactor, made of stainless steel No. 316L, having a capacity of 0.15 L. 3.0 g of straw and 45 mL of diluted sulfuric acid solution were put and 1.0 MPa of nitrogen gas was injected into the reactor. The heating equipment was an electronic furnace with a heating power of 2 kW. When the reactor was heated to the set temperature, the agitation switch was turned on to adjust the agitating speed into 500 r/min, while the time was counted. The temperature of lignocellulose hydrolysis ranged from 170°C to 220°C and the reaction time was 2.5–30 min. When the hydrolysis experiment finished, the reactor was put into the cool water. After the temperature inside the reactor fell to room temperature, the reactor was opened. The liquid and solid products/residues were separated by filtration. Then the filtrate and filter cake was respectively analyzed. The concentration of reducing sugars in the samples was analyzed using the 3,5-dinitrosalicylic acid method [16].

Establishment of hydrolysis kinetics model

Both cellulose and hemicellulose are polysaccharides that can be hydrolyzed into reducing sugar. Meanwhile, reducing sugar can decompose to small molecular compounds like furan, acetaldehyde, acetic acid, butanone etc. under the high temperature and dilute acid conditions [17,18]. The following kinetic model was applied to describe the process of biomass hydrolysis:

\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\left(S\right)\stackrel{k_{\mathrm{1}}}{\to }\mathrm{Re}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}\mathrm{u}\mathrm{g}\mathrm{a}\mathrm{r}\left(P\right)

\stackrel{k_{\mathrm{2}}}{\to }\mathrm{S}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\left(C\right),

where k₁ is the rate constant of hydrolysis of biomass, k₂ is the rate constant of decomposition of reducing sugar.

In the process of hydrolysis, the biomass particles can be regarded as spherical. As the hydrolysis proceeds, these particles will gradually shrink to the center of the sphere. Based on the characteristics of the hydrolysis, some assumptions could be proposed: ① The bulk concentration was well distributed in the high-speed stirring reactor, and the diffusion resistance of reactants and products mainly focused on the laminar sublayer of particle surface; ② The biomass particles were seen as dense spherical, and there were no free water molecules in the particles in the initial reaction. The diffusion of water molecules to the particle surface and the diffusion of products to the solution could be conduced through the laminar sublayer of the particle surface, which could be considered as equimolecular reverse diffusion; ③ Because there was no consumption of H⁺ in the process of biomass hydrolysis, the concentration of H⁺ in the laminar sublayer of particle surface and the particle surface was consistent with that of the bulk solution; ④ Under high temperature and high pressure conditions, the rate of lignocellulose acid hydrolysis was relatively fast [19]. Therefore, it could be assumed that the concentrations of water molecules on cellulose and hemicellulose surface were zero.

According to the principle of lignocellulose hydrolysis, α unit of glycosidic bonds can be broke by α unit of water molecules to generate α + 1 unit of sugar molecules. Considering that the α is relatively large, it can be approximately assumed that one water molecule can break one glycosidic bond and one sugar molecule can be generated, which diffuses into the solution. As a result, the rates of cellulose and hemicellulose hydrolysis, sugar molecules formation and water molecules diffusion are equal in value:

(1)-r_{\mathrm{S}}=\left(\alpha +\mathrm{1}\right)r_{\mathrm{P}}=-\alpha r_{\mathrm{W}},

where r_{\mathrm{S}} is the rate of cellulose and hemicellulose hydrolysis, while r_{\mathrm{P}} is the rate of sugar molecules formation and r_{\mathrm{W}} is the rate of water molecules diffusion.

The consumption of lignocellulose in \mathrm{d}t:

(2)-\mathrm{d}{n}_{\mathrm{S}}=\mathrm{4}\mathrm{\pi }{r}^{\mathrm{2}}{\rho }_{\mathrm{S}}{\omega }_{\mathrm{S}}\mathrm{d}r/{\mathit{M}}_{\mathrm{S}}.

The consumption of water molecules in \mathrm{d}t:

(3)-\mathrm{d}{n}_{\mathrm{W}}=\mathrm{4}\mathrm{\pi }{r}^{\mathrm{2}}{k}_{\mathrm{L}}\left(C_{\mathrm{W},\mathrm{L}}-C_{\mathrm{W},\mathrm{L}}^{*}\right)\mathrm{d}t,

where {\rho }_{\mathrm{S}} is the density of particle, {\omega }_{\mathrm{S}} is the content of cellulose and hemicellulose in the straw, r is the radius of shrinking core model during the reaction, M_{\mathrm{S}} is the average molecular weight of cellulose and hemicellulose, k_{\mathrm{L}} is the coefficient of mass transfer, C_{\mathrm{W},\mathrm{L}} is the concentration of water in the reaction system, C_{\mathrm{W},\mathrm{L}}^{*} is the concentration of water in biomass particle surface, and t is the reaction time.

Since the polymerization degree of cellulose and hemicellulose is great (7000–10000) [20], \alpha /(\alpha +\mathrm{1})\approx \mathrm{1}.

The formation of sugar molecules in \mathrm{d}t:

(4)\mathrm{d}{n}_{\mathrm{P}}=-\mathrm{d}{n}_{\mathrm{W}}=-\alpha \mathrm{d}{n}_{\mathrm{S}}.

So

(5)\mathrm{4}\mathrm{\pi }{r}^{\mathrm{2}}{k}_{\mathrm{L}}\left(C_{\mathrm{W},\mathrm{L}}-C_{\mathrm{W},\mathrm{L}}^{*}\right)\mathrm{d}t=\mathrm{4}\mathrm{\pi }{r}^{\mathrm{2}}\alpha {\rho }_{\mathrm{S}}{\omega }_{\mathrm{S}}\mathrm{d}r/M_{\mathrm{S}}.

By the assumption, C_{\mathrm{W},\mathrm{L}}^{*} was approximately zero. Equation (5) can be simplified as

(6)k_{\mathrm{L}}{C}_{\mathrm{W},\mathrm{L}}\mathrm{d}t={\rho }_{\mathrm{S}}\alpha {\omega }_{\mathrm{S}}\mathrm{d}r/M_{\mathrm{S}},

or

(7)k_{\mathrm{L}}{C}_{\mathrm{W},\mathrm{L}}t={\displaystyle \frac{{\rho }_{\mathrm{S}}\alpha {\omega }_{\mathrm{S}}}{M_{\mathrm{S}}\left(R_{\mathrm{S}}-r\right)}},

where R_{\mathrm{S}} is the initial radius of particle.

In the process of hydrolysis, the conversion rate of single biomass particle x_{\mathrm{S}} can be expressed as

(8)x_{\mathrm{S}}={\displaystyle \frac{m_{\mathrm{S}}-m_{\mathrm{R}}}{m_{\mathrm{S}}}}={\displaystyle \frac{n_{\mathrm{S}}-n_{\mathrm{R}}}{n_{\mathrm{S}}}}=\mathrm{1}-{\left({\displaystyle \frac{r}{R_{\mathrm{S}}}}\right)}^{\mathrm{3}},

where m_{\mathrm{S}} is the original quality of the biomass particles, m_{\mathrm{R}} is the remaining quality of the biomass particles, n_{\mathrm{S}} is the original amount of substance, n_{\mathrm{R}} is the remaining amount of substance.

Combined with Eqs. (7) and (8), these can be expressed as follow:

(9){\displaystyle \frac{k_{\mathrm{L}}{C}_{\mathrm{W},\mathrm{L}}{M}_{\mathrm{S}}}{{\rho }_{\mathrm{S}}{R}_{\mathrm{S}}\alpha {\omega }_{\mathrm{S}}}}t=\mathrm{1}-{\left(\mathrm{1}-x_{\mathrm{S}}\right)}^{\mathrm{1}/\mathrm{3}}.

Through integration, assuming

k_{\mathrm{1}}={\displaystyle \frac{k_{\mathrm{L}}{M}_{\mathrm{S}}{C}_{\mathrm{W},\mathrm{L}}}{{\rho }_{\mathrm{S}}{R}_{\mathrm{S}}\alpha {\omega }_{\mathrm{S}}}}.

Eq. (10) can be obtained from Eq. (9).

(10)k_{\mathrm{1}}t=\mathrm{1}-{\left(\mathrm{1}-{\mathit{x}}_{\mathrm{S}}\right)}^{\mathrm{1}/\mathrm{3}}.

From Eq. (10), t_{\mathrm{C}} represents the time of cellulose and hemicellulose were completely hydrolyzed:

(11)t_{\mathrm{C}}=\mathrm{1}/k_{\mathrm{1}}.

Compared to individual particles, the equations above were also applicable to the particle swarms when the particles were uniformly distributed in the high-speed stirring reactor. So, analytical solution can be obtained as follow:

(12)

where C_{\mathrm{S},\mathrm{0}} is the concentration of solid, C_{\mathrm{S}} is the concentration of biomass.

The reducing sugar decomposition rate is defined as

(13){\displaystyle \frac{\mathrm{d}{C}_{\mathrm{C}}}{\mathrm{d}t}}=k_{\mathrm{2}}^{\prime }f\left(C_{\mathrm{P}}\right),

where C_{\mathrm{P}} is the concentration of reducing sugar, and C_{\mathrm{C}} is the concentration of small molecular compound.

The linear fitting f\left(C_{\mathrm{P}}\right) (expanding it into Taylor series at t = 0, and omitting the higher order terms) was obtained as

(14)f\left(C_{\mathrm{P}}\right)=C_{\mathrm{P}}+\gamma .

The rate of reducing sugar decomposition can be described as

(15){\displaystyle \frac{\mathrm{d}{C}_{\mathrm{C}}}{\mathrm{d}t}}=k_{\mathrm{2}}\left(C_{\mathrm{P}}+\gamma \right).

The different rates between the reducing sugar formation and its decomposition with reaction time can be expressed by Eq. (16) based on the above kinetic model.

(16)

When t=\mathrm{0}, C_{\mathrm{P}}=\mathrm{0}, Eq. (16) can be simplified as

(17)

where

(18)A=\mathrm{3}{\displaystyle \frac{k_{\mathrm{1}}}{k_{\mathrm{2}}}}{\left(\mathrm{1}-k_{\mathrm{1}}t\right)}^{\mathrm{2}}+\mathrm{6}{\left({\displaystyle \frac{k_{\mathrm{1}}}{k_{\mathrm{2}}}}\right)}^{\mathrm{2}}\left(\mathrm{1}-k_{\mathrm{1}}t\right)+\mathrm{6}{\left({\displaystyle \frac{k_{\mathrm{1}}}{k_{\mathrm{2}}}}\right)}^{\mathrm{3}},

(19)B=\gamma -C_{\mathrm{S},\mathrm{0}}\left[\mathrm{3}{\displaystyle \frac{k_{\mathrm{1}}}{k_{\mathrm{2}}}}+\mathrm{6}{\left({\displaystyle \frac{k_{\mathrm{1}}}{k_{\mathrm{2}}}}\right)}^{\mathrm{2}}+\mathrm{6}{\left({\displaystyle \frac{k_{\mathrm{1}}}{k_{\mathrm{2}}}}\right)}^{\mathrm{3}}\right].

According to the Arrhenius law, which expresses the relationships among the frequency factors, the activation energy, the temperature, k_{\mathrm{1}}and k_{\mathrm{2}}can be rewritten in detail as

(20)k_{\mathrm{1}}=k_{\mathrm{10}}\exp \left(-E_{\mathrm{1}}/RT\right),

(21)k_{\mathrm{2}}=k_{\mathrm{20}}\exp \left(-E_{\mathrm{2}}/RT\right).

Results and discussion

Verification and calculation of kinetics model

The reaction temperature and reaction time are main factors which can greatly influence the dilute acid hydrolysis of biomass. Under the conditions of sulfuric concentration of 0.05%, liquid to solid ratio of 15∶1 (V/m), pressure of 1.6 MPa and stirring speed of 500 r/min, the hydrolysis processes of five species of crop straw (rice, wheat, cotton, rape and corn) were examined. The relationship between reducing sugar concentration and reaction time at different temperatures and the contrast between the experimental data and the curves calculated from kinetic model were illustrated in Fig. 1. As can be seen from Fig. 1, the variation of reducing sugar concentration was generally consistent with the theory of Saeman [7]. When reaction time increased, the reducing sugar concentration first increased and then decreased. Just as the model assumed, the reducing sugar was the intermediate product in the process of straw hydrolysis. The higher of the temperature was, the earlier the time the reducing sugar concentration reached the maximum. The reason for this is that the increasing temperature can obviously accelerate the hydrolysis of straw and that high temperatures make reducing sugar concentration reach the maximum a short period of time. However, the decomposition of reducing sugar is also accelerated, which can explain the decrease of reducing sugar concentration.

In order to determine the values of kinetic parameters, the least square method was employed. Defining the sum of squares of residuals of the experimental value C_{\mathrm{P}\mathrm{e}\mathrm{x}\mathrm{p}} and analog value C_{\mathrm{P}\mathrm{c}\mathrm{a}\mathrm{l}} as the objective function S, the objective function S can be expressed as Eq. (22). Let

(22)S={\displaystyle \sum _{i=\mathrm{1}}^n{\left(C_{\mathrm{P}\mathrm{c}\mathrm{a}\mathrm{l}}-C_{\mathrm{P}\exp }\right)}^{\mathrm{2}}}

have the minimum value.

The calculating equations of decisive index is

(23)R^{\mathrm{2}}=\mathrm{1}-{\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^n{\left(C_{\mathrm{P}\mathrm{c}\mathrm{a}\mathrm{l}}-C_{\mathrm{P}\exp }\right)}^{\mathrm{2}}}}{{\displaystyle \sum _{i=\mathrm{1}}^n{C}_{\mathrm{P}\exp }^{\mathrm{2}}}}}.

The results of statistical simulation are presented in Table 2.

A good fit between the experimental data and the kinetic model was achieved, as shown in Fig. 1 and Table 2, which indicated that under dilute acid, the set of kinetics model in line with the hydrolysis behavior of lignocellulose described the reaction process well.

With the kinetics model above, the parameters like pre-exponential factor and apparent activation energy were calculated, as given in Table 3. Obviously, in the process of hydrolysis, apparent activation energy varied from different kinds of straws. Besides, for the same kind of straw, the apparent activation energy of formation of reducing sugar was greater than decomposition, which demonstrated the increasing of reaction temperature could better benefit for the formation of reducing sugar.

With the numerical calculation method, the value \gamma of each kind of straw the five straws was 6.99×10^-43, which indicated that the degradation of reducing sugar obeyed first-order kinetics.

Application of hydrolysis kinetics model and discussion

Effect of particle size on concentration of reducing sugar

Lignocellulose hydrolysis under dilute acid, high temperature and high pressure was greatly controlled by diffusion, while the diffusion was closely related to the particle size. In the hydrolysis processes, there existed optimal reducing sugar formation condition, which was different when the sizes of straw particle varied. The reason for this is that the diffusion distance of reactants and products were different.

Generally speaking, for the same kind of straw, the optimal reaction time for reducing sugar formation would be shortened when the sizes of straw particle decreased. This was mainly because that as the size of straw particle decreased, the hydrolysis rate of straw increased and the specific surface of particle increased, and correspondingly, the hydrolysis rate would be promoted. The optimal hydrolysis time and temperature could be obtained by the model from the principles of mathematical \partial C_{\mathrm{P}}/\partial t=\mathrm{0}, when the reducing sugar concentration reached the maximum. By using Eqs. (18)–(22), t_{\mathrm{o}\mathrm{p}\mathrm{t}}, T_{\mathrm{o}\mathrm{p}\mathrm{t}} and C_{\mathrm{P}\mathrm{o}\mathrm{p}\mathrm{t}} can be calculated in the range of experimental temperature as demonstrated in Table 4. It can be seen that, the optimal reaction time, temperature and the maximum reducing sugar concentration were almost the same for the hydrolysis of straws from Hubei province under dilute acid, while those of the rape straw were slightly different.

According to k_{\mathrm{1}}=k_{\mathrm{L}}{M}_{\mathrm{S}}{C}_{\mathrm{W},\mathrm{L}}/\left({\rho }_{\mathrm{S}}{R}_{\mathrm{S}}\alpha {\omega }_{\mathrm{S}}\right), k_{\mathrm{1}} and R_{\mathrm{S}} were inversely proportional when other parameters were constant. The straw was milled and screened with 180 mesh (particle radius was 4×10^-5m) in this experiment, and the effects of particle size on reducing sugar concentration was found. Therefore, the optimal hydrolysis time of each kind of straw was gained by the simulation of different particle sizes at its optimal hydrolysis temperature. It was advised that 300 meshes be the upper limit of mechanical grinding, considering the limitation of the grinding technology and energy consumption [21]. In Table 5, the maximum reducing sugar concentrations of rice straw at the optimal time were listed when straw particle ranged from 80 to 300 meshes and the effect of particle size on reducing sugar concentration was depicted in Fig. 2.

As the sizes of straw particle increased, the hydrolysis constant decreased, which meant that more time was needed to reach the maximum reducing sugar concentration. Besides, there was substantial amount of reducing sugar decomposed in the process demonstrated above, and the maximum reducing sugar concentration declined. As a result, smaller particle size was more proper for lignocellulose hydrolysis.

Effect of particle uniformity on reducing sugar concentration

Table 5 showed that the smaller sizes of straw particle contribute to the higher reducing sugar concentration. In fact, the hydrolysis of lignocellulose was so called nonuniform hydrolysis because the straws were usually mechanically grinded without screening. Table 6 illustrated the relationship between maximum reducing sugar concentration and uniformity of straw particle. In this experiment, there existed optimal reaction temperatures and reaction time, which were different with different sizes of straw particle. Some smaller straw particle had reached the optimal reaction temperatures and reaction time. At that condition, the continued hydrolysis of larger particles may cause the lower concentration of reducing sugar. Regarding the average particle radius as the standard of the uniformity of the mixed straw particles, it was concluded that high uniformity of straw particles had a high reducing sugar concentration. Therefore, small size of straw particles and high uniformity of straw particles contributed to the improvement of straw hydrolysis efficiency.

Conclusions

1) Through the research of lignocellulose hydrolysis under high temperature and dilute acid conditions, a kinetics model describing the hydrolysis process of lignocellulose was suggested and verified. A comparison of the calculated results from the equations and experimental ones proved that a good fit between the experimental data and the kinetic model was achieved. The set of kinetics model could satisfactorily verbalize the hydrolysis reaction of lignocelluloses by dilute acid.

2) In the process of hydrolysis, it was concluded that the apparent activation energy of hydrolysis varied for different kinds of straws. Besides, the value of \gamma (Eq. (14) above) of each kind of straw of the five strws was 6.99×10^-43, which meant the degradation of reducing sugar obeyed first-order kinetics;

3) The smaller sizes and higher uniformity of straw particles contributed to better concentration of reducing sugar and the improvement of straw hydrolysis efficiency.

4) The shrinking core model was initially established and verified based on the dilute acid hydrolysis under high temperatures. However, the decomposition of reducing sugar wasn not considered when it was diffused from the surface of straw particle to the bulk. Meanwhile, the hydrolysis products were not all reducing sugar because the glycosidic bonds couldn not be broken by free water molecules on the surface of straw particle. Therefore, a further study is needed.

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