The proximate and ultimate compositions of the feedstock including wood chips, daily manure, sorghum, and grapevine (Lapuerta et al., 2008; Huang, 2009; Maglinao et al., 2015; Rodriguez-Alejandro et al., 2016) are presented in Table 1. Among the four biomass, the hydrogen contents of wood chips and sorghum are higher, while daily manure owns the lowest volatile content and hydrogen content. The simplified flow diagram of the designed system for producing hydrogen and electricity is shown in Figure 1. The system consists of five main units: the 1) biomass gasification unit, 2) steam methane reforming unit (SMR), 3) water–gas shift unit (HTS and LTS), 4) hydrogen separation unit (PSA), and 5) organic Rankine cycle (ORC). The key parameters and main assumptions associated with these modules are listed in Table 2, and the thermodynamic calculations and the system evaluation are performed using Python.

Thermodynamic equilibrium models usually ignore the conversion efficiency of carbon, but in fact, carbon cannot be completely converted during the gasification process (Eq. 10) (Marandi et al., 2019). Meanwhile, thermodynamic equilibriums such as the water–gas shift reaction (Eq. 3) and methanation reaction (Eq. 4) are usually hard to achieve in actual experiments. Therefore, correction factors based on experimental data were used to reflect the actual carbon conversion efficiency and nonequilibrium factors shown as follows: K 1 , n o n − e q =   K 1 , e q F K 1 (21) K 2 , n o n − e q =   K 2 , e q F K 2 (22) where K i , n o n − e q is the modified nonequilibrium constant, K i , e q is the equilibrium constant, and F K i is the correction factor of the equilibrium constants based on experimental data.

Compared with the original thermodynamic equilibrium model, correcting the equilibrium constants can improve the accuracy of hydrogen yield prediction. Besides that, F K 1 reduces the error of methane production yield, while   F K 2 gives more accurate carbon monoxide production yield in most cases (Basu, 2013; Marandi et al., 2019; Behzadi et al., 2020). The correction factors of carbon conversion efficiency and equilibrium constant of different biomass under specific conditions are summarized in Supplementary Table S2. The RMS (root mean square) is used to compare the differences of syngas compositions between the modified model and the experimental data, as shown in Eq. 23: R M S =   ∑ i = 1 N | n i , c a l − n i , e x p | N (23) where n i , c a l and   n i , e x p are the calculated and experimental syngas composition in vol％, respectively, and N is the specific gas including H2, CO, and CH₄.

Once establishing the full process model as aforementioned, hydrogen production and power generation can be projected according to various combinations of input operating parameters. To investigate the variation of key parameters simultaneously, the response surface methodology (RSM) was employed based on Design-Expert (DX10) version 10.0.3 software. The operating conditions of the overall system were designed by using the Box–Behnken (BBD) method, and the corresponding data were incorporated to meet the design requirements. After that, a response surface model was constructed to formulate the mathematical relationship between the target outputs such as hydrogen yields and power output and the input operational conditions, which was further illustrated by the contour plots. Therefore, the impacts of the key input parameters on the target indicator can be thoroughly explored from the sensitivity analysis.

Built upon the regression model, the multi-objective optimization of target indicators could be performed using the genetic algorithm (NSGA-Ⅱ), which transforms the problem-solving process into a mechanism similar to the crossing and mutation of chromosome genes in biological evolution. The genetic algorithm was employed in this work due to its capability of speeding up the search for optimal solutions and the set of optimal solutions constituting the Pareto front and was invoked from the Geatpy platform.

The syngas compositions from four biomass types including wood chips and sorghum were compared between different models (M1: the original equilibrium model, M2: the modified model considered the carbon conversion efficiency, and M3: the modified model considered the carbon conversion efficiency and nonequilibrium constants) and the experimental data of specific biomass. The main operating parameters (gasification temperature and equivalence ratio) of the simulation were kept consistent with the actual experimental conditions.

Figure 2 shows the results of wood chip gasification under the operating conditions of gasification temperatures varying from 813 to 1,058 K and ER of 0.33. The experimental data were derived from a pilot-scale fluidized bed gasifier, and air was used as the gasification agent (Rodriguez-Alejandro et al., 2016). As shown in Figure 2 A, the modified model considering carbon conversion efficiency (M2) could not improve the hydrogen production and the calculated error exceeds 100%. When both the carbon conversion efficiency and equilibrium constants were modified simultaneously (M3), the error between the predicted hydrogen production value and the experimental data was reduced to 42%. Figure 2B shows a comparison of the carbon monoxide production yield on a dry basis between different levels of models. The results of M2 were relatively close to the experimental values with a calculated error of 24.4%, while the error between M3 and the experimental values was 25.1%. Figure 2C shows a comparison of the methane production yield, and the average error was reduced by 20.9% from M3 to M1. Only when the temperature was higher than about 923 K, the predicted methane yield of theoretical models was close to the experimental data.

Figure 3 shows the results of sorghum gasification at the operating conditions of 1,013 < T < 1,073 K and ER = 0.35. The reactor was a pilot-scale fluidized bed gasifier and used air supplied by a blower as the fluidizing medium. Experimental data came from Maglinao et al. (2015). As shown in Figure 3A, the correction of the carbon conversion efficiency and the nonequilibrium constants (M3) could reduce the average error of the hydrogen production prediction values from more than 100 to 35.9% compared with the model that only modified the carbon conversion efficiency (M2). Figure 3B shows a comparison of the carbon monoxide production yield. The average error between M2 and the experimental values was 48.5%, while the error between M3 and the experimental values was 21.8%. Figure 3C shows a comparison of the methane production yield. Compared with the experimental results, M2 resulted in an average error of 42.7% and the error would decrease as the temperature increased.

As shown above, the original equilibrium model (M1) overestimated the production contents of hydrogen and carbon monoxide, while the production of methane was underestimated (George et al., 2016). The errors of carbon monoxide yield prediction were reduced in M2, and M3 could effectively improve the prediction of hydrogen yield. Besides that, M3 improved the methane prediction yield of wood chips, while M2 showed higher accuracy for sorghum. RMS values gradually decreased by applying the carbon conversion efficiency and the nonequilibrium constants, as summarized in Table 4 for different biomass. In general, the modified equilibrium model is desirable for the prediction of the syngas productions of these four kinds of biomass.

Figure 4 shows the comparison of hydrogen production yield out of the gasifier between different biomass at the same operating condition of 973 < T < 1,073 K and ER of 0.3. As shown in Table 5, the trend in the hydrogen yield was as follows: wood chip (11.59 mol/kg dry biomass) > sorghum (8.80 mol/kg dry biomass) > grapevine pruning (6.41 mol/kg dry biomass) > daily manure (5.72 mol/kg dry biomass). The differences in the yields of hydrogen might be attributed to the different biomass volatiles (Wei et al., 2014; Zhang et al., 2019) or the hydrogen contents based on the ultimate analysis.

Different fluids were investigated to select the best working fluids for the proposed system, as illustrated in Supplementary Figure S1. Output power was used as a standard to measure the performance of the fluids. The results show that R123 is the best working fluid by generating a total power of 2,268.93 kW. Results were derived by thermodynamic modeling and considering the assumptions given in Table 6.

Furthermore, the detailed stream states of the system are shown in Sankey diagram of the energy flows (see Figure 5). The produced syngas heat is recovered to preheat the reaction agent and supplies heat to the ORC, which contributes to improving the energy conversion efficiency. Under the given design conditions, the largest energy loss occurs in the biomass gasification process since a certain proportion of biomass carbon does not react in the modified equilibrium model.

As mentioned above, wood chips produced the most maximum amount of hydrogen and showed a good degree of regression, so it was used as the biomass feedstock for further analysis. The hydrogen production (the mole of hydrogen per kilogram of biomass, mol/kg) and the output power are the evaluation parameters, while the independent variables were gasification temperature (923–1,223 K), equivalence ratio (0.1–0.6) and steam-to-biomass ratio (0.1–1.5).

The empirical prediction models of produced hydrogen yield and output power were statistically analyzed using an ANOVA (analysis of variance) as shown in Supplementary Table S3. The terms of “A, B, and C” refer to gasification temperature, equivalence ratio, and steam-to-biomass ratio, respectively. Generally speaking, a p-value of less than 0.05 indicates a significant term in the regression model (Cuevasglory et al., 2017). Both the gasification temperature (A) and ER (B) were highly correlated with the production yield of hydrogen and the system output power. Both models were considered significant since p-values were less than 0.001. R-squared values of 0.9988 and 0.9976 for the hydrogen production model and output power model are observed, respectively. Additionally, “Adeq Precision” measures the signal-to-noise ratio, and a value greater than 4 is desirable. The values of the models (45.28, 39.30) indicate adequate signals. Therefore, both models are desirable to navigate the design space.

From Figure 6, it can be seen that the yield of hydrogen increased with the increasing equivalence ratio under the condition of relatively low equivalence ratio. When the equivalence ratio exceeded a certain level, the hydrogen yield turned down. An appropriate ER value could maximize the hydrogen production yield. Temperature and steam-to-biomass ratio made same impacts. From the empirical regression model, the highest hydrogen production was calculated as 41.28 (mol/kg) at conditions of 1,031.73 K, 0.325, and 0.886 (temperature, equivalence ratio, and steam-to-biomass ratio). Figure 7 shows the effects of gasification temperature, ER, and S/B on output power. The energy recovery system which utilizes the heat of the exhaust gas transfers energy to the ORC system, and the heat of gasifier outlet syngas increases with the gasification temperature and S/B. Therefore, larger operating parameters (gasification temperature and S/B) can improve the output power of the ORC system. The highest output power was calculated as 4,733.11 (kW) at conditions of 1,223 K, 0.579, and 1.5 (temperature, equivalence ratio, and steam-to-biomass ratio). Figures 6D and 7D show the actual and predicted response values of the regression model. The values were concentrated near the line, which indicated that it is a reliable regression model with small errors.

The equation in terms of actual equation can be used as the regression model to make predictions, while the coded coefficients are useful for identifying the relative impact of the factors by comparing the factor coefficients. Actual factors should not be used to determine the relative impact of each factor because the coefficients are scaled to accommodate the units of each factor, and the intercept is not at the center of the design space. As shown in Supplementary Table S4, the coded coefficients for the hydrogen production yield were gasification temperature (A = −1.46), equivalence ratio (B = −5.06), and steam-to-biomass ratio (C = −0.73), which indicated that the equivalence ratio was the major influential independent variable. The influential coded coefficients contributing to the increasing output power were the linear terms of gasification temperature (A = 866.00), equivalence ratio (B = 790.34), and steam-to-biomass ratio (C = 633.79). Gasification temperature was the major parameter contributing to the increasing output power since the heat exchanger could recover more energy into the ORC system with the increasing gasification temperature.

The formulated multi-objective optimization (MOO) problem for the designed system is shown in Table 7. In this study, two important optimization objectives were studied using the genetic algorithm method (NSGA-Ⅱ) incorporated in Python: 1) maximization of hydrogen production yield and 2) maximization of output power (Li et al., 2019).

Figure 8 depicts the Pareto frontier diagram of the optimal solution points of objective functions for the model. Selecting the relatively best point depends on the policy of decision since all the points on the Pareto front are the optimal points. For instance, if the system needs to be optimized from the hydrogen yield aspect alone, point C is the best solution point, while the value of the output power is minimized. Point A is the best point if maximized output power is the focus. In this research, the LINMAP (linear programming technique for multidimensional analysis of preference) selection method was used to find the preferred optimal solution (Zhiyuan et al., 2017). The LINMAP method is executed with the following three steps:

The points of the Pareto front curve are made nondimensional by Eq. 24.