### Specimen preparation

Figure 1 shows three species of softwood purchased from a Korean wood market (Jeonil timber Co., Ltd), 20-year-old hinoki [*Chamaecyparis obtusa *(Siebold & Zucc.) Endl] from Japan, 26-year-old Douglas fir (*Pseudotsuga menziesii*) from North America, and 20-year-old hemlock (*Tsuga heterophylla*) from North America. The logs were cut into cross-sections with thickness of 1 cm. In hinoki, the entire diameter was 20 cm, and the diameter of the heartwood was 14 cm. The entire diameter of the Douglas fir was 32 cm, and the diameter of the heartwood was 20 cm. In the hemlock, the entire diameter was 29 cm, and the diameter of the heartwood was 20 cm. From the cross-sectional discs, 10 cylindrical specimen (30 mm diameter × 10 mm thickness) of heartwood, intermediate wood, and sapwood were cut. Intermediate wood samples were distinguished by interfacing with approximately 50% of the area of the heartwood and sapwood. The cylindrical specimens were dried at 40 °C using a dryer for 1 week and controlled within a 10% moisture content (MC) to exclude the influence of MC between heartwood and sapwood to focus on pore structure.

To measure the true density of the wood substance, internal voids must be ignored. Wood samples from the sapwood and the heartwood were pulverized into fine wood powder [34, 37, 38].

### Scanning electron microscope (SEM) imaging for cross-sections of specimens

To observe the pore morphology of a specimen, its cross-sections were cut into dimension of approximately 5 mm (radial) × 5 mm (tangential) × 4 mm (longitudinal), and the surfaces were smoothed using a microtome (model: HM400S, Microm GmbH, Germany). Further, specimens were coated with gold ions by an ion sputter-coater (model: SCM, Emcrafts, Korea) and observed at an acceleration voltage of 13 kV and 400× magnification using scanning electron microscopy (SEM; model: Genesis-1000, Emcrafts, Korea).

### Measurement of bulk density and true density

Bulk density of the cylindrical specimens was measured by the dimension method. True density of cylindrical specimens and sawdust was measured by gas pycnometer (model: PYC-100A-1, Porous Material Inc., USA) [5, 37, 38]. Before measuring the specimen, the gas pycnometer was calibrated to a standard stainless-steel cylindrical sample from the manufacturer, the volume and mass of which were 15.4346 cm^{3} and 41.1767 g, respectively. The volumes of the reference chamber and sample chamber were 35.5310 cm^{3} and 33.5224 cm^{3}, respectively. For convenience, the true density of sawdust intermediate wood was calculated as the average of heartwood and sapwood.

### Measurement of gas permeability

Gas permeability was measured using a capillary flow porometer (model: CFP-1200AEL, Porous Materials, Inc., USA). To prevent air leakage from edge of a cylindrical specimen, the side surface was sealed with a silicon O-ring. Increasing pressure slowly, air flow through the pore was measured, and the Darcy permeability constant was calculated from Eq. (1) shown below:

$$ C = 8{\text{FTV}}/\pi D^{2} \left( {P^{2} - 1} \right), $$

(1)

where *C* is the Darcy permeability constant; *F *is the flow; *T* is the sample thickness; *V* is the viscosity of air; *D* is the sample diameter; and *P* is the pressure.

### Measurement of pore diameter

Pore diameter of specimens was measured using a capillary flow porometer (model: CFP-1200AEL, Porous Material Inc, USA). The ASTM F316-03 [39] method was used to selectively measure the constricted part of a through pore related with permeability and is widely used for analysis of pore structure of various porous materials [40]. It is also a possible way to selectively measure only through pores in line with permeability of wood [36, 37]. As shown in Fig. 2, in the process of gas permeability estimation by flow rate under pressure, the graph of flow rate versus pressure is called a ‘dry curve’. Next, the specimens were wetted in Galwick solution that has an extremely low surface tension (surface tension: 0.159 mN/m) and non-volatility to penetrate well into the cavity. Pressure was measured sequentially from the moment when the flow rate of the gas was detected with solution extrusion, and the pressure at the time of initial flow increase is called the ‘bubble point’. In the wet state, the graph of flow rate versus pressure is called a ‘wet curve’. Here, an imaginary curve having a slope of 1/2 of that of the ‘dry curve’ can be drawn and is called a ‘half-dry curve’. The point where the ‘wet curve’ and ‘half-dry curve’ meet is called ‘mean flow pore pressure’, and the pore size is determined by Eq. (2) as below:

$$ D = \frac{{C_{\tau } }}{p}, $$

(2)

where *D* is the limiting diameter, *τ* is the surface tension, *p* is the pressure, and *C* is the constant of 2860 when *p* is in Pa, 2.15 when *p* is in cmHg, and 0.415 when *p* is in psi units.

### Porosity of through pore, blind pore, and closed pore types

Following IUPAC [41], pore types of solid porous materials can be classified as through pores, blind pores, and closed pores (Fig. 3). Hence, this study measured the content of each type of pores in the three species of wood as in previous studies [5, 37]. Specifically, content was measured for through pore porosity (*ϕ*_{through}), blind pore porosity (*ϕ*_{blind}), and closed pore porosity (*ϕ*_{closed}) of the cylindrical specimens using the following method.

Total porosity *ϕ*_{total} (%) was calculated from Eq. (3) measuring true volume (*V*_{true}) of the sawdust by gas pycnometry and bulk volume (*V*_{bulk}) of the cylindrical specimens by the dimensional method:

$$ \phi_{{{\text{total}}}} \left( \% \right) = \left( {1 - \frac{{V_{{{\text{true}}}} }}{{V_{{{\text{bulk}}}} }}} \right) \times 100. $$

(3)

Pore volume of the cylindrical specimen by gas pycnometer was obtained as the sum of through pore volume (*V*_{through}) and blind pore volume (*V*_{blind}). Thus, the sum of through pore porosity (*ϕ*_{through}) and blind pore porosity (*ϕ*_{blind}) was calculated as in Eq. (4):

$$ \phi_{{{\text{through}}}} + \phi _{{{\text{blind}}}} = \frac{{ V_{{{\text{through}}}} + V_{{{\text{blind}} }} }}{{V_{{{\text{bulk}}}} }} \times 100. $$

(4)

Finally, from the results of Eqs. (3) and (4), closed pore porosity (*ϕ*_{closed}) was obtained with Eq. (5):

$$ \phi_{{{\text{closed}}}} = \phi_{{{\text{total}}}} - \left( {\phi_{{{\text{through}}}} + \phi_{{{\text{blind}}}} } \right) . $$

(5)

To distinguish through pore porosity (*ϕ*_{through}) from blind pore porosity (*ϕ*_{blind}), this study wetted cylindrical specimens in Galwick solution (surface tension: 0.159 mN/m) and intruded the liquid into the pores utilizing a vacuum pump. After that, the specimens were placed in a chamber of which both sides were sealed with O-rings, and the air pressure was increased in the longitudinal direction so that only Galwick in the through pores could be extruded since blind pores were blocked at one end.

We obtained the mass of Galwick solution in blind pores by measuring the difference between specimen mass after extrusion (*M*_{after extrusion}) and dried specimen mass (*M*_{dried}). Also, the volume of blind pore (*V*_{blind}) was calculated as the difference between specimen mass (*M*_{after extrusion} − *M*_{dried}) and specific gravity of Galwick solution (*ρ*_{Galwick}) using Eqs. (6, 7, and 8):

$$ V_{{{\text{blind}}}} = \frac{{M_{{{\text{after}}\;{\text{extrusion}}}} - M_{{{\text{dried}}}} }}{{\rho_{{{\text{Galwick}}}} }}, $$

(6)

$$ \phi_{{{\text{blind}}}} = \frac{{V_{{{\text{blind}}}} }}{{V_{{{\text{bulk}}}} }} \times 100, $$

(7)

$$ \phi_{{{\text{through}}}} = \left( {\phi_{{{\text{through}}}} + \phi_{{{\text{blind}}}} } \right) - \phi_{{{\text{blind}}}} . $$

(8)

### Statistical analyses

This study applied a statistical approach to corroborate reliability of the experimental results.

Physical properties (pore type, pore size, and density) of wood can affect gas permeability. Among the three types of pores for solid porous materials defined by IUPAC, only through pores can permit fluid inflow. Thus, through pore porosity may have a significant effect on gas permeability [5, 37]. Moreover, as pore size increases, the flow of fluid generally increases; as density increases, the flow of fluid generally decreases. In short, pore size, bulk density, and through pore porosity are significant factors affecting gas permeability. Thus, this study statistically investigated the effects of through pore porosity, mean pore size, and bulk density on gas permeability.

Specifically, this study compared the average gas permeability, pore size, and porosity of three parts of heartwood, intermediate wood, and sapwood using analysis of variance (ANOVA).

In addition, this study analyzed statistical correlation by Pearson correlation analysis to understand univariate associations among the variables. Furthermore, this study utilized multivariate regression to analyze effects of physical factors on gas permeability to enable investigation of factor-specific effects on dependent variables after controlling the other factors. Multivariate regression has another advantage in that it provides the simultaneous effects of several variables on the dependent variable.

The multivariate regression model was used to display the effects of through pore porosity, mean pore size, and bulk density on gas permeability as displayed in the equation below:

$$ Y\, = \,\alpha_{0} \, + \,\beta_{1} X_{1} \, + \,\beta_{2} X_{2} \, + \,\beta_{3} X_{3} \, + \,\beta_{4} D_{1} \, + \,\beta_{5} D_{2} \, + \,\varepsilon , $$

(9)

where *Y* is the gas permeability; *X*_{1} is the through pore porosity; *X*_{2} is the mean pore size; *X*_{3} is the bulk density; *D*_{1} is the wood dummy variable (1: if the wood is hinoki, otherwise 0); *D*_{2} is the wood dummy variable (1 if the wood is Douglas fir, otherwise 0); *α*_{0} is the constant (intercept term); and *ε* is the residuals (error term).

This study uses Eq. (9) as an ordinary least square (OLS) regression model that formulates a linear function. Thus, *α*_{0} in Eq. (9) represents a constant (intercept term) of the linear function model, while *ε* indicates residuals (error term) of the regression model. Basically, regression analysis such as Eq. (9) assumes that the expected value of the error term is zero [*E*(*ε*_{i}) = 0], resulting in an estimated value of 0 (zero) for *ε*.

If estimated coefficients of *β*_{1}, *β*_{2} and *β*_{3} in Eq. (9) are significant, the three physical properties (*X*_{1}, *X*_{2}, and *X*_{3}) substantially affect gas permeability. Wood dummy variables (*D*_{1} and *D*_{2}) were included in Eq. (9) to control the effect of wood species. Specifically, *D*_{1} has a value of 1 if the wood is hinoki and 0 (zero) if the woods are other species. Likewise, *D*_{2} has a value of 1 if the wood is Douglas fir and 0 (zero) if the woods are other species. Therefore, hemlock has a value of 0 (zero) for both *D*_{1} and *D*_{2}, and those two dummy variables (*D*_{1} and *D*_{2}) control the effect of the difference among the three species of wood. Further, this study analyzes VIF (variance inflation factor) values of all independent variables in Eq. (9) to assess the multi-collinearity among the independent variables. Multi-collinearity is not serious if the estimated VIF value does not exceed 10.

All sample data were analyzed using both Pearson correlation analysis and regression analysis (*n* = 90). Also, measured values of all variables were winsorized at 2% of both sides to minimize the effect of extreme values.

All statistical analyses were performed using IBM SPSS statistics v25 software (IBM Corp., Armonk, NY, USA).