Characterizing the Pore Structure of BiocharsUsing Multiscale Models and Reactivity Data
Ashton Gooding1, Pauline Markenscoff 2 and Kyriacos Zygourakis1
1. Department of Chemical and Biomolecular Engineering, Rice University, 6100 Main Street, Houston, TX 77005, USA
2. Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77005, USA
Biochar is charcoal generated for intentional soil amendment by pyrolyzing sustainable biomass feedstocks. Properly engineered (or "designer") biochars can provide significant agricultural benefits by increasing the water holding and cation exchange capacities of soils, and by reducing fertilizer runoff into watersheds. The environmental performance of biochars depends on their ability to absorb, retain and release water and nutrients. These biochar properties are controlled by their pore structure and surface chemistry, which can vary widely depending on the composition of the biomass feedstocks and on the pyrolysis conditions employed during biochar production.
Biochars have complex pore structures consisting of multiple interconnected networks of micropores, mesopores and macropores that span multiple length scales: from sub-nanometer micropores to macropores with sizes of the order of 10 microns. Such pore structures cannot be characterized by a single analytical technique. Instead, a combination of time-consuming analytical techniques must be used to bridge the vastly different length scales: adsorption of multiple gases (like nitrogen, carbon dioxide and water) for the micropores, mercury porosimetry for the mesopores and sectioning with optical microscopy and 3-D reconstruction techniques for the macropores.
At low temperatures, combustion of biochars takes place in the regime of kinetic control and the entire surface area attributed to micropores (or even the sub-micropores) is completely accessible to the reactant. As the temperature rises, the reaction regimes shifts to diffusion control and strong diffusional resistances start appearing first in the sub-micropores, then in the micropores, the mesopores and, eventually, in the macropores. As a result, larger and larger fractions of the micropore and mesopore structure will become inaccessible to oxygen as the combustion temperature is raised.
In a recent publication, we have shown how experimental reactivity data can be used to probe and characterize the pore structure of biochars and other solid reactants. The nanoscale model developed in that study used discrete simulations to describe the reactivity of solids consisting of multiple components and having a mixture of ordered and random pores whose size ranges from a fraction of a nanometer to several nanometers. Since biochars consist of a mixture of amorphous and crystalline phases, the model considered two subpopulations of micropores: randomly distributed pores and domains of orderly arranged pores. The latter pores were the slits formed between the graphitic-like layers of aromatic carbon clusters that are turbostratically arranged in nanometer-size crystallites in biochars. Such structures have been confirmed with NMR and XRD measurements. Simulation results were then used to analyze and interpret reactivity data obtained by burning biochars in air at low temperatures where the reactions occur primarily on the surface of micropores.
When reaction takes place at high temperatures, however, strong diffusional resistances will appear first in the micropores and, subsequently, in the mesopores. As a result, progressively larger fractions of the micropore and mesopore structure will become inaccessible to the gaseous reactant. At sufficiently high temperatures, reaction will take place only on the micropore and mesopore mouths, where they open up into the large macropore cavities. Eventually, the overall reaction rate will be determined by the temporal evolution of the surface of large macropores identified in SEM or optical microscopy images.
(A) Corn stover biochar (B) Apple wood biochar
Figure 1: Normalized reactivity patterns for combustion of biochars with air at different temperatures. Both biochars were produced by heating #20 mesh particles of the two feedstocks at 1 C/min to 600 C and holding them there for 1 hour. The rates at 5% conversion were used as reference values  for computing the normalized rates.
The two panels of Figure 1 show the reactivity patterns obtained for apple wood and corn stover biochars during the transition from the kinetic to the diffusion control regime. As the combustion temperature increases above 350 C, the normalized reaction rates for both chars exhibit pronounced maxima for conversions between 20-40% as strong diffusional limitations appear in the smallest pores and control of the reaction rates shifts to the mesopores. At even higher temperatures, the reactivity patterns for both chars become similar with a plateau at intermediate conversions and a sharp decline as the reaction approaches completion.
To model reaction in the diffusion control regime, we developed a hybrid model that uses (a) the continuous diffusion-reaction PDEs to describe the mass and energy balances in the microporous and mesoporous solid and (b) discrete (erosion) simulations to describe the growth and eventual coalescence of the large macropores. Models of the macropore structure of biochars were generated on cubic computational grids to match experimental macroporosity measurements and information obtained from SEM or optical microscopy images providing information about the size and spatial arrangement of the large macropore cavities. The computational cells representing solid biochar were assumed to be porous and the gas reactant (oxygen) was allowed to diffuse in them. The reaction rate in every cell was controlled by the local reactant concentration computed by solving the transient mass and energy balance PDEs and the transient reactivity pattern was calculated using the nanoscale model of Zygourakis et al. Reaction could also take place of the exterior of a computational cell if that cell had one or more faces exposed to macropores.
Multiple realizations of a solid with the same macropore structural properties were generated and reacted to obtain the reactivity patterns during the transition from the regime of kinetic control to the regime of diffusion control. Simulation results revealed that the reactivity patterns in the transition regime were influenced both by the volume ratio of the crystalline over the amorphous phase and by the size distribution of the random pores of the amorphous phase. In all cases, however, similar reactivity patterns were observed when the temperatures were high enough so that reaction took place only on the mesopore mouths opening up into the large macropore cavities identified in SEM images. At that point, the temporal evolution of the surface of large macropores controlled the overall reaction rate. The combustion rates measured at high temperatures changed relatively little for intermediate conversions (20-60%) and dropped sharply as reaction approached completion (see, for example, the reactivity patterns of Figure 1 for combustion at 500 or 550 C). These results are indicative of macropore structures consisting of large cylindrical cavities separated by walls of similar thickness, an observation that is consistent with the SEM images of our biochars.
To validate our model, we compared simulation results with experimental data from the combustion of several biochars over a range of reaction temperatures. Biochars from apple wood, slash pine, eucalyptus and corn stover were produced in a thermogravimetric analyzer using different heating rates (1 and 10 C/min), various final pyrolysis temperatures (400-600 C) and different durations of heat treatment at the maximum temperature. These results will be analyzed to demonstrate that reactivity patterns measured at different temperatures can provide important information about the pore structure and, in particular, the accessibility of the interconnected pore networks of biochars.
 H. Sun, W.C. Hockaday, C.A. Masiello and K. Zygourakis*, "Multiple Controls on the Chemical and Physical Structure of Biochars," Industrial and Engineering Chemistry Research, 51 (9), 3587–3597 (2012).
 K. Zygourakis*, H. Sun and P. Markenscoff, "A Nanoscale Model for Characterizing the Pore Structure of Solid Reactants with Ordered and Random Pores," AIChE Journal, 59(9), 3412–3420, (2013)