Brucite CO2 Capture - 2D Packed Bed and Shrinking Core

Controls

Live readouts

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Numerical check

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Performance graph

How to use

A packed bed of brucite, Mg(OH)2, particles captures CO2 from a gas stream by carbonation. The bed turns lighter as the particles convert; the blue tint shows how much CO2 is still in the gas. The circle shows one particle at the inspected position: the dark unreacted core shrinks inside a growing carbonate shell that CO2 must diffuse through.

The left graph shows the conversion front moving down the bed; the right shows the breakthrough curve (when CO2 starts to leave) and the mean conversion over time.

Try: raise the temperature and the capture speeds up (Arrhenius); halve the particle size and diffusion-limited conversion becomes four times faster; reduce the shell diffusivity to see the last 20 percent of conversion stall; lengthen the bed to delay breakthrough.

The science

Reaction. Carbonation of brucite binds CO2 in a solid carbonate:Mg(OH)2 + CO2 -> MgCO3 + H2OThe stoichiometric capacity is 44.01/58.32 = 0.755 kg CO2 per kg of brucite, reached only at 100 percent conversion.

Shrinking-core model. For a spherical particle of radius R with a growing product layer (Levenspiel), the time to reach conversion X with gas concentration C ist = tau_r [1 - (1-X)^(1/3)] + tau_d [1 - 3 (1-X)^(2/3) + 2 (1-X)], tau_r = rho R/(k_s C), tau_d = rho R^2/(6 D_e C)where rho is the molar density of brucite (about 41,000 mol/m3), k_s the surface rate constant and D_e the effective diffusivity of CO2 through the carbonate layer. The first term is reaction control (time scales with R), the second diffusion control (time scales with R^2).

Temperature. Arrhenius: k = k_ref exp(-(E_a/R)(1/T - 1/T_ref)), with E_a = 40 kJ/mol for the reaction and 30 kJ/mol for diffusion in this model.

Packed bed. A plug-flow gas balance along the bed, u dC/dz = -(1-eps) rho dX/dt, couples all particles; the gas profile is quasi-steady because gas moves through the bed much faster than the solid converts.

Simplified: the rate constants are illustrative round numbers chosen for a slow, laboratory-scale carbonation, not fitted to a specific brucite. In reality, carbonation of brucite is often assisted by water films, high pressure or temperature, and forms hydrated carbonates such as hydromagnesite, which this single-step model ignores. No heat release, no pressure drop, no particle-size distribution and no water vapour effects are included.

Keyboard, touch and accessibility

Space pauses or resumes the simulation.
R resets it to its initial state.
C re-runs the numerical check.
All sliders are native range inputs and work with arrow keys, Home and End; on touch devices drag on the canvas where the sim supports pointer input.
Rendering is capped at a device pixel ratio of 2 so phones stay smooth; the frame-time graph above shows the cost of the current settings (green line is 16.7 ms, i.e. 60 frames per second).

What is checked and why you can trust it

Every time the page loads, and whenever you press Re-run check, the simulation evaluates its own mathematics against an independent reference, such as a closed-form formula, a finite-difference derivative or an exhaustive count. Each line above reports PASS or FAIL together with the measured numbers, so you can see by how much it agrees. Results are also published on window.__msChecks for automated testing. The check never uses the same code path as the animation it validates, otherwise it would only confirm itself.

How to read a failure: a FAIL line means the measured discrepancy exceeded the stated tolerance for the current slider values. Try Reset, then move the sliders back toward their defaults; if a check still fails at the defaults it is a bug worth reporting. Tolerances are chosen from the numerical method itself, never tuned to make a test pass: round-off level (1e-9) for exact algebra, about 1e-3 for finite differences and Monte Carlo estimates with a few hundred thousand samples, and a documented margin for stochastic learning runs.

Reproducibility: the particle and pen simulations use the browser random generator for initial positions, so exact pixels differ between visits, but the checks depend only on mathematics and not on those positions. Fixed wave tables (curl noise) and fixed grammars (L-system) are deterministic.

This is an educational model. It shows the mechanism clearly, but it is deliberately simplified; the science panel lists what was left out.