Nucleation reactive surface area

Hi all,

I'm running some models where calcite is not initially present but precipitates kinetically during the simulation. There is an option to have initial reactive surface area be very large at the initial stages of precipitation by using the RAD (mineral grain radius) and RNUCL (initial volume fraction) parameters in chemical.inp. The initial reactive surface area (Anucl) is calculated using a simple cubic packing model, but I don't understand how the final formula is derived. It says in the users guide Appendix G:

"By default, Anucl is always set to zero if the value of RAD (on record Imin-6.1 in file chemical.inp) is set to zero. If RAD ≠0, a simple model is implemented to compute Anucl as a function of mineral grain size, with RAD entered as the initial grain radius (in m). This is done by assuming simple cubic packing of spherical grains of radius r. This cubic arrangement of spheres yields, in a cube of side 4r and volume (4r)^3, a total of 8 spheres, each of radius r, volume 4/3 πr^3, and area 4πr^2. Thus the surface area Anucl (as the area of the spheres divided by the volume of the cube) is computed as Anucl = 0.5/r (equation G.5)".

This doesn't seem correct to me. I get the following:

Surface area of 8 spheres: 8*4πr^2 = 32πr^2

Volume of cube: (4r)^3 = 64r^3

So, surface area divided by volume of cube: Anucl = 32πr^2/ 64r^3 = π/2r

Have I misunderstood this? Seems like an easy calculation, but I can't get this to add up, which is really annoying... I'm using an executable version of TOUGHREACT, so I'm not able to check the source code. Would really appreciate if someone could explain this.

Kind regards,

Eivind B. Vagle

PhD student at the University of Manchester