Mass Balance

[vss0015@auburn.edu]

Greetings Dr. Jirka,

I am working with a Dual porosity model with both physical and chemical non-equilibrium. We are adding 30000 ug of ortho-p on the top and the entire 50 cm soil profile has an initial total concentration of ortho-p of 0.93 ug/cm3. Area of c-s = 176.625 cm3. I am using 2 mass balance and 2 soil materials for the simulation process.

If I add the ortho-p to top 0.24186 cm of the soil, the total concentration in that depth = ((0.93*176.625*0.24186)+(30000))/(176.625*0.24186) = 704.95 ug/cm3.

1. If I set subregion 1 depth = 0.24186 cm and also the material distribution 1 depth as 0.24186 cm. For sub-region 1, I get the Cmean = 534.66 ug/cm3, which is what we are supposed to get using the formula: s= c*theta + rho*kf*(c^beta). But what about the Cmean of the sub-region 2? Shouldn't also follow the same formula? Cause mine gives me a lot higher value.

2. If I get the value of cmean for the 2nd sub-region follows the s= c*theta + rho*kf*(c^beta), I need to increase the sub-region 1 depth to the next value (0.30779 cm in my case), but now Cmean for the sub-region is not accurate.

As I am only working at t=0, so kinetic sorption will not play any role. The values of Frac, Frac_m and omega are hypothetical as I am trying to understand how hydrus works the mass balance.

Kindly, help me understand this process. I am attaching my model with the email.
Thank you.

[Jirka]

If you are interested in mass balance, I would not focus on cMean (which is the mean liquid-phase concentration, calculated as an arithmetic average of nodal concentration values), which has very little to do with mass balance, but rather on VoncVol (Amount of solute in the entire flow domain or a specified subregion in equilibrium phases, including sorbed and gaseous, if applicable), ConcVolIm (Amount of solute in the entire flow domain, or in a specified subregion in the immobile liquid region), and SorbVolIm2 (Amount of solute in the entire flow domain, or in a specified subregion in the nonequilibrium phase, i.e., adsorbed at type-2 (kinetic) adsorption sites).

For the “Dual porosity model with both physical and chemical non-equilibrium”, these are calculated for region 1 as follows (for your case):
VoncVol=length*[ c*theta_m + Frac*frac_M*rho*kf*(c^beta)] = 0.241*(533.72*0.2+0.3*0.99*1.3*33*533.72^0.37)= 57.1
ConcVolIm: length*[ c*theta_im + (1-Frac) *rho*kf*(c^beta)] = 0.241*(533.72*0.3+0.7*1.3*33*533.72^0.37)= 112.5
SorbVolIm2: Length*(rho*s_k)=0.241*1.3*2.36=0.74

J.

[vss0015@auburn.edu]

Thank you Dr. Jirka for the reply. It sure is really helpful.
Have a good day sir.

[vss0015@auburn.edu]

Greetings Dr. Jirka,

I am vey thankful for your reply and was working on the calculations myself. For the sorbvolIm2 calculations, as per the hydrus Manual equations 3.3 and 3.7, we can calculate total sorption and kinetic sorption. I know I maybe wrong but just wanted to check it with you.

sk (total sorption) = Kf*(c^beta) = 33*(533.72^0.37) = 336.99
but for sorption in mobile phase, shouldn't we need to multiply it with Frac ?

sk (total sorption in mobile phase) = Kf*(c^beta)*Frac = 33*(533.72^0.37)*0.3 = 101.09

than the kinetic sorption part wil be:
s_k = (1-Frac_m)*sk = (1-0.99)*101.36 = 1.01

SorbVolIm2: Length*(rho*s_k)=0.241*1.3*1.01= 0.316

[Jirka]

The “Dual-Porosity Model with One Kinetic Site (Physical and Chemical Nonequilibrium)” is fully described in Section 3.1.4 and equations 3.36 and 3.37. From these equations, you should be able to figure all this out, since the definition of all terms is given by these equations. J.

[vss0015@auburn.edu]

Thank you Dr. Jirka.