Greetings Dr. Jirka,
I am working with a Dual porosity model with both physical and chemical nonequilibrium. We are adding 30000 ug of orthop on the top and the entire 50 cm soil profile has an initial total concentration of orthop of 0.93 ug/cm3. Area of cs = 176.625 cm3. I am using 2 mass balance and 2 soil materials for the simulation process.
If I add the orthop 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 subregion 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 subregion 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 subregion follows the s= c*theta + rho*kf*(c^beta), I need to increase the subregion 1 depth to the next value (0.30779 cm in my case), but now Cmean for the subregion 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.
Mass Balance

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 Location: USA
Mass Balance
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Re: Mass Balance
If you are interested in mass balance, I would not focus on cMean (which is the mean liquidphase 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 type2 (kinetic) adsorption sites).
For the “Dual porosity model with both physical and chemical nonequilibrium”, 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 + (1Frac) *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.
For the “Dual porosity model with both physical and chemical nonequilibrium”, 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 + (1Frac) *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.

 Posts: 17
 Joined: Thu Nov 10, 2022 8:58 pm
 Location: USA
Re: Mass Balance
Thank you Dr. Jirka for the reply. It sure is really helpful.
Have a good day sir.
Have a good day sir.

 Posts: 17
 Joined: Thu Nov 10, 2022 8:58 pm
 Location: USA
Re: Mass Balance
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 = (1Frac_m)*sk = (10.99)*101.36 = 1.01
SorbVolIm2: Length*(rho*s_k)=0.241*1.3*1.01= 0.316
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 = (1Frac_m)*sk = (10.99)*101.36 = 1.01
SorbVolIm2: Length*(rho*s_k)=0.241*1.3*1.01= 0.316
Re: Mass Balance
The “DualPorosity 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.

 Posts: 17
 Joined: Thu Nov 10, 2022 8:58 pm
 Location: USA
Re: Mass Balance
Thank you Dr. Jirka.