|
[Sponsors] |
Analytical solution of the 1D advection-dispersion equation |
|
LinkBack | Thread Tools | Search this Thread | Display Modes |
June 29, 2021, 11:28 |
Analytical solution of the 1D advection-dispersion equation
|
#1 |
New Member
Anelechi Ibekwe
Join Date: Jun 2021
Posts: 1
Rep Power: 0 |
The Ogata and Banks analytical solution of the ADE for a continuous source of infinite duration and a 1D domain with initial condition: C(x,0) = C, and BCs: C(0,t) = C, and C(x,t) = 0.
is given as: C(x,t) = [erfc() + exp()erfc()] where C [mol/L] is the concentration, x [m] is the distance, R is the retardation factor, D [m2/day] is the effective dispersion/diffusion, v [m/day] is the flow velocity, Ci [mol/L] is the initial concentration in the column, and Co [mol/L] is the influent (or injected) concentration. The time-evolution of production and degradation of species obtained from the numerical solution of the ADE shows that specie production increases with time, whereas degradation (inversion of the production) reduces with time. However, the analytical equation above only matches the production (Ci = 0, Co > 0) but not the degradation (Ci > 0, Co = 0). So, I have been looking for the equivalent analytical expression that describes the degradation process (meaning that Ci would be contained therein). I am thus hoping that there is someone who may know this equation or could point me in the right direction. Thank you in advance. |
|
July 1, 2021, 00:00 |
|
#2 |
Senior Member
Lucky
Join Date: Apr 2011
Location: Orlando, FL USA
Posts: 5,754
Rep Power: 66 |
Abuse linearity. Define a new dynamic variable equal to K(x,t)=C(x,t)-Ci, re-cast the BC's and IC in terms of this new variable and you can make it work backwards. Basically, just do a substitution. As you've noticed, the solution only works for Ci=0 and Co>0 but not Ci>0 and Co=0. But it still works for Ki=0 and Ko>0 (which also satisfies your desire for Ci>0 and Co=0). =)
|
|
Tags |
analytical solution, cfd, convection-diffusion, numerical computation |
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Solver Validation chemFoam using analytical Solution | Hanzo | OpenFOAM Running, Solving & CFD | 5 | April 4, 2019 09:08 |
Calculation of the Governing Equations | Mihail | CFX | 7 | September 7, 2014 07:27 |
Exact solution of Burgers equation | mcaro | Main CFD Forum | 3 | January 25, 2011 07:46 |
Analytical solution of poisson equation | kostaspan | Main CFD Forum | 1 | April 22, 2010 13:24 |
IcoFoam parallel woes | msrinath80 | OpenFOAM Running, Solving & CFD | 9 | July 22, 2007 03:58 |