Page 57 - Geochemical Remote Sensing of The Sub-Surface

34 O.F. Putikov and B. Wen

OC -[3 ~o c(x,y,z,~ )d~ OC
Ver ~ + qmax Ce +--Ot -- 0 (2.2)

This non-linear integro-differential equation is equivalent to the following system of
non-linear differential equations,

OC OC Oq
--+ Vel f .... + = 0 (2.3)
Ot OZ Ot

Oq
= ~C(qma x - q) (2.4)
c3t

where, q - qmax 1 - e -~ C(x, y, z~ )d~ (2.5)
o

Solution of equations (2.3) and (2.4) under the following boundary and initial
conditions,

CIz_o - C O (2.6)
Cl,=o - 0 (2.7)

q],-o - 0 (2.8)

where, Co is the concentration of the soluble components at source and is considered
constant in geological time, with the form (Panchenkov, 1964),

C(z,t) 1
, z < v~Lrt (2.9)
C O (e f~q ..... "/"~ -- 1)e ~c~ + 1

C(z,t)
=0, z > v~fft (2.9')
Co

[SCo ( z / v,,r t -t )
1-e < (2.10)
e f~c~ .... z/v"rr -e f~C~ ~Z V eff t
qmax