5.2. The Multiple Cell Balance Method
119
For the second integral on the right-hand side of Eq. (5.1.12), we may
arrive at
-f r c[o(mv,,) + o(mv,)]dXd Y = f r ~(sOh + W)dXd Y
JO) OX
oY
JD) n ot
= L (Yi~Ci + YijCj + Yt"Ck), (5.2.14)
e,
where
and with Se being the value of storage coefficient, S, in element (e).
In the calculation of Eqs. (5.2.13) and (5.2.14), the following formulas are
used:
With the aid of the variable substitution,
{ X = Xi~ + X/1 + xk(1 - ~ - '1),
Y = Yi~ + Yj'1 + Yk(1 - ~ - '1),
all integrals in Eq. (5.2.15) can be computed in the ~'1 plane.
Dividing the right-hand side of Eq. (5.2.3) into three parts:
(5.2.16)
f r [O(~C)+C'WJdXdy=fr m°:.Cdxdy+f r C°:.mdxdy
JD) ut
n
JO) ut
JO) ut
fi
C'W
+
-dxdy
(D)
n
(5.2.17)
and ca1culating each part on the right-hand side, we have
fi
oe
L (e OCi eOCj e OCk)
m-dxdy=
B .. -+B .. -+B· k -
(D)
ot
e " ot
'J ot
' a t '
(5.2.18)