7.1. The Classification ofGroundwater Quality Models
195
FIGURE 7.3. Water balance and
solute mass balance in element i.
0.i
With the above factors considered, the water mass balance equation for
element i is
!l.t {I Qij + Ni + Ri - Pi} = Ui(t + !l.t) - Ui(t),
UJ
(7.1.16)
where I represents the summation of all the elements adjacent to element
(j)
i, U i the water contained in element i, and Ui(t + At) - Ui(t) denotes the
change of water volume in element i within !l.t. If a side of the element is a
section ofthe inflow (or outflow) boundary ofthe region, then we should add
(or deduct) the water passing through the boundary in the balance equation
(7.1.16).
Using the area Ai, porosity ni and the height of aquifer bottom b i of
element i, and using the hydraulic conductivity Kij' aquifer thickness mij' the
width of water carrying section lij' and the distance rij between nodes i and j,
all flux terms in Eq. (7.1.16) can be represented by the hydraulic head. Let hi
and hj be the water heads ofnodes i andj, respectively, we then have
(7.1.17)
Ui = niAi(hi - b;).
(7.1.18)
Inserting these equations into Eq. (7.1.16), we arrive at
hi(t + At) - hi(t)
I Äij(hj - h;) + Ni + R i - Pi = ni Ai
A
'
UJ
t
(7.1.19)
where
Readers may recognize that Eq. (7.1.19) is actually a finite difference equation
of ground water flow associated with the polygonal element. Solving the
balance equations for all elements simultaneously, we can obtain the water