Defining 



(28) 



then. 



Q = Q - ^? 



This equation is now applied to both lines, y, (x) and y^(x) 



9yi 



Qi = Q.T - q 



1 ^ol ^1 9x 



(29) 



3y^ 



Q9 = Q.9 - <^ 



2 ^o2 ^2 3x 



(30) 



The equation of continuity. 



3x 9t 



(31) 



is modified by the term Q due to onshore-offshore transport so that 



3Qt 3yi 



9^ - Qy = °13t- 



(32) 



3Q 



3^ ^Qy 



2 3t 



(33) 



Substituting equations (1), (2), and (3) for Q , Q , Q gives: 



i z y 



9/^ 



^\ 





S ^^1 " ^2^ 



1 3t 



(34) 



35 



