Page 24 - Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation

VA - DF: Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation p 23/23
where






  
   
   
2 2 2
2 2
2
2
2 2
2 2
1
2
1 1
R z h g
R b h g L z b
R b h g Lz b
z
Some special cases of interest can be derived from there, the uniform point source
distribution, 1 )(  s  is readily given in Cartesian coordinates as:

















 
 
 
  
 
 
  
  
  
 
  
  
 
    )
) (
) (
( tan )
) (
) (
( tan )
) (
) (
( tan )
) (
) (
( tan
) (
) (
) (
) (
) (
) (
) ( ) (
) ( ) (
) ( ) (
) ( ) (
) , , , , (
2
2 1
2
2 1
1
1 1
1
1 1
2 2
1 1
2 2
1 1
2
2
2
1
1
1
Hz Rg
Hzb
Hz Rg
Hzb
Hz Rg
Hzb
Hz Rg
Hzb
R
b Hzg
b Hzg
Log Hz
b Hzg
b Hzg
Log Hz
Hz Hzg
Hz Hzg
Log b
Hz Hzg
Hz Hzg
Log b HLFM rec
u  
  sin , cos ) ( ) ( )(
) ( ) ( )(
2 2 2
2 2
2 2 2
1 1
L dy L dx dy y dx x h hg L
L
dy
y
L
dx
x b
L
dy
x
L
dx
y R dy y dx x h hg L
L
dy
y
L
dx
x b
         
         
  FM zyx   , , , F the panel centre.