GATE-2018 (24) :Wyllie – Time average equation

114. Self potential (SP) logs from two shaly sandstone reservoirs A and B record their pseudo-static self potential (PSP) and static self potential (SSP). The ratio of PSP to SSP in A and B are 0.4 and 0.7, respectively. For both A and B, the mud filtrate resistivity is more than the formation water resistivity (Rmf > Rw). This implies that the shale volume of A is

1. half of that in B

2. twice that in B

3. one-fourth of that in B

4. four times of that in B

Solution:

Volume of the Shale (V_sh) or Volume of the clay

$V_{sh} = 1-\frac{PSP}{SSP}$

PSP = SP log read in a thick homogeneous shaly sand zone (Value of SP deflection at a given depth)

SSP= SP log read in the thick clean sand zone(maximum value of SP deflection in sand line)

Reservoir ‘A’ record their ratio of pseudo-static self potential (PSP) and static self potential (SSP) = 0.4

Reservoir ‘B’ record their ratio of pseudo-static self potential (PSP) and static self potential (SSP) = 0.7

Reservoir ‘A’

$V_{sh} = 1-\frac{PSP}{SSP}$

V_sh = 1 – 0.4

         
      =0.6

Reservoir ‘B’

V_sh = 1 – 0.7

        =0.3

Therefore, Volume of the shale in ‘A’ is twice that of the volume of the shale in ‘B’