Chapter 4 conclusion

Today, I finish reading the Chapter 4 of the thesis.

Summary

k_along=∑_(i=1)^3▒〖α_i k_i 〗

k_across=1/(∑_(i=1)^3▒α_i/k_i )

From the distribution of possible shale permeabilities, a probability plot of k from very shaly intervals shows an LND with log k~N with log mean and log-variance.

From the LND, k is estimated by the following two equations:

(k_1 ) ̅=e^(logx) ̅ ∙ψ_n (s^2/2)

ψ_n (t)=1+(n-1)/n t+〖(n-1)〗^3/(n^2 (n+1))  t^2/2!+〖(n-1)〗^5/(n^3 (n+1)(n+3))  t^3/3!+⋯

After calculating k_1, we can calculate k_(2+3) by the same way.

This equation k_1 α_1+k_(2+3) (1-α_1 )=k can remove the effect of k_1.

SDR: Schlumberger-Doll Research model

TIM: Timur-Coates model

FFI: free fluid volume

BVI: bound fluid volume

LND: log-normally distributed

XRD: X-ray diffraction

Next week, I will read another book called ‘Reservoir Properties from Well Logs Using Neural Networks’.