Step 1: Rewrite the formula in a simplified squared form:
Since $10^4 = (100)^2$, the permeability formula can be regrouped as $k = \left[100 \, \phi^2 \, \frac{FFI}{\phi - FFI}\right]^2$. This form lets everything be combined inside a single bracket before squaring only once at the end, instead of squaring the ratio and multiplying separately.
Step 2: Find FFI from the porosity balance:
Total porosity equals the sum of irreducible bound water and free fluid, so $FFI = \phi - BVI = 0.1 - 0.04 = 0.06$. Check: $FFI + BVI = 0.06 + 0.04 = 0.10 = \phi$, so the split is consistent.
Step 3: Compute $100\phi^2$:
With $\phi = 0.1$, $\phi^2 = 0.01$, so $100 \times 0.01 = 1$.
Step 4: Compute the FFI over (phi minus FFI) ratio:
$\phi - FFI = 0.1 - 0.06 = 0.04$, and $\frac{FFI}{\phi - FFI} = \frac{0.06}{0.04} = 1.5$.
Step 5: Multiply inside the bracket and square once:
Multiplying the two pieces from Step 3 and Step 4 gives $1 \times 1.5 = 1.5$. Squaring this single number gives $1.5^2 = 2.25$.
Step 6: State the result:
Both the direct substitution method and this regrouped method give the same permeability of 2.25 mD, confirming the answer.
Final Answer:
\[ \boxed{2.25 \text{ mD}} \]