Question

A drawdown test is analyzed to find the permeability and skin factor of a reservoir using a semi-log plot, where the flowing bottomhole pressure (in psi) is plotted on a linear scale against time (in hours). The flow rate is 1500 STB/day, the oil formation volume factor is 1.2 RB/STB, and the oil viscosity is 1 cP. The thickness of the producing bed is 10 ft. The slope of the straight line fitting the data in the middle time region of the semi-log plot is 60 psi/log cycle.
The permeability of the reservoir (in mD) is _______ (rounded off to one decimal place).

Hint:

Use the semi-log drawdown slope formula k = 162.6 q B mu / (m h) with field units for q, B, mu, m and h.

Answer 1

Correct Answer: 487.8

Step 1: Write down the known quantities in a different grouping order:
$q = 1500$ STB/day, $B = 1.2$ RB/STB, $\mu = 1$ cP, $h = 10$ ft, $m = 60$ psi per log cycle
Step 2: Instead of substituting everything in one shot, compute the denominator term m h first:
$m h = 60 \times 10 = 600$
Step 3: Compute the product of q and B separately:
$q B = 1500 \times 1.2 = 1800$ RB/day
Step 4: Multiply this product by the viscosity to complete the numerator term:
$q B \mu = 1800 \times 1 = 1800$
Step 5: Apply the semi-log permeability relation using these grouped terms:
\[ k = 162.6 \times \frac{qB\mu}{mh} = 162.6 \times \frac{1800}{600} \]
Step 6: Reduce the fraction 1800/600 before multiplying by the constant:
$1800 / 600 = 3$
$k = 162.6 \times 3 = 487.8$ mD
Step 7: Check the result against the direct substitution method:
Both the direct calculation and this rearranged grouping give the same value, confirming that the arithmetic is correct and the permeability estimate is reliable.
Final Answer:
\[ \boxed{k = 487.8 \text{ mD}} \]