Question

Matthews-Brons-Hazebroek (MBH) plots are used to calculate the Dietz shape factor (C_A) for reservoirs of various shapes. The MBH plot for a right-angled triangle reservoir with the well located at the centre shows a reading of dimensionless pressure P_D(MBH) = 3.0, at a modified dimensionless time t_DA = 1.0.
The Dietz shape factor of this right-angled triangle reservoir is ____________ (rounded off to one decimal place).

Hint:

At t_DA = 1.0 the logarithmic time term in the MBH relation vanishes, so P_D(MBH) reduces directly to ln(C_A).

Answer 1

Correct Answer: 20.1

Step 1: List the given data:
Dimensionless MBH pressure, P_D(MBH) = 3.0
Modified dimensionless time, t_DA = 1.0
Step 2: Write the relation connecting the MBH dimensionless pressure reading to the Dietz shape factor:
The value read off an MBH plot at a given modified dimensionless time is related to the Dietz shape factor of the drainage area through \[ P_{D(MBH)} = \frac{1}{2}\ln(t_{DA}) + \ln(C_A) \]
Step 3: Substitute the given modified dimensionless time:
Since t_DA = 1.0, the natural log of t_DA is zero, because ln(1) = 0. So the time dependent term drops out and the relation reduces to \[ P_{D(MBH)} = \ln(C_A) \]
Step 4: Substitute the given MBH dimensionless pressure:
3.0 = ln(C_A)
Step 5: Solve for the shape factor by taking the exponential of both sides:
C_A = e^3.0
Step 6: Evaluate e^3.0 using e = 2.71828:
e^2 = 2.71828 x 2.71828 = 7.38906
e^3 = 7.38906 x 2.71828 = 20.0855
Step 7: Round the result to one decimal place:
C_A = 20.1
Final Answer:
\[ \boxed{C_A = 20.1} \]