Question:hard

One dimensional oil flow occurs in a horizontal porous medium of length 2000 ft, with a constant cross sectional area of 6000 ft\(^2\) and absolute permeability of 50 mD. The oil has a viscosity of 2 cP and flows along the length of the medium. The pressure at the inlet is 2500 psig and at the outlet is 2200 psig. Using Darcy's equation for single phase, linear flow, the flow rate of oil (in bbl/day, rounded to one decimal place) is _______. [1 bbl = 5.61 ft\(^3\)]

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Use the field unit form of Darcy's law, q(bbl/day) = 1.127x10^-3 x k x A x deltaP / (mu x L), and plug in the given values directly.
Updated On: Jul 28, 2026
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Correct Answer: 25.4

Solution and Explanation

Step 1: Convert every quantity into consistent Darcy, cgs units: 
In the Darcy unit system, Darcy's law reads $q(\text{cm}^3/\text{s}) = \dfrac{k(\text{darcy}) \, A(\text{cm}^2) \, \Delta p(\text{atm})}{\mu(\text{cP}) \, L(\text{cm})}$. Convert each given quantity: permeability $k = 50\ \text{mD} = 0.05$ darcy. Area $A = 6000\ \text{ft}^2$, and since $1\ \text{ft}^2 = 929.03\ \text{cm}^2$, this gives $A = 6000 \times 929.03 = 5{,}574{,}182\ \text{cm}^2$. Length $L = 2000\ \text{ft}$, and since $1\ \text{ft} = 30.48\ \text{cm}$, this gives $L = 2000 \times 30.48 = 60{,}960\ \text{cm}$. Pressure drop $\Delta p = 300\ \text{psi}$, and since $1\ \text{atm} = 14.696\ \text{psi}$, this gives $\Delta p = 300/14.696 = 20.414\ \text{atm}$. Viscosity stays $\mu = 2\ \text{cP}$. 

Step 2: Substitute into the Darcy unit equation: 
Numerator: $k \times A \times \Delta p = 0.05 \times 5{,}574{,}182 \times 20.414$. First, $0.05 \times 5{,}574{,}182 = 278{,}709$. Then $278{,}709 \times 20.414 = 5{,}689{,}540\ \text{cm}^3\cdot\text{cP/s}$ approximately. Denominator: $\mu \times L = 2 \times 60{,}960 = 121{,}920$. Dividing gives $q = 5{,}689{,}540 / 121{,}920 = 46.67\ \text{cm}^3/\text{s}$. 

Step 3: Convert the flow rate from cm³/s to bbl/day: 
First convert to cm3/day: $46.67 \times 86400 = 4{,}032{,}000\ \text{cm}^3/\text{day}$. Since $1\ \text{bbl} = 5.61\ \text{ft}^3$ and $1\ \text{ft}^3 = 28{,}316.8\ \text{cm}^3$, one barrel equals $5.61 \times 28{,}316.8 = 158{,}898\ \text{cm}^3$. Dividing the daily volume by this gives $q = 4{,}032{,}000 / 158{,}898 = 25.38\ \text{bbl/day}$. 

Step 4: Compare with the field unit result and round: 
This matches the value obtained directly from the field unit form of Darcy's law within rounding, confirming the calculation. Rounding to one decimal place: $q \approx 25.4\ \text{bbl/day}$. 

Final Answer: 
\[ \boxed{25.4 \text{ bbl/day}} \]

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