Question:
For a single-phase dry gas reservoir having a well producing only dry gas, \(E\) represents gas expansion factor and \(B_g\) represents gas formation volume factor. Which of the following options is CORRECT?
For a single-phase dry gas reservoir having a well producing only dry gas, \(E\) represents gas expansion factor and \(B_g\) represents gas formation volume factor. Which of the following options is CORRECT?
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Compare the definitions of gas expansion factor and gas formation volume factor.
Updated On: Jul 28, 2026
- \(E \propto \dfrac{1}{B_g}\)
- \(E \propto B_g\)
- \(E \propto B_g^{2}\)
- \(E \propto B_g^{3}\)
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The Correct Option is A
Solution and Explanation
Step 1: Meaning of gas formation volume factor Bg:
Bg is defined as the ratio of the volume occupied by a given mass of gas at reservoir conditions of pressure and temperature to the volume occupied by the same mass of gas at standard surface conditions. In symbols, \(B_g = \dfrac{V_{reservoir}}{V_{standard}}\), and it is usually expressed in units of reservoir barrels per standard cubic foot or reservoir cubic feet per standard cubic feet.
Step 2: Meaning of gas expansion factor E:
The gas expansion factor E is defined in the opposite sense, as the number of standard cubic feet of gas obtained from one reservoir volume of gas as it expands from reservoir conditions to standard surface conditions. In symbols, \(E = \dfrac{V_{standard}}{V_{reservoir}}\).
Step 3: Relating E and Bg:
Since \(B_g = \dfrac{V_{reservoir}}{V_{standard}}\) and \(E = \dfrac{V_{standard}}{V_{reservoir}}\), it follows directly that E is simply the reciprocal of Bg, that is \(E = \dfrac{1}{B_g}\), so E is inversely proportional to Bg.
Step 4: Checking option A:
Option A states \(E \propto \dfrac{1}{B_g}\), which matches the reciprocal relationship derived above, so option A is correct.
Step 5: Checking option B:
Option B states E is directly proportional to Bg, which would mean both quantities increase or decrease together. This contradicts the reciprocal relationship, so option B is incorrect.
Step 6: Checking options C and D:
Options C and D propose E proportional to the square and cube of Bg respectively. Neither the definition of E nor the definition of Bg involves any power relationship between them, only a simple reciprocal, so both C and D are incorrect.
Final Answer:
\[ oxed{E \propto \dfrac{1}{B_g}} \]
Bg is defined as the ratio of the volume occupied by a given mass of gas at reservoir conditions of pressure and temperature to the volume occupied by the same mass of gas at standard surface conditions. In symbols, \(B_g = \dfrac{V_{reservoir}}{V_{standard}}\), and it is usually expressed in units of reservoir barrels per standard cubic foot or reservoir cubic feet per standard cubic feet.
Step 2: Meaning of gas expansion factor E:
The gas expansion factor E is defined in the opposite sense, as the number of standard cubic feet of gas obtained from one reservoir volume of gas as it expands from reservoir conditions to standard surface conditions. In symbols, \(E = \dfrac{V_{standard}}{V_{reservoir}}\).
Step 3: Relating E and Bg:
Since \(B_g = \dfrac{V_{reservoir}}{V_{standard}}\) and \(E = \dfrac{V_{standard}}{V_{reservoir}}\), it follows directly that E is simply the reciprocal of Bg, that is \(E = \dfrac{1}{B_g}\), so E is inversely proportional to Bg.
Step 4: Checking option A:
Option A states \(E \propto \dfrac{1}{B_g}\), which matches the reciprocal relationship derived above, so option A is correct.
Step 5: Checking option B:
Option B states E is directly proportional to Bg, which would mean both quantities increase or decrease together. This contradicts the reciprocal relationship, so option B is incorrect.
Step 6: Checking options C and D:
Options C and D propose E proportional to the square and cube of Bg respectively. Neither the definition of E nor the definition of Bg involves any power relationship between them, only a simple reciprocal, so both C and D are incorrect.
Final Answer:
\[ oxed{E \propto \dfrac{1}{B_g}} \]
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