Natural gas (assume pure methane) is delivered to a city via pipeline at a volumetric rate of 150 million standard cubic feet per day. If the selling price of the gas is $5.00 per GJ of higher heating value, what is the expected revenue in dollars per day? Standard conditions are 60(°F) and 1(atm).
The Correct Answer and Explanation is:
To calculate the expected revenue in dollars per day from the sale of natural gas (assumed to be pure methane), follow these steps:
🔢 Step 1: Convert standard cubic feet to energy (GJ)
We are given:
- Flow rate: 150 million standard cubic feet per day (scfd)
- Price: $5.00 per GJ (gigajoule)
- Standard conditions: 60°F and 1 atm
- Gas: pure methane (CH₄)
🔹 Energy content of methane:
The higher heating value (HHV) of methane is approximately:
1 standard cubic foot (scf) of CH₄ ≈ 1,030 BTU
Now, convert BTU to joules:
1 BTU ≈ 1,055.06 J
So,
1 scf CH₄ ≈ 1,030 × 1,055.06 = 1,087,711.8 J = 0.0010877 GJ
🔹 Total energy per day:
150,000,000 scf/day×0.0010877 GJ/scf=163,155 GJ/day150,000,000 \, \text{scf/day} × 0.0010877 \, \text{GJ/scf} = 163,155 \, \text{GJ/day}
💰 Step 2: Calculate Revenue
Given price: $5.00 per GJ Revenue=163,155 GJ/day×5.00 $/GJ=815,775 $/day\text{Revenue} = 163,155 \, \text{GJ/day} × 5.00 \, \text{\$/GJ} = 815,775 \, \text{\$/day}
✅ Final Answer:
$815,775 per day\boxed{\$815,775 \text{ per day}}
📘 Explanation (300+ words):
To estimate the revenue generated from natural gas delivery, we begin by understanding how energy content relates to volume. The gas delivered is assumed to be pure methane (CH₄), the principal component of natural gas, which makes the energy content calculation more straightforward. Energy from natural gas is measured by its heating value — in this case, the higher heating value (HHV), which includes the heat released from condensing water vapor produced during combustion.
Methane’s HHV is about 1,030 BTU per standard cubic foot (scf). A British Thermal Unit (BTU) is a standard energy unit, and 1 BTU equals 1,055.06 joules (J). Thus, each cubic foot of methane holds around 1.0877 megajoules (MJ), or 0.0010877 GJ.
With a flow rate of 150 million scf per day, we multiply the volume by the energy content per unit volume: 150,000,000×0.0010877=163,155 GJ/day150,000,000 × 0.0010877 = 163,155 \text{ GJ/day}
Next, the pricing structure is applied. Since the gas is sold at $5.00 per GJ, multiplying by the daily energy content gives: 163,155×5=$815,775 per day163,155 × 5 = \$815,775 \text{ per day}
This is the gross daily revenue from selling 150 million scf of natural gas at the specified rate. Such calculations are essential for energy companies, utility pricing, and economic feasibility assessments in the natural gas sector.