Temperature calculations

Temperature at a Point

Piper will calculate the temperature of each calculation segment of pipe based on the following equation, and using the two boundary conditions (the Wellsite Line Temperature and Surroundings Temperature) specified by the user.

Where:

Similarly, the average temperature over a link is calculated using the following equation:

The equation for the temperature at a point in a pipe segment is shown below.

Where: T₀ is the temperature at the beginning of the pipe, T is the temperature of the surroundings, D is the inner pipeline diameter, x is the pipeline distance measured from the beginning of the pipe, U is the overall heat transfer coefficient.

Where:

Where: m is the total mass of each component and C is the specific heat capacity.

Mixing Temperature

Piper will calculate the temperature of the mixture at junctions with the assumption of perfect mixing of all the phases. The equation used to calculate the Mixed Temperature is as follows:

Where 1,2…n refer to the fluid phases and fluid streams present.

Specific Heat Capacity Calculations

Each of the temperature calculations depend on the specific heat capacity of the fluids present.

For water, Piper will always assume that is equal to 1 Btu/lbm-°F.

The correlation for specific heat of oil was taken from the book Multiphase Flow in Wells (1). The correlation is shown below.

This correlation shall be used in Piper to determine the specific heat of the oil phase.

For gas, the following correlation, published in the Oil & Gas Journal (2), and is shown below.

This correlation is used to determine the specific heat of the gas phase.

1. Brill, James P. and Mukherjee, Hemanta.Multiphase Flow in Wells. Richardson : Society of Petroleum Engineers Inc., 1999. p. 122.

2. Correlation for Natural Gas Heat Capacity Developed.Moshfeghian, Mahmood. October 3, 2011, Oil & Gas Journal, Vol. 109, pp. 123-127.