Thermal expansion is the unit change in oil volume with the temperature at constant pressure. In equation form, the thermal expansion,βo, is defined as
The thermal expansion is a point function with the dimension of reciprocal temperature, 1/ºF. The following equation estimates the average thermal expansion coefficient between two temperatures at the same pressure:
Where ß̄o is the average thermal expansion between T1 and T2; v1 and v2 are the oil volumes at T1 and T2.
The thermal expansion correlation was developed based on the following assumed general relationship:
The following correlation describes the best relation to predicting thermal expansion.
Where the values of regression fit are
For pressures equal to bubblepoint pressure, the thermal expansion at the bubblepoint is
If the bubblepoint thermal expansion is known, the thermal expansion at any pressure for the given bubblepoint condition is calculated using the following equation.
These equations predict the instantaneous or point thermal expansion. However, the average thermal expansion can be calculated by averaging βo estimated from these equations at T1 and T2 without ignoring that pb is different at different temperatures.
Also, Eq. 18 can calculate the average thermal expansion by averaging βo estimated from the ANN model at T1 and T2.