water vapor factor 2 different formula

I have 2 formula for calculation the water vapor factor.
Formula 1 ; Water vapor Factor = (1-0.0000210181*Water content(lbs/MMscf))/0.9826

Formula 2 ; Water vapor Factor = 1/(1-0.0174*(1-(Water content/828)))


I would like to know 2 formula,they are diferent or not ? and help to show the solution.

[JohnS]

Originally Posted by Unregistered

I have 2 formula for calculation the water vapor factor.
Formula 1 ; Water vapor Factor = (1-0.0000210181*Water content(lbs/MMscf))/0.9826

Formula 2 ; Water vapor Factor = 1/(1-0.0174*(1-(Water content/828)))


I would like to know 2 formula,they are diferent or not ? and help to show the solution.

In formula 1, carry out the division by 0.9826
Formula 1': WF = 1.0177 - 0.0000213902*WC

In formula 2, 1/(1-x) can be expanded in Taylor series as 1 + x + x² + x³ +higher order terms. If x is small only a few terms are needed. Take x = 0.0174(1 - WC/828). Note when x² and x³ are expanded, you will get constant and linear terms

The constant is 1 + 0.0174 + 0.0174² + 0.0174³ = 1.0177
The linear terms are -0.0174*WC/828 +2*0.0174²*WC/828² +... = 0.210136

So the constant term agrees and the linear term is only slightly different.