PVT Data Measurement Error Analysis for Compressibility Factor and Second Virial Coefficient

(a) To determine the allowable percentage errors in the measured variables (m, M, V', T, and P) to maintain a maximum allowable error in the calculated compressibility factor Z of ±1%, we can use the equation for Z:

Z = PV / RT

Taking the derivative of Z with respect to each variable and then multiplying by the respective relative error gives:

ΔZ/Z = (ΔP/P) + (ΔV/V) + (ΔR/R) + (ΔT/T)

Assuming that the errors in each variable are independent, we can estimate the allowable percentage errors in each variable by equating the sum of their respective relative errors to ±1%.

For example, if we assume that the error in Z comes entirely from the pressure measurement, we can set ΔP/P = ±1% and set the other relative errors to zero. Then we can solve for the other variables:

(ΔP/P) = ±1% = (ΔV/V) + (ΔR/R) + (ΔT/T)

We can repeat this calculation for each variable to determine the allowable percentage errors. Keep in mind that this is an approximate calculation and assumes that the errors in each variable are independent.

(b) To determine the allowable percentage errors in the measured variables to maintain a maximum allowable error in the calculated values of the second virial coefficient B of ±1%, we can use Eq. (3.32):

B = Z - 1

Taking the derivative of B with respect to each variable and then multiplying by the respective relative error gives:

ΔB/B = ΔZ/Z

Assuming that the error in B comes entirely from the compressibility factor Z, we can set ΔZ/Z = ±1%. Then we can set the relative errors in the other variables to zero.

Again, this is an approximate calculation and assumes that the errors in each variable are independent.