Question

. A 0.65 specific gravity natural gas contains 10% nitrogen, 8% carbon dioxide, and 2% hydrogen sulfide. Brill and Beggs correlation can used in estimating the z-factor values accurately enough for many engineering calculations. Brill and Beggs’ z-factor correlation is expressed as follows: With your knowledge in computer literacy and information technology coupled with Matlab programming, develop either a Microsoft excel spreadsheet program or a Matlab script to compute the z-factor of the gas at initial pressure and temperature of 5,000 psia and 180 °F respectively. Your application should be able to compute the z-factor for the gas at varying temperature and pressure.

Answer 1

Brill and Begg's Correlation is an important correlation in finding out the compressibility factor of natural gas when

• It's composition of hydrocarbon is unknown, however we have data on the specific gravity of the hydrocarbon.
• When viscosity data is unavailable. If viscosity data is available we go with Carr, Kobayashi and Burrows correlations.
• We need to have composition data of .

Compressibility Factor (Z) is the ratio of actual volume of the gas to the volume of the gas as described by the ideal gas law.

Brill and Begg's Z factor Correlation - Calculation Algorithm

Step 1: Determine the pseudocritical pressure and temperature

Note: The values of and will be in (psia) and (^oR) respectively

Step 2: Calculate the reduced pseudopressure and reduced pseudotemperature

Step 3: Calculate Brill and Begg's Parameters

Step 4: Calculate Z value

Note : Z value is an unitless value.

Excel Sheet

The below solution steps will guide on how to calculate Z factor(Compressibility factor) for any hydrocarbon system as per Brill and Begg's Correlation using a Excel Spreadsheet.

Step 0: Setup the Input parameters

Note: In the problem it has been reported as 180^oF. This has to be converted to ^oR. Hence 180^oF is 639.67 ^oR. Inorder to convert ^oF to ^oR, we need to add 459.67 to the fahrenheit value.

Step 1: Calculate the pseudocritical pressure and pseudocritical temperature.

Inorder to do this we need to the enter the formula for pseudocritical pressure and pseudocritical temperature as mentioned above into the Excel formula box. The formula will be cell referenced inorder to make sure that for any change in input parameters we get the corresponding values.

For pseudocritical pressure the formula cell will look as shown below

For pseudocritical temperature the formula cell will look as shown below

Step 2: Calculate the reduced pseudopressure and reduced pseudotemperature.

For reduced pseudopressure

For reduced pseudotemperature

Step 3: Calculate Brill and Begg's Parameters (A,C,E,F)

Here we keep the parameters B and D for step 4 as they are dependent of E and F respectively.

For parameter A

For parameter C

For parameter E

For parameter F

Step 4: Calculate Brill and Begg's Parameters (B and D)

For parameter B

For parameter D

Step 5 : Calculate Z

The formula bar for correlation factor will look as follows,

Final answer: The final Z factor

For a pressure of 5000 psia and 180^oF

NOTE: - Hence the Z value as per our problem would be 0.97875

This excel sheet can be used to predict the correlation factor for any hydrocarbon whose input parameters are defined by specific gravity, pressure, temperature, mole composition of .

For example : For the same compound at a pressure of 2500 psia and 360^oF, according to Brill-Begg's Correlation,

The Z value would be 0.997878.

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