Question

Calculate the density of the following fluid mixtures. Report your answers in units of lbm/ft3 and kg/m3. You will need to use equation 1.A from the textbook, and you will need to clearly state a basis for your calculations. Consider using either an appropriate mass basis or a volume basis, whichever fits each sub-problem statement the best.

A solution of ethanol and water, containing 30% ethanol and 70% water (by volume). The density of water is 62.3 lbm/ft3, while the density of ethanol is 49.2 lbm/ft3.

A drilling mud that contains 32 weight (wt) % barite (BaSO4) and 68 wt% water. The specific gravity of barite is 4.7 (density of barite is 4.7 times greater than the density of water).

A gas volume that is 80% air (density of 1.23 kg/m3) and 20% carbon dioxide (density of 1.98 kg/m3), combined in a closed container at final pressure of 1 atmosphere and ambient temperature.

Answer 1

SOLUTION.

1) ethanol water system.

A)Basis= 100 ft³ of SolutioSolution.

Componant	Water	ethanol
Volume, ft³	70	30
Density , lbm/ft³	62.3	49.2
mass , lbm	4361	1476
Total mass of Solution, lbm	5837
Total volume of Solution,ft³	100 ft³

Density of ethanol-water system = total mass/total volume

= 5837/100 =58.37 lbm/ft³

B)Basis = 100 m³ ethanol-water system

Componant	Water	ethanol
Volume, m³	70	30
Density , kg/m³	1000	788.108
mass , kg	70000	23643
Total mass of Solution, kg	93643
Total volume of Solution,m³	100

Density of ethanol-water system = total mass/total volume

= 93643.24/100 =936.43 kg/m³

2).let

Basis = 100 kg total mud

Water density = 1000 kg/m³

Density of berite = 4.7*density of berite

= 4700 kg/m³

Berite mass = 32 kg, volume =32kg/(4700kg/m³)=0.0068 m³

Water mass = 68 kg, volume = 68kg/(1000kg/m³)=0.068 m³

Total mud volume = 0.0748 m³

Total mud mass = 100 kg

Mud density =

mass/volume =

100kg/0.0748m³=1337 kg/m³

WKT 1 lbm/ft³ ~ 16 kg/m³

Mud density = 1337kg/m³ *(1 lbm/ft³/(16 kg/m³)=83.56 lbm /ft³

Mud has density of 83.56 lbm/ft³ or 1337 kg/m³

3) for air -CO2 system.

let assume air -CO2 system as ideal gas mixure because air -CO2 system is far above their critical conditions

where P is absolute pressure = 101.325 kPa(1atm)

T = temp = 25 °C

Basis === 100 m³ air - CO2 mixure

wkt Volume%= mole%=pressure% for ideal gas

Air=80 m³ , mass =80 m³*(1.23kg/m³)=98.4 kg

CO2 = 20 m³, mass = 20 m³*(1.98kg/m³)=39.6

total gas mass = 98.4 + 39.6 kg= 138 kg

total gas volume = 100 m³

Density of gas = 138 kg /100 m³ = 1.38 kg/m³

or 1.38 kg/(m³) *( lbm/ft³/ 16 kg/m³)

= 0.08625 lbm/ft³.

or we can find density of gas mixure

fraction of air =0.8

Fraction of CO2=0.2

Mix density =fraction of air *air density+fraction of Co2 *CO2 density

=0.8*1.23+0.2*1.98=1.38 kg/m³ or 0.08625 lbm/ft³.

​​​

​