Transcript LAWS OF NATURAL GAS Fundamentals of Petroleum Engineering. By: Bilal Shams Memon

Fundamentals of Petroleum Engineering.
By: Bilal Shams Memon
LAWS OF NATURAL GAS
BOYLE’S LAW
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At constant temperature, the volume of a given quantity of gas is inversely
proportional to its pressure : V - 1/P
So at constant temperature, if the volume of a gas is doubled, its pressure
is halved.
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At constant temperature for a given quantity of gas, the product of its
volume and its pressure is a constant : PV = constant, PV = k
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At constant temperature for a given quantity of gas : PiVi = PfVf
where Pi is the initial (original) pressure, Vi is its initial (original) volume, Pf
is its final pressure, Vf is its final volume
Pi and Pf must be in the same units of measurement (e.g., both in
atmospheres), Vi and Vf must be in the same units of measurement (e.g.,
both in liters/cu. ft).
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All gases approximate Boyle's Law at high temperatures and low pressures.
A hypothetical gas which obeys Boyle's Law at all temperatures and
pressures is called an Ideal Gas. A Real Gas is one which approaches
Boyle's Law behavior as the temperature is raised or the pressure lowered.
BOYLE’S LAW
P1V1=P2V2
CHARLES’ LAW
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At constant pressure, the volume of a given quantity of gas is directly proportional to the
absolute temperature : V - T (in Kelvin)
So at constant pressure, if the temperature (K) is doubled, the volume of gas is also doubled.
OR
At constant pressure for a given quantity of gas, the ratio of its volume and the absolute
temperature is a constant : V/T = constant, V/T = k
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At constant pressure for a given quantity of gas : Vi/Ti = Vf/Tf
where Vi is the initial (original) volume, Ti is its initial (original) temperature (in Kelvin), Vf is its
final volume, Tf is its final temperature (in Kelvin)
Vi and Vf must be in the same units of measurement (e.g., both in liters/cu. ft.), Ti and Tf must
be in Kelvin NOT Celsius.
temperature in Kelvin = temperature in Celsius + 273 (approximately)
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All gases approximate Charles' Law at high temperatures and low pressures. A hypothetical gas
which obeys Charles' Law at all temperatures and pressures is called an Ideal Gas. A Real Gas
is one which approaches Charles' Law as the temperature is raised or the pressure lowered.
As a Real Gas is cooled at constant pressure from a point well above its condensation point, its
volume begins to increase linearly. As the temperature approaches the gases condensation
point, the line begins to curve (usually downward) so there is a marked deviation from Ideal Gas
behavior close to the condensation point. Once the gas condenses to a liquid it is no longer a
gas and so does not obey Charles' Law at all.
Absolute zero (0K, -273⁰C approximately) is the temperature at which the volume of a gas
would become zero if it did not condense and if it behaved ideally down to that temperature.
CHARLES LAW
V1/V2=T1/T2
COMBINING BOYLE’S & CHARLES LAWS…
P1V1/T1=P2V2/T2
Or PV/T = constant ------- (1)
AVOGADRO’S LAW - MOLECULAR CONSTANTS
In the kinetic theory of gases, there are certain constants which
constrain the ceaseless molecular activity. A given volume V of any ideal
gas will have the same number of molecules. The mass of the gas will
then be proportional to the molecular mass. A convenient standard
quantity is the mole, the mass of gas in grams equal to the molecular
mass in amu. Avogadro's number is the number of molecules in a mole
of any molecular substance.
V-n
THE MOLE
A mole (abbreviated mol) of a pure substance is a mass of the material
in grams that is numerically equal to the molecular mass in atomic
mass units (amu). A mole of any material will contain Avogadro's
number of molecules. For example, carbon has an atomic mass of
exactly 12.0 atomic mass units -- a mole of carbon is therefore 12
grams.
One mole of an ideal gas will occupy a volume of 22.4 liters or 379.4
Cu. Ft at STP (Standard Temperature and Pressure, 0°C and one
atmosphere pressure).
Avogadro's number
COMBINING EQUATION 1 & AVOGADRO'S LAW…
LEADING TO GENERATION OF IDEAL GAS LAW
PV/nT = constant
PV = nRT - (ideal gas equation)
Where R is the gas constant (atm cu.ft/mol. ⁰K),
value depends on system of units used.
Or
Pressure
Volume
Temperature
R
Atm
Cc
⁰K
82.1
atm
Litres
⁰K
.0821
Mm mercury
Cc
⁰K
62369
Gm. Per sq. cm
Cc
⁰K
8.315
Lb. per sq. inch
CF
⁰R
10.7
Lb. per sq. ft.
CF
⁰R
1545
Atm
CF
⁰R
0.73
IDEAL GAS LAW
How can the ideal gas law be applied in dealing with how gases behave?
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PV = nRT
Used to derive the individual ideal gas laws:
For two sets of conditions: initial and final set of conditions:
P1V1 = n1RT1 and P2V2 = n2RT2
Solving for R in both equations gives:
R = P1V1 / n1T1 and R = P2V2 / n2T2
Since they are equal to the same constant, R, they are equal to each other:
P1V1 / n1T1 = P2V2 / n2T2
For the Volume Pressure relationship (ie: Boyle's Law):
P1V1 = P2V2 (mathematical expression of Boyle's Law)
For the Volume Temperature relationship (ie: Charles's Law):
V1 / T1 = V2 / T2 (mathematical expression of Charles's Law)
For the Pressure Temperature Relationship (ie: Gay-Lussac's Law):
P1 / T1 = P2 / T2 (math expression of Gay Lussac's Law)
For the Volume mole relationship (Avagadro's Law)
V1 / n1 = V2 / n2 (math expression for Avagadro's Law)
Used to solve single set of conditions type of gas problems where there is no observable change in the four variables of a gas
sample. Knowing three of the four variables allows you to determine the fourth variable. Since the universal Gas Law constant,
R, is involved in the computation of these kinds of problems, then the value of R will set the units for the variables.
IDEAL GAS LAW
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An Ideal Gas (perfect gas)is one which obeys Boyle's Law and Charles' Law exactly.
An Ideal Gas obeys the Ideal Gas Law (General gas equation):
PV = nRT
where P=pressure, V=volume, n=moles of gas, T=temperature, R is the gas constant
which is dependent on the units of pressure, temperature and volume
An Ideal Gas is modeled on the Kinetic Theory of Gases which has 4 basic postulates
Gases consist of small particles (molecules) which are in continuous random motion
The volume of the molecules present is negligible compared to the total volume occupied
by the gas
Intermolecular forces are negligible
Pressure is due to the gas molecules colliding with the walls of the container
Real Gases deviate from Ideal Gas Behavior because
at low temperatures the gas molecules have less kinetic energy (move around less) so
they do attract each other
at high pressures the gas molecules are forced closer together so that the volume of the
gas molecules becomes significant compared to the volume the gas occupies
Under ordinary conditions, deviations from Ideal Gas behavior are so slight that they can
be neglected
A gas which deviates from Ideal Gas behavior is called a non-ideal gas.
IDEAL GAS LAW PARAMETERS @ STANDARD
TEMPERATURE AND PRESSURE (STP CONDITIONS)
STP is used widely as a standard reference point for expression
of the properties and processes of ideal gases. The standard
temperature is the freezing point of water and the standard
pressure is one standard atmosphere. These can be quantified
as follows:
Pressure ( P ) is the ratio of the force applied to a surface (F) to the surface area ( A ).
P=F/A
Standard temperature: 0°C = 273.15 K = 32 F
Standard pressure = 1 atmosphere = 760 mmHg = 101.3 kPa =14.696 psi
Standard volume of 1 mole of an ideal gas at STP: 22.4 liters or 379.4 Cu. Ft.
REAL GAS LAW
A gas which deviates from Ideal Gas behavior
and does not obeys Boyle’s & Charles’ laws is
called a non-ideal/real gas.
 Real gas law equation: PV=znRT
Where z is the gas deviation factor occur due to
its compressibility effect, used to account for
the difference between actual and ideal gas
volumes.
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Z VALUE DETERMINATION
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Value of z for natural gas mixtures have been
experimentally correlated as function of
pressures, temperatures and composition.