Fundamentals of Petroleum Engineering. By: Bilal Shams Memon

 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. OR At constant temperature for a given quantity of gas, the product of its volume and its pressure is a constant : PV = constant, PV = k  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).  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.Ideal Gas

P 1 V 1 =P 2 V 2

 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  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 (approximately)  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, -273 ⁰ C 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.Ideal Gas

V 1 /V 2 =T 1 /T 2

P 1 V 1 /T 1 =P 2 V 2 /T 2 Or PV/T = constant  (1)

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

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 Cu. Ft at STP (Standard Temperature and Pressure, 0°C and one atmosphere pressure). Avogadro's number

PV/nT = constant Or PV = nRT -  (ideal gas equation) Where R is the gas constant (atm cu.ft/mol. ⁰ K), value depends on system of units used. PressureVolumeTemperatureR AtmCc ⁰K⁰K 82.1 atmLitres ⁰K⁰K.0821 Mm mercuryCc ⁰K⁰K Gm. Per sq. cmCc ⁰K⁰K Lb. per sq. inchCF ⁰R⁰R 10.7 Lb. per sq. ft.CF ⁰R⁰R 1545 AtmCF ⁰R⁰R 0.73

How can the ideal gas law be applied in dealing with how gases behave?  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):Boyle's Law  P1V1 = P2V2 (mathematical expression of Boyle's Law)  For the Volume Temperature relationship (ie: Charles's Law):Charles's Law  V1 / T1 = V2 / T2 (mathematical expression of Charles's Law)  For the Pressure Temperature Relationship (ie: Gay-Lussac's Law):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.

 An Ideal Gas (perfect gas)is one which obeys Boyle's Law and Charles' Law exactly.Boyle's LawCharles' Law  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.

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 = K = 32 F Standard pressure = 1 atmosphere = 760 mmHg = kPa = psi Standard volume of 1 mole of an ideal gas at STP: 22.4 liters or Cu. Ft.

 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.

 Value of z for natural gas mixtures have been experimentally correlated as function of pressures, temperatures and composition.