05 thermo dyanamics

Fundamentals of Gas Processing Jan 2017

THERMODYNAMICS OF NATURAL GAS


Introduction

• Knowledge of natural gas properties is essential for designing and analyzing natural gas production and processing systems.

• Because natural gas is a complex mixture of light hydrocarbons with a minor amount of inorganic compounds, it is always desirable to find the composition of the gas through measurements.

• Once the gas composition is known, gas properties can usually be estimated using established correlations with confidence


Properties Used in Equations• Density, need z-factor and molecular weight• Flow in wells, need z-factor and viscosity• Pressure drop in pipelines, need density and viscosity• Temperature in pipelines, need heat capacity• Compressor power and exhaust temperature, need molecular

weight and heat capacity ratio• Molecular weight, need relative density (gravity)• Reynolds number, need density and viscosity• Wobbe index, need calorific value and relative density• Hydrates and water, need water vapor in natural gas (diagram or

PVT package)


Equation of State• The behavior of natural gas must be understood for designing and operating

equipments for its production , processing and transportation

All fluids follow physical laws that define their state

under given physical conditions, equations of state

(EOS).These equations

essentially correlate, P, V, and T for any fluid and can be expressed, on a mole basis,

as:Ø(P,V,T)= 0

Ideal Gas LawAn ideal gas is a gas in which:

• The molecules occupy negligible volume• There is no interaction between the molecules

• Collisions between the molecules are purely elastic, implying no energy loss on collision.

At low pressures (< 400 psi) most gases exhibit an almost ideal behaviorPV = nRT

Behavior of Real GasesIn general, gases deviated from ideal behavior for reasons summarized as

follows: Molecules for even a sparse system, such as gas, occupy a finite

volume. Intermolecular forces are exerted between molecules.

Molecular collisions are never perfectly elastic. The deviation from ideal behavior is greater for heavier gases because of

the larger size of their molecules. Most gases compress more than ideal gas at low pressures, whereas the

opposite is true at high pressures.

where P and T are the absolute pressure and temperature of the gas, n is the number of moles, and V is the volume occupied by the gas. R, the constant of proportionality, is called the universal gas constant.


To correct for non-ideality, the simplest equation of

state uses a correction factor known as the gas

compressibility factor, Z


Compressibility Factor• Gas compressibility factor is also called deviation factor, or z-factor. • Its value reflects how much the real gas deviates from the ideal gas at given

pressure and temperature. • Definition of the compressibility factor is expressed as:

• The simplest equation of state uses a correction factor, the gas compressibility factor Z to correct for non-ideality

PV = nzRT• Where n is the number of moles of gas. When pressure P is entered in psia, volume V

in ft 3 , and temperature in °R, the gas constant R is equal to


Compressibility Factor• The gas compressibility factor can be determined on the basis of

measurements in PVT laboratories. • For a given amount of gas, if temperature is kept constant and volume is measured at 14.7 psia and an elevated pressure P1, z-

factor can then be determined with the following formula:

Where V0 and V1 are das volumes at 14.7 psia and P1 , respectively.


Compressibility Factor ApproachThe Z-factor can therefore be considered as being the ratio of the volume occupied by a real gas to the volume occupied by it under the same temperature and pressure

conditions if it were ideal. This is the most widely used real gas equation of state. The major limitation is that

the gas deviation factor, Z, is not a constant but varies with changes in gas: CompositionTemperature Pressure

The Z-factor is determined experimentally. The results of experimental determinations of compressibility factors are

presented graphically.


Real gas factor with reduced p & T

Real gas factor with pressure at 25 C


Real Gas Pseudopressure and Pseudotemperature

• The shapes of isobars of compressibility factors of natural gas constituents are very similar.

• This led to the development of the law of corresponding states and the definition of the terms "reduced temperature" and "reduced pressure".

• The law of corresponding states – expresses that all pure gases have the same compressibility factor at the same

values of reduced pressure and reduced temperature.– extended to cover mixtures of gases, which are closely related chemically.– It is difficult to obtain the critical point for multi-component mixtures

• The quantities of pseudocritical temperature and pseudocritical pressure have been defined as:


Real Gas Pseudopressure and Pseudotemperature

• When pressure and temperature are normalized using critical pressure and temperature, then all properties become the same/similar, irrespective of composition.

• Normalized pressure or temperature are called reduced pressure or temperature in one component systems.

• Normalized pressure or temperature are called pseudoreduced pressure or temperature in multi-component systems.

• Commonly used when gas properties (natural gas and other gases) are to be correlated and/or presented.


Example Calculation for Natural Gas

• Calculation of pseudocritical temperature and pseudocritical pressure and average molecular mass for a natural gas mixture


Compressibility factor for natural gas

The pseudocritical quantities are used for mixtures of gases in exactly same manner as the actual critical temperatures and critical pressures are used for pure gases. The compressibility factors for natural gases have been correlated using there pseudocritical properties

GPA (1998)

Fundamentals of Gas Processing Jan 2017 Rojey o.a. (1997)


Formation Volume Factor and Expansion Factor

• Formation volume factor is defined as the ratio of gas volume at reservoir condition to the gas volume at standard condition

The unit of the formation volume factor is ft3/scf.

• If expanded in rb/scf, it takes the form of:


Compressibility of Natural Gas

• Gas compressibility is defined as:

• Because the gas law for real gas gives

• This yields:


Gas Density• Because natural gas is compressible, its density depends upon

pressure and temperature. • Gas density can be calculated from gas law for real gas with good

accuracy:

Where m is mass of the gas and ρ is gas density

Taking air molecular weight 26 and

Then the density formula become: , the gas density is in Ibm/ft3.


VISCOSITYKnowledge of the viscosity of hydrocarbon fluids is essential for a study of the dynamic or flow behavior of these fluids through:

• pipes• porous media

The unit of viscosity is g/cm.s, or the poiseThe kinematic viscosity is the ratio of the absolute viscosity to the density:

corrections to the value of hydrocarbon viscosity, due to the effect of the pressure of low concentrations of :

H2S, N2 or CO2

The effect of each of the non-hydrocarbon gases is to increase the viscosity of the gas mixture.

graphical rapid and reliable method for obtaining the viscosities of mixtures of hydrocarbongases at 1.0 atmosphere of pressure


• Diagram shows viscosity against temperature for gas components (methane, ethane, propane etc.) at atmospheric pressure.

• Empirical equation

(shown under) gives estimate of viscosity to natural gas (mixture of methane, ethane, propane etc.) at atmospheric pressure.

Katz o.a. (1959), fra Rojey o.a. (1997)

Viscosity from Diagram


Viscosity from Diagram

Correlation of gas viscosity ratio with

reduced temperature and pressure

Turn to a method for calculating the viscosity at pressures other than one atmosphere, the pseudocritical temperature and pressure are required to obtain reduced temperature

and pressure for entry into the graph.

Katz o.a. (1959), fra Rojey o.a. (1997)


Viscosity from Correlation

• Several correlations in literature, for example Carr et al. (1954), Lee et al. (1966) and Pedersen et al. (1987).

• Lee et al. (1966) correlation has recently been evaluated by Jeje and Mattar (2004) and has the form shown below. K, X and y are given by empirical equations.

• The correlation is available as spreadsheet on home page to course, link shown below.

www.ipt.ntnu.no/~jsg/undervisning/naturgass/BeregningerDiverse.xls


What is Thermodynamics?Thermodynamics can be defined as the science of energy

The first law of thermodynamics defines the internal energy (E) as equal to the difference of the heat transfer (Q) into a system and the work (W) done by the system. E2 - E1 = Q - W • From the first law of thermodynamics:

wqE Conservation of EnergySays Nothing About Direction of Energy Transfer


Second Law of ThermodynamicsPreferred (or Natural) Direction of Energy TransferDetermines Whether a Process Can OccurThree Types of Thermodynamic Processes

Natural (or Irreversible)ImpossibleReversible

• Physical processes that proceed in one direction

• Tends towards equilibrium (at end of process)• Examples: Free Expansion of Gas

ValveClosedVacuum Gas

ValveOpen Gas

Increase in Entropy

Equilibrium

Gas

Thermal Conduction

Hot ColddQ Warm

Increase in Entropy

Equilibrium

Equilibrium: Time independent , Properties do not change with time


Physical processes that do not occur naturallyProcess that takes system from equilibrium


Natural (or Irreversible)ImpossibleReversible Examples: Free Compression of Gas

ValveOpen GasGas

ValveOpenVacuum Gas

Decrease in EntropyThermal Conduction

Warm

Cannot Occur without Input of Work

Hot ColdDecrease in Entropy



Natural (or Irreversible)ImpossibleReversible

Reversal in direction returns substance & environment to original states


THERMODYNAMIC PROPERTIESThe principles of thermodynamics find very wide application in correlating and predicting the properties of hydrocarbons. For example:

• The effect of pressure on the enthalpy of gas can be computed from PVT data.

• Latent heats can be computed from the slopes of vapor pressure curves.

The properties of greatest interest are:• Specific heats of gases and liquids• Heats of vaporization• The effects of pressure on the enthalpies of compressible fluids. • Enthalpy-entropy charts for natural gases permit prediction of

temperature change when gases are expanding or when reversible work is done by compression.


Specific Heat

• Defined as the amount of heat required raising the temperature of a unit mass of a substance through unity

• It can be measured at :– constant pressure (Cp)

– constant volume (Cv)

Where: h is the molal enthalpy (BTU/lbmole)U is the molal internal energy (Btu/lbmole)Cp is the molal specific heat at constant pressure (BTU/lbmole-R)Cv is the molal specific heat at constant volume (Btu/lbmole-R)


For an ideal gas

where R is the universal gas constant (8,314 kJ/kmol.k).

For a real gas: • Cp and Cv are functions of both pressure as well as temperature• The specific heats of gases and liquids are determined experimentally in a

calorimeter, usually at 1 atm.

For natural gases:• The specific heat at 1 atm pressure is a function of temperature and of gas

gravity or molecular weight. • For a given heat release in combustion, the temperature is governed by the

specific heat of the combustion products of the flue gases.


Specific Heat

Campbell (1984)


Mean modal heat capacities of gases between 15 °C and temperature (Btu/((Btu/(lbmol°F))4.1868=(kJ/(kmol°C)))


Approximate heat-capacity ratios of

hydrocarbon gases

Beggs (1984)


Heating Value• Combustion is used to provide heat in the field or plant as well as the

power for gas engines, and engineers need to understand it.• The heating or calorific value of combustion is a prime characteristic

of a natural gas, often a factor in the price received in the sale.• The heating value of natural gas is the heat liberated when a unit of

fuel is burned with oxygen under specified conditions.

Methane has a heating value of 37.694 MJ/m3 of gas at 15 °C and 1 atm, when burned with air. This heating value is obtained by cooling the products of combustion to 15 °C.

the net heating value is the energy recovered when water remains as vapor.

the total or gross heating value the is the recovered energy when moisture is condensed.


Gross Heating Values of Gases

Component Gross heating value (MJ/m3)

Nitrogen 0.0

Methane 37.694

Ethane 66.032

Propane 93.972

i-butane 121.426

n-butane 121.779

Pentane+ 163.521

Gross heating value of mixture = ∑(mole fraction gross heating value) of pure

components


Limits of Flammability - Safety• Composition limits of flammability represent a safety problem that should be

familiar to engineers.• Air and natural gas in the proper proportions will ignite, liberating heat, which is

absorbed primarily by the products of combustion. The temperature rise of the gas causes an increase in pressure and, under confinement, can result in an explosion

• There are two composition limits of flammability for air and a gaseous fuel under specified conditions.– The lower limit corresponds to the minimum concentration of combustible

gas that will support combustion • The lower limits of gaseous mixtures can be predicted from the limits of

the pure constituents by a simple formula:

where n is the mole fraction of each constituent in the total mixture at lower limit and N is the lower limit for each constituent as a pure hydrocarbon.

– The higher limit the maximum concentration.


Limits of flammability of gases with air at 1 atm (volume or mol%)

• Pressure influences the flammability limits.• At low pressures( say 50 mm Hg) natural gas-air mixtures are not combustible. • At high pressures, the upper limit rises rapidly.

• The diluting of a fuel-air mixture with inert constituents, such as nitrogen and carbon dioxide also changes the limits of flammability.• Natural gas or any fuel is very combustible when mixed with oxygen-enriched air or

pure oxygen.• Usually odorant is added into natural gas to alert operators when the natural gas

concentrations in air reaches 20 percent of the lower flammability limits.


Joule-Thomson Effect

• The Joule-Thomson coefficient is defined as the change in temperature upon expansion which occurs without heat transfer or work

• It is a useful and practical property for estimating the isenthalpic temperature drops of the gas per unit pressure drop.

Where:Tr, Pr = reduced temperature and pressure of the gasTc, Pc = critical temperature and pressure of the gasm=Joule-Thomson coefficientCp = specific heat capacity of the gasAccording to the definition, the gas cools down when the coefficient is positive and heats up when the coefficient is negative.


Natural Gas – Phase Diagram• When an extractive sample conditioning system is used to measure pipeline gas,

it is essential that the sample gas is representative of the gas in the pipeline. Condensation in the sample gas would alter the composition and must be avoided.

Example (A): assume a pipeline is at 800 psi and 50 degrees F; the gas would be in the gas phase. If the temperature dropped to zero degrees, liquid would begin to form. If the temperature decreased more, additional liquid would form as gas properties go deeper into the 2-phase region.

pres

sure

temperature

Typical Phase Diagram for Natural Gas


Effects of Gas Composition on the Phase Diagram

less heavy hydrocarbons

Example (B) : Assume a temperature drop from 50 degrees to zero which is accompanied by a pressure drop from 800 to 50psi. The gas would end up in the vapor region.Most pipeline operators prefer not to allow temperature drops because it is critical to keep the gas above the dew point line. In the case of an analyzer that requires an extracted sample of the gas, the pressure may need to be dropped in order to stay within the operating specs of the analyzer . When the pressure is decreased, the Joule-Thomson effect causes a temperature decrease as well.Example (B) : If the pipeline is operating at

800 psi, the temperature change is about 50 degrees.By using a heated regulator or a probe regulator, the result is an adiabatic (constant temperature) process.

Example C: the gas moves farther away from the dew point line using this method, making condensation less likely in the sample conditioning system than in the pipeline.

05 thermo dyanamics

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