ENCH 607 Lecture 1

ENCH 607 Lecture 1 Introduction and Equations of State

Introduction Natural gas produced from formations is unlikely to be able to be put into a pipeline and sold for consumption. Depending on the reservoir the gas will contain water, a mixture of hydrocarbons from methane to C30

+, acid gases such as CO2 and H2S, non-condensable gases such as N2, H2, and He, and trace sulphur compounds such as mercaptans, COS, and CS2. Some gas streams may also contain elemental sulphur, asphaltenes, diamonoids, or wax. All product streams from a gas treating facility are required to meet certain specifications and as such treatment is required to remove or separate the various components. In order to treat gas, two critical pieces of information are required: the gas you are starting with, and the specifications of the products you are required to make.

Raw Gas Composition When a project is being conceived, a Reservoir Engineer may have some indication of the expected gas composition based on well analogues. Once a well is drilled the composition may be determined by testing the well. If the well is sweet, a long period of testing may be possible, resulting in an accurate composition. Production testing of sour wells is problematic due to environmental considerations and sour gas test results are often less accurate. Although the plant process flow drawing will show one composition for the raw gas feed, it should be remembered that this is usually only a best guess, and the actual feed gas composition will vary. In some reservoirs the gas composition from individual wells varies and the inlet composition is dependant on the relative flow rates. Variation may also result if a plant is fed from multiple reservoirs, or as a result of retrograde condensation in the reservoir as the field is produced. When adding compression to a field that has been producing for years, the gas composition can be expected to be accurate. There are a number of important items to consider when looking at the raw gas.

Water Content Most reservoirs are saturated with water at reservoir conditions and as the gas is produced to surface both temperature and pressure decrease. Decreasing the temperature reduces the ability of the gas to hold water in the vapour phase, while decreasing the pressure has the opposite effect. The net effect is usually condensation of water from the gas stream. If the gas composition and reservoir conditions are known, the amount of water is easy to calculate. Many gas reservoirs are underlain by an aquifer containing brine. Generally Reservoir and Production Engineers try to perforate and produce the well to avoid producing any of this connate water. In reality the total water produced may be a

ENCH 607 Lecture 1 1 of 14

combination of water of condensation and connate water, which may also change over time. Measuring chloride content of the water provides a means to estimate the ratio of each type of water produced.

Hydrocarbon Content The hydrocarbon content is usually determined by doing a well test where the well is produced into a series of test separators operating at different pressures. The flow rates and compositions of the liquid and gas streams are determined and then recombined to give the overall composition. Gas and liquid analyses are done using gas chromatographs. Identification of the lighter components C1 through C5 is strait forward. The heavier components are somewhat trickier, as there is a difference if the C6 component is hexane or benzene. A good analysis should identify these individual components. This allows the designer to base detailed calculations on a detailed analysis, or to lump components when the details are not required.

Acid Gas Content The acid gases, H2S and CO2 are usually determined as part of the hydrocarbon analysis. When the H2S content is in the ppmv range, it is important to take the sample into a Teflon lined bomb and have the analysis done quickly. Failure to do this may result in the H2S reacting with the wall of the bomb giving low H2S results. Believing that there is little or no H2S present in the gas stream may result in the wrong process design and failure to meet the required produce specifications.

Trace Sulphurs Trace sulphurs usually refer to mercaptans (RSH), carbonyl sulphide (COS), carbon disulphide (CS2), and various disulphides (RSSR). These are more likely to be found when the gas contains H2S. Identification of these compounds is important as they behave differently than H2S in various treating processes, and will impact the total sulphur content of the treated products. Specialized sampling and analysis is required to obtain an accurate assessment.

Elemental Sulphur Reservoirs that contain H2S often contain elemental sulphur that is tied up with the H2S in the form of hydrogen polysulphides (H2Sx). The maximum amount of H2Sx that may be present is a function of temperature, pressure, and H2S concentration. The actual amount of H2Sx present may however be less than the maximum. As the gas is produced to surface the temperature and pressure decrease shifting the polysulphide equilibrium. The shift in the equilibrium may result in the deposition of elemental sulphur if the saturation point is reached. Sulphur may deposit as a liquid or solid depending on the local temperature. Deposition may occur in the reservoir or in the production tubing. Deposition is more like to occur and cause problems when the raw gas is very light and lacks heavy hydrocarbon components. The heavy hydrocarbon components will dissolved the sulphur or at least transport it in the tubing. The amount of


polysulphide present is determination by taking a downhole sample at reservoir conditions. Alberta Sulphur Research Ltd. (ASRL) has the equipment and skills to complete this sort of testing and analysis.

Product Specifications The main product of a treating facility is usually sales gas that is delivered to a pipeline for transportation to markets. Liquid products may be delivered in a variety of ways. The lighter streams can be delivered as mixed streams like Natural Gas Liquids (NGLs), or Liquified Petroleum Gases (LPGs). These lighter streams might also be delivered as fractionated stream like ethane, propane, or butane. Ethane and NGLs are delivered by pipeline due to their high vapour pressure. LPGs, propane, and butane can be delivered by pipeline, truck, or rail car. The heavy hydrocarbon stream is produced as a condensate stream (C5+) and can be shipped by pipeline, truck, or rail car.

Sales Gas The detailed sales gas specifications that must be met are determined by the particular pipeline company. Standard gas conditions at 15 oC and 101.325 kPa(abs). Typical Alberta sales gas specifications are given below, but one should always refer to the specific sales gas contract. Typical Sales Gas Specifications Specification SI value Traditional value Higher Heating Value (minimum) 34.5 MJ/Sm3 950 BTU/scf H2S Content (maximum) 23 mg/Sm3 1 grain/100 scf Total Sulphur (maximum) 115 mg/Sm3 5 grain/100 scf Hydrocarbon Dew Point (minimum) -10 oC @

5500 kPa(abs) 15 oF @ 800 psia

Water Content (maximum) 65 mg/Sm3 4 lb/MMscf Delivery Temperature (maximum) 49 oC 120 oF Delivery Pressure (minimum) 6200 kPa(g) 900 psig CO2 2% by volume 2% by volume Oxygen, and mercaptans might also be specified in some contracts, and there is usually a clause prohibiting “waxes, gums, and other deleterious substances”. Contracts may also specify a Wobbe index, which is:

avitySpecificGrHHVWobbeIndex =


NGLs NGLs are a mixture of hydrocarbons, usually in the C2-C4 range that are recovered at cryogenic temperatures and sent to another location for fractionation into separate products. A typical NGL specification is:

Ethane Ethane is a fractionated product containing primarily C2H6. A typical specification for ethane is: C2H6 95 mole% minimum CO2 2.0 mole% maximum CH4 2.0 mole % maximum C3H8 2.0 mole % maximum H2S 100 ppmw maximum Total Sulphur 200 ppmw maximum

LPGs LPGs are liquefied petroleum gases recovered by cooling a gas stream with a refrigerant. The product is a mixture of propane and butane if recovered at a gas plant, and may contain propylene and butylenes if recovered from a refinery. LPGs may be fractionated and sold as separate products. Typical specifications are: Typical LPG Specifications Specification Commercial

Propane Commercial Butane

Commercial B-P Mixtures

Vapour Pressure at 37.8 oC

1434 kPa(g) 483 kPa(g) 1434 kPa(g)

Residue 2.5 vol% butane 2.0 vol% C5+ 2.0 vol% C5+ 95% boiling point -38.3 oC 2.2 oC 2.2 oC Corrosion No. 1 Copper strip No. 1 Copper strip No. 1 Copper strip Total Sulphur 185 mg/kg 140 mg/kg 140 mg/kg Water Content No free water No free water No free water

Condensate (C5+) Condensate or Pentanes plus is usually just the heavy ends recovered from a gas processing facility. Typical specifications include a Reid vapour pressure (RVP), a maximum butane content, maximum basic sediment and water (BS&W), maximum density, and a maximum H2S content. The Reid vapour pressure is the pressure exerted by a sample at 100 oF. Typical numerical values are: RVP 90 kPa(abs) max BS&W 0.5 vol% max


Butane 5 vol% max Density 927 kg/m3 max H2S 20 ppmw max

Sulphur Sulphur is produced as a liquid product if H2S is present in the feed gas. Sulphur may be transported as liquid in trucks or rail cars, but most sulphur is sold as a solid. Typical sulphur specifications are: Purity 99.5% by weight (dry basis) Acidity < 0.05% by weight (as H2SO4) Moisture < 1.0% by weight Ash <0.1% by weight Carbonaceous matter <0.15% by weight Arsenic <0.25 ppmw Selenium <2.0 ppmw Tellurium <2.0 ppmw Colour Bright yellow at ambient temperature. There is current no North American specification for H2S in a sulphur product, but degassing is becoming more common. Many facilities provide sulphur with an H2S content below 10 ppmw.

Water Water produced from the reservoir usually has to be disposed of by deep well injection. There is no standard specification for the product but some specifications may be required depending on the particular disposal option. Reservoir engineers are likely to want the water to be filtered so that there are no particles larger than 10 microns. Disposal by off site trucking or storage in vented atmospheric tanks may require that the H2S content be below 10 ppmw.

Treating Requirements The treating required by a particular stream is dependant on the raw feed gas and the product specifications. The feed gas is subject to uncertainty, but the product specifications should be well defined. There may however be cases when product specifications may be variable. This may occur when a product may be sold into two markets with different specifications. The treating scheme must be able to handle the variation in feed composition to deliver specification products. If products are not on spec, they must either be flared, reprocessed, or sold at a discount. Another consideration in determining the treating requirements is the local infrastructure available. Recovery of a separate LPG product may not be worthwhile if shipping the product from site is prohibitively expensive. Gas not meeting a specification, especially the H2S spec must be flared as there is no storage or resale option. Flaring means a loss in sales revenue and often has implications with the public. Although the flared gas may be almost sweet,


the sight of a large fire ball on the end of a flare stack does not bode well with the community. It may be possible to reprocess NGL, LPG, and Condensate streams if a rerun pump is available to bring the stored product back into the processing train, and if there is spare capacity in the unit. If reprocessing is not available it may be necessary to sell the product at a discount. Sulphur not meeting the specification may be sold at a discount, but more likely will need to be disposed of in an industrial landfill.

Physical Properties Engineering problems often require physical properties of the fluids in order to arrive at a proper design. Most engineering calculations are now done on computers and there is often little opportunity for the engineer to become proficient in the application. It is important to understand the fundamentals that govern the many applications that are employed. When using computer programs, there are a number of “laws” that are worth remembering:

1. The utility of a computer calculation is limited by the user’s knowledge of the system and not by the capability of the computer.

2. The precision of an answer can be no better than the worst input data. 3. There is no such thing as a single equation or program that is equally valid

for all compositions and all physical conditions. 4. The validity of a computation is not necessarily proportional to its

complexity.

With the above in mind, it is often worthwhile to perform hand calculations prior to starting a computer simulation, or to check the validity of results after you have done some preliminary computer calculations.

Fundamental Concepts The most important fundamental concepts that will be covered are:

• Physical properties of fluids and solids. • Vapour-liquid-solid behaviour of a substance as a function of pressure,

temperature. and composition. • The concept of equilibrium. • The use of equations of state to predict the behaviour and properties of

systems. • The use of mixing rules for the prediction of mixture behaviour from that of

the individual components of the mixture. • Thermodynamic concepts that govern the conservations laws of energy

and matter. • Rate equations that express the speed of a process in terms of driving

force and resistance to change. • The molecular theory of matter.


Units of Measurement Canada has been using the System International (SI) units in the Oil & Gas industry since about 1978. Because of close ties with the United States, where the Imperial system (FPS) is used, there will be many instances where unit conversions are required. We will use SI for essentially all of our work, but occasionally data may come in other units. A number of unit conversion programs and website can easily be found.

Mass, force, and weight If relativistic effects are ignored, the mass of a body is a measure of the quantity of matter. Most common units are kilograms, with tonnes, grams, milligrams, and micrograms being common. In the FPS system, tons, pounds, ounces, and grains are commonly used. Force is required to accelerate a mass. The relationship between force and mass is:

gmaF =

where: m = mass (kg) a = acceleration (m/s2) g = proportionality constant for force (kg·m/N·s2) In SI unit of force is the Newton. Weight is a term that should be avoided even though it is often used to denote mass. Weight is a measure of the attraction of gravity on a given mass. The standard acceleration of gravity is: gc = 9.81 m/s2.

Length, area, and volume The standard unit of length is the metre (m). Other units are millimetre (mm), centimetre (cm), decimetre (dm), and kilometre (km).

1 m = 1000 mm = 100 cm = 10 dm = 0.001 km 1 m = 3.28 ft, 1 ft = 0.305 m

Area is expressed in the same length units squared. m2, mm2, cm2, dm2,km2

1 m2 = 1x106 mm2 = 100 dm2 = 10.76 ft2

The basic volume term is the cubic metre, m3. The litre (L) is an allowable term for the cubic decimetre. The API barrel (bbl), which is 42 U.S. gallons is not part of the SI system but is widely used in the industry.


1 m3 = 1000 dm3 = 1000 L = 35.31 ft31 bbl = 0.159 m3 = 159 L = 5.61 ft3 = 42 U.S. gal = 35 U.K. gal

Density The usual units are kg/m3 or lbm/ft3. Density is a function of temperature and pressure, so standard or reference density is usually reported at standard atmospheric pressure and some temperature like 0 oC, 15 oC, 25 oC, 60 oF, and 77 oF. For most engineering calculations standard density is adequate. For custody transfer and gases, an actual density is required. 1 kg/m3 = 0.0624 lb/ft3 Relative density is the density of the system divided by that of a reference substance at specified conditions. Relative density is the SI term for specific gravity. The reference for liquids is water; for gas it is air.

water

liquidL ρ

ργ =

air

gas

air

gasg M

M==

ρρ

γ

where: M = molecular mass The relative density for oil may be expressed in oAPI. The equation is:

APIoL +

=5.131

5.141γ 5.1315.141−=

L

o APIγ

Pressure Pressure is the force exerted per unit area. The standard term for pressure is the pascal (Pa) = 1 N/m2. This is a small pressure unit, so kilopascal (kPa) and megapascal (Mpa) are commonly used. In Europe it is common to use the term bar, which is 100 kPa. Absolute pressure is used in most engineering calculations. In FPS an “a” is added to denote absolute pressure (psia) and a “g” is added to denote gauge pressure (psig). In SI, it is common to use no suffix for absolute pressure, so that P = 150 kPa implies an absolute pressure. In some instances absolute pressures are written as kPa(abs). A gauge pressure would be written as 49 kPa(g). 100 kPa = 1 bar =0.987 atm = 14.50 psia 14.696 psia = 1 atm (std) = 101.325 kPa = 1.01 bar Fluid head A vertical column of fluid exerts a pressure on the bottom. This head, expressed as a length can be converted to a pressure by the equation:


P = A·ρ·H·gc/g Where: P = pressure (kPa) A = unit conversion factor (pascal to kilopascal) (0.001) ρ = density (kg/m3) H = height (m) gc = acceleration due to gravity (9.81 m/s2) g = proportionality constant (1.0 kg·m/N·s2)

Temperature The SI units are degrees Celsius (oC) and Kelvin (K). The term centigrade is obsolete. K = oC + 273.15 oC = (oF - 32) / 1.8 oF = 1.8 x oF + 32 oR = oF + 459.67 Degrees Fahrenheit (oF) and Rankin (oR) are the units in the FPS system. Absolute temperatures are used in most engineering calculations.

Work and power The units of work are force times distance. Power is the time rate of performing work. The standard SI unit of work is the joule (J) = 1 N·m. The joule is a small unit so kilojoule (kJ) and megajoule (MJ) are normally used. 1 kJ = 0.001 MJ = 737 ft-lbf Engineers are concerned with the rate of doing work, or power. The watt (W) and horsepower (hp) are the most common units. 1 W = 1 J/s 1 kW = 3600 kJ/h = 1.34 hp 1 hp = 0.746 kW = 2686 kJ/h

Heat energy Heat energy must have the same units as work and power in order to make calculations involving the conversion between them. In SI the joule is also used for heat energy, while the British Thermal Unit (Btu) is used in the FPS system. 1 kW = 3600 kJ/h = 3412 Btu/h Energy per unit mass is expressed in kJ/kg and Byu/lbm 1 Btu/lbm = 2.326 kJ/kg = 6.46 x 10-4 kWh/kg


Viscosity The dynamic viscosity is a shear force per unit area. The poise was the original unit; 1 poise = 1 dyne-sec/cm2. For petroleum systems the centipoises (cp) is the most convenient unit. In SI the Pa·s is the preferred unit. 1 cp = 0.001 Pa·s = 0.001 kg/(m·s) = 6.72 x 10-4 lbm/(ft-sec) Kinematic viscosity is dynamic viscosity divided by density with the primary unit being centistokes (cSt). 1 cSt = 1 mm2/s = 1.08 x 10-5 ft2/sec

Equations of State Any equation that relates pressure, temperature, and volume is called an equation of state. This all started with the Boyle-Charles law that stated pressure times volume is proportional to temperature.

Ideal gas law Adding a proportionality constant (R) normally called a universal gas constant gives a practical form: PV = nRT Where: P = pressure (kPa) V = volume (m3) n = amount of substance (kmol) T = temperature (K) This is known as the ideal gas law and is valid for pressures up to about 400 kPa. If n = 1, the “V” is the molar volume and is designated as “v”. If “V” is a mass specific volume (reciprocal density), then “n” is the reciprocal of molecular mass. P/ρ = RT/MW The value of R is 8.3145 kPa·m3/kmol·K The ideal gas law is used to calculate the standard volume of a gas (Sm3). SI standard conditions are 15 oC and 101.325 kPa. Some gas volumes are given at normal conditions, which are 0 oC and 101.325 kPa.

Compressibility factor Because of its simplicity, the ideal gas law is often corrected by using a compressibility factor, z. The equation then becomes:

PV = znRT


One must then determine z for the gas. A number of methods are applicable, but the concept of corresponding states must first be addressed.

Corresponding states The corresponding states concept states that physical and thermodynamic properties are related to the critical properties in a universal way. Mathematically, if an equation of state for any fluid is written in terms of reduced properties, that equation is also valid for any other fluid. The reduced properties are defined as: Tr = T/Tc Pr = P/Pc vr = v/vc Where “r” denotes the reduced property and “c” denotes the critical property. Critical properties can be found for many hydrocarbons in Chapter 23 of the GPSA Engineering Data Book. The concept of corresponding states is illustrated by the charts below.

1

10

100

1000

10000

-200 -150 -100 -50 0 50 100

Temperature C

Pre

ssur

e kP

a

MethanePropane

When the vapour pressure curves for methane and propane are plotted, they show a large deviation as shown above. If the same curves are plotted on reduced parameter scales they align much more closely as shown below. The correlation is not perfect, and a third parameter, the Pitzer acentric factor, ω, is often used. The parameter ω is defined as: ω = -log(Pr) - 1 where: Pr = P*/Pc; P* is the vapour pressure at T = 0.7 Tc


The acentric factor is a measure of the difference between the reduced vapour pressure of a component at Tr = 0.7 and the reduced vapour pressure of an ideal molecule at Tr = 0.7, which is Pr = 0.1

0.0001

0.0010

0.0100

0.1000

1.0000

0.00 0.20 0.40 0.60 0.80 1.00

Reduced Temperature

Redu

ced

Pres

sure

MethanePropane

Katz correlation and Kay’s rule This is the simplest method to calculate z. The correlation of Katz et al for lean sweet natural gas is given in FIG. 23-4 in the GPSA Engineering Data Book. To use the correlation the pseudo-critical properties for the gas mixture are used to determine the pseudo-reduced properties. Kay’s rule is a mole weighted average and states: and ciic PyP ∑='

ciic TyT ∑=' where: yi = mole fraction of component in gas phase Pci and Tci are the critical values for each component The pseudo-reduced pressure and temperature are then: and '' / cr PPP = '' / cr TTT = Kay’s rule also applies to the molecular mass: iiMWyMW ∑='

An example calculation is presented in FIG. 23-3 of the GSPA Engineering Data Book.


Modifications for sour gas When the gas contains appreciable quantities of H2S or CO2 the Katz correlation is modified by applying one of two methods:

• Robinson et. al • Wichert and Aziz

Robinson’s approach was an earlier work based on limited data, and the work by Wichert and Aziz is usually used. The method applies a correction factor to the pseudo-critical parameters calculated using Kay’s rule. The correction factor, ε is a function of the mole fraction of H2S and CO2 in the gas and is presented in FIG. 23-8 in the GPSA Engineering Data Book. Once ε is determined, adjusted critical parameters are calculated as follows:

ε+= '''cc TT

ε)1('

'''''

BBTTPP

c

ccc −+=

where: and are adjusted pseudo-critical values ''

cT ''cP

and are pseudo-critical values calculated from Kays rule 'cT '

cP ε is from FIG. 23-8 B is the mole fraction of H2S in the gas The value of ε in figure 23-8 can be estimated by the equation: )(33.8)(67.66 45.06.19.0 BBAA −+−=ε where A is the mole fraction of H2S plus CO2 in the gas

Benedict-Webb-Rubin (BWR) Equation The BWR equation was developed in 1940 and modified by Starling (BWRS) in 1970. It is rather cumbersome because of all the terms and is suitable only for computerized calculations. The form of the equation is:

( ) 222

3632

40

30

20

0 1 χρχρραρρρρ −−+⎟⎠⎞

⎜⎝⎛ ++⎟

⎠⎞

⎜⎝⎛ −−+⎟

⎠⎞

⎜⎝⎛ −+−−+= e

Tc

Tda

TdabRT

TE

TD

TCARTBRTP

Coefficients for the equation can be found in Younger’s notes.

Cubic equations of state Cubic equations of state have in them a volume term raised to the third power. They are widely used due to their ease of use and the performance they provide. When the roots of a cubic equation of state are found, one real root is the volume of the vapour, while the other is the volume of the liquid. Three of the most used cubic equations of state are given below. The constants used are functions of the critical temperature and pressure, and usually a third parameter, ω, the


acentric factor. For mixtures of gases, mixing rules must be applied to the constants. For cubic equations of state the mixing rules are: ( ) ( )ijjijim kaaxxa −=∑∑ 12/1 iim bxb ∑= where: am and bm = the a anb parameters for the mixture ai, aj, bi = a and b parameters for any component xi, xj = mole fraction for any two components kij = binary interaction parameter Once am and bm are determine the calculations are done as if a and b were for a pure component. The binary interaction parameters kij has no theoretical basis, but is regressed from experimental data. van der Waals

2va

bvRTP −−

=

where: a and b = correlation constants v = molar volume Redlich-Kwong

)(5.0 bvvT

abv

RTP+

−−

=

Peng-Robinson

)()( bvbbvv

aTbv

RTP−++

−−

=

Homework Assignment Younger’s 607 Notes – Chapter 1 – Introduction GPSA Engineering Data Book – Section 1 – Introduction GPSA Engineering Data Book – Section 2 – Product Specifications GPSA Engineering Data Book – Section 23 – Physical Properties, pages 23-1 to 23-17 Problem Assignment #1


ENCH 607 Lecture 1

Documents

Transcript of ENCH 607 Lecture 1