Fraction – part of mixture which consist of compounds evaporated within the given temperature range

Lecture 1

• Caustobolites – burned minerals – natural energy resource

• Firm state – peat, coal, anthracite

• Liquid state  – petroleum

• Gas state– natural and associated gases

• Mendeleyev D.I. – inorganic theory:

 CaC2 + H2O = C2H2

2FeC + 3H2O = Fe2O3 + C2H6 ­

FeC, TiC, Cr2C3, WC, SiC

• Sokolov M.A. - Space hypothesis

• He stated the dust cloud from which the Earth and other planets of the solar system were formed consisted of HC

• Lomonosov M.V. – Organic theory

• It is expelled from underground with heat, prepared from stone coal and brown coal, this black oily material…And this is a birth of different grade of combustible liquid and dry hard matter.

• H.Hefer,K. Engler 1888 year - the experiments were performed by evaporation of fish fat at 4000, 1 bar – oil, gases, water, different acids.

• Zelinskiy N.D. - 1919 year, - initial material-organic silt of mainly vegetative origin from lake Balkhash – evaporation products - crude pitch, coke and gases, gasoline, jet oil, heavy oil

• Coal – contain of hydrogen is about 5%

• Carbon (С) - 83 - 87 %

• Hydrogen (Н) - under  12-14 %

• Oxygen (О) - 0,05 - 3,6 %

• Nitrogen (N) – 0,00001 - 1,7 %

• Sulfur (S) – 0,02 - 14%

• Metals – V, Ni, Fe, Mg, Cr, Ti, Co, K, Na,

• Other elements - P,  Si, Ge

Fraction – part of mixture which consist of compounds evaporated within the given temperature range

Boiling Ranges   - (temperature range) temperatures of the beginning and ending of fraction boiling point

• Fractions which are evaporated under 300⁰С

• Mazut (bottom product) is residue after oil rectification and removing light distillations

• Goudron is a vacuum residue after vacuum rectification of atmospheric residue

• Ligth products,

• Heavy products

Lecture 2

Alkanes - C n H2 n +2             where n = 1,2,3,…

•   only single covalent bonds

•  saturated hydrocarbons (they contain the maximum number of hydrogen atoms that can bond with the number of carbon atoms in the molecule)

What is the structure of 2-propyl-4-methylhexane?

• Cycloalkanes (cycloparaffins) - CnH2n (n ≥ 3),

• They include the basic mass of oil hydrocarbons

• Saturated HC

• Cyclic skeleton

• Only single covalent bond.

Lecture 3

• Naphtens have more higher melting points, boiling points and more bigger density then respective alkanes.

Chemical reactions of naphthens

• Less reactivity and very hard oxidable HC

• 1. Hydrogenation reactions at high temperature

•            СН2

•    Н2С   СН2 + Н2 ® СН3-СН2-СН3

• 2. Dehydrogenation reactions for hexane HC

Arenas

• Unsaturated HC, ring type compounds with special cyclic group from six carbon atoms –benzene ring

• All carbon atoms take part in stable single p - system formation by p-electrons

• Arenas  – are very desirable components of auto motor fuel, but not desirable for jet and diesel fuel in any kind

• (Arenas concentrate in the medium fractions, its contain varies from 15 to 25%)

• In gasoline fractions (under 200°С) are presented just benzene homologies.

• In the crude oil are found all benzene and naphthalene homologies.

• Phenyl - С6Н5

• С6Н5 -СН3 - methylbenzene (toluene)

• phenylmethane

• С6Н4 -(СН3) - ксилол

• High thermal stability

• Reactions of hydrogenation with naphtenes formation

• Oxidize

• 2С6Н6 + 15О2 →12СО2 +6Н2О.

• Reaction of condensation (with coke formation)

• Crude oil also consist of various kind of HC which are formed by hybrid HC

• They can contain aromatic cycles with alkyl substituted chains or aromatic HC with naphtenic cycles and others.

• Indan, Tetralin, Fluoren - cycloalkanoarenas and their homologies are presence in diesel fractions

• Sulfur containing compounds

• Elemental sulfur   S

• Hydrogen Sulfide,  H2S

• Mercaptans R-SH

• Sulfides (cyclic and non cyclic) R –S –R1

• Disulfides R –SS –R1

• More than 200 kinds of different sulfurous compounds

• Mercaptanes  (thiol) – R- S- H

• R – radicals can be different (paraffinic, naphtanic, aromatic, hybrid est.)

• Tengiz Oil  – about 10% of mercaptanes

• Mercaptanic sulfur are concentrated mostly in leading fractions

• Light fractions b.b.p. - 600С consist of   85% of mercaptanes

• Mercaptans are used in industry – odorant of gases (C2H5-SH-ethanethiol), in pharmacology, cosmetology

• All types of SCC have neutral characteristics

•  

• During oil refining SCC are hydrogenated with producing of hydrogen sulfide and then – go to getting the elemental sulfur and sulfuric acid

•     RSH + H2 = RH + H2S

Oxygen containing compounds

• Amount of oxygen compounds in crude oil increases with b.p. of fraction

• Over 20% - concentrated in asphaltenes and resins

• Acidic oxygen compounds

• Neutral oxygen compounds

• Usually presented by carbon acids and phenols

• Oil acids – С nHmCOOH – cyclopentane and cyclohexane carbon acids or mixture naphtenoaromatic acids

• Naphtenic acids and their salts are used in industry

• Sodium and potassium salts of naphtenic acids - (мылонафт) have strong emulsifying properties - detergent properties

• They are produced when kerosene and diesel fractions are cleaned by alkaline

• Neutral oxygen compounds concentrated in medium and high boiling fractions of crude oil

• Ketone – fluorenon, kumaron

• (benzofuran)

Asphaltenes and Resins

• Large molecular weight, amorphous nature

• Contain in crude oil – under 45%

• Very complicated, multicomponent polidispersive mixture of the largest molecular weight HC (above 1000) and heteroatomic compounds including metals

Lecture 6

• Density

• Viscosity

• Molecular mass

• Sulfur and water content

• Impurities content

• Temperatures (ignition, combustion, crystallization

Density Determination

• Density is not only just one of the most important physical parameters of crude oil and its products, but it is also an important characteristic for measuring the quality for crude oil and its products.

d = W/V     (absolute density)

Viscosity

• Characterize liquids and gases fluidity at engine operation

• Influence on transport, filtration and mixing

• Depends of chemical composition, and international forces

• The heavy oil fractions have more large viscosity than light oil fractions because of molecular mass

• Dynamic Viscosity (or absolute viscosity)– viscosity is the quantity that describes a fluid's resistance to flow.

• Fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them.

• The SI unit of viscosity is the pascal second [Pa·s]

• The most common unit of viscosity is the dyne second per square centimeter [dyne·s/cm2],

•  which is given the name poise [P] after the French physiologist Jean Louis Poiseuille (1799-1869).

• Ten poise is equal one pascal second [Pa·s] making the centipoise [cP] and millipascal second [mPa·s] identical.

1 pascal second =10 poise =

Millipascal second

1 centipoise =1 millipascal second

• Kinematic viscosity n is the ratio of the absolute viscosity to the density.

•  

• n = m/ r

             

• m - absolute viscosity, kg/(m· s);

•  d - density, kg/ m3.

• The SI unit of kinematic viscosity - [m2/s]

• A more common unit of kinematic viscosity is the square centimeter per second [cm2/s], which is given the name stokes [St] after the Irish mathematician and physicist George Gabriel Stokes (1819-1903).

• the most common unit is the square millimeter per second [mm2/s] or centistokes [cSt].

• 1 m2/s = 10,000 cm2/s [stokes] = 1,000,000 mm2/s [centistokes]
1 cm2/s = 1 stokes
1 mm2/s = 1 centistokes

• The viscosity of gasoline at 20°С is about 0,6 mm2/s,

• for heavy residue oil - about 300—400 mm2/s.

• Naphtenes - most viscosity

• Arenas  - medium state

• Paraffines - less viscosity

Specific viscosity

• The ratio of absolute viscosity of oil or oil products to the absolute viscosity of water at the same conditions

• m water= 1 centipoise  at  Т=20,2⁰С

Conditional Viscosity

• The ratio of outflow time of 200 ml of oil sample from viscosimeter under experimental conditions to outflow time of 200 ml of distilled water at 200С

• Defined in   (⁰ CV) units

•    n t = 0,0731 × CVt  - 0,0631/ CVt

• Where n t - kinematics viscosity

• CVt – conditional viscosity at the same T

• Viscosity index

• An arbitrary scale for lubricating oils that indicates the extent of variation in viscosity with variation of temperature.

• VI  is a commonly used method of measuring a fluid's change of viscosity in relation to temperature.

• The higher the VI, the smaller the relative change in viscosity with temperature.

• VI improvers (also known as viscosity modifiers) are additives that increase the viscosity of the fluid throughout its useful temperature range.

• The VI scale was set up by the Society Automotive Engineeres (SAE).

• The temperatures chosen arbitrarily for reference are 100 °F (40⁰ C) and 210 °F (100⁰C).

• The original scale only stretched between

• VI=0 (worst oil, naphthenic) and

• VI=100 (best oil, paraffinic)

Molecular mass

Formula of Voinov B.P.

          М = a + bt + ct2

А,в,с - coefficients

Creg Formula

• М = 44,29 d¹⁵₁₅  / (1,03 - d¹⁵₁₅)

Temperature properties

• Flash point

• Fire point

• Autoignition point (autogeneous ignition)

• Pour point

• Freezing point

• Lower limit of explosibility

• Minimum concentration of combustible gas mixture with air which will be flared up if the fire is made

• Higher limit of explosibility

• Maximum concentration of combustible gas mixture above that do not flash because of shortage of air oxygen

Flash Point

Fire Point

• The fire point is defined as the temperature at which the vapor continues to burn after being ignited.

• The fire point of a fuel is the temperature at which it will continue to burn after ignition for at least 5 seconds

• At the flash point, a lower temperature, a substance will ignite,

• but vapor might not be produced at a rate to sustain the fire.

• Fire point and autogenous ignition are additional considerations when selecting fire resistant greases.

• Industrially, fire point is the lowest temperature at which industrial greases produce sufficient vapors to form a mixture in air that continuously supports combustion after ignition.

•

• The fire point usually slightly higher then flash point

• This difference may be about 500C

AutoIgnition Point

• The autoignition temperature or kindling point of a substance is the lowest temperature at which it will spontaneously ignite in a normal atmosphere without an external source of ignition, such as a flame or spark.

• It is usually applied to a combustible fuel mixture.

• The heaver residue spontaneous ignite under 210 °С, gasoline fraction – above 280 °С.

• n-alkanes have the lowest autoignition point

Pour Point

• The lowest temperature at which an oil is observed to flow under the conditions of the test.

• It is a rough indication of the lowest temperature at which oil is readily pumpable.

• Also, the pour point can be defined as the minimum temperature of a liquid, particularly a lubricant, after which, on decreasing the temperature, the liquid ceases to flow.

• Pour point data indicates the amount of long-chain paraffins (petroleum wax) found in a crude oil.

• Handling and transporting crude oils and heavy fuels is difficult at temperatures below their pour points.

• Pour point depressants are used to improve the flow properties of the fuel.

• Long-chain n-paraffins ranging from 16–60 carbon atoms in particular, are responsible for near-ambient temperature precipitation.

• In middle distillates, less than 1% wax can be sufficient to cause solidification of the fuel

• The bigger amount of solid paraffins the higher pour point

• The bigger amount of resins the lower pour point

• Pour Point

• for auto and diesel fuel -10 до -40⁰С

• For lubricating oils and aircraft engines

•     -55⁰С

Freezing Point

• The maximum temperature at which wax will begin crystallize and become visible

• Maximum temperature at which crystals of hydrocarbons are found out by visually

• Mostly – aromatic HC that crystallize at 5,5⁰С.

Octane Number

• The octane rating is a measure of the autoignition resistance of gasoline (or petrol) and other fuels used in spark-ignition internal combustion engines.

• It is a measure of anti-detonation of a gasoline or fuel.

• Incorrect work of motor engines.

• If only part of combustible mixture are burnt after spark ignition

• but small part (20%) of this mixture are autoignited very rapidly and such noises and knocking are formed inside the cylinder

•  tool deterioration -износ двигателя

• The octane number is determined by comparing, under standard conditions, the knock intensity of the fuel with that of blends of two reference fuels: isooctane, which resists knocking, and heptane which knocks readily.

• Octane rating is measured relative to a mixture of isooctane (2,2,4-trimethylpentane, an isomer of octane) and n-heptane

.

• An 87-octane gasoline, for example, has the same octane rating as a mixture of 87 vol-% isooctane and 13 vol-% n-heptane.

• This does not mean, however, that the gasoline actually should contain these chemicals in these proportions.

• It simply means that it has the same autoignition resistance as the described mixture.

Additives

• ways to improve the octane number of gasoline

• change the composition of gasoline (difficult and expensive),

– add additives that destroy peroxides and prevent knock effects.

• The additive added in a very small amount in gasoline allows the increase of the octane number by about 5 – 10 units.

Oil Classifications

l <ll < lll - sulfur content

T1 >T2 > T3 - light fractions with b.r. under 3500C content

M1 >M2 >M3  – potential lubricating oils content

И1 >И2 >И3 >И4 – viscosity index

П1 < П2 < П3 - paraffin wax content

Chemical classification

1. paraffinic,
2. paraffinic- naphtenic,
3. naphtenic,
4. paraffinic-naphtenic-aromatic,
5. naphtenic-aromatic,
6. aromatic.

In according to density

• In according to viscosity mm2/s:

• Low viscous 0÷40

• Viscous           40÷80

• High viscous >80

• Jetybai Oil

• Sulfur content   - 0,1% mass:

• Content light fractions under 3500С %mass – 41,2

• Potential content of lubricating oils %–34,8

• Viscosity index – 95

• Paraffin wax, % mass. - 23,4

• Gasoline fraction of Tengiz oil

• (gasoline   (b.r.  65-180⁰С)

• Sulfur content  0,16%

• Octane Number  -39

• Density d²⁰₄ =0,7557

• Arenas - 15 %

• Cycloalkanes – 29%

• Alkanes  -56%

Natural Gases

• Raw natural gas comes from three types of wells:

• oil wells,

• gas wells,

• condensate wells.

 

• 1. Non-associated

• 2. Associated

• 3. Oil Refinery Gases

Non-Associated Gases

• - 98-99% СН4, other -   С3Н8, С4Н10, С5Н12

• Impurities: H2S, CO2, CS2, COS, RSH, N2 sometimes – He, Ar, also water.

• All components – saturated HC, (unsaturated HC do not present).

Associated Gases

• Natural gases which are extracted along with crude oil

• Besides methane - C2H6, C3H8, C4H10 and more heaver HC

• Also are present – H2S and not combustible components – N2, CO2, He, Ar

• Percentage of С 3Н 8-С 4Н 10 are bigger then in natural gases and varies from 30 to 70%.

• All HC saturated

• Sometimes gas can be dissolved in crude oil and it can be extracted just together with oil.

Gas condensate

• condensate wells produce free natural gas along with a semi-liquid hydrocarbon condensate.

• Gas condensate – is a mixture of gaseous hydrocarbons with light liquid hydrocarbons (C5-C12) which are found in vaporized state.

• Most condensates are composed of saturated hydrocarbons in the light gasoline range (butane, pentane and hexane).

• Gas produced from a field containing significant quantities of condensate is characterized as wet gas.

• Natural Gas Liquids (NGL) - liquid light hydrocarbons

• Liquefied Petroleum Gas (LPG) - gas is liquefied under very low T and high P

Gases are used for

• producing energy (gas turbine engine)

• producing motor fuel (fueling)

• as a source for petrochemistry

• in oil and gas refinery as fuel gases

• heating homes,

• heating water,

• cooking and refrigerating

Condensation

• Gas is converted into two phase system – liquid-gas

• Refriagents - air, water, ammonium, freon,, gases – propane and ethane

• About 70% of ethane and 90% of propane is liquefied

Oil Emulsions

• Dispersion – раздробленность

• Dispersed system – mixture where one substance is dispersed evenly throughout another

• And dispersed substance is suspended in the mixture

• Dispersed system is a dispersion of one substance  (dispersed phase) in the another (dispersion medium)

• dispersed phase (or internal phase) – dispersed particles

• continuous phase (or dispersion medium)

• Colloidal particles – aggregates of molecules

• Particle size ranges from 5 to 1000 nm. 

 

 

• Coagulation – cohesion of colloidal particles in to more bigger aggregates under gravity forces

 

 

• Sedimentation   - falling down to the bottom under gravity

 

Emulsion – is a system of two  immiscible (unblendable) liquids where one liquid is

evenly dispersed in the another as a droplets (globules)

 

• Surface tension is measured as the energy required to increase the surface area of a liquid by a unit of area.

 

• The surface tension of a liquid results from an imbalance of intermolecular attractive forces, the cohesive forces between molecules

 

 

• Substances which decrease the surface tension of liquid – surface active substances

• The less surface tension the less liquid resists to increasing their surface the either to cohere of droplets

 

 

• Emulsifiers – surfactants that promote emulsion formation and influence the ability to form an emulsion

 

• Demulsifies – surfactants that decrease the emulsion’s stability

 

Crude oil consist of:

- associated gas - 50-100 m3/t,

- reservoir water 200-300 kg/t,

- mineral salts under 35%

- other impurities (sand, clay etc.)

 

When crude oil is extracted

• Stable oil emulsions can be formed because of there is intensive blend of crude oil and reservoir water 

 

• The stability of oil emulsion is provided by formation of very stable adsorptive layer around the colloidal particle

            

 

• Hydrophilic: oil-in-water - is evenly dispersed in water

 

•     Hydrophobic: water-in-oil – is evenly dispersed in gasoline or in crude oil

 

• Over 95% of the crude oil emulsions - are hydrophobic emultions.

 

 

• The presence of water in crude oils is caused by:

• Natural mixing with oils during their migration

• Washing of tubing for scale dissolving

• Washing of oil for salts dissolving

• Seawater contamination during marine transportation.

 

• Not all emulsions are equal in stability. There are several factors that contribute to the stability of an emulsion:

 

• Size of Dispersed Water Drops

• Viscosity and Density of Crude Oil.

• Salinity of Brine.

• Age of Emulsions.

 

 

Emulsifies

 

• Oil surfactants   - sulfur contain compounds, resins, asphaltens, salts and others

 

• They adsorb on the surface of the droplet and form the protective layer which covers the droplet with a preserving layer thereby stabilizing the droplet.

 

Mechanical methods

• Settling - heating under 120-160°С under pressure 8-15 atm within 2-3 hours

 

• Separation occurs because of preservative layer begin dissolve in crude oil at high temperature.

• Centrifugation

• Filtration

 

• Several methods are used to break water-oil emulsions:

• Demulsifiers – They may decreasing and cancel the electrostatic forces of repulsion reacting between the water droplets. They also modify the wettability of the solid micro-particles absorbed at the interface or form some inverse emulsion oil-in-water, thus destabilizing the water-in-oil emulsion.

• Agitation – Mixing increases the collision number between particles and their coalescence. In practice, the mixing is natural during the flow of the emulsion in surface equipment.

 

Requirements to crude oil

 

• Before transportation:

• - water content   W water<0,5%;

• - salts content Р salt<200 mg/L.

 

• Before rectification:

• - water content W water<0,05%;

• - salts content Р salts<20 mg/L.

 

 

• Salts could hydrolyze and as result they can form a hydrochloric acid.

 

• Sand, Silts, Salt deposit and Foul Heat Exchangers

 

• Water Heat of Vaporization reduces crude Pre-Heat capacity

 

• Sodium, Arsenic and Other Metals can poison Catalysts

 

• Potassium, Calcium, Magnesium Chlorides and Bicarbonates 

 

• CaCl2 is hydrolyzed  about 10%

• MgCl2 - -   90%

 

•       М gCl ₂ + Н2О = М gОН Cl + Н Cl

•      CaCl2 + H2O = CaOHCl + HCl

 

 

• Sulfur corrosion

•   Fe + H₂S ® FeS + H₂

• FeS + 2HCl ® FeCl₂ + H₂S

Oil pretreatment:

• 1. Stabilization and separation

 

• 2. Desalting

 

• 3. Dewatering (dehydration or drying)

 

 

Pretreatment of Crude Oil

• Gas separators - for removing of dissolving gases from crude oil

 

 

• At the same time the separation of crude oil from mechanical impurities and the majority of water are occurred

 

 

Electrostatic Desalting

• Polar water molecules are replaced with a strong electrostatic charge which drives the separation water from oil

 

• Electrical desalting is the application of high-voltage electrostatic charges to concentrate suspended water globules in the bottom of the settling tank.

 

 

 

Atmospheric Rectification

 

Heat and mass exchange process for separation of liquid into its components by their boiling points using the countercurrent multiply contact between vapor and liquid

 

 

• Reflux (liquid) –condensed overhead liquid which returns to the upper part of column for better separation of products

 

 

•    Reflux (steam) – water steam which puts into bottom of column for better boiling

Refux (steam)

Reflux (steam) – water vapor is added into bottom of the column for decreasing of partial pressure of HC that decreases their boiling point

 

Due to reflux water vapor are intensively mixed with liquid hydrocarbons that promote the evaporation of low boiling HC

Trays Towers

• Main principle

 

• Continues contact between vapor and liquid and mutual concentration of definite hydrocarbons on the definite tray due to countercurrent flow

 

 

Packed column

• Packing materials are used in PC instead of trays as in the TC

 

• The main property of the PC is the specific surface area which determines the efficiency of the packing

• Packing materials are the different geometric forms from different materials.

• They have under 70 mm diameters and the ratio of surface area to the volume is above 500 times

• Differently shaped packing materials have different surface areas and void space between the packing. Both of these factors affect packing performance.

• Atmospheric rectification column

• Vacuum rectification column

• Tray column

• Packed column

• Simple columns

• Complicated columns

Vacuum rectification

• Under vacuum conditions

• The less pressure the less boiling point of liquid

• Vacuum distillation is used to distill or separate compounds that have a high boiling point or any compounds which might undergo decomposition on heating at atmospheric pressure.

 

• The vacuum is provided either by a water aspirator or by a mechanical pump.

• Vacuum distillation is distillation at a reduced pressure.

 

• Since the boiling point of a compound is lower at a lower external pressure,

• the compound will not have to be heated to as high a temperature in order for it to boil.

• Vacuum gas oils – are used for producing of lubricating oils

 

 

• Vacuum residue - for producing of lubricating oils, building and construction bitumen, oil coke, road asphalts, etc.

 

• Adsorption – adsorbent, adsorptive

• Absorption - absorbent, absorptive

 

• Desorption – 

 

• Chemical sorption – is the process where sorption is occurred by chemical interaction between molecules

• Gas absorption

• (also known as scrubbing) is an operation in which a gas mixture is contacted with a liquid for the purpose of preferentially dissolving one or more components of the gas mixture and to provide a solution of them in the liquid.

From the top

From the bottom

Extraction

Liquid-liquid extraction, also known as solvent extraction is a method to separate compounds based on their relative solubility in two different immiscible liquids, usually water and an organic solvent.

This is the separation of a substance from a mixture by preferentially dissolving that substance in a suitable solvent. By this process a soluble compound is usually separated from an insoluble compound.

 

 

Lecture 1

• Caustobolites – burned minerals – natural energy resource

• Firm state – peat, coal, anthracite

• Liquid state  – petroleum

• Gas state– natural and associated gases

• Mendeleyev D.I. – inorganic theory:

 CaC2 + H2O = C2H2

2FeC + 3H2O = Fe2O3 + C2H6 ­

FeC, TiC, Cr2C3, WC, SiC

• Sokolov M.A. - Space hypothesis

• He stated the dust cloud from which the Earth and other planets of the solar system were formed consisted of HC

• Lomonosov M.V. – Organic theory

• It is expelled from underground with heat, prepared from stone coal and brown coal, this black oily material…And this is a birth of different grade of combustible liquid and dry hard matter.

• H.Hefer,K. Engler 1888 year - the experiments were performed by evaporation of fish fat at 4000, 1 bar – oil, gases, water, different acids.

• Zelinskiy N.D. - 1919 year, - initial material-organic silt of mainly vegetative origin from lake Balkhash – evaporation products - crude pitch, coke and gases, gasoline, jet oil, heavy oil

• Coal – contain of hydrogen is about 5%

• Carbon (С) - 83 - 87 %

• Hydrogen (Н) - under  12-14 %

• Oxygen (О) - 0,05 - 3,6 %

• Nitrogen (N) – 0,00001 - 1,7 %

• Sulfur (S) – 0,02 - 14%

• Metals – V, Ni, Fe, Mg, Cr, Ti, Co, K, Na,

• Other elements - P,  Si, Ge

Fraction – part of mixture which consist of compounds evaporated within the given temperature range