20 Oilfield Review

When Rocks Get Hot: Thermal Properties ofReservoir Rocks

For many years, thermal stimulation has been the leading method for enhanced oil

recovery. Operators are using new techniques on heavy oil, tar sands, bitumen and oil

shale to liberate a vast store of liquid energy that could provide transportation fuels

for worldwide use for a century or more. Design of stimulation programs to produce

these resources efficiently over long periods of time requires better understanding

and measurement of thermal properties of rocks.

Evgeny ChekhoninAnton ParshinDimitri PissarenkoYury PopovRaisa RomushkevichSergey SafonovMikhail SpasennykhMoscow, Russia

Mikhail V. ChertenkovVladimir P. SteninLukoilMoscow, Russia

Oilfield Review Autumn 2012: 24, no. 3.Copyright © 2012 Schlumberger.For help in preparation of this article, thanks to YevgeniyaGelman, Houston; and Sidney Green and Roberto Suarez-Rivera, Salt Lake City, Utah, USA.Micarta® is a trademark of Norplex-Micarta.Plexiglas® is a registered trademark of ATOFINA.TerraTek is a mark of Schlumberger.

When reservoir fluid gets hot, its viscositydecreases, and a greater amount of fluid usuallycan be produced from the reservoir rock.Stimulation of conventional petroleum reservoirswith heat from injected steam or hot water hasbeen practiced for more than 50 years with some

remarkable successes. At the Kern River oil fieldin California, USA, for example, a massive pro-gram of cyclic steam injection, starting in the1960s, revived this supergiant field by increasingits production rate more than tenfold after ithad stagnated for decades (below). Today, about

> Kern River field, operated by Chevron near Bakersfield, California, USA.Production of heavy oil at Kern River field peaked within its first 10 years ofoperation and went into a 50-year decline. A program of thermal EOR bycyclic steam injection, accompanied by intensive infill drilling, rejuvenatedthe field in the 1960s, with high production levels continuing today.

Bakersfield

C a l i f o r n i a

Kern River field

U N I T E D S T A T E S

160,000

Oil p

rodu

ctio

n, b

bl/d

140,000

120,000

100,000

80,000

60,000

40,000

20,000

01900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

Year

Kern River Field Production History

Steam stimulation

Autumn 2012 2121Autumn 2012

22 Oilfield Review

60% of world oil production attributed to methodsof enhanced oil recovery (EOR) comes fromthermal stimulation. For the future, heavy oildeposits, tar sands, bitumen and oil shale—unconventional resources that represent Earth’slargest store of liquid fuels—are now beingcoaxed into releasing the oil they contain byhighly evolved forms of thermal recovery.1

This article examines an important, but oftenoverlooked, facet of thermal EOR—the thermalbehavior of reservoir rocks. Heating reservoir flu-ids means also heating large volumes of rock.And, while engineers designing a stimulation pro-gram usually know the thermal properties of thefluids, thermal properties of formation rocks are

often only loosely constrained, even though theseproperties help determine project economics.

After a brief look at an unusual thermal recov-ery operation taking place in the Yarega heavy oilfield in Russia, this article reviews the basic ther-mal properties of rocks and their measurementby often time-consuming conventional tech-niques. It also introduces a new measurementtechnique that employs optical sensors to rapidlyquantify thermal properties of rock. Since the1980s, scientists have scanned thousands of rocksamples with this optical method, including igne-ous and metamorphic rocks from deep scientificboreholes around the world and, more recently,

sandstones, shales and carbonates from manypetroleum reservoirs. The measurements haverevealed important new results about the hetero-geneity and anisotropy of thermal rock proper-ties. Investigators are also finding intriguingcorrelations between thermal and other petro-physical properties.

Research on cores from Russian oil fieldsrevealed surprising variability in reservoir ther-mal properties over spatial scales ranging fromcentimeters to tens of meters. Reservoir simula-tions show why it is important for engineers tounderstand this variability when they attempt topredict the outcome of thermal EOR. In the casessimulated, incorrect values caused estimates ofkey metrics for thermal stimulation to vary by upto 40% after just 10 years of production.

Yarega Oil FieldThe Yarega heavy oil field in the Komi Republic,Russia, illustrates the enormous potential ofthermal EOR. Discovered in 1932, and now oper-ated by Lukoil, Yarega lies in a prolific oil prov-ince west of the Ural Mountains called theTiman-Pechora basin (left). The reservoir holdslarge quantities of bitumen, a highly viscous,semisolid hydrocarbon formed during the pro-cess of petroleum generation. Natural bitumenoccurs at depths shallower than 370 m [1,200 ft]in many Russian oil fields, where it constitutes aresource estimated at more than 16 billion m3

[100 billion bbl] of oil. The pay zone in Yarega isat depths between 180 and 200 m [590 and 660 ft]and is composed of fine-grained quartz sandstoneof Middle Devonian age, with a porosity of 20% to25% and nearly 100% oil saturation.2

Production from the shallow reservoirs atthe Yarega field resembles a mining operation.Operators have used several configurations toheat the reservoir with steam and extract the lib-erated fluids. In the most common scheme, devel-oped in the 1970s and called the two-level, ortwo-horizon, system, steeply inclined steaminjection wells, drilled from overlying chambersreached by conventional mine shafts, penetrateand heat the reservoir. Additional mine shaftslead to a second set of galleries near the bottomof the reservoir, from which gently sloping pro-duction wells are drilled upward into the oil-bearing layers.

The effect of thermal stimulation on produc-tion from the Yarega field has been dramatic.Before thermal mining began in the late 1960s,production in conventional wells drilled fromthe surface recovered barely 4% of the originaloil in place. Thermal mining has raised the

> Yarega oil field, operated by Lukoil near Ukhta in the Komi Republic, Russia. Primary production of oilfrom bitumen in the shallow Yarega field started in the 1930s and peaked in the early 1950s. Productionwas declining rapidly around 1970, when new programs of thermal mining by steam injection wereintroduced.

R U S S I A

Yarega field

Ukhta

0 km

0 mi 200

200

KomiRepublic Timan-Pechora

basin

Oil p

rodu

ctio

n, M

g ×

103

Stea

m in

ject

ion,

Mg

× 10

3

0

250

1940 1950 1960 1970 1980 1990 2000

2,000

1,000

0

3,000

4,000

500

750

1,000

Year

Thermalmining

Oil production

Steaminjection

Autumn 2012 23

average recovery to 33% and in some zones, tonearly 70%. Lukoil recently introduced newforms of steam-assisted gravity drainage(SAGD) at Yarega, which are expected toincrease annual production to 3.5 million met-ric tons (3,500,000 Mg) [25 million bbl] of oil inthe near future.3

Thermal Rock PropertiesEngineers often use reservoir simulations todesign thermal EOR programs and predict theamount of additional oil attributed to thermalstimulation and its production rate over time atvarious wells in the field. To accomplish this, sim-ulators employ sophisticated algorithms to com-pute the evolution of temperature and heat flowwithin a reservoir after stimulation. These twoquantities—temperature and heat—are linkedby the thermal properties of rocks and their porefluids (see “Physics of Temperature and Heat,”page 24). The most important of these propertiesare volumetric heat capacity, thermal conductiv-ity and thermal diffusivity. Volumetric heat capac-ity specifies the amount of heat required to raisethe temperature of a unit volume of rock (and anypore fluids within) by one degree. Thermal con-ductivity determines where and how much heatflows in response to temperature differences inthe reservoir. Thermal diffusivity determinesthe speed at which a temperature front movesthrough the reservoir.4

A fourth property, the coefficient of thermalexpansion, links the thermal and mechanicalresponses of reservoir rocks by determining theamount by which a volume of rock expands as itstemperature increases. Knowledge of this prop-erty is needed, for example, to assess changes inmechanical wellbore stability and in caprockintegrity caused by changing temperature condi-tions in the reservoir.

In the enormous volume of petrophysical datafrom geologic formations around the world, thereare relatively few measurements of thermal prop-erties of reservoir rocks made in the laboratory orin situ. As a result, engineers often calculatethese thermal properties by using crude predic-tive models, without reference to actual mea-surements on core samples. This lack of thermalmeasurements represents a big gap in currentknowledge of reservoir rock properties.

One reason for the lack of data is that it isdifficult to measure thermal rock properties.The long-time standard for measuring thermalconductivity, the divided bar method, obtainsthe property by placing a disk-shaped sample ofmaterial between two cylindrical metal barsheld at constant temperature (above right).

After a steady state is reached, the sample’sthermal conductivity is estimated by comparingthe temperature drop across its faces with thedrop across those of reference materials of knownconductivity flanking the sample. The divided

bar method defines the standard for accuracy inmeasuring thermal conductivity, but is time-consuming. The measurement of a typical cylin-drical sample, 3 to 5 cm [1.2 to 2.0 in.] indiameter and 1 to 3 cm [0.4 to 1.2 in.] long, takes

1. For more on Kern River and modern methods of thermalEOR: Curtis C, Kopper R, Decoster E, Guzmán-Garcia A,Huggins C, Knauer L, Minner M, Kupsch N, MarinaLinares L, Rough H and Waite M: “Heavy-Oil Reservoirs,”Oilfield Review 14, no. 3 (Autumn 2002): 30–51.Alboudwarej H, Felix J, Taylor S, Badry R, Bremner C,Brough B, Skeates C, Baker A, Palmer D, Pattison K,Beshry M, Krawchuk P, Brown G, Calvo R, Cañas Triana JA,Hathcock R, Koerner K, Hughes T, Kundu D, López deCárdenas J and West C: “Highlighting Heavy Oil,”Oilfield Review 18, no. 2 (Summer 2006): 34–53.Allix P, Burnham A, Fowler T, Herron M, Kleinberg Rand Symington B: “Coaxing Oil from Shale,”Oilfield Review 22, no. 4 (Winter 2010/2011): 4–15.Butler RM: Thermal Recovery of Oil and Bitumen.Englewood Cliffs, New Jersey, USA: Prentice Hall, 1991.For a comprehensive report on methods developed in theformer Soviet Union: Bokserman AA, Filippov VP,Filanovskii VYu: “Oil Extraction,” in Krylov NA,Bokserman AA and Stavrovsky ER (eds): The Oil Industry

>Measuring rock thermal conductivity. The divided bar method is thestandard laboratory technique for determining rock thermal conductivity. Themethod sandwiches a disk-shaped rock sample between brass plates—twoends of a divided bar—held at different temperatures. The sample is flankedby disks of a reference material of known thermal conductivity; fused silica,with a thermal conductivity of 1.38 W/m°K, is a commonly used reference.After a steady state is reached, as indicated by steady temperatures in thetransducer wells, the sample’s thermal conductivity is determined bycomparing the temperature drop across its length with the drop across thereference material. The hydraulic ram compresses samples formeasurements under high pressure. (Adapted from Popov et al,reference 12.)

50 mm

Steel Hydraulic ram

Micarta

Micarta

Fused silicaTemperature

transducerwells

MicartaCopper

Copper

Copper

Copper

Micarta

Brass cold bath

Brass warm bath

Rock or cell

Rubber

Steel

Steel head plate

Increasing temperature

of the Former Soviet Union: Reserves and Prospects,Extraction, Transportation. Amsterdam: Gordon andBreach Publishers (1998): 69–184.For a recent comprehensive review of enhanced recovery:Alvarado V and Manrique E: “Enhanced Oil Recovery:An Update Review,” Energies 3, no. 9 (2010): 1529–1575.

2. Mamedov YG and Bokserman AA: “Development ofHeavy Oils and Natural Bitumens in the Former SovietUnion and Eastern and Central Europe: State-of-the-Artand Outlook,” Proceedings of the Sixth UNITARInternational Conference on Heavy Crude and Tar Sands,Houston, February 12–17, 1995: 11–18.Chertenkov MV, Mulyak VV and Konoplev YP: “TheYarega Heavy Oil Field—History, Experience, andFuture,” Journal of Petroleum Technology 64, no. 4(April 2012): 153–160.

3. Chertenkov et al, reference 2.4. The three thermal properties are not independent;

thermal diffusivity is the ratio of thermal conductivity tovolumetric heat capacity.

(continued on page 27)

Thermal properties connect temperature andheat flow, which are fundamental conceptsin physics and classical thermodynamics.Temperature is a measure of the averageenergy content of macroscopic bodies—solids,liquids and gases—while heat flow representsthe transfer of thermal energy between bodiesor regions at different temperatures.Temperature has its own basic SI unit,degrees kelvin (°K), with absolute zero (0°K)as the lowest possible temperature. In thecommonly used Celsius scale (°C), thefreezing point of water is taken as 0°C, placingabsolute zero at −273.15°C. A difference ofone degree in either scale represents thesame change in temperature.

Volumetric heat capacity, thermal conduc-tivity, thermal diffusivity and the coefficient ofthermal expansion are the main thermal prop-erties of interest for engineers. Volumetricheat capacity (VHC) measures the amount ofheat needed to raise the temperature of a unitvolume (1 m3) of a substance by 1°K (below).The original unit of heat, the Calorie, wasdefined in 1824, by the French physicist andchemist Nicolas Clément, as the amount ofheat needed to raise 1 kg of water by 1°C. Thelater discovery, by the English physicist andbrewer James Prescott Joule, of the equivalenceof heat and mechanical energy led toreplacement of the Calorie as a basic physicalunit by the derived unit for mechanical orkinetic energy, kg m2/s2—now called the

joule (J). Clément’s Calorie, which is equiva-lent to about 4.2 kJ, survives today as the com-mon unit for measuring the energy content offood. Since 1 m3 of water weighs 1,000 kg,the volumetric heat capacity of water is about4.2 MJ/m3°K. The volumetric heat capacityof rocks is generally lower, in the range1 to 4 MJ/m3°K (next page, bottom left).

Temperature differences drive the flow ofthermal energy—the flow of heat (above).Like the flow of fluid or electrical current,heat flow has both magnitude and directionand is therefore represented as a vectorquantity. The magnitude of the heat flowvector gives the amount of thermal energy persecond crossing a surface of unit area orientedperpendicular to the direction of the vector.The units of heat flow are thus energy per unittime per unit area, or power per unit area andare conventionally taken as watt per squaremeter (W/m2).

24 Oilfield Review

Physics of Temperature and Heat

> Volumetric heat capacity. Volumetric heat capacity is the amount of thermalenergy in the form of heat needed to raise the temperature of a unit volume ofmaterial—1 m3 in SI units—by 1°K, starting from a given temperature T0.There can be no change of phase, such as melting, during the temperaturerise. The volumetric heat capacity of dry sandstone typically falls betweenthat of bitumen and water.

26°C

25°C

1.7 MJ

Bitumen

2.7 MJ

Sandstone

4.2 MJ

Water

Volumetric Heat Capacity

1 m 1 m

1 m

> Heat flow. Heat flow is a vector quantity, q,whose magnitude, at any point in a material,gives the amount of thermal energy flowing perunit time across a surface of unit area orientedperpendicular to the vector direction. If theheat flow vector (red arrow) is oriented at anangle, θ, to the surface, energy flow across thesurface is reduced by the cosine of the angle.

Heat Flow

1 m

1 m

qHeat flowvector

θ

Thermal conductivity provides the quanti-tative connection between heat flow andtemperature differences (right). It can bedefined by considering a cube of homoge-neous material with a temperature differ-ence between two opposite faces. Theamount of heat flowing through the cube,from the high- to low-temperature faces, is

proportional to the temperature differencedivided by the distance between the faces.The constant of proportionality is the ther-mal conductivity, which thus has units ofW/m°K. The thermal conductivity of water isabout 0.6 W/m°K. The thermal conductivityof rocks is generally higher, in a range fromabout 0.5 to 6.5 W/m°K.

Some materials, including rocks, exhibitmacroscopic thermal anisotropy; for example,different numerical values for thermal con-ductivity result from measurements acrossdifferent pairs of opposing faces on a cube ofthe material. The simplest type of thermalanisotropy, common in rocks, arises when thematerial has a layered structure at fine scales.The thermal conductivity in the direction per-pendicular to the layering is generally lowerthan the conductivity in any direction parallelto the layering.

Autumn 2012 25

> Thermal properties of common materials.

Carbon dioxide

Air

Motor oil, grade SAE 50Bitumen

GlassCarbon

Methanol

Water

Stainless steel

LeadSteel

Nickel

AluminumGoldCopperSilver

0.01

0.1

1.0

10

100

1,000

Sandstone

Shale, siltstone

Limestone

Thermal Conductivity,W/m°K

Air, dry at sea level

Lead

0

1

2

3

4

5

Petroleum

BitumenEthanol

Paraffin

Gold

Ammonia

Sandstone

Shale, siltstone

Limestone

Copper

Humantissue

Water at 25°C

Water at 100°C

Volumetric HeatCapacity, MJ/m3°K

> Thermal conductivity. Thermal conductivityrelates temperature gradients and heat flow. Ablock of material with a temperature differenceΔT across two opposing faces separated by adistance Δz sustains a heat flow whosemagnitude is proportional to the temperaturedifference divided by the distance (top). Theproportionality constant is the block’s thermalconductivity k. Many materials displayanisotropic thermal conductivity, in whichtemperature differences placed acrossdifferent pairs of opposing faces of a cuberesult in different magnitudes of heat flow(bottom). Thermal anisotropy is common infinely layered materials, such as rocks, wherethe thermal conductivity parallel to layers (k ||)is up to 50% higher than thermal conductivityperpendicular to layers (k⊥).

qz

q

qx

T

T

TxΔ

T + TΔq = –k Δz

TΔ

T + TΔ

T + TΔqz = –k Δz

TΔ qx = –k ΔxTΔ

zΔ

zΔ

Thermal Conductivity

Anisotropic Thermal Conductivity

26 Oilfield Review

> Thermal expansion. The coefficient of thermal expansion measures afractional change in linear dimension of a uniform cube for a unit temperaturerise. Each side of the cube may expand by a different amount in anisotropicmaterials.

1 m + Δx

Block of materialat temperature T0

Block of materialat temperature T0 + 1°K

1 m 1 m1 m + Δy

1 m

1 m

+Δ

z

Thermal Expansion

> Thermal diffusivity. Thermal diffusivity controls the rate at whichtemperature rises in a uniform block of material when more heat is flowinginto the block than flowing out. If an initial temperature gradient is establishedbetween the block and its surroundings, the heat fluxes in and out aredetermined by the block’s thermal conductivity, while the temperature risecaused by the heat imbalance is determined by the block’s volumetric heatcapacity. Thermal diffusivity is thus the ratio of thermal conductivity tovolumetric heat capacity.

qout

T

qout

q in q in

Time0 + 1 sTime0

T + TΔ

Thermal Diffusivity

Volumetric heat capacity and thermalconductivity combine to determine a thirdthermal property, called thermal diffusivity(left). Imagine a cube of uniform materialwith more heat flowing in through the bot-tom face than is flowing out through the topface. The difference in the two flows is therate at which heat is being added to thecube, which will cause its temperature torise. Since the rate of heat flow is deter-mined by the material’s thermal conductivityand the temperature increase by its volumet-ric heat capacity, the rate of temperatureincrease is obtained by dividing the thermalconductivity by the volumetric heat capacity.This ratio, called thermal diffusivity, governsthe speed at which temperature changespropagate through a material.

Temperature is not the only property thatchanges when a cube of material is heated:Most substances also expand. The rate oflinear expansion—defined as the fractionalincrease in length of a cube’s sides per unittemperature rise—is called the coefficientof linear thermal expansion (below left).The thermal expansion of reservoir rocksprovides an important link between the ther-mal and mechanical responses of the reser-voir during thermal EOR.

Thermal conductivity, heat capacity,thermal diffusivity and the coefficient ofthermal expansion are properties that applyto macroscopic chunks of matter. The con-cepts break down when applied to individualatoms or molecules of a substance. Like allmacroscopic properties—including petro-physical properties such as porosity, permea-bility and electrical conductivity—thermalproperties may vary from point to point in arock formation and depend on its tempera-ture and pressure.

Autumn 2012 27

5. Beck A: “A Steady State Method for the RapidMeasurement of the Thermal Conductivity of Rocks,”Journal of Scientific Instruments 34, no. 5 (May 1957):186–189.Pribnow DFC and Sass JH: “Determination of ThermalConductivity for Deep Boreholes,” Journal of GeophysicalResearch 100, no. B6 (June 10, 1995): 9981–9994.Beck AE: “Methods for Determining Thermal Conductivityand Thermal Diffusivity,” in Haenel R, Rybach L andStegena L (eds): Handbook on Terrestrial Heat FlowDensity Determination. Dordrecht, the Netherlands:Kluwer (1988): 87–124.

6. Jaeger JC: “The Measurement of Thermal Conductivitywith Cylindrical Probes,” EOS Transactions AmericanGeophysical Union 39, no. 4 (1958): 708–710.

about 10 to 15 minutes. In addition, laboratorytechnicians must spend an hour or two cutting,trimming and polishing the disk to ensure goodthermal contact with the heating bars. This laststep is difficult to complete with fractured orpoorly consolidated reservoir rocks.5

Alternatives to the steady state method aretransient methods in which a scientist applies apulse of heat to the sample, usually with a needle-shaped probe, and records the temperatureresponse at one or more locations on the sample(right). Thermal conductivity or diffusivity isthen calculated from a theoretical model thatpredicts how the material should respond in thegiven configuration. One configuration of thistransient line source method, which is useful formeasuring loose samples such as unconsolidatedsediments and soils, applies the pulse of heatalong a thin wire that carries a temperature sen-sor at its midpoint. This wire is inserted, like ahypodermic needle, into the material and mea-sures the temperature as a function of time. Inanother configuration, a scientist places theneedle-shaped probe with its sensor on the flattop of a cylindrical core and records this surface’stemperature response to a pulse of heat.6

Because thermal conductivity relates twodirectional quantities, the temperature gradientand the heat flow vector, its value may depend onthe direction of measurement, for example, onthe direction of the temperature gradientimposed on a sample. The line source methodprovides a convenient way of characterizingdirectional dependence: Any variation of thetemperature response as the needle is rotatedthrough various directions on the surface of thecore indicates that its thermal conductivity isanisotropic—heat flows preferentially in certaindirections through the rock.

The most common form of anisotropy incrustal rocks is the result of features such as thinlayers or oriented fractures that determine thedirectional characteristics of a rock’s bulk physi-cal properties. The simplest example is fine layer-ing or bedding, which is present in nearly allclastic reservoir and source rocks—sandstonesand shales—and distinguishes the direction per-pendicular to the layers from the directions par-allel to the layers. This type of anisotropy inducedby layering—also called transverse isotropy,axial anisotropy or cross anisotropy—may bepresent in sedimentary and igneous rocks perme-ated by thin oriented fractures, and in metamor-phic rocks that have been compressed strongly in

>Measuring thermal conductivity of unconsolidated or anisotropic materials. The line source methoddetermines thermal conductivity by placing a thin probe with a heating element and temperaturesensor in contact with a sample. A theoretical model predicting the temperature response to a pulse ofheating is used to calculate the sample’s thermal conductivity. For unconsolidated samples, the probeis inserted, like a hypodermic needle, inside the material (top). For solid rocks, the probe is attached tothe bottom of a Plexiglas block placed on the surface of the sample. For laminated samples cut at anangle to the measurement surface, the response of the probe changes as it rotates through variousdirections (bottom). Variations in response with angle may be used to determine the thermal anisotropyof layered rocks.

Sample

Sample

Azimuth, degree0 30 60 90 120 150 180

90 120 150 180 210 240 270

Azimuth, degree

Maximum

Maximum

Maximum

Maximum

Minimum

Minimum

Minimum

Minimum

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mal

con

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ivity

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mal

con

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Needle probe forthermal propertymeasurements

Connection wires

Connectionwires

Pressure-resistantsteel cell

Drainagechannel

Plunger systemfor pressure control

Unconsolidatedrock sample

Von Herzen R and Maxwell AE: “The Measurement ofThermal Conductivity of Deep-Sea Sediments by aNeedle-Probe Method,” Journal of GeophysicalResearch 64, no. 10 (October 1959): 1557–1563.Waite WF, Gilbert LY, Winters WJ and Mason DH:“Estimating Thermal Diffusivity and Specific Heat fromNeedle Probe Thermal Conductivity Data,” Review ofScientific Instruments 77, no. 4 (April 2006): 1–5.Woodside W and Messmer JH: “Thermal Conductivity ofPorous Media. I. Unconsolidated Sands,” Journal ofApplied Physics 32, no. 9 (September 1961): 1688–1699.Woodside W and Messmer JH: “Thermal Conductivity ofPorous Media. II. Consolidated Rocks,” Journal ofApplied Physics 32, no. 9 (September 1961): 1699–1706.

28 Oilfield Review

one direction and, as a result, have acquired a distinctive planar fabric.7

In finely layered rocks, the value of thermal conductivity in the direction perpendicular to the layers—and therefore the heat flow for a given temperature drop—is usually 5% to 30% lower than its value in directions parallel to the layers; in some rocks, the difference is as high as 50%. The physics and mathematics of thermal anisotropy are similar to those of electrical

anisotropy, which is critical to the proper evalua-tion of laminated reservoirs.8

Measuring Thermal Properties by Optical ScanningMost of the fundamental science of rock thermal properties was carried out in two waves. The first took place in the 1930s, when scientists began to unravel the thermal structure of Earth’s interior; the second occurred during the years of the plate

tectonics revolution of the 1960s and 1970s, when scientists recognized that the Earth’s internal heat and its flow to the surface were driving forces of global tectonics. Much of the latter research was devoted to mapping heat flow through ocean basins, which shows the thermal signature of convection patterns in the Earth’s deep interior (below).9 Scientists study thermal rock properties as a necessary component for heat flow determination and to understand the

> Earth’s surface heat flow. Flow of heat from the Earth’s deep interior to the surface is a driving force of global tectonics. A map of surface heat flow highlights ocean ridges, where magma derived from partial melting of the upper mantle rises to the surface to create new oceanic crust (bottom, adapted from Davies and Davies, reference 9). To produce this map, Davies and Davies compiled nearly 40,000 measurements, from which correlations of heat flow with geologic regions were derived to extend the discrete measurements using a digital map of global geology. At ocean ridges (top right), heat flow is dominated by convection—the movement of hot material (white arrows) from depth to the surface. Over the continents, average heat flow is determined by the geothermal gradient—the variation of temperature with depth—and the thermal conductivity of crustal rocks. The graph shows geothermal gradients in the shallow crust for several regions of the US (top left). Each geothermal gradient corresponds to a different value of surface heat flow.

Oilfield Review SUMMER 12 Thermal Properties Fig. 6ORSUM 12-THMPTS 6

23 to 45 45 to 55 55 to 65 65 to 75 75 to 85 85 to 95 95 to 150 150 to 450

Heat flow, mW/m2

Surface Heat Flow

Cross Section of Ocean Ridge

Shallow Geothermal GradientsTemperature, °C

North American

PlateEurasian

Plate

Surface heat flow, mW/m2

0

0 50 100 150 200 2500

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Battle Mountain, NevadaBasin and Range provinceEast of Rocky MountainsSierra Nevada Mountains

Autumn 2012 29

potential of geothermal energy. Beginning in the1980s, researchers looked at thermal propertiesof sedimentary rocks to provide input to modelthe thermal history of basins in early quantita-tive attempts at petroleum system modeling.10

These lines of research converged in a study ofthermal and other petrophysical measurementson rocks from deep scientific boreholes, includingthe 12,262-m [40,230-ft] Kola Superdeep Boreholein the Soviet Union, the deepest hole ever drilled.The work was driven by the recognition thatthermal properties measured along the track oflong scientific boreholes were much more hetero-geneous than previously imagined. Scientistsrealized that new methods were needed to char-acterize the thermal properties of rocks, includ-ing better methods of measuring these propertiesin situ, as well as laboratory methods that workedmore rapidly and at higher resolution on smallercore samples.11

In the 1990s, scientists from Russia, Germanyand the US participated in a joint study of majorlaboratory methods for measuring thermal con-ductivity, focusing on cores from the superdeepKTB borehole in Germany.12 One method in thisstudy used an optical device developed in theearly 1980s in the former Soviet Union. Unlikeprior techniques for measuring thermal proper-ties, the optical method is contactless—no sen-sor touches the material; instead, the device usesremote optical thermal sensors to scan the sam-ple surface for the thermal signature of a con-stant, focused heat source (right). The sourceand sensors move together along the sample—acore, for example—in a fixed arrangement that

7. Transverse isotropy, axial anisotropy and crossanisotropy are synonymous terms referring to theparticular directional character of materials in whichproperties have the same values in all directions parallelto planes of isotropy and different values perpendicularto or crossing the planes of isotropy; this perpendiculardirection is the axis of cylindrical symmetry.

8. Thin oil-bearing layers in laminated reservoirs significantlyincrease the resistance to current flow, but only in thedirection perpendicular to the beds. A resistivity loggingtool that measures resistance in directions parallel to thebeds generally will not detect the presence of oil. Formore on the anisotropy of finely layered formations:Anderson B, Barber T, Leveridge R, Bastia R, Saxena KR,Tyagi AK, Clavaud J-B, Coffin B, Das M, Hayden R,Klimentos T, Minh CC and Williams S: “TriaxialInduction—A New Angle for an Old Measurement,”Oilfield Review 20, no. 2 (Summer 2008): 64–84.

9. The earliest systematic studies of Earth’s surface heatflow were a series of papers in the late 1930s:Anderson EM: “The Loss of Heat by Conduction fromEarth’s Crust,” Proceedings of the Royal Society ofEdinburgh 60, part 2. Edinburgh, Scotland: Robert Granand Son, Ltd. (1939–1940): 192–209.Benfield AE: “Terrestrial Heat Flow in Great Britain,”Proceedings of the Royal Society of London A 173,no. 955 (December 29, 1939): 428–450.

> Principle of the optical scanning method. Optical scanning provides a fast, contactless method ofmeasuring thermal properties (top right). This method determines thermal conductivity and thermaldiffusivity by heating a spot on the sample with a moving optical heat source—a laser or focusedelectric light (top left). Three infrared sensors, moving in tandem with the source, measure temperatureat the surface of the sample. Sensor 1 is situated ahead of the heat source along the scan lineto register surface temperature before the sample is heated. Two trailing sensors register thetemperature rise induced by the heating: Sensor 2 measures along the scan line, and Sensor 3, alonga parallel line (dashed black). A theoretical model predicting the temperature at these two locations asa function of time is used to calculate the thermal conductivity and thermal diffusivity at variouslocations under the scan line. By scanning the sample in three different directions, the method candetermine anisotropic thermal properties of laminated rocks (bottom right).

Infraredsensors

Temperatureprofiles

2

1

3

Opticalheatsource

Infraredsensor

Scan line

Sample

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Krige LJ: “Borehole Temperatures in the Transvaal andOrange Free State,” Proceedings of the Royal Society ofLondon A 173, no. 955 (December 29, 1939): 450–474.Bullard EC: “Heat Flow in South Africa,” Proceedings ofthe Royal Society of London A 173, no. 955 (December29, 1939): 474–502.Birch AF and Clark H: “The Thermal Conductivity ofRocks and Its Dependence on Temperature andComposition, Part I,” American Journal of Science 238,no. 8 (August 1940): 529–558.Birch AF and Clark H: “The Thermal Conductivity ofRocks and Its Dependence on Temperature andComposition, Part II,” American Journal of Science 238,no. 9 (September 1940): 613–635.Many researchers contributed to mapping surface heatflow over the globe and unraveling its relation to platetectonics. For more: Sclater JG and Francheteau J:“The Implications of Terrestrial Heat Flow Observationson Current Tectonic and Geochemical Models of theCrust and Upper Mantle of the Earth,” GeophysicalJournal of the Royal Astronomical Society 20, no. 5(September 1970): 509–542.The most recently published compilation of surface heatflow data: Davies JH and Davies DR: “Earth’s SurfaceHeat Flux,” Solid Earth 1, no. 1 (February 22, 2010): 5–24.

10. Brigaud F, Chapman DS and Le Douaran S: “EstimatingThermal Conductivity in Sedimentary Basins UsingLithologic Data and Geophysical Well Logs,”AAPG Bulletin 74, no. 9 (September 1990): 1459–1477.

McKenna TE, Sharp JM Jr and Lynch FL: “ThermalConductivity of Wilcox and Frio Sandstones in SouthTexas (Gulf of Mexico Basin),” AAPG Bulletin 80, no. 8(August 1996): 1203–1215.For more on petroleum system modeling: Al-Hajeri MM,Al Saeed M, Derks J, Fuchs T, Hantschel T, Kauerauf A,Neumaier M, Schenk O, Swientek O, Tessen N,Welte D, Wygrala B, Kornpihl D and Peters K: “Basinand Petroleum System Modeling,” Oilfield Review 21,no. 2 (Summer 2009): 14–29.

11. Orlov VP and Laverov NP (eds): Kola Superdeep Well:Scientific Results and Research Experience. Moscow:Technoneftegaz, 1998 (in Russian).Burkhardt H, Honarmand H and Pribnow D: “TestMeasurements with a New Thermal ConductivityBorehole Tool,” Tectonophysics 244, nos. 1–3 (April 15,1995): 161–165.

12. Popov YA, Pribnow DFC, Sass JH, Williams CF andBurkhardt H: “Characterization of Rock ThermalConductivity by High-Resolution Optical Scanning,”Geothermics 28, no. 2 (April 1999): 253–276.KTB is the Kontinentales Tiefbohrprogramm derBundesrepublik Deutschland, or German ContinentalDeep Drilling Program. For more on the KTB borehole:Bram K, Draxler J, Hirschmann G, Zoth G, Hiron S andKühr M: “The KTB Borehole—Germany’s SuperdeepTelescope into the Earth’s Crust,” Oilfield Review 7, no. 1(January 1995): 4–22.

30 Oilfield Review

allows the first sensor to register the ambientsurface temperature under laboratory condi-tions. After a spot on the surface has been heatedby the source—either a laser or a focused elec-tric light—one or two trailing sensors record therise in temperature along lines parallel to thetrace of the heated spot.13

Optical scanning uses tailored theoreticalmodels to determine thermal properties from the

recorded temperature profiles. According to amodel for the arrangement with two thermal sen-sors flanking the heat source, the maximum tem-perature rise seen by the trailing sensor is directlyproportional to the source power, in watts, andinversely proportional to the product of the source-sensor separation and the sample’s thermal con-ductivity. This model can be inverted for theunknown thermal conductivity, given the mea-

sured temperature rise, source-to-sensor distancesand source power. Alternatively, thermal conduc-tivity can be determined by comparing the tem-perature rise in the sample with that in a standardmaterial of known conductivity placed next to it inthe scan line. Another common configuration addsa second trailing sensor offset from the main scanline and uses two different standards flanking thesample to determine both thermal diffusivity andthermal conductivity. Aligning the axis of the scanalong various directions through the rock allowscharacterization of the thermal conductivity of ananisotropic sample; full characterization requiresscans along three distinct directions lying in twononparallel planes.

Nearly all of the core samples from the KTBborehole were crystalline metamorphic rocks,chiefly amphibolites and gneisses, possessing a dis-tinctive foliation and requiring measurement ofthermal conductivity parallel and perpendicular totheir planar fabric.14 The joint international study ofcores from the KTB borehole demonstrated thatmeasurements of thermal properties by opticalscanning compare well in precision, or repeatabil-ity, and in accuracy with measurements made by thedivided bar and line source methods (left). Thedivided bar measurements were conducted with adevice maintained and continually improved sincethe late 1960s by the US Geological Survey; the linesource measurements were conducted with a unitspecially constructed at the Technische UniversitätBerlin to work on cores from deep scientific wells.Differences between optical scanning and dividedbar measurements averaged 2.1%, with a standarddeviation of 6.5%; the closest agreement was formeasurements in directions parallel to rock folia-tion. Differences between optical scanning and linesource measurements were generally less than 5%.15

The accuracy and reliability of thermal propertiesmeasured by optical scanning have since been con-firmed on thousands of core samples. Many of thesecores come from deep scientific wells drilled intolarge impact structures such as the Puchezh-Katunkiimpact structure in Russia, the Ries impact structurein Germany, the Chesapeake crater in the US and theChicxulub crater in Mexico.16 This work establishedthat optical scanning measurements can be accurateto within 1.5% for thermal conductivity within therange 0.1 to 50 W/m°K and to within 2% for thermaldiffusivity in the range 0.1 × 10–6 to 5 × 10–6 m2/s. Theremote sensing and nondestructive nature of opticalscanning allows easy, repeated testing of samplesof a variety of sizes; the laboratory instrument usedin the scientific studies characterizes samples from1 to 70 cm [0.4 to 28 in.] long.

Optical scanning measurements are also rela-tively immune to the shape and quality of the sample

> Thermal properties of rock samples from the superdeep KTB borehole. A study of core samples fromthe KTB borehole in Germany (top) demonstrated that measurements of thermal conductivity by opticalscanning compare well with measurements made by the divided bar and line source methods. Thecrossplot at upper left, for example, shows good agreement between optical scanning measurementsof thermal conductivity and divided bar measurements on 36 different samples cut from the KTB cores.Scientists prepared this collection so that the same physical rock sample could be used in bothinstruments. The remaining crossplots compare one method against another when two different rocksamples are cut from the same core. Open diamonds represent measurements in the direction parallelto the rock foliation; solid diamonds represent measurements perpendicular to the foliation. (Adaptedfrom Popov et al, reference 12.)

Thermal conductivity by line source, W/m°K

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Autumn 2012 31

surface, tolerating up to 1 mm [0.04 in.] of roughnesswith little loss of accuracy. The scan speed is routinelyset between 1 and 10 mm [0.04 and 0.4 in.] per sec-ond, which usually allows a throughput of about onesample per minute. Slower speeds and a smaller dis-tance between the heating spot and temperature sen-sor enlarge the measurement’s depth of investigation,which can be up to 3 cm in samples with moderate tohigh thermal conductivity.

A new instrument developed at SchlumbergerMoscow Research Center and engineered at theSchlumberger Innovation Center in Salt Lake City,Utah, USA, has further refined the specificationsfor rapid, high-resolution optical measurement ofthermal properties (right). This instrument forrock profiling, housed at TerraTek Rock Mechanicsand Core Analysis Services laboratory, can detectheterogeneity in thermal conductivity and thermaldiffusivity—or volumetric heat capacity, as calcu-lated from these two quantities—with a resolutionbetter than 0.4 mm [0.016 in.] at a core scanningvelocity of 3.0 mm/s [0.12 in./s] (below right).17

13. Popov Yu A: “Theoretical Models for Determination ofthe Thermal Properties of Rocks on the Basis of MovableSources of Thermal Energy, Part I,” Geologiya i Razvedka(Geology and Prospecting) no. 9 (September 1983): 97–105(in Russian).Popov Yu A: “Theoretical Models for Determinationof the Thermal Properties of Rocks on the Basis ofMovable Sources of Thermal Energy, Part II,” Geologiya iRazvedka (Geology and Prospecting) no. 2(February 1984): 81–88 (in Russian).Popov Yu A: “Peculiarities of the Method of DetailedInvestigations of Rock Thermal Properties,” Geologiya iRazvedka (Geology and Prospecting) no. 4 (April 1984):76–84 (in Russian).

14. Foliation is the layered fabric—the orientation,arrangement and texture of minerals, grains and otherconstituents in rock—of metamorphic rocks that havebeen strongly compressed in one direction.

15. Popov et al, reference 12.16. Popov Yu, Pohl J, Romushkevich R, Tertychnyi V and

Soffel H: “Geothermal Characteristics of the Ries ImpactStructure,” Geophysical Journal International 154, no. 2(August 2003): 355–378.Popov Yu, Romushkevich R, Korobkov D, Mayr S,Bayuk I, Burkhardt H and Wilhelm H: “ThermalProperties of Rocks of the Borehole Yaxcopoil-1 (ImpactCrater Chicxulub, Mexico),” Geophysical JournalInternational 184, no. 2 (February 2011): 729–745.Mayr SI, Burkhardt H, Popov Y, Romushkevich R,Miklashevskiy D, Gorobtsov D, Heidinger P andWilhelm H: “Physical Rock Properties of the EyrevilleCore, Chesapeake Bay Impact Structure,” in Gohn GS,Koeberl C, Miller KG and Reimold WU (eds): TheICDP-USGS Deep Drilling Project in the Chesapeake BayImpact Structure: Results from the Eyreville Core Holes.Boulder, Colorado, USA: The Geological Society ofAmerica, Special Paper 458 (2009): 137–163.The Chicxulub crater is believed to be an imprintof the catastrophic asteroid impact that ended theage of dinosaurs. For more: Barton R, Bird K,Garcia Hernández J, Grajales-Nishimura JM,Murillo-Muñetón G, Herber B, Weimer P, Koeberl C,Neumaier M, Schenk O and Stark J: “High-ImpactReservoirs,” Oilfield Review 21, no. 4 (Winter 2009/2010):14–29.

17. Popov Yu, Parshin A, Chekhonin E, Gorobtsov D,Miklashevskiy D, Korobkov D, Suarez-Rivera R andGreen S: “Rock Heterogeneity from Thermal ProfilesUsing an Optical Scanning Technique,” paper ARMA12-509, presented at the 46th US Rock Mechanics/Geomechanics Symposium, Chicago, June 24–27, 2012.

> High-resolution optical scanner at the Schlumberger Innovation Center inSalt Lake City, Utah.

Thermal conductivity range 0.2 to 6.0 W/m°K

(0.1 to 2.5) × 10–6 m2/sThermal diffusivity range

4%Accuracy of thermal conductivity

5%Accuracy of thermal diffusivity

Better than 0.4 mmSpatial resolution in rock profiling

3.0 mm/sScanning velocity

Parameter Value

>Resolution and repeatability of optical scanning. Two optical scans (red and blue, top) of a gravellysandstone core illustrate the strong heterogeneity of thermal properties in rocks and the repeatabilityof optical measurements. Excess surface temperature—the temperature rise measured along a scanline (yellow, bottom) after heating by the laser—is proportional to thermal conductivity. The differencebetween the maximum and the minimum, divided by the average, gives a measure of propertyheterogeneity.

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32 Oilfield Review

Thermal Properties of Reservoir Rocks:A Growing DatabaseBecause scientists are now better able to mea-sure thermal properties, new avenues of petro-physics are opening up. Like many rockproperties, thermal conductivity depends in com-plex ways on the composition and distribution ofminerals in the rock matrix and fluids in its porespace. Studies going back to the 1950s have pro-vided data on this dependence, but until recentlysuch studies were limited by measurement tech-niques that were unable to resolve layers andfractures at scales finer than a few centimeters.Moreover, conventional techniques cannot deter-mine thermal conductivity and diffusivity simul-taneously and have difficulty characterizingunconsolidated rocks and core samples and plugssaturated with brine, oil or gas.18

Optical scanning avoids nearly all of theobstacles hindering accurate, routine determina-tion of thermal rock properties. This methodenabled a large petrophysical study of more than8,000 samples, including sedimentary rocks ofvarious lithologies, ages and geologic settingsfrom eight geologic regions, to uncover new con-nections between thermal rock properties andthe usual staples of petrophysical reservoir evalu-ation: porosity, permeability, electrical conduc-tivity, acoustic velocity and fluid saturation.19

Most of the cores in this study came frombasins in petroleum provinces of the formerSoviet Union (above left). Scientists measuredthe thermal conductivity of all samples underboth dry and fluid-saturated conditions, and thehigh-resolution scans revealed several key fea-tures of this diverse collection.

Scientists first discovered a wide variation ofthermal properties within individual dry samples.A simple measure of heterogeneity within a sam-ple is the difference between the maximum andminimum thermal conductivity measured along ascan line, divided by the average conductivityalong the same line. This heterogeneity factor,expressed as a percentage, characterizes therange of conductivity in the sample as seen byoptical scanning. Measured on dry samples, thefactor varied from about 4% to 50% for rocks inthe collection (left).

Second, and more interesting, was that theheterogeneity factor went no higher than about15% when measured on samples saturated withwater. This result could be explained by highervalues of porosity in samples whose heterogene-ity factor, when dry, was above about 15%. Voidspace, or air, has essentially zero thermal con-ductivity, in contrast to most solid rock, and isdistributed in a complex way at scales below the

OkhotskbasinTiman-

Pechorabasin

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SouthernVolga-Urals

NorthernVolga-Urals R U S S I A

Yeniseisk-Anabar

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> Core samples from Russian oil provinces. Scientists have compared thermal conductivity measuredby high-resolution optical scanning with other petrophysical properties on more than 8,000 core samplesof sedimentary rocks from various petroleum provinces in Russia. The collection was supplemented bysamples from deep scientific boreholes and oil fields in Germany, Mexico and the US.

> Heterogeneity of thermal conductivity and porosity. Heterogeneity of rockthermal properties is closely related to variations in porosity. In this plot,50 clay-rich limestone samples, studied under dry and water-saturatedconditions, are arranged in order of increasing heterogeneity as measuredunder dry conditions (blue). Heterogeneity is quantified as the differencebetween the maximum and minimum thermal conductivities measured alonga scan line, divided by the average value along the line. When thisheterogeneity factor of a dry sample is less than about 15%, it changes byonly a few percent when the sample is saturated with water and scannedagain (red). When the heterogeneity factor of a dry sample is greater than15%, it generally changes dramatically after water saturation. Scientiststraced this effect to large spatial variations of porosity in samples with dryheterogeneity factors above 15%. (Adapted from Popov et al, reference 12.)

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Autumn 2012 33

resolution of the optical scans—about 1 mm.When its low thermal conductivity is averagedwith that of the rock matrix, void space has largeeffects on the result because an optical scansenses low and high values of conductivitydepending on whether the heated spot containsmore or less pore space. In contrast, when porespace is saturated with water, whose thermalconductivity is relatively close to that of solidrock, its effect on the average thermal conductiv-ity is much less significant.

Scientists have known for some time thatchanges in thermal properties are caused by theopening of microscopic cracks and fissures inrock samples brought from high pressure deepunderground to atmospheric pressure at the sur-face.20 But high-resolution optical scans con-firmed the importance, for thermal properties, ofeven small variations in natural porosity in sedi-mentary rocks. The threshold of 15% to 20% in theheterogeneity factor is significant: When varia-tions along a scan line remain below this level ondry samples, saturating the rock with water doesnot change the measured range of scanned con-ductivity values. In such rocks, heterogeneityalong a scan line arises directly from variations incomposition or mineralogy of the rock matrix.

Optical scans have also revealed that anisot-ropy may be a key to unlocking new relationshipsamong thermal and other petrophysical proper-ties. One example is the relationship betweenthermal conductivity and permeability (right).These two properties depend not only on theamount of pore space, but also on its distributionthrough the rock volume—in isolated pores or inconnected pathways. When compared on a col-lection of rock samples, permeability and ther-mal conductivity often show a wide scatter. Butwhen the samples are limited to rocks with aheterogeneity factor above 20%—that is, to sam-ples in which thermal conductivity is stronglyaffected by pore fluids—there appears to be adirect correlation between permeability and thepercentage change in thermal conductivity ingoing from dry to water-saturated conditions. Therelationship is strongest when both thermal con-ductivity and permeability are measured parallel

> Anisotropic thermal conductivity and permeability. Most sedimentary rocks have anisotropic thermalproperties: Thermal conductivity measured in a direction parallel to the layering generally is 5% to50% higher than its value measured perpendicular to the layering. Moreover, the value measured ineach direction changes in going from dry to water-saturated conditions. The degree of thermalanisotropy and its change with fluid saturation are both related to permeability (top). Samples withhigher thermal anisotropy generally have lower permeability. Moreover, the percentage change inthermal conductivity parallel to layering when going from dry to water-saturated conditions—aquantity labeled δk || in these plots—closely tracks the logarithm of permeability. Measurements oncore samples collected throughout a 140-m [450-ft] depth interval in the Middle Ob’ province of Russiashow that this correlation holds across different lithologies (bottom). (Adapted from Popov et al,reference 19.)

X80

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Fine-grained massive mica-quartz sandstone

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Fine- and coarse-grained massive andbedded mica-quartz sandstone

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18. Early studies of the thermal properties of fluid-saturatedporous rocks include the following:Asaad Y: “A Study of the Thermal Conductivity of FluidBearing Porous Rocks,” PhD thesis, University ofCalifornia, Berkeley, USA, 1955.Zierfuss H and van der Vliet G: “LaboratoryMeasurements of Heat Conductivity of SedimentaryRocks,” AAPG Bulletin 40, no. 10 (October 1956):2475–2488.Somerton WH: “Some Thermal Characteristics ofPorous Rocks,” Petroleum Transactions, AIME 213(1958): 375–378.

A large, published compilation of thermal rockproperties is maintained by the US Geological Survey:Robertson EC: “Thermal Properties of Rocks,” Reston,Virginia, USA: US Geological Survey, Open FileReport 88-441 (1988).

19. Popov Y, Tertychnyi V, Romushkevich R, Korobkov D andPohl J: “Interrelations Between Thermal Conductivityand Other Physical Properties of Rocks: ExperimentalData,” Pure and Applied Geophysics 160, no. 5–6(2003): 1137–1161.

20. Walsh JB and Decker ER: “Effect of Pressure andSaturating Fluid on the Thermal Conductivity of CompactRock,” Journal of Geophysical Research 71, no. 12(June 15, 1966): 3053–3061.Pribnow D, Williams CF, Sass JH and Keating R:“Thermal Conductivity of Water-Saturated Rocks fromthe KTB Pilot Hole at Temperatures of 25 to 300°C,”Geophysical Research Letters 23, no. 4 (February 15,1996): 391–394.

34 Oilfield Review

to any layering. A conclusion of the large studyof samples from Russian oil fields was that aspecific relative change of thermal conductiv-ity—defined as the percentage change in ther-mal conductivity in the direction parallel tolayering when going from dry to water-saturatedconditions—may be the single most importantthermal property for the petrophysical charac-terization of reservoir rocks.21

Understanding these subtleties enabled sci-entists to discern new correlations relating ther-mal conductivity to porosity, acoustic velocityand electrical resistivity (left). These functionalmappings hold promise in both directions: Goingfrom the standard petrophysical properties tothermal conductivity opens the possibility ofdetecting changes in thermal properties far fromthe wellbore by remote geophysical sensing withelectrical or seismic methods; going in thereverse direction enables high-resolution opticalscans to explore the petrophysical heterogeneityof rocks at both macroscopic and microscopicscales. Thermal rock properties may also help toquantify this multiscale heterogeneity in theevaluation of unconventional reservoirs such asgas shale.22

Thermal Properties at Reservoir ConditionsOptical scanning provides rapid measurementsof thermal properties under normal laboratoryconditions—ambient temperature and atmo-spheric pressure. To calibrate these measure-ments to conditions in the reservoir, a specialchamber was built at the Schlumberger MoscowResearch Center to study the influence of ele-vated temperature and pressure on thermalproperties (next page). The new device employsa variation of the line source method to deter-mine thermal conductivity and diffusivity attemperatures up to 250°C [480°F] and at pres-sures up to 200 MPa [29,000 psi]. Pore pressurein the sample and axial and lateral componentsof confining stress can be varied independentlywithin the chamber.23

Thermal conductivity and diffusivity usuallyhave an inverse relationship with temperature.For example, under an increase of temperaturefrom 25°C to 100°C [77°F to 212°F], thermal con-ductivity in core samples from the Yarega oil fielddecreased by 50% while thermal diffusivitydecreased by 70%. A suite of measurements onsamples selected from different reservoir rocksdetermined average trends for changes in thermalproperties with temperature, which were thenapplied to all measurements in the database.

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> Correlation of thermal conductivity with porosity, acoustic velocity andelectrical resistivity. Thermal conductivities of samples from the Yarega fieldshow good correlation with porosity (top) and acoustic velocity (center). Thesolid lines in the top two panels are based on best least-squares fits to themeasurements for curves with an exponential dependence of thermalconductivity on porosity or on acoustic velocity. Measurements on samplesfrom western Siberia (bottom) show a correlation between thermalconductivity and resistivity. The solid lines in the bottom plots are best fits tothe measurements for curves with a logarithmic dependence of thermalconductivity on the logarithm of resistivity.

Autumn 2012 35

To connect thermal and mechanical proper-ties, a new instrument was developed at theSchlumberger Moscow Research Center to mea-sure the thermal expansion of core samples over arange of typical reservoir temperatures. Theinstrument, which uses a standard test methodcalled a quartz-rod dilatometer, accommodateseither cube-shaped samples or standard cylindri-cal core plugs used in petrophysical studies—3 cm in diameter and length—and can measureanisotropic thermal expansion coefficients by ori-enting the same sample in different positions.This measurement technique gives results thatare more consistent than conventional approachesin which thermal expansion along a variety ofdirections is measured on three different samplescut from the same rock core. A typical measure-ment sequence, which takes up to 12 hours, deter-mines the coefficient of thermal expansion attemperatures from 20°C to 300°C [70°F to 572°F]in temperature steps of 20°C.24

A second instrument at TerraTek providesthermal expansion measurements at elevatedpressure. The device accommodates dry or satu-rated cylindrical plugs 5 cm [2 in.] long and 2.5 to3.8 cm [1 to 1.5 in.] in diameter. The specimencan be loaded axially and radially in two direc-tions and subjected to a maximum hydrostaticconfining stress of 27 MPa [3,900 psi]. The devicemeasures thermal expansion coefficients at tem-peratures up to 200°C [400°F] in a few tempera-ture steps.25

Thermal Properties in RussianHeavy Oil FieldsSince its introduction in the 1980s, the opticalscanning method has measured thermal proper-ties of more than 80,000 rock samples. About 10%of the samples come from 15 oil and gas fields inRussia.26 This growing database of reservoir ther-mal properties is beginning to change the waypetrophysicists regard the importance of hetero-geneity in EOR processes.

Thermal rock properties measured by scansof more than 500 cores from the production zoneand surrounding formations at Yarega field, forexample, showed variations up to 150% over dis-tances of a few meters. The largest variations cor-related generally with changes in lithology, butthe degree of heterogeneity in individual drysamples was not expected. Moreover, differencesin thermal conductivity and diffusivity of up to

21. Popov et al, reference 19.22. Popov et al, reference 17.23. Popov YA, Spasennykh MY, Miklashevskiy DE,

Parshin AV, Stenin VP, Chertenkov MV, Novikov SV andTarelko NF: “Thermal Properties of Formations fromCore Analysis: Evolution in Measurement Methods,Equipment, and Experimental Data in Relation to ThermalEOR,” paper CSUG/SPE 137639, presented at theCanadian Unconventional Resources and InternationalPetroleum Conference, Calgary, October 19–21, 2010.

>Measuring thermal properties at high temperature and pressure. Scientists at Schlumberger MoscowResearch Center constructed a chamber (top) to determine rock thermal properties at reservoirconditions. The measurement cell (bottom left), which employs a version of the line source method,was calibrated on quartz crystals, a material with well-known anisotropic thermal properties.Measurements (bottom right) indicate that values for the thermal conductivity along the principal axes(1, 2 and 3) of the quartz thermal conductivity tensor measured at different temperatures and pressureswith the new instrument (solid circles) compare well with published results (open circles). (Adaptedfrom Popov et al, reference 23.)

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24. Popov Yu, Parshin A, Miklashevskiy D and Abashkin V:“Instrument for Measurements of Linear ThermalExpansion Coefficient of Rocks,” paper ARMA 12-510,presented at the 46th US Rock Mechanics/Geomechanics Symposium, Chicago, June 24–27, 2012.ASTM International: “Standard Test Method for LinearThermal Expansion of Solid Materials with a Push-RodDilatometer,” West Conshohocken, Pennsylvania, USA,ASTM E228-11, April 2011.

25. Popov et al, reference 24.26. Popov et al, reference 23.

36 Oilfield Review

120% were observed among nearly identical rocksamples saturated with air, oil or water (left).

Overall, the ranges of thermal properties seenin the Yarega study ran from 0.8 to 5.2 W/m°K forthermal conductivity and from 1.1 to 3.4 MJ/m3°Kfor volumetric heat capacity. Coefficients of lin-ear thermal expansion, measured on samplesfrom Yarega under reservoir conditions, varied bymore than a factor of two, from 8 × 10–6 to 17 ×10–6 per °K.

This variation far exceeds what had beenobserved in previous studies. Optical scanningand complementary measurements are revealing,possibly for the first time, the natural variabilityof thermal properties in reservoirs—causedeither by natural heterogeneity in rock texture,mineral and organic composition, or by changesin fluid saturation, temperature and pressure. Allthese factors affect the flow of heat into the res-ervoir and therefore the production forecasts fora thermal recovery project.

Precise Design and Control of Thermal EOREstimating the economics of thermal EOR requiresthat operators accurately predict the amount ofadditional hydrocarbon that will be produced froma field and the production rates of wells followingstimulation by a given amount of heat. The thermalproperties used in these reservoir simulations areoften derived from theoretical models, called mix-ing laws, that estimate the combined thermalproperties of a volume of rock and pore fluid fromthe volume fractions of its constituents.27

27. The bulk physical properties of a composite materialgenerally cannot be precisely calculated withoutknowledge of the microscopic distribution of itsconstituents. Mixing laws are mathematicalcombinations of the constituent properties to estimatebulk properties. Examples are the weighted arithmeticmean, weighted harmonic mean, weighted geometricmean and Hashin-Shtrikman model.For more on mixing laws see: Berryman JG: “MixtureTheories for Rock Properties,” in Ahrens TJ (ed): RockPhysics & Phase Relations: A Handbook of PhysicalConstants. Washington, DC: American GeophysicalUnion (1995): 205–228.Zimmerman RW: “Thermal Conductivity of Fluid-Saturated Rocks,” Journal of Petroleum Science andEngineering 3, no. 3 (1989): 219–227.

28. Popov Y, Parshin A, Ursegov S, Taraskin E, Chekhonin E,Andrianov N, Bayuk I and Pimenov V: “ThermalReservoir Simulation: Thermal Property DataUncertainties and Their Influence on SimulationResults,” paper WHOC12-291, presented at the WorldHeavy Oil Congress, Aberdeen, September 10–13, 2012.

29. For more on cementing: Boisnault JM, Guillot D,Bourahla A, Tirlia T, Dahl T, Holmes C, Raiturkar AM,Maroy P, Moffett C, Pérez Mejía G, Ramírez Martínez I,Revil P and Roemer R: “Concrete Developments inCementing Technology,” Oilfield Review 11, no. 1(Spring 1999): 16–29.

30. For more on asphaltenes: Akbarzadeh K, Hammami A,Kharrat A, Zhang D, Allenson S, Creek J, Kabir S,Jamaluddin A, Marshall AG, Rodgers RP, Mullins OC andSolbakken T: “Asphaltenes—Problematic but Rich inPotential,” Oilfield Review 19, no. 2 (Summer 2007): 22–43.

> Variation of rock thermal properties. Thermal properties at the Yarega oil field show largevariations—up to 150%—over a 50-m [166-ft] interval covering the depths of thermal mining. Eachdata point represents a separate core sample measured under various conditions. Colored linesrepresent moving averages of the data. (Adapted from Popov et al, reference 23.)

X850 1 2 3 4 5 6 0.5 1.0 1.5 2.0 2.5 0.5 4.0

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Quartz sandstone and leucoxene sandstone

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Siltstone with layers of sandstone and silty sandstone

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Basalt

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Thermal Conductivity, W/m°K Thermal Diffusivity, 10–6 m2/s Volumetric Heat Capacity, MJ/m3°K

>Models of rock thermal properties. Reservoir engineers use predictivemodels called mixing laws to calculate a rock’s bulk thermal conductivityas a function of porosity from the conductivities of the solid matrix andsaturating fluid. Each model employs different assumptions about thedistribution of pore space. Predictions of standard mixing laws foroil-saturated quartz sandstones, with matrix thermal conductivity of6.6 W/m°K and varying porosity, overlap the range of thermal conductivitiesmeasured by optical scanning of oil-saturated sandstones from the Yaregaoil field (blue shading), but can differ from actual values for specific samplesby more than 100%.

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Values of thermal conductivity obtained fromstandard mixing laws may be compared withexperimental results obtained by optical scan-ning (previous page, bottom). Although the mix-ing laws provide helpful bounds, the predictedvalues may differ from measured values by morethan a factor of two. Similar large discrepanciesare found between the default settings for ther-mal conductivity and volumetric heat capacityprogrammed in most reservoir simulators and theaverage values calculated from the database ofmeasured thermal properties maintained at theSchlumberger Moscow Research Center.28

A simplified model of a SAGD process illus-trates the importance of using accurate rock prop-erties in simulations of thermal EOR (above). This

model has two horizontal wells crossing a150-m by 500-m by 25-m [490-ft by 1,640-ft by 80-ft]pay zone of uniform thermal and production prop-erties, typical of tar sand reservoirs. The key met-rics for a SAGD operation are the cumulative oilproduction (COP) and the cumulative steam/oilratio (CSOR), which is the volume ratio of steaminput to oil produced. This ratio largely determinesefficiency of a steam injection process. Simulationsin which the thermal conductivity and volumetricheat capacity were varied by factors of up to two—to reflect a range of uncertainties in reservoirproperties—show production scenarios with rela-tive deviations in COP and CSOR of 20% to 50%persisting over the duration of the simulatedSAGD operation.

The economic implications for the variousscenarios differ dramatically from one anotherand, given the typical life of an EOR project, havelong-term consequences. Production predictionsbased on empirically derived thermal rock prop-erties may provide field operators with realisticexpectations for returns on capital investments.

Other ApplicationsMany oilfield processes other than thermal stim-ulation may benefit from operators having accu-rate knowledge of thermal properties surroundingthe wellbore. A cementing operation, for exam-ple, has to maintain pressure in the annulusbetween the casing and the formation in the nar-row range between formation pore pressure andformation fracture pressure. This requirementholds over the full length of the wellbore from thestart of the job until the cement fully cures. Sincethe curing process can raise the temperature ofthe slurry by more than 100°C [180°F], pressureand temperature in the annulus may be stronglyaffected by the thermal response of the surround-ing rock and its pore fluids. Knowing the actualvalues of thermal properties in a formation helpsoperators determine the best choice of cementmixtures and additives.29

Another important process governed in partby the temperature regime near the wellbore,and therefore by the surrounding distributionof thermal properties, is the precipitation ofasphaltenes, which can choke off productionby clogging flow pathways. Knowing whereasphaltenes are likely to precipitate helps engi-neers design better well completions.30

Petroleum production is essentially a ther-momechanical process. Modern reservoir simu-lators calculate the pressure, volume andtemperature changes accompanying mass andheat transfer during production or testing, butthey often use average values of thermal proper-ties, usually based on point measurements oncores, to characterize the entire reservoir. Thegrowing database of measurements made possi-ble by optical scanning shows that thermal rockproperties vary significantly at both macroscopicand microscopic scales. Understanding theeffects of heterogeneity in scaling up from high-resolution thermal scans of cores to full reser-voir simulations is a fundamental challenge forengineers constructing the next generation ofreservoir models. —MO

> Sensitivity of a SAGD operation to reservoir thermal properties. In SAGD operations (top), steam isinjected into a heater well and oil is produced from a producer well. Predictions of the performanceover time of a SAGD operation—in terms of cumulative oil production (bottom left) and cumulativesteam/oil ratio (bottom right)—vary with the modeled thermal properties of the reservoir zone. Thebase scenario (dashed black line) is modeled with an assumed, or measured, average volumetric heatcapacity (VHC) and thermal conductivity (TC) for the reservoir zone. Variation in cumulative oilproduction from the base scenario is determined, on the low side, by doubling volumetric heat capacity(left, dashed red line), thereby reducing the temperature rise for a given amount of injected heat.Variation in oil production on the high side is determined by doubling thermal conductivity (left, redline), thereby increasing the speed at which the temperature rise at the heater well propagates into thereservoir. Increasing thermal conductivity or volumetric heat capacity drives the cumulative steam/oilratio higher (right, red line) than its value in the base scenario (dashed black line). Relative changes(green) in oil production and steam/oil ratio in these different scenarios are as high as 40% in the earlyyears of production and persist at levels above 20% for 10 years or more. (Adapted from Popov et al,reference 28.)

Number of years

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