Fundamental Properties of Reservoir RocksAdrian C ToddHeriot-Watt UniversityDEPARTMENT OF PETROLEUM ENGINEERING

IntroductionProperties of rocks with respect to the fluids contained and injected are important characterisation parameters.Influence reserves and mobility.Reservoir engineer concerned with:

The quantities of fluids contained The transmissivity of fluids through the rocks and related properties

Chartacteristics of Reservoir RocksFactors which effect capacity and flow of fluids are:

porosity permeability capillary pressure compressibility fluid saturation

Chartacteristics of Reservoir RocksFor economic viability for oil & gas production reservoir rock must exceed a:

minimum porosity minimum thickness minimum permeability minimum area

Chartacteristics of Reservoir RocksFor fluid production the rock must be permeable.Sufficient large and interconnecting pores.A permeable rock is porous.Porous does not necessarily imply permeable.Volcanic rocks, porous BUT pores not interconnecting.Shale, porous BUT pores very small.

Physical Characteristics of Reservoir RocksA typical reservoir rock - sandstone.The shape and size and size distribution reflect:

source physical and chemical processes exposed to: crushing & grinding tumbling action in streams or on dunes.

Physical Characteristics of Reservoir RocksPore spaces in the reservoir rock provide the container for accumulation of fluids.Most commercial reservoirs occur in :

sandstones limestone dolomite. Some occur in fractured shale basement rocks.Porosity is one of the most important rock properties.Measure of the space available for accumulation of fluids

PorosityComplexSpace between grains or limestone cavessometimes good estimates from laboratory studiessometimes such measurement irrelevant

PorosityComplicated nature illustrated by metal cast of pores

PorosityOne classification based on pores space.whether original or formed subsequently

PorosityIsolated pores cannot contribute to recoverable reserves

Porosity

PorosityTotal Porosity

is the ratio of volumes of ALL pores to the bulk materialregardless of pore interconnectivityEffective Porosity

is the ratio of interconnected pore volume to bulk material volume

Porosity-Range of valuesConsider a assembly of mono size spheresMinimum packing gives porosity of 47.6% Maximum packing gives porosity of 26%

Porosity-Range of valuesPacking & size of grains

Absolute size does not have a large impact.Particle size distribution

Wide size distribution leads to low porosityParticle shape

Strong impact in sedimentary processCementing material

Clays and minerals

Porosity-Range of valuesSize distribution of grains effects porosity

Porosity-Range of valuesReservoir Porosity can range from 50% to 1.5%Typical values are:

35 - 45%Unconsolidated (young) Sands20 - 35%Consolidated Sandstone15 - 20%Strong (low permeability) Sandstone 5 - 20%Limestone10 - 30%Dolomites 5 - 40%Chalk

Subsurface MeasurementSurface measurements made on recovered core.Down hole measurements very sophisticated.Downhole porosity related to acoustic and radioactive properties of the rock.

Density LogDensity log attributed to the porosity of the rock.Needs good description of the mineralology.

r - Quartz = 2.65 g/cm3r Limestone = 2.71 g/cm3

Sonic LogMeasures response to acoustic energy through sonic transducersTime of travel related to acoustic properties of the formation.If mineralogy is not changing then travel time related density and hence porosity.Formation fluids will effect response.

DT - Quartz = 55ms ft-1DT Limestone = 47 ms ft-1DT Water =190 ms ft-1

Neutron LogAnother radioactive logging techniqueMeasures response of the hydrogen atoms in the formationNeutrons of specific energy fired into formation.The radiated energy is detected by the tool.This is related to the hydrogen in the hydrocarbon and water phase.The porosity determined by calibration

Average PorosityPorosity normally distributedAn arithmetic mean can be used for averaging.

PermeabilityThe permeability of a rock is the description of the ease with which fluid can pass through the pore structureCan be so low to be considered impermeable.Such rocks may constitute a cap rock above permeable reservoir.Also include some clays,shales, chalk, anhydrite and some highly cemented sandstones.

PermeabilityTerm is used to link flowrate and pressure difference across a section of porous rock.In a rock the pore space , size and interconnection is very complex.The application of energy equations developed for flow in pipes is difficult.The parameter used for this flow behaviour is termed permeabilityThe unit of permeability is the Darcy, named after a French scientist investigating flow through filter beds.

PermeabilityDarcys Law

PermeabilityDarcys Law

The rate of flow of fluid through a given rock varies directly with the pressure applied, the area open to flow and varies inversely with the viscosity of the fluid flowing and the length of the porous rock. The constant of proportionality is termed Permeability

PermeabilityUnit of permeability - DarcyPermeability which will permit flow of one centipoise fluid to flow at linear velocity of one cm per second under a pressure gradient of one atmosphere per centimetre.

PermeabilityDarcys ExperimentA sandpack through which water flowed

Permeability

There is a very strong relationship between porosity and permeability

PermeabilityComparing equations.

DarcyCarmen KozenyIt is not surprising therefore that there is a strong relationship between permeability and porosity

PermeabilityPractical unit-millidarcy, mD, 10-3 DarcyFormations vary from a fraction of a millidarcy to more than 10,000 millidarcy.Clays and shales have permeabilities of 10-2 to 10-6 mD.These very low permeabilities make them act as seals between layers.

Factors Affecting PermeabilityPermeability is anisotropicHorizontal permeabilities in a reservoir are generally higher than vertical permeabilities.Due to reservoir stressesParticle shape as influenced by depositional process.

Anisotropic permeabilityImpact of ordered deposition

Anisotropic permeabilityHorizontal permeabilities can be affected by the deposition process

Anisotropic permeabilityPorosity is a non directional propertyIt is isotropic

Dimensions of PermeabilityDarcys EquationDimensions

Assumptions in Darcys LawDarcys Law assumes

Steady State Flow Laminar Flow Single phase only occupying 100% of porosity No reaction between fluid & rock Homogenous rock

Steady State FlowNo transient flow regimesUnrealistic in reservoir flowOK for laboratory testsCores are small enough for transients to only last for a few minutes.

Laminar Flowi.e. no turbulent flowpressure drop due to viscous forcesValid for most reservoirs

Turbulent FlowNon Darcy FlowAttributed to higher velocitiesPressure drop due to kinetic energy lossesFor example near well bore flow in gas production Essentially appears as an extra pressure loss term in the flow system

Single phase onlyAchieved in the laboratory through cleaning coresIn the reservoir except for aquifer water flow there is more than one phase present.Concept of relative permeability used to describe more complex flow regime.

No reaction between fluid & rockSome cases when this will not happenHydraulic fracturingAcidising.Water flooding sometimes generates fines from clays etc.

Applications of Darcys Law -Horizontal Linear Incompressible System

Applications of Darcys Law -Horizontal Linear Compressible Ideal Gas SystemThe laboratory set up for this would be:Flow rate, Qb, measured at ambient pressure, PbQ in the core at P,For ideal gas:

Horizontal Linear Compressible Ideal Gas System

Comparing EquationsGasLiquidIn some circumstances the mean flow rate is measured at a mean pressure.For a core this is the mean of the upstream and downstream pressure.

Comparing EquationsThe ideal gas permeability can be calculated from the liquid equation using the mean flow measured at mean pressure.

Radial Linear Incompressible Liquid Systemds = -dr since the direction of flow is opposite to the co-ordinate system

For radial geometry the area A is radius dependentA=2prh

Radial Linear Incompressible Liquid SystemRadial Darcy EquationIncompressible flow

Horizontal-Radial Linear Compressible Gas System

Field UnitsMeasurements in the field often quoted in field units. A conversion is required for compatibility with Darcy equation.

Flow rate, Q - bbl/day or ft3/day or m3/day Permeability, k - darcy Thickness, h - feet or metre Pressure, P - psia Viscosity, m- centipoise Radius. R - feet or metre Length, L - feet or metreto oil field unitsgives

Klinkenberg EffectDarcys law should be the same irrespective of transmitted fluids.Since viscosity is in the equationMeasurements on gas compared to liquid give higher values than the liquid for some conditions.The phenomena is attributed to Klinkenberg.

Klinkenberg EffectConsidered due to the effect of slippage of gas molecules along grain surfaces.Occurs when the diameter of the pore throat approaches mean free path of the gas.Darcys law assumes laminar flow and viscous theory specifies zero velocity at the boundary.Not valid when mean free path approaches diameter of pore.Result there is insufficient gas molecules to form a zero velocity.

Klinkenberg EffectMean free path function of size of molecule.Smaller the molecule , the larger the effectGas permeabilty is plotted versus reciprocal mean pressure

Klinkenberg EffectMeasurements made in gas permeability set upLiquid permeabilty0 reciprocal mean pressuremean pressure infinity Klinkenberg equationb =Slope of lineEffect greatest for low permeabilty rock at low mean pressures.

Reactive FluidsDarcys law assumes no reaction with the formation.Many formation with clays react with water to give lower permeability.Lower permeability in formation than gas based measurements in the laboratory.Water injected into the formation may severely reduce permeability due to clay swelling.

Average PermeabilityPermeability is not normally distributed but has an exponential function.Geometric mean is used to obtain average reservoir permeability.

Stress Effects on Core Measurements-Stress RegimesImpact of reservoir stresses on reservoir flow and capacity an increasing interest.Removing a core from the formation is to remove all confining forces.Allows rock matrix to expand in all directions.Partially changing fluid flow paths.

Influence of Reservoir StressesCertain formations are subject to consolidation when the net overburden stress is increased.Subsidence of reservoir and surface formations.Reduction in permeability and porosity of formationRelevance of measurements under simulated reservoir stress conditions

Stresses associated with rock properties

Stresses associated with rock propertiesWithin a reservoir stresses can be expressed in three directions

Stresses associated with rock properties

These are a combination of major and minor stressesThis is more acceptable but only applies to a vertical core plug and therefore vertical permeability

Impact of Overburden StressNet overburden pressure = overburden pressure - pore pressure

Isothermal CompressibilityCf is the isothermal compressibility.V is the volumedV is the change in volumedP is the change in pressure.Negative sign as pressure increases volume decreases.

Types of CompressibilityMatrix volume compressibility

The change in volume of the rock grains. This is very small and usually not of interest in sandstonesBulk volume compressibility

The change in unit volume of the rock. This is of interest in reservoirs on the impact at the surface where subsidence might occur.Pore volume compressibility

Change in pore volume. Of interest since it affects porosity

Effect of Stress on PermeabilityAs effect of stress effects pore volume.It also effects permeability as the pore throat radii reduces and the permeability declines.

Effect of Stress on PermeabilityIn true triaxial stress regime stresses are not identical and therefore the strain ( pore throat radii changes ), may cause dilation in different directions.

Influence of stresses

Influence of stresses on permeabilityUniaxialBiaxialTriaxialConventional core analysis measurements

Porosity-Permeability RelationshipsWhereas for porosity there are downhole measurement techniques.There are no downhole methods for permeability.Downhole permeability is usually obtained by flow and pressure monitoring. - Well Testing.Continued interest in porosity-permeability correlations.If there is no recovered core for the section of interest, the approach is to use downhole porosity to determine lab equivalent porosity and then use a porosity-permeability correlation to calculate permeability.

Porosity-Permeability RelationshipsPorosity is an absolute propertyPermeability is a secondary property.It is influence by a range of basic parameters.Size, shape and porosity.Carmen -Kozeny equation

Porosity-Permeability CorrelationsDownhole porosityLab. porosityDownhole permeability

Surface Kinetics

Ideas discussed so far assume ONLY one fluid present in the pore spacesReservoir rocks contain two or more phases and other issues need to be considered.Multiple phases introduce the concept of:

Wettability Capillary PressureRelative Permeability

Surface tensionSurface free energy exists on all surfaces between states of matter and between immiscible fluidsSurface tension results from molecular forces that cause the surface of a liquid to assume smallest possible size.The equilibrium in force between two dissimilar fluids is disrupted at the interface

Oil-Water Boundary

Surface tensionSurface or Interfacial tension deforms the outer surface of immiscible liquids to produce droplets.If the two liquids are on a surface, the IFT deforms the liquids to produce a contact angle.

WettabilityA wetting phase is one which spreads over the solid and preferentially wets the solid.The contact angle approaches zero and will always be less than 90o.

A non-wetting phase has little affinity for the surface

The contact angle will be greater than 90o.

WettabilityThe composition of the surface affects the interfacial tension.

Wetting on Reservoir RocksWater droplets on silica grains and claysSilicaClaysWettingNon wetting

Adhesion tensionDifference between solid water and solid oil interfacial tension.

Capillary Rise in TubeInterface is at equilibriumCapillary PressureIs the pressure difference across an interface

Distribution of CapillariesFree water level is the level with zero capillary pressure Capillary rise is also a function of capillary radiusPorous media consist of a range of pore sizes (capillaries) which result in a transition zone from 100% water to the residual water saturation

Distribution of CapillariesFree Water level, FWLOil water contact,OWC100% saturation above FWLIrreducible water saturationTransition zone

Capillary Pressure in RockThe shape of capillary pressure curve depends on nature of rockRock is more than a series of different size tubes.It is a complex network of interconnected poresThe height at which wetting liquid will stand above free water level is directly proportional to capillary pressure which is related to size and size distribution of pores.It is also proportional to the IFT and contact angleInversely proportional to the pore radius and fluid density difference

Fluid Distribution in Reservoir Rocks

Fluid Distribution in Reservoir RocksWater wet, coarse grained sand and oolitic and vuggy carbonates with large pores have low capillary pressure..Silty, fine grained sands have high capillary pressure and water saturation.Water saturation reduces with increased height above the hydrocarbon water contact.The base of the 100% water satn limit is termed the water table.The non identifiable level, the free water level is the level of zero capillary pressure.

Fluid Distribution in Reservoir Rocks

Fluid Distribution in Reservoir Rocks

Parameters affecting capillary pressure

Rock wettability affects Pc.Oil wet rocks have reduced transition zonesLower IFT reduces transition zoneHigh IFT extends transition zone

Saturation historyDrainage saturation

Drainage of the wetting phase Represents saturation before fluid production Level of saturation dictated by capillary pressure.Imbibition saturation

Results from increase in wetting phase and expulsion of hydrocarbonsThe situation resulting from natural or forced water driveThe rising water table

Saturation historyDrainage effect

Small pore holding up water above larger pore

Saturation historyImbibition effect

Larger pore limiting entry to water by cap.pressure

Density DifferenceLarge density (water-gas) difference supresses transition zone.Small density differences (water-oil ) increases transition zone.

Layered ReservoirsA characteristic of many reservoirs is their layered nature with each layer having its oqn capillary pressure characteristic

Free water levelThe basis for the saturation profile

Relative PermeabilityRelative permeability provides an extension of Darcys Law to the presence of more than a single fluid within the pore space.

kro,krw - relative permeabilityk - absolute permeability

Relative PermeabilityPermeability to a particular phase is reduced when a second or third phase is present

Relative Permeability =phase permeability when more than one phase is presentpermeability to that phase aloneRelative permeability is normally reported as a fraction or percentage. It equals 1.0 or 100% when the phase is present on its own

Relative permeability water -oil system

Relative permeability gas -oil system

Relative Permeability Curves for Water-wet and Oil -wet systemsShape of rel perm curves characteristic of wetting qualities.Shape of rel. perm curves different for water wet and oil wet phases.Drainage curvesand imbibition curves

Relative Permeability Curves for Water-wet and Oil -wet systemskro -end point relative permeability to oilRelative perm. to oil in presence of irreducible waterkrw -end point relative permeability to waterRelative perm. to water in presence of irreducible oil

Relative permeabilityImbibition relative permeability

Is displacement where the wetting phase saturation is increasing.For example in a water flood of a water wet rock.Drainage relative permeability.

Is where the non wetting phase saturation is increasingFor example gas expulsion during primary depletion.The condition existing in the transition zone at discovery.

Water displacement of oilPrior to water displacement water exists as film around grain or in dead end pores.Presence of water has little effect on oil flow.Relative perm approaches 100%.Water invasion results in water invasion into small and large pores.Imbibition relative permeability influences flow behaviourOil saturation decreases with decrease in oil relative permeability.Oil remaining after flood out is termed residual oil

Oil remaining immobile after waterfloodOil remaining is influenced by capillary pressure and interfacial tension.High residual oil saturation is a result of oil ganglia retained in large pores as a result of capillary forces.Explained by Pore Doublet Model

Oil remaining immobile after waterflood

Pore Doublet Model

Pore Doublet ModelCaplillary forces have drawn water into narrower pore

Pore Doublet ModelCapilliary forces have now isolated oil in large poreOil trapped by following equationOil can be moved by enhanced oil recovery methods

Enhanced oil recovery methods:Surfactant flooding reduces IFT to reduce PcMiscible flooding -there is no interfacial tension enabling oil ganglia to be pushed out

Mobility RatioAn important perspective in oil displacement.Relates mobility of displacing fluid to that of displaced fluid.A ratio of Darcys law for each fluid.At residual saturation of the other fluid.

krw is the relative permeability at residual oil saturationkro is the relative permeability at irreducible water saturationEnd point relative permeabilities

Mobility Ratio

Water displacement of oilAs water table rises

Gas Displacement of OilGas is a non-wetting phase.Gas permeability is zero until a critical gas saturation is reached.

Gas Displacement of Oil

Gas Displacement of OilImportant in understanding solution gas drive