COMPRESSIBILITY OFCOMPRESSIBILITY OFRESERVOIR ROCKSRESERVOIR ROCKSRESERVOIR ROCKSRESERVOIR ROCKS

Lecture Outline

Overburden pressure and rock compressibilitycompressibility

Definition of overburden pressure- Definition of overburden pressure

- Pore pressure and effective overburden pressure

- Types of rock compressibility

- Relationship between porosity and compressibility

- Porosity-compressibility correlations

Net pay gross pay net to gross and cut-off values- Net pay, gross pay, net to gross, and cut-off values

Overburden Pressure and Rock Overburden Pressure and Rock CompressibilityCompressibility

Definition of overburden pressure:Definition of overburden pressure:

CompressibilityCompressibility

The total pressure at any reservoir depth, due to the weight of overlying fluid saturated rock column, is called the overburden pressure Pthe overburden pressure, Pov

The total pressure at any depth is the sum of the overlaying fluid-column pressure Pf and the overlaying overlaying fluid column pressure Pf and the overlaying grain or matrix column pressure Pm

Pov = Pf + Pm Pov Pf + Pm

A typical value of overburden pressure is approximately one psi per foot of depthfoot of depth.

Overburden pressure depends on: depth, structure, consolidation of the formation, geologic age and history of the rock.g g g y

Overburden Pressure and Rock Overburden Pressure and Rock CompressibilityCompressibilityCompressibilityCompressibility

Pore pressure and effective overburden pressure:Pore pressure and effective overburden pressure:

The weight of the overburden simply applies a compressive force to the reservoir. The pressure in the rock pore spaces does not normally approach the overburden pressure A typical pore normally approach the overburden pressure. A typical pore pressure, commonly referred to as the reservoir pressure, is approximately 0.5 psi per foot of depth, assuming that the

i i ffi i tl lid t d th b d i reservoir is sufficiently consolidated so the overburden pressure is not transmitted to the fluids in the pore spaces.

The pressure difference between overburden and internal pore pressure is referred to as the effective overburden pressure. During pressure depletion operations, the internal pore pressure g p p p , p pdecreases and, therefore, the effective overburden pressure increases. This increase causes the following effects:

• The bulk volume of the reservoir rock is reduced.• Sand grains within the pore spaces expand.

Relationship of Original Formation Porosity to Overburden Pressure

50

40

30

40Sandstones

30

2020

10Shales

10

0

Overburden pressure, psi

00 1,000 3,0002,000 4,000 5,000 6,000

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITY

General DefinitionGeneral Definition

The relative volume change of matter per unit pressure change under conditions of constant pressure change under conditions of constant temperature

Usually, petroleum reservoirs can be considered isothermal (an exception: thermal stimulation)

Increasing pressure causes volume of material to decrease (compression) - e.g. reservoir fluids

Decreasing pressure causes volume of material to increase (expansion) - e.g. reservoir fluids

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITY

⎞⎜⎜⎛ ∂

=V1C p

fUnder static conditions, downward overburden force must be balanced by upward forces of the

1.

F

⎠⎜⎜⎝ ∂pVp

fforce must be balanced by upward forces of the matrix and fluid in pores

FO2. Thus: FFF fmo +=

AND

FM F Fppp mo +=

3.

As fluids are produced from reservoir, fluid pressure (p) usually4.

Pressure Gradients, Normal Reservoirs:

dp /dZ = 1 0 psia/ft As fluids are produced from reservoir, fluid pressure (p) usually decreases while overburden is constant, and:

(a) force on matrix increases ( “net compaction pressure”,pm=po-p)

(b) b lk l d d

4.dpo/dZ = 1.0 psia/ft

dp/dZ = 0.465 psia/ft

(b) bulk volume decreases, and(c) pore volume decreases.

General Equation

C: Coefficient of Isothermal CompressibilityALWAYS positive valueoilfield units: 1/psia

⎞⎛ ∂V1V: Volume

oilfield units: ft3⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−=pV

V1C

oilfield units: ft

p: Pressure exerted on material

⎠⎝ ∂pVp: Pressure exerted on material

oilfield units: psia

Negative sign in equation determined by ∂V/∂p term, to force the coefficient C to be positiveVolume is a function of pressure only (temperature isVolume is a function of pressure only (temperature is constant, and amount of material is constant)

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITYImportanceImportance

F i ibili h i ifi iFormation compressibility can have a significant impact on reservoir performance

Subsidence can have significant environmental impact

Types of rock compressibility:Types of rock compressibility:Types of rock compressibility:Types of rock compressibility:

R k M t i C ibilitRock Matrix Compressibility

Pore Compressibility ( Cf )p y ( f )

Bulk Compressibility ( Cb )

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITY

Rock Matrix Compressibility

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITY

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITY

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITY

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITY

FORMATION COMPRESSIBILITYFORMATION COMPRESSIBILITY

Relationship between porosity and compressibilityRelationship between porosity and compressibilitye at o s p bet ee po os ty a d co p ess b tye at o s p bet ee po os ty a d co p ess b ty

Relationship between porosity and compressibilityRelationship between porosity and compressibility

Relationship between porosity and compressibilityRelationship between porosity and compressibility

PorosityPorosity--Compressibility Correlations:Compressibility Correlations:

PorosityPorosity--compressibility correlations:compressibility correlations:yy p yp y

Net pay gross pay and net to gross value:Net pay gross pay and net to gross value:Net pay, gross pay and net to gross value:Net pay, gross pay and net to gross value:

Net pay gross pay and net to gross value:Net pay gross pay and net to gross value:Net pay, gross pay and net to gross value:Net pay, gross pay and net to gross value:

Net pay gross pay and net to gross value:Net pay gross pay and net to gross value:

Net to gross value is the ratio between net pay to gross pay

Net pay, gross pay and net to gross value:Net pay, gross pay and net to gross value:

Net to gross value is the ratio between net pay to gross pay, e.g., the ration between the part of the reservoir thickness which contribute in the oil recovery to the total or gross Thickness.

The net pay values are different from one reservoir to another depending on economic limits but as general theanother depending on economic limits but as general the following present the cut-off values for oil and gas reservoirs:

Cut-off values

φ, %

k, mD

Sw, % Clay content, %values % mD %

Oil reservoirs <<1010 <<5050 >>5050 >>1515

Gas reservoirs <<55 <<11 >>7575 >>1515

Net pay gross pay and net to gross value:Net pay gross pay and net to gross value:Net pay, gross pay and net to gross value:Net pay, gross pay and net to gross value:

Laboratory Determination of Laboratory Determination of CCff

In reservoirs, overburden pressure is constant and the , ppressure of fluid in pores changes, resulting in pore volume change

In the laboratory, we change the confining pressure on the core plug (overburden) while holding the pore pressure constant

Remember that the net compaction pressure on the Remember that the net compaction pressure on the matrix is the difference between the overburden and pore pressures

This allows us to obtain useful results in the laboratorylaboratory

Laboratory Determination of Laboratory Determination of CCffLaboratory Determination of Laboratory Determination of CCff

Laboratory Procedure

Core plug is 100% saturated with brine

Core plug is placed in rubber or soft copper sleeve

As pressure outside sleeve is increased, As pressure outside sleeve is increased, pore volume decreases and the volume of expelled brine is measured

Formation CompressibilityHysteresis Effect Hysteresis Effect

Hysteresis is used by Petroleum Engineers to describe the effects of path dependence and irreversibilities we observe in reservoir behavior

For example, if we decrease reservoir pressure from initial conditions, pore volume decreases. If we then increase reservoir pressure back to the initial pressure, pore volume does not increasepressure back to the initial pressure, pore volume does not increase all the way back to the initial pore volume.

REFERENCES:REFERENCES:Ahmed, Tarek : “Reservoir Engineering Handbook-

Ch.4:

Fundamentals of Rock Properties”, Second Edition, Gulf Professional Publishing 2001Professional Publishing, 2001.

Subsidence and Bulk CompressibilitySubsidence and Bulk Compressibility

• Process of subsidenceB lk l d fl id d d• Bulk volume decreases as fluids are produced

• Area is constant• ∴ Formation thickness decreases (causing subsidence• ∴ Formation thickness decreases (causing subsidence

of strata above)

• Porosity: φ = Vp/Vb = 1-(Vm/Vb); where Vb=Vp+Vm

• Net compaction pressure: pm = po – pp p pm po p

• Overburden (po) is constant ∴ dpm= -dp

Subsidence and Bulk Compressibility

• As net compaction pressure increases• Bulk volume decreases; Cb = -1/Vb (∂Vb/∂pm) • Pore volume decreases; Cf= -1/Vp (∂Vp/∂pm)

M t i l d C 1/V (∂V /∂ )• Matrix volume decreases; Cm= -1/Vm (∂Vm/∂pm)

• Substituting from definitions aboveC = ( 1/V ) [(∂V /∂p ) + (∂V /∂p ) ]• Cb = (-1/Vb) [(∂Vp/∂pm) + (∂Vm/∂pm) ]

• Cb = (-1/Vb) [(- Cf Vp) + (- Cm Vm)]• Cb = φCf + (1-φ)Cm; usually Cm << Cfb φ f ( φ) m; y m f

Formation Compressibility

Calculation of Pore Volume Change

Separate pf VV1pC dd = p

pf V

p

p22 Vp 1and Integrate ∫∫ =

p11 Vp

ppf V

V1pC dd

Two common approaches for constant value of Cfpp fExact Integration1st Order Approximation

Formation Compressibility

Pore Volume Change - Continued

Exact Integration [ ] [ ] p2

1

2

1

VVp

ppf )Vln(pC =

p11 Vpp

Exponentiating (Inverse of Natural Logarithm) and rearranging

)(C

OR

)p(pCp1p2

12feVV −=

OR[ ]1eV V )p(pC

p1p12f −=∆ −

Formation Compressibility

Pore Volume Change - Continued

1st Order Approximation

VV1V

V1C pp

f ⎟⎠

⎞⎜⎜⎝

⎛∆

∆≅⎟

⎠

⎞⎜⎜⎝

⎛=

dd

VV1C

pVpV

p1p2

ppf

⎞⎜⎛ −

⎠⎜⎝ ∆⎠

⎜⎝ d

)(CVV

ppVC

12

p1p2

p1f

∆⎠

⎜⎜⎝ −

=

[ ])p(pC1VV

)p(pCVV

12fp1p2

12fp1p

−+=

−=∆

pp

COMPACTION OF SEDIMENTSCOMPACTION OF SEDIMENTS

Porosity is reduced by compactionPorosity reduction is determined by maximum y yburial depthPrincipal effects are:

Changes in packingPressure solutionR t lli tiRecrystallizationDeformation of rock fragments

Compaction effects are not reversed byCompaction effects are not reversed by erosional unroofing (hysteresis effect)

MECHANICS OF COMPACTIONMECHANICS OF COMPACTION

P S l tiRotation and Closer

PackingDuctile GrainDeformation

Breakage of Brittle Grains

Pressure SolutionAt GrainContacts

Platy GrainsPlaty Grains(e.g., clays)

Non-Platy Grains(e.g., qtz., feldspar)

Modified from Jonas and McBride, 1977

Ductile FrameworkGrain, e.g., Shale RockFragment)

Formation CompressibilityEquation

⎟⎠

⎞⎜⎜⎝

⎛∂

∂=

pV

V1C p

f

Cf: Formation Compressibility (Pore Volume Comp.)ALWAYS positive value

⎠⎜⎝ ∂pVp

ALWAYS positive valueoilfield units: 1/psia

Vp: Pore volumeoilfield units: ft3

p: Pressure of fluid in poresoilfield units: psia

Positive sign in equation determined by ∂Vp/∂p term, to force Cf to be positivePore volume is function of pressure only (temperature is constant, amount of reservoir rock is constant)

ImportanceFormation compressibility can have a significant p y gimpact on reservoir performanceSubsidence can have significant environmental impact

TypesypMatrix Compressibility ( Cm ): relative change in volume of solid rock material (grain volume) per unit pressure change (usually Cm ≅ 0).Pore Compressibility ( Cf ): relative change in

l it hpore volume per unit pressure change.Bulk Compressibility ( Cb ): relative change in bulk volume per unit pressure change ( usuallybulk volume per unit pressure change ( usually ∆Vb ≅ ∆Vp). Significant decrease in bulk volume can cause subsidence.