COMPRESSIBILITY OF RESERVOIR ROCKS

• Porosity is reduced by compaction– Porosity reduction is determined by maximum

burial depth– Principal effects are:

• Changes in packing• Pressure solution• Recrystallization• Deformation of rock fragments

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

COMPACTION OF SEDIMENTS

MECHANICS OF COMPACTION

Modified from Jonas and McBride, 1977

Platy Grains(e.g., clays)

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

Rotation and Closer Packing

Ductile GrainDeformation

Breakage of Brittle Grains

Pressure SolutionAt GrainContacts

Ductile FrameworkGrain, e.g., Shale RockFragment)

Relationship of Original Formation Porosity to Overburden Pressure

50

Overburden pressure, psi

Po

rosi

ty, % 30

40

20

10

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

Sandstones

Shales

Isothermal Compressibility

• General Definition– The relative volume change of matter per unit

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

Isothermal Compressibility• General Equation

– C: Coefficient of Isothermal Compressibility• ALWAYS positive value• oilfield units: 1/psia

– V: Volume• oilfield units: ft3

– p: Pressure exerted on material • oilfield units: psia

– Negative sign in equation determined by V/p term, to force the coefficient C to be positive

– Volume is a function of pressure only (temperature is constant, and amount of material is constant)

p

V

V

1C

Formation Compressibility• Importance

– Formation compressibility can have a significant impact on reservoir performance

– Subsidence can have significant environmental impact

• Types– Matrix 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 pore volume per unit pressure change.

– Bulk Compressibility ( Cb ): relative change in bulk volume per unit pressure change ( usually Vb Vp). Significant decrease in bulk volume can cause subsidence.

FORMATION COMPRESSIBILITY

FO

FM FF

p

V

V

1C p

pf

Under static conditions, downward overburden force must be balanced by upward forces of the matrix and fluid in pores

2. Thus:

ppp

FFF

mo

fmo

AND

3.

1.

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

4.

Pressure Gradients, Normal Reservoirs:

dpo/dZ = 1.0 psia/ft

dp/dZ = 0.465 psia/ft

Formation Compressibility• Equation

– Cf: Formation Compressibility (Pore Volume Comp.)• ALWAYS positive value• oilfield units: 1/psia

– Vp: Pore volume• oilfield units: ft3

– p: Pressure of fluid in pores• oilfield units: psia

– Positive sign in equation determined by Vp/p term, to force Cf to be positive

– Pore volume is function of pressure only (temperature is constant, amount of reservoir rock is constant)

p

V

V

1C p

pf

Subsidence and Bulk Compressibility Process of subsidence

Bulk volume decreases as fluids are produced Area is constant Formation thickness decreases (causing subsidence of strata above)

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

Net compaction pressure: pm = po - p

Overburden (po) is constant dpm= -dp

As net compaction pressure increases Bulk volume decreases; Cb = -1/Vb (Vbpm)

Pore volume decreases; Cf= -1/Vp (Vppm)

Matrix volume decreases; Cm= -1/Vm (Vmpm)

Substituting from definitions above Cb = (-1/Vb) [(Vppm) + (Vmpm) ]

Cb = (-1/Vb) [(- Cf Vp) + (- Cm Vm)]

Cb = Cf + (1-)Cm; usually Cm << Cf

Formation Compressibility• Calculation of Pore Volume Change

– Separate

– and Integrate

– Two common approaches for constant value of Cf

• Exact Integration

• 1st Order Approximation

pp

f VV

1pC dd

p2

p1

2

1

V

V

pp

p

p

f VV

1pC dd

Formation Compressibility• Pore Volume Change - Continued

– Exact Integration

• Exponentiating (Inverse of Natural Logarithm) and rearranging

• OR

p2

p1

2

1

V

Vpppf )Vln(pC

)p(pCp1p2

12feV V

1eV V )p(pCp1p

12f

Formation Compressibility• Pore Volume Change - Continued

– 1st Order Approximation

)p(pC1VV

)p(pCVV

pp

VV

V

1C

p

V

V

1

p

V

V

1C

12fp1p2

12fp1p

12

p1p2

p1f

p

p

p

pf

d

d

Laboratory Determination of Cf

• In reservoirs, overburden pressure is constant and the pressure 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 matrix is the difference between the overburden and pore pressures– This allows us to obtain useful results in the laboratory

Laboratory Determination of Cf

• 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, pore volume decreases and the volume of expelled brine is measured

pconfining

Hysteresis Effect - Formation Compressibility• Hysteresis: The lagging of an effect behind its cause, as when the

change in magnetism of a body lags behind changes in the magnetic field. (definition from dictionary.com, 2002)

• 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 increase all the way back to the initial pore volume.

Po

re V

olu

me

Pore Pressure

Initial Conditions