COMPRESSIBILITY OF
RESERVOIR ROCKS
COMPACTION OF SEDIMENTS
• 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)
MECHANICS OF COMPACTION
Rotation and Closer
Packing
Ductile Grain
Deformation
Breakage of
Brittle Grains
Pressure Solution
At Grain
Contacts
Platy Grains
(e.g., clays)
Non-Platy Grains
(e.g., qtz., feldspar)
Ductile Framework
Grain, e.g., Shale Rock
Fragment)
Modified from Jonas and McBride, 1977
Relationship of Original Formation
Porosity to Overburden Pressure
50
40
Sandstones
30
20
Shales
10
0
0
1,000
2,000
3,000
4,000
5,000
Overburden pressure, psi
6,000
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
1  V 

C   
V  p 
– 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)
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 DVb  DVp).
Significant decrease in bulk volume can cause
subsidence.
FORMATION COMPRESSIBILITY
1  Vp 


Cf 
Vp  p 
F
O
F
M
F
F
Under static conditions, downward
1. overburden force must be balanced by
upward forces of the matrix and fluid in
pores
2. Thus:
F F
o
m

F
f
AND
p p  p
o
3.
Pressure Gradients,
Normal Reservoirs:
dpo/dZ = 1.0 psia/ft
dp/dZ = 0.465 psia/ft
m
4.
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.
Formation Compressibility
• Equation
1  Vp 

Cf  
Vp  p 
– 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)
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 (Vb/pm)
 Pore volume decreases; Cf= -1/Vp (Vp/pm)
 Matrix volume decreases; Cm= -1/Vm (Vm/pm)
 Substituting from definitions above
 Cb = (-1/Vb) [(Vp/pm) + (Vm/pm) ]
 Cb = (-1/Vb) [(- Cf Vp) + (- Cm Vm)]
 Cb = Cf + (1-)Cm; usually Cm << Cf
Formation Compressibility
• Calculation of Pore Volume Change
– Separate
1
Cf dp  dVp
Vp
p2
– and Integrate
Vp2
1
p Cf dp  V Vp dVp
1
p1
– Two common approaches for constant value of Cf
• Exact Integration
• 1st Order Approximation
Formation Compressibility
• Pore Volume Change - Continued
– Exact Integration


Cf p  ln( Vp ) V
p2
p1
Vp2
p1
• Exponentiating (Inverse of Natural Logarithm) and rearranging
Vp2  Vp1eCf (p2 p1 )
• OR


DVp  Vp1 eCf (p2 p1 ) 1
Formation Compressibility
• Pore Volume Change - Continued
– 1st Order Approximation
1  dVp  1  DVp 
 


C f  
Vp  dp  Vp  Dp 
1  Vp2  Vp1 


Cf 
Vp1  p 2  p1 
DVp  Vp1C f (p 2  p1 )
Vp2  Vp11  C f (p 2  p1 )
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
Pore Volume
– 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.
Initial
Conditions
Pore Pressure