COMPRESSIBILITY OF

1
COMPRESSIBILITY OF RESERVOIR ROCKS
2
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)

3
MECHANICS OF COMPACTION
4
Relationship of Original Formation Porosity to
Overburden Pressure
5
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

6
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)

7
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.

8
FORMATION COMPRESSIBILITY
Under static conditions, downward overburden
force must be balanced by upward forces of the
matrix and fluid in pores
1.
2. Thus
4.
3.
As fluids are produced from reservoir, fluid
pressure (p) usually decreases while overburden
is constant, and (a) force on matrix
increases ( net compaction pressure, pmpo-p)
(b) bulk volume decreases, and (c)
pore volume decreases.
Pressure Gradients, Normal Reservoirs dpo/dZ
1.0 psia/ft dp/dZ 0.465 psia/ft
9
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)

10
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
  VbVpVm
• 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 ltlt Cf

11
Formation Compressibility

• Calculation of Pore Volume Change
• Separate
• and Integrate
• Two common approaches for constant value of Cf
• Exact Integration
• 1st Order Approximation

12
Formation Compressibility

• Pore Volume Change - Continued
• Exact Integration
• Exponentiating (Inverse of Natural Logarithm) and
  rearranging
• OR

13
Formation Compressibility

• Pore Volume Change - Continued
• 1st Order Approximation

14
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

15
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
16
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.

Initial Conditions
Pore Volume
Pore Pressure