COMPRESSIBILITY OF RESERVOIR ROCKS

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. Pressure Solution At Grain Contacts Rotation and Closer Packing Ductile Grain Deformation Breakage of Brittle Grains 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 MECHANICS OF COMPACTION

4. 50 40 Sandstones 30 Porosity, % 20 Shales 10 0 1,000 2,000 3,000 4,000 5,000 6,000 0 Overburden pressure, psi 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”, pm=po-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 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

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