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) Hysteresis is discussed in more detail at the end of this presentation.

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 Grain Deformation Breakage of Brittle Grains Pressure Solution At Grain Contacts Ductile Framework Grain, e.g., Shale Rock Fragment)

Relationship of Original Formation Porosity to Overburden Pressure 50 Overburden pressure, psi Porosity, % 30 40 20 10 1,000 3,000 2,000 4,000 5,000 6,000 Sandstones Shales Figure shows typical formation porosity trend as burial depth increases. This porosity is at original reservoir pressure for that depth. Compaction occurred over geologic time periods. The behavior shown here is not related to changing the overburden or pore pressure of a particular reservoir during the time period of development (a few years/decades). Note that when speaking and in many older references, porosity is referred to as “percent”. Remember that porosity is a dimensionless ratio of two volumes, and should be thought of as a fraction.

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) The equation for C is an ODE (Ordinary Differential Equation)

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. Impact on Reservoir Performance: If we think of the reservoir as a tank of fluid, then pore compressibility can act to reduce the volume of the tank as we decrease reservoir pressure; like a piston helping “squeeze out” reservoir fluids. Pore Compressibility is usually of greatest interest to Petroleum Engineers

FORMATION COMPRESSIBILITY Under static conditions, downward overburden force must be balanced by upward forces of the matrix and fluid in pores 1. 2. Thus: p is fluid pressure in the pores, and can be easily measured with a pressure gauge. Remember: Force = (Pressure) *(Area) 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

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)

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 Lake Maracaibo Venezuela - Levees have been built along the lake shore to protect towns. The water level of the lake has not increased, but instead the towns have sunk 10-12 meters as petroleum reservoirs have been produced. North Sea - Production platforms have been raised in oilfields at great expense because production from chalk formations with large compressibility has resulted in subsidence. It would have been much less expensive to have prevented or designed for this subsidence Houston - Measureable subsidence has occurred in Houston area due to production of ground water for drinking One way to prevent subsidence: inject fluids to maintain reservoir pressure (fluids in pores) and prevent compaction of reservoir rock. Other examples: Pisa, Italy (groundwater) , Venice Italy (groundwater) Injection of water to maintain pressure is being tried in Pisa to slow/remediate the leaning of the famous tower.

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

Formation Compressibility Pore Volume Change - Continued Exact Integration Exponentiating (Inverse of Natural Logarithm) and rearranging OR If p2<p1 then Vp2 < Vp1 and DVp is negative.

Formation Compressibility Pore Volume Change - Continued 1st Order Approximation We use Vp1 in the denominator of the 2nd equation because we know the pore volume at p1 and wish to calculate Vp2 as pressure changes The 1st order approximation can be useful when we have discrete data such as a few experimental points from the laboratory, or in computer modeling of reservoir performance using discrete time periods. Remember: A 1st order approximations assume the function is a straight line, dVp/dp = DVp/Dp = constant. This equation can also be derived from the exact solution by considering the Taylor Series expansion for ex about x=0 and truncating after the 1st order term.

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 The lab process is like sqeezing a saturated sponge to remove water. The reservoir process is like putting the saturated sponge in a sealed plastic bag, then setting several heavy bricks on top, then poking a hole in the bag. Either way water is sqeezed out 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. Initial Conditions Pore Volume Pore Pressure