*Kompresibiltas batuan reservoir Terjadi kompaksi pada batuan sediment

*Porositas akan turun yang besarnya ditentukan oleh maksimum burial depth Over burden pressureYang efeknya adalah : Changes in packing Pressure solution Recrystallization Deformation of rock fragments Compaction effects are not reversed by erosional unroofing (hysteresis effect)

Akibat kompaksi pada batuan sedimen maka :

*MECHANICS OF COMPACTION

*Relationship of Original Formation Porosity to Overburden Pressure

*Isothermal CompressibilityGeneral DefinitionThe relative volume change of matter per unit pressure change under conditions of constant temperatureUsually, petroleum reservoirs can be considered isothermal (an exception: thermal stimulation)Increasing pressure causes volume of material to decrease (compression) - e.g. reservoir fluidsDecreasing pressure causes volume of material to increase (expansion) - e.g. reservoir fluids

*Isothermal CompressibilityGeneral Equation

C: Coefficient of Isothermal CompressibilityALWAYS positive valueoilfield units: 1/psiaV: Volumeoilfield units: ft3p: Pressure exerted on material oilfield units: psiaNegative sign in equation determined by V/p term, to force the coefficient C to be positiveVolume is a function of pressure only (temperature is constant, and amount of material is constant)

*Formation CompressibilityImportanceFormation compressibility can have a significant impact on reservoir performanceSubsidence can have significant environmental impactTypesMatrix 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 COMPRESSIBILITYUnder static conditions, downward overburden force must be balanced by upward forces of the matrix and fluid in pores2. Thus:

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/ftdp/dZ = 0.465 psia/ft

*Formation CompressibilityEquation

Cf: Formation Compressibility (Pore Volume Comp.)ALWAYS positive valueoilfield units: 1/psiaVp: Pore volumeoilfield units: ft3p: Pressure of fluid in poresoilfield units: psiaPositive sign in equation determined by Vp/p term, to force Cf to be positivePore volume is function of pressure only (temperature is constant, amount of reservoir rock is constant)

*Subsidence and Bulk CompressibilityProcess of subsidenceBulk volume decreases as fluids are producedArea is constant Formation thickness decreases (causing subsidence of strata above)Porosity: = Vp/Vb = 1-(Vm/Vb); where Vb=Vp+VmNet compaction pressure: pm = po - pOverburden (po) is constant dpm= -dpAs net compaction pressure increasesBulk 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 aboveCb = (-1/Vb) [(Vp/pm) + (Vm/pm) ]Cb = (-1/Vb) [(- Cf Vp) + (- Cm Vm)]Cb = Cf + (1-)Cm; usually Cm

*Formation CompressibilityCalculation of Pore Volume Change

Separate

and Integrate

Two common approaches for constant value of CfExact Integration1st Order Approximation

*Formation CompressibilityPore Volume Change - Continued

Exact Integration

Exponentiating (Inverse of Natural Logarithm) and rearranging

OR

*Formation CompressibilityPore Volume Change - Continued

1st Order Approximation

*Laboratory Determination of CfIn reservoirs, overburden pressure is constant and the pressure of fluid in pores changes, resulting in pore volume changeIn the laboratory, we change the confining pressure on the core plug (overburden) while holding the pore pressure constantRemember that the net compaction pressure on the matrix is the difference between the overburden and pore pressuresThis allows us to obtain useful results in the laboratory

*Laboratory Determination of CfLaboratory ProcedureCore plug is 100% saturated with brineCore plug is placed in rubber or soft copper sleeveAs pressure outside sleeve is increased, pore volume decreases and the volume of expelled brine is measuredpconfining

*Hysteresis Effect - Formation CompressibilityHysteresis: 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 behaviorFor 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.Pore VolumePore PressureInitial Conditions

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

**The equation for C is an ODE (Ordinary Differential Equation)*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*p is fluid pressure in the pores, and can be easily measured with a pressure gauge.

Remember: Force = (Pressure) *(Area)

**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.**If p2