Rock Compressibility
The concept of rock compressibility is similar to that of squeezing a sponge. Sponges are highly porous media used for many applications, including washing dishes due to their high capacity to store water. Pressure is applied to the wet sponge to reduce the pore volume and push the water out. The higher the pressure applied, the higher the reduction in the pore volume, resulting in more water coming out. Similarly, rocks are subjected to an overburden (or compaction) pressure that reduces their pore volume.
The compressibility of a petroleum reservoir rock is the measure of how much the rock volume changes in response to a change in pressure. It is an important property of the rock because it affects the amount of oil and gas that can be produced from the reservoir.
Porosity is a function of the degree of compaction of the rock and compaction forces are f (maximum depth of burial of the rock).
All materials exhibit some irreversible change in porosity under extreme compaction pressures.
This is due to distortion and crushing of the grain or matrix elements of the materials, and in some cases, recrystallization. The change in porosity with pressure can be represented by:
where and - are porosities at pressures P2 and P1 respectively, and C_f- is formation compressibility.
Formation compressibility is defined as the sum of both grain and pore compressibility. For most petroleum reservoirs, grain compressibility is considered to be negligible.
The effect of natural compaction on porosity is shown in Figure 3.1. Compaction greatly reduces the porosity of shale.
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Figure. 3.1 Effect of natural
compaction on porosity (from Krumbein and Sloss) |
Decompression of the field leads to changes in internal rock strains. This change in constraints leads to changes in grain volume, solid volume, and pore volume. These volume changes result in rock porosity reductions of the order of 0.5% for a pressure variation of 70 bars in internal fluid pressure, i.e., porosity falls from 20% to 19.9%.
The main source of stress (the rock) is the following:
• External stress:
the burial depth induces stress by vertical loading from the weight of solid material above.
• Internal stress:
the fluids inside the pore space of the rock exert a counteracting hydrostatic force due to the hydrostatic head and any overpressurization.
• Stress induced laterally as a result of geological deformation and lateral confinement. The depletion of fluids from the pore space of a reservoir rock results in a change in the internal stress in the rock, thus causing the rock to be subjected to a different resultant stress.
This change in stress results in changes in the grain, pore, and bulk volume of the rock. Of principle interest to the reservoir engineer is the change in the pore volume of the rock. The rock and bulk compressibilities are considered small in comparison with the pore compressibilities Cp.
The formation compressibility Cf is the term commonly used to describe the total compressibility at the formation and can be expressed as:
where pore volume of porous medium the temperature is held constant. Formation compressibility is a complex function of:
1. Rock type (consolidated, unconsolidated).
2. Pore pressure.
3. Overburden pressure.
4. The stress in different direction in the formation.
5. Maximum depth.
Types of compressibility
Three kinds of compressibility
1-Rock matrix compressibility:
is the fractional change in volume of solid rock material (grain) with a unit change in pressure.
Where Vg - volume of solids, and Cgr - rock matrix compressibility, psi-1
2- Rock bulk compressibility:
the fractional change in volume of the bulk volume of the rock with a unit change in pressure,
Where Cb - rock-bulk compressibility psi-1, Vb- bulk volume, and P^* - external hydrostatic pressure on a rock
3- Pore compressibility:
the fractional change in pore volume of the rock with a unit change in pressure.
Where P -pore pressure, C_p - pore compressibility coefficient, and V_p - pore volume
Due to the sediments above it, a rock buried deep is susceptible to an overburden load. In general, the internal hydrostatic stress of the formation fluids is smaller than the outward hydrostatic stress exerted by this overburden load.
Determination of Compressibility
1 - Correlation method
Measuring of pore volume compaction
In Figure 3.2 illustrated equipment for measuring pore volume compaction.
- A core sample is enclosed in a copper jacket, which is then placed in a pressure vessel and connected to a jereguson sight gauge.
- The hydraulic pressure system is arranged so that a saturated core can be subjected to variable internal pressures and overburden (external pressures).
- The resulting internal volume changes are indicated by the position of the mercury slug in the sight gauge.
Experimental equipment for measuring pore volume, compaction, and compressibility
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Figure.3.2 Experimental equipment
for measuring pore volume compaction and compressibility |
Correlations
Several authors have attempted to correlate the pore compressibility with various parameters, including the formation porosity.
- Hall (1953) correlated the pore compressibility with porosity (Figure.3.3) as given by the following relationship:
Where Cf is formation compressibility, psi-1, and ∅ - porosity, fraction
- Newman (1973) used 79 samples of consolidated sandstones and limestones to develop a correlation between the formation's compressibility and porosity. The proposed generalized hyperbolic form of the equation is:
Where
a =97.32 106
b = 0.699993
c = 79.8181
For limestones
a = 0.8535
b = 1.075
c=2.202 106
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Figure
3.3 Formation compaction component of total rock compressibility (From hall) |
Factors Affecting petroleum Reservoir rock Compressibility
The compressibility of a petroleum reservoir rock is affected by a number of factors, including:
1. The type of rock: Different types of rocks have different compressibilities. The compressibility of a rock is affected by its mineral composition, grain size, and cementation. For example, sandstones are generally more compressible than limestones because sandstones have more interconnected pores.
2. The porosity of the rock: The porosity of a rock is the percentage of the rock volume that is pore space. the more porous the rock, the more compressible it will be because there is more space for the rock to expand or contract.
3. The pore fluid: The compressibility of the pore fluid also affects the compressibility of the rock. Oil is less compressible than water, so a rock with oil will be less compressible than a rock with water. This is because oil molecules are closer together than water molecules, and they are less easily compressed.
4. The temperature of the rock: The temperature of the rock affects its compressibility. As the temperature increases, the rock becomes more compressible. the molecules in the rock move faster as the temperature increases. This causes the rock to expand slightly.
5. The pressure of the rock: The pressure of the rock also affects its compressibility. As the pressure increases, the rock becomes less
compressible. because the weight of the overlying rock presses down on the rock, forcing the molecules closer together. This makes the rock less compressible.
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compressibility, External stress, internal stress, Pore compressibility, Correlation method.