Pore fluid properties

Hydrocarbons occur in a variety of conditions, in different phases, and with widely varying properties, This page will cover the important geophysical properties of pore fluids. Pore fluids are fluids that occupy pore spaces in a soil or rock.

Relationship between different mixtures

Fig. 1 shows schematically the relation among the different mixtures. For a single, constant composition mixture, as we vary temperature and pressure over a wide range, we would encounter the boundary between the single and multiphase regions. In contrast, if we restrict the temperatures and pressures to those typical of reservoirs, we could again move in this phase "space" by changing compositions. Velocities and densities will be high (close to water) for heavy "black" oils to the left of the figure and decrease dramatically as we move right toward lighter compounds.

• 

  Fig. 1 – General fluid phase behavior for hydrocarbon mixtures. Above the critical point, there is a continuum of compositions and properties from heavy oil to light gas.

In many cases, the hydrocarbons are greater than critical pressure and temperature conditions (greater than critical point). Properties then can vary continuously from liquid-like, for oils with gas in solution, to gas-like, for mixtures of light molecular weight. With changing pressure and temperature conditions, phase boundaries can be crossed, resulting in abrupt changes in fluid properties. Additional components are often injected during production, further complicating the distribution of compositions and properties. (See also Phase diagrams.)

Gas

The gas phase is the easiest to characterize. The compounds are usually relatively simple, and the thermodynamic properties have been thoroughly examined. Hydrocarbon gases usually consist of the light hydrocarbons of methane, butane, and propane. Additional gases, such as water vapor and heavier hydrocarbons, will occur in the gas depending on the pressure, temperature, and history of the deposit. The specific weight of these gases, as compared to air at standard temperature and pressure, will vary from about 0.6 for nearly pure methane to over 1.5 for gases with heavier components. Fortunately, when a rough idea of the gas weight is known, a fairly accurate estimate can be made of the gas properties at pressure and temperatures. Thomas et al. did a complete analysis of the acoustic properties of natural gases, and the discussion below follows a similar analysis.

Ideal gas law

The important seismic characteristics of a fluid (the bulk modulus, density, and sonic velocity) are all related to primary thermodynamic properties. Therefore, for gases, we are obliged to start with the ideal gas law.

....................(1)

where:

• P is pressure
• V is volume
• n is the number of moles of the gas
• R is the gas constant
• T_a the absolute temperature

This leads to a density ρ, of

....................(2)

where M is the molecular weight. The isothermal compressibility β_T is

....................(3)

for compressibility defined as a positive number.

If we calculate the "isothermal" velocity V_T, we find

....................(4)

for an ideal gas. The acoustic velocity is controlled by the stiffness of the material and its density (see the derivation Compressional and shear velocities). Therefore, velocity would increase with temperature and be independent of pressure.

Modification for real gasses

Two mitigating factors bring the relationship closer to reality. First, because there are rapid temperature changes associated with the passage of an acoustic wave, we must use the adiabatic compressibility, β_S, rather than the isothermal compressibility γ β_S = β_T.

Here, γ is the ratio of heat capacity at constant pressure to the heat capacity at constant volume. In most solid materials, the difference between the isothermal and adiabatic compressibilities is negligible. However, in fluid phases, particularly gases, the isothermal compressibility can be twice the adiabatic value.

The second, more obvious factor stems from the inadequacies of the ideal gas law ('Eq. 1). The gas law can be corrected by adding a compressibility factor (Z). The relationships are thus modified:

....................(5)

....................(6)

and

....................(7)

The heat capacity ratio can itself be derived if the equations of state of the material are known. The seismic characteristics of the gas can, therefore, be described if we have an adequate description of Z with

• Pressure
• Temperature
• Composition.

Thomas et al. made use of the Benedict-Webb-Rubin (BWR) equation to define the gas behavior. The BWR equation of state is a rational equation, with numerous constants based on the behavior of natural gas mixtures. These gas mixtures range in gravity G (relative to air) from about 0.5 to 1.8. The results of the density calculations are shown in Fig. 2 . As would be expected, the gas densities increase with pressure and decrease with temperature. However, the densities also strongly depend on the gas gravity, which is composition dependent.

• 

  Fig. 2 – Hydrocarbon gas densities as a function of pressure and temperature for gas gravities of G = 0.6 and G = 1.2 (from Batzle and Wang).

The adiabatic gas modulus K (the inverse of β) also strongly depends on the composition as well as the pressure and temperature conditions. Fig. 3 shows the calculated modulus from the Thomas relationships. Again, the modulus increases with pressure and decreases with temperature, but the relationship is not as linear. The impact of variable composition (gravity) is again obvious.

• 

  Fig. 3 – Hydrocarbon gas modulus as a function of pressure and temperature for gas gravities of 0.6 and 1.2 (from Batzle and Wang).

Oil

Crude oils can be mixtures of extremely complex organic compounds. Natural oils range from the lightest condensate liquids of low carbon number to very heavy tars. At the heavy extreme are bitumen and kerogen, which may be denser than water and act essentially like solids. At the light extreme are condensates that may become gas with decreasing pressure. Oils can absorb large quantities of hydrocarbon gases under pressure, thus significantly decreasing the moduli. Under room conditions, the densities can vary from 0.5 to greater than 1 gm/cc with most produced oils in the 0.7 to 0.8 gm/cc range. The American Petroleum Institute (API) [gravity] number is defined as

....................(8)

This results in API [gravity] number of about 5 for very heavy oils to near 100 for light condensates. The extreme variations in composition and ability to absorb gases produce greater variations in the seismic properties of oils.

If we had a general equation of state for oils, we could calculate the moduli and densities as we did for the gases. Such equations abound in the petroleum engineering literature. Unfortunately, the equations are almost always strongly dependent on the exact composition of a given oil. For the purposes of this topic, we will develop only very general relations. Often, in petrophysical analysis we only have a rough idea of what the oils may be like. In some reservoirs, individual yet adjacent zones will have quite distinct oil types. We will, therefore, proceed along empirical lines based on the density of the oil. (See also Oil density.)

The acoustic properties of numerous organic fluids have been studied as a function of pressure or temperature (see, for example, Rao and Rao). Generally, the velocities, densities, and moduli are quite linear with pressure and temperature away from phase boundaries. In organic fluids typical of crude oils, the moduli decrease with increasing temperature and increase with increasing pressure. Wang and Nur did an extensive study of several light alkanes, alkenes, and cycloparaffins and found simple relationships among the density, moduli, temperature, and carbon number or molecular weight.

Velocity

For velocity:

....................(9)

where V_o is the initial velocity, V_T is the velocity at temperature T, ΔT is the temperature change, and b is a constant for each compound of molecular weight M:

....................(10)

Similarly, the velocities are related in molecular weight by

....................(11)

where:

• V_TM is the velocity of oil of weight M
• V_TOMO is the velocity of a reference oil of weight M_o at temperature T_o.

The variable a_m is a positive function of temperature. We can see from the rightmost term in Eq. 11 that the velocity of the fluid will increase with increasing molecular weight. When compounds are mixed, Wang and Nur found that the resulting velocity is a simple fractional average of the end components. This is roughly equivalent to a fractional average of the bulk moduli of the end components. Pure simple hydrocarbons, therefore, behave in a simple predictable way. We must extend this analysis to include crude oils, which are generally much heavier and have more complex compositions. The influence of pressure must also be determined. In the petroleum engineering literature, broad empirical relationships are available.

Density

By empirically fitting equations to these data, we can get density as functions of initial density (or API number), temperature, and pressure

....................(12)

These densities are shown in Fig. 4.

• 

  Fig. 4 – Oil density as a function of pressure and temperature for three weights of oil: API = 10, 30, and 50 (from Batzle and Wang).

Isothermal compressibility

By differentiating Eq. 12, we obtain the isothermal compressibility β_T,

....................(13)

Adiabatic bulk moduli

If we assume a reasonable and constant heat capacity ratio γ of 1.15, we obtain the adiabatic bulk moduli K.

....................(14)

General relationship of oil velocity

The ultrasonic velocities of a variety of crude oils measured recently are reported in Wang et al. A general relationship of oil velocity was derived.

....................(15)

where:

• V is in m/s
• T in °C
• P in bars
• API is the API degree of the oil

....................(16)

for V in ft/s, T in °F, and P in psi.

Using these velocities and the densities as shown in Fig. 4, we find the moduli shown in Fig. 5.

• 

  Fig. 5 – Oil modulus as a function of pressure and temperature for three weights of oil: API = 10, 30, and 50 (from Batzle and Wang).

Gas/oil ratio

Very large amounts of gas or light hydrocarbons can go into solution in crude oils. In fact, the lighter crudes are condensates from the gas phase. We would expect the "live" or gas-saturated oils to have significantly different properties than the "dead" or gas-free oils commonly available and measured. The amount of gas that can be dissolved is a function of:

• Pressure
• Temperature
• Composition of both the gas and the oil.

....................(17)

where R is the gas-oil ratio in liters/liter (1 liter/liter = 5.615 cu ft/bbl) at atmospheric pressure and at 15.5°C and G is the gas gravity. Eq. 17 indicates that much larger amounts of gas can go into the light (high API number) oils. In fact, heavy oils may precipitate heavy compounds if much gas goes into solution.

The effect of this gas in solution on the oil acoustic properties has not been well documented. Sergeev noted that gas in solution will reduce both oil and brine velocities. He calculated that this mix would change some reservoir reflection coefficients by more than a factor of two. A rough estimate of this dissolved gas effect can be made by assuming that the relationship in Eq. 18 remains valid and by adjusting the oil density to include the gas component. We are assuming here that the gas is a liquid component with its own volume and density and that the result is an ideal liquid mixture. The simple additive relations found in Wang and Nur support this concept. The estimated density becomes

....................(18)

where:

• ρ_O is the dead oil density
• ρ_G is the gas saturated live oil density

The factor F is derived from the gas/oil ratio

....................(19)

Fig. 6 shows the live and dead oil velocities measured in Wang et al. along with the estimates using Eqs. 16, 18, and 19.

• 

  Fig. 6 – Acoustic velocity of a 23 API oil both “dead” or gas-free and “live” with 85 L/L gas in solution. Dissolved lowers both the effective density and velocity of the live oil mixture.

Brines

The great bulk of the pore fluids consists of brines. Their composition can range from almost pure water to saturated saline solutions. Gulf of Mexico area brines often have rapid increases in concentration with increasing depth. In other areas, the concentrations are often lower but can vary drastically between adjacent fields.

Thermodynamic properties of aqueous solutions

The thermodynamic properties of aqueous solutions have been studied in detail. Keenan et al. give a relation for pure water that can be iteratively solved to give densities at pressure and temperature. Helgeson and Kirkham use this and other data to calculate a wide variety of water properties over an extensive temperature and pressure range. One obvious effect of salinity is to increase the density of the fluid. Rowe and Chou presented a polynomial to calculate both specific volume and compressibility of various salt solutions at pressure over a limited temperature range. Extensive additional data on sodium chloride solutions is provided in Zarembo and Fedorov and Potter and Brown. Using all these data, a simple polynomial can be constructed that will adequately calculate the density of sodium chloride solutions:

....................(20a)

and

....................(20b)

Here,

• T and P are in °C and bars, respectively
• x is the weight fraction of sodium chloride;
• ρ_B is the density of the brine in gm/cm³

The calculated brine densities, along with selected data from Zarembo and Federov, are plotted in Fig. 7. The accuracy of this relationship is limited largely to the extent that other mineral salts, particularly divalent ions, are in solution.

• 

  Fig. 7– Brine density as a function of temperature pressure and salinity (ppm = parts per million NaCl). Solid circles are from Zarembo and Fedorov.

A vast amount of acoustic data is available for brines, but generally for pressure, temperature, and salinity expected under oceanic conditions. Wilson provides a relationship for the velocity V_w of pure water to 100°C and about 1000 bars

....................(21)

Millero et al. and Chen et al. give additional factors to be added to the velocity of water to calculate the effects of salinity. Their corrections, unfortunately, are limited to 55°C and 1 molal ionic strength (55,000 ppm). We can extend their results by using the data of Wyllie et al. to 100°C and 150,000 ppm NaCl. Still, this leaves the high-temperature and -pressure region with no data. Here we can use the isothermal modulus calculated from Eq. 20 to estimate the adiabatic moduli. We can also use the velocity function provided in Chen et al. but with the constants modified to fit the additional data.

Heat capacity ratio of the brine

The heat capacity ratio for the brine can be estimated from the PVT relationship in Eq. 20 and estimates of the isobaric heat capacity from Helgeson and Kirkham:

....................(22)

and

....................(23)

In this equation, m is the molal salt concentration and c_ij, d_ij, and e_i are constants. Using the calculated density and velocity of brine produces the modulus, and this is shown in Fig. 8.

• 

  Fig. 8 – Brine modulus as a function of temperature, pressure, and salinity (ppm = parts per million NaCl). Water and brines are peculiar fluids in that they have a modulus (and velocity) maximum around 70°C.

Nomenclature

aij	=	water density coefficients
b	=	velocity/temperature constant, m/sC
B	=	bulk modulus/porosity factor
G	=	shear modulus, GPa or MPa
M	=	molecular weight, g/mole
MA, MB	=	modulus of component a, b, etc., GPa or MPa
P	=	pressure, MPa
R	=	gas constant, (L MPa)/(K mole)
t	=	time, s
T	=	temperature, °C
Ta	=	absolute temperature, K
VTM	=	oil weight m compressional velocity, m/s
VTOMO	=	oil weight m compressional velocity at to, m/s
VT	=	isothermal fluid compressional velocity, m/s
n	=	number of moles
Ks	=	saturated bulk modulus, GPa or MPa
β	=	strength factor, numeric
βS	=	adiabatic compressibility, MPa–1
βT	=	isothermal compressibility, MPa–1
ρ	=	density, kg/m3 or g/cm3
ρO	=	oil density, kg/m3 or g/cm3
y	=	directional component, m

Noteworthy papers in OnePetro

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External links

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See also

Rock density and porosity

PEH:Rock_Properties