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Difference between revisions of "Pore fluid properties"
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Revision as of 06:28, 17 September 2013
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.
In many cases, the hydrocarbons are greater than critical pressure and temperature conditions (greater than critical point). Properties then can vary continuously from liquidlike, for oils with gas in solution, to gaslike, 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.^{[1]} 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.
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
where M is the molecular weight. The isothermal compressibility β_{T} is
for compressibility defined as a positive number.
If we calculate the "isothermal" velocity V_{T}, we find
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:
and
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.^{[1]} made use of the BenedictWebbRubin (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.
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.
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
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^{[3]}). 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^{[4]} 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:
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:
Similarly, the velocities are related in molecular weight by
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^{[4]} 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
These densities are shown in Fig. 4.
Isothermal compressibility
By differentiating Eq. 12, we obtain the isothermal compressibility β_{T},
Adiabatic bulk moduli
If we assume a reasonable and constant heat capacity ratio γ of 1.15, we obtain the adiabatic bulk moduli K.
General relationship of oil velocity
The ultrasonic velocities of a variety of crude oils measured recently are reported in Wang et al.^{[5]} A general relationship of oil velocity was derived.
where:
 V is in m/s
 T in °C
 P in bars
 API is the API degree of the oil
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.
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 gassaturated oils to have significantly different properties than the "dead" or gasfree 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.^{[6]}
where R is the gasoil 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^{[7]} 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^{[4]} support this concept. The estimated density becomes
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
Fig. 6 shows the live and dead oil velocities measured in Wang et al.^{[5]} along with the estimates using Eqs. 16, 18, and 19.
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.^{[8]} give a relation for pure water that can be iteratively solved to give densities at pressure and temperature. Helgeson and Kirkham^{[9]} 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^{[10]} 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^{[11]} and Potter and Brown.^{[12]} Using all these data, a simple polynomial can be constructed that will adequately calculate the density of sodium chloride solutions:
and
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/cm^{3}
The calculated brine densities, along with selected data from Zarembo and Federov,^{[11]} 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.
A vast amount of acoustic data is available for brines, but generally for pressure, temperature, and salinity expected under oceanic conditions. Wilson^{[13]} provides a relationship for the velocity V_{w} of pure water to 100°C and about 1000 bars
Millero et al.^{[14]} and Chen et al.^{[15]} 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.^{[16]} to 100°C and 150,000 ppm NaCl. Still, this leaves the hightemperature 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.^{[15]} 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^{[9]}:
and
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.
Nomenclature
a_{ij}  =  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 
M_{A}, M_{B}  =  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 
T_{a}  =  absolute temperature, K 
V_{TM}  =  oil weight m compressional velocity, m/s 
V_{TOMO}  =  oil weight m compressional velocity at t_{o}, m/s 
V_{T}  =  isothermal fluid compressional velocity, m/s 
n  =  number of moles 
K_{s}  =  saturated bulk modulus, GPa or MPa 
β  =  strength factor, numeric 
β_{S}  =  adiabatic compressibility, MPa^{–1} 
β_{T}  =  isothermal compressibility, MPa^{–1} 
ρ  =  density, kg/m^{3} or g/cm^{3} 
ρ_{O}  =  oil density, kg/m^{3} or g/cm^{3} 
y  =  directional component, m 
References
 ↑ ^{1.0} ^{1.1} Thomas, L.K., Hankinson, R.W., and Phillips, K.A. 1970. Determination of Acoustic Velocities for Natural Gas. J Pet Technol 22 (7): 889895. SPE2579PA. http://dx.doi.org/10.2118/2579PA.
 ↑ ^{2.0} ^{2.1} ^{2.2} ^{2.3} Batzle, M. and Wang, Z. 1992. Seismic properties of pore fluids. Geophysics 57 (11): 1396–1408. http://dx.doi.org/10.1190/1.1443207.
 ↑ Rao, K.S. and Rao, B.R. 1959. Study of Temperature Variation of Ultrasonic Velocities in Some Organic Liquids by Modified FixedPath Interferometer Method. The Journal of the Acoustical Society of America 31 (4): 439441. http://dx.doi.org/10.1121/1.1907731.
 ↑ ^{4.0} ^{4.1} ^{4.2} Wang, Z. and Nur, A. 1988. Effect of Temperature on Wave Velocities in Sands and Sandstones With Heavy Hydrocarbons. SPE Res Eng 3 (1): 158164. SPE15646PA. http://dx.doi.org/10.2118/15646PA.
 ↑ ^{5.0} ^{5.1} Wang, Z., Nur, A.M., and Batzle, M.L. 1990. Acoustic Velocities in Petroleum Oils. J Pet Technol 42 (2): 192200. SPE18163PA. http://dx.doi.org/10.2118/18163PA.
 ↑ Standing, M.B. 1962. Oilsystem correlations. In Petroleum Production Handbook, T.C. Frick, Vol. 2, Part 19. New York: McGrawHill Book Company.
 ↑ Sergeev, L.A. 1948. Ultrasonic velocities in methane saturated oils and water for estimating sound reflectivity of an oil layer. Fourth AllUnion Acoust. Conf. Izd. Nauk USSR (English trans).
 ↑ Hill, P.G., Keenan, J.H., Moore, J.G. et al. 1969. Steam Tables: Thermodynamic Properties of Water Including Vapor, Liquid & Solid. New York: John Wiley and Sons.
 ↑ ^{9.0} ^{9.1} Helgeson, H.C. and Kirkham, D.H. 1974. Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes: I. Summary of the Thermodynamic/Electrostatic Properties of the Solvent. Am. J. Sci. 274 (December): 10891198.
 ↑ Rowe, A.M. and Chou, J.C.S. 1970. Pressure–Volume–Temperature–Concentration Relation of Aqueous NaCl Solutions. J. Chem. Eng. Data 15 (1): 61–65.
 ↑ ^{11.0} ^{11.1} ^{11.2} Zarembo, V.I. and Fedorov, M.K. 1949. Density of sodium chloride solutions in the temperature range 25–350°C at pressures up to 1000 kg/cm (English translation). Journal of Applied Chemistry USSR 48: 1949–1953.
 ↑ Potter, R.W. and Brown, D.L. 1977. The Volumetric Properties of Sodium Chloride Solutions From 0 to 500°C at Pressures up to 2,000 Bars Based on a Repression of Available Data in the Literature. USGS Bulletin 1421C, US Geological Survey, Reston, Virginia.
 ↑ Wilson, W.D. 1959. Speed of Sound in Distilled Water as a Function of Temperature and Pressure. The Journal of the Acoustical Society of America 31 (8): 10671072. http://dx.doi.org/10.1121/1.1907828.
 ↑ Millero, F.J., Ward, G.K., and Chetirkin, P.V. 1977. Relative sound velocities of sea salts at 25[degree]C. The Journal of the Acoustical Society of America 61 (6): 14921498. http://dx.doi.org/10.1121/1.381449.
 ↑ ^{15.0} ^{15.1} Chen, C.T., Chen, L.S., and Millero, F.J. 1978. Speed of sound in NaCl, MgCI2, Na2So4, and MgSO4 aqueous solutions as functions of concentration, temperature, and pressure. The Journal of the Acoustical Society of America 63 (6): 17951800. http://dx.doi.org/10.1121/1.381917.
 ↑ Wyllie, M., Gregory, A., and Gardner, L. 1956. Elastic wave velocities in heterogeneous and porous media. Geophysics 21 (1): 4170. http://dx.doi.org/10.1190/1.1438217.
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