# Batzle and wang relationship

### Pore fluid properties -

Download Table | Calculated fluid properties from Batzle and Wang Model (for reservoir modeling showing the relationship of fluid properties to seismic. the brine density correlation of Batzle and Wang, and the brine The McCain, Kemp et al., Batzle & Wang and Rowe & Chow correlations predict very. For pure compounds. we get the relationship for adiabatic bulk modulus KS. and volume 7P Batzle and Wang heat capacity at constant pressure to heat.

The relationships are thus modified: The seismic characteristics of the gas can, therefore, be described if we have an adequate description of Z with Pressure Temperature Composition.

### Rock physics for seismic modelling - Seismic Amplitude - page

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. The results of the density calculations are shown in Fig. 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.

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. 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.

Physical properties of reservoir fluids are dependant on composition, pressure and temperature. Unless thermal recovery techniques are used, the variations of temperature in a reservoir are negligible during its production history, and pressure and composition are the dominant parameters affecting the changes observed between two surveys.

Brine physical properties are extremely dependant on its salinity S. In the Gulf of Mexico, the presence of the buried Jurassic salt generates a significant increase of salinity with depth.

In most reservoirs, brine samples are collected and their salinity measured, but Batzle and Wang [] offer a relationship to estimate salinity as a function of depth that can be used for gulf coast sediments.

They also provide relationships for the velocity and density of brine as a function of salinity, pressure and temperature See Appendix. Brine density and velocity increase with pressure in standard hydrocarbon reservoir conditions.

The gaseous phase present in the pore space of a reservoir is a mixture of the lightest hydrocarbon fractions. Its composition can vary during production when reservoir pressure decreases and the lightest oil components come out of solution.

The properties of the gas mixture can be characterized by the gas specific gravity G measured at standard temperature and pressure conditions If a complete PVT Pressure-Volume-Temperature analysis of the physical properties of gas samples is not systematically performed, the measure of its gravity is most often available and allows a good estimation of its properties as function of pressure and temperature [Batzle and Wang, ].

## Fluid Properties Calculator

The formulas in the Appendix show that the density and the bulk modulus of gas mixtures increase significantly with pressure. In addition to the crude oil produced at the surface, the oil phase in a reservoir can include dissolved light hydrocarbons that are gaseous at lower pressure. One of the key parameters controlling the properties of oil is the bubble point pressure, which is the maximum pressure where free gas can be present.

As long as reservoir pressure is above bubble point, oil is under-saturated with regard to gas, its composition remains fixed and the density and bulk modulus both increase with increasing pressure.

**SHEN YUE AND DYLAN WANG: RELATIONSHIP STATUS REVEALED 💏**

If reservoir pressure falls below bubble point during production, the lightest dissolved gas start coming out of solution. As pressure decreases and more light component leave the liquid phase, only the heaviest hydrocarbon remain in this phase, and the density and bulk modulus of the oil phase increase with decreasing pressure [Batzle and Wang,England et al.

The value of the bubble point and the relationships between pressure and elastic properties should be determined from PVT analysis of actual oil samples. If such analysis is not performed, the values of oil and gas density at surface conditions can be used to determine these relationships and the bubble point pressure [Batzle and Wang,Beggs,see equations in Appendix]. One of the standard indicators of fluid properties is the produced Gas-Oil ratio GORwhich is the ratio of the volumes of gas and oil produced at the surface.

The GOR remains constant as long as the reservoir pressure is above bubble point, but increases as soon as pressure falls below this value and free gas saturation exceeds a critical value, at which point it becomes mobile and gets preferably produced [Batzle and Wang,Steffensen, ].

This is shown clearly in K8 Figure 3. The evolution of the GOR is one of the key control parameters in monitoring production simulation.

While one of the goals of the reservoir simulation is to determine the evolution of these distributions during production, the original fluids in place before production can be totally determined from the fluid PVT properties if we assume the reservoir in hydrostatic equilibrium.

The density-pressure relationships provide the pressure gradient within each phase and the entire pressure and fluid distributions can be integrated from the knowledge of the depth of the oil-water contact OWC and of one pressure value at one depth within the oil or gas zone. Additional parameters necessary for the most accurate distribution include capillary pressures between each phase and the connate water fraction, or irreducible water saturation, which depends on matrix properties and is measured on reservoir samples.

In the case of K8, the original oil-water contact in was detected at mbsf, downdip from the study area. These two data points and the oil gravity define the pressure distribution at equilibrium shown in Figure 3. We use geostatistical simulations for this characterization, assuming that within an individual reservoir petrophysical and acoustic properties are closely related and can be associated with calibrated cross-correlation functions [He, ].

Using well logs as "Hard" accurate data and impedance volumes as "Soft" data, this method combines the high vertical resolution and accuracy of logs with the wide aerial coverage of 3D seismics. He [] provides a complete description of the Markov-Bayse conditional soft indicator technique used. The lithology is expressed in terms of shaliness.

The soft "inaccurate" data, which have to be of the same type, are approximate shaliness values gs calculated from the impedance volume by a simple weighted average: For the porosity distribution, the hard data come from porosity logs, and the soft data are calculated from the impedance volume by a modified time-average relationship: Both porosity and shale distributions show a high level of heterogeneity, illustrating the channelled deposition of the reservoir.

The bulk of the porosity is located immediately downdip from the two producing wells and in the South East corner of the study area. Having previously established the fluid and pressure distribution before production in K8, we can compare the estimations of the different models with the impedance inversion to determine which formulation offers a better representation of the observed reservoir properties.

Two additional impedance volumes were calculated with the complete KT model Eqs. We refer to these values as the KT and Han impedances, respectively. All the parameters used for grain and fluid properties are given in Tables 1 and 2. In all these figure, a perfect formulation should result in an identical linear fit with the inverted values.

This comparison seems to indicate the better readiness of these two formulations to represent the acoustic properties of the reservoir in hydrostatic equilibrium. It will be necessary, however, to make a similar comparison after simulation to evaluate how fluid substitution affects the comparison between the calculated and the inverted impedance.

A traditional view of the fluid movements within a producing reservoir is of a uniform buoyancy-driven movement of the different phases, the contact surfaces between adjacent phases remaining horizontal. Because the BHPs measured in the two wells after were below the bubble point, this indicates that the GOC has migrated down to at least these depths mbsf.

Assuming that the GOC and WOC have been simply sweeping uniformly along dip, and that the reservoir is still globally in hydrostatic equilibrium at any time, we have calculated as previously the pressure and fluid distribution that would exist in if an horizontal gas cap had formed down to mbsf and the WOC had moved up to mbsf.

The impedance changes over time Figures 3. However, the pattern and the absolute values of the observed impedance changes are much more heterogeneous in Fig 3. The bright areas in the observed impedance changes correspond to isolated impedance decreases, that could indicate areas with low connectivity where hydrocarbon, mostly gas, would remain trapped as the reservoir pressure decreases.

The comparison of Figs 3. The fact that the impedances calculated after the reservoir sweep Fig 3. Assuming that our inversion results are correct, the heterogeneity observed in the impedance difference over time suggests a migration process more complex than the simple gravitationnal sweep.

Numerical simulation of the migration of the different phases can be used to identify the actual behavior of the reservoir under production. While permeability is directly related to porosity, it can also be affected considerably by the presence of shales [Audet,McCarthy, ].

The relative permeability of each phase increases with its saturation and can be calculated in three phases fluid as a combination of the relative permeabilities of two-phases fluid mixtures: Swco is the connate, or irreducible, water saturation. The variations of krg and krog as a function of gas saturation and of krw and krow as a function of water saturation, called saturation functions, have to be explicitely provided to the simulator.

The lower end member of each saturation function is the critical saturation, which is the minimum saturation value for each phase to become mobile. Because of their dependance on the fluid compositions and on the pore structure, saturation functions should be measured in laboratory for every reservoir.

## Pore fluid properties

However, relative permeability measurements are rarely performed, in part because the experimental procedures to measure them are not universally established [Rose, ]. No relative permeability measurements were available for either K8 or the Eugene Island LF field, and since this absence has to be expected in most reservoirs, saturation functions are among the prime parameters to adjust within the 4D loop.

The saturation functions used in K8 are shown in Figure 3. The position and the shape of each grid block is defined by the coordinates of its eight "corners". The coordinates and the attributes of the grid blocks porosity and permeability are directly imported from the reservoir characterization grid.

The numerical formulation of Eq. Since the only actual measurable effects of the reservoir drainage are the volumes of hydrocarbons collected at the surface, the production history recorded on the rig floor is the principal constraint on the simulator. It is expressed in terms of daily production rate of oil or gas for each well, and averaged monthly.

This imposed production is translated into pressure gradients between the wellbores and the formation, which are echoed in the reservoir at each time step of the simulation.

In addition to the perforated well intervals, the only flows allowed in and out the reservoir model are from eventual aquifers.