Technical Notes

This section presents technical notes explaining thermodynamic phenomena and provides recommendations on which methods and models to use to solve problems within fluid phase behavior.

Importance of Critical Point for the Phase Behavior of a Reservoir Fluid.


The phase behavior of a pure hydrocarbon component is throughout the gas and liquid region essentially determined by the critical temperature and pressure of the component. As discussed in this Technical Note, the phase behavior of a petroleum reservoir fluid is also strongly influenced by the location of the critical point. Reservoir fluids are multicomponent mixtures, and compared to a pure component, this adds an extra dimension. The below analysis shows that the saturation pressure at the reservoir temperature in addition to the critical point is all that is needed to generate a complete phase diagram for a reservoir fluid. A measured critical point is rarely available for reservoir fluids, but as shown in two recent Kapexy publications, the critical point of a reservoir fluid can be simulated from its composition. This allows a reliable equation of state model to be developed if only a fluid composition and a measured saturation pressure at the reservoir temperature are available. By utilizing this finding, versatile EoS models applicable to both reservoir and process conditions, as well as when gas injection is used as a means of enhancing recovery, can be developed with far less experimental PVT data than is standard today.

The famous Dutch scientist, van der Waals (vdW) presented the first cubic equation of state in 1873.
It is built on the Principle of Corresponding States, which basically says: “If you know the critical point of a hydrocarbon component, you can simulate the behavior of that component at any P and T”. The vdW equation relates P, V and T through two parameters, a and b, both of which are unique functions of the critical temperature, Tc, and the critical pressure, Pc. The considerations behind the vdW equation are illustrated in Figure 1. Far from the critical point, the gas and liquid properties on either side of the vapor pressure line are much different, but they become progressively more similar when approaching the critical point, at which the properties of the two phases are identical. The critical temperature and pressure differ between components, but the qualitative pattern as illustrated in Figure 1 is the same for all hydrocarbons.
Figure 1 How van der Waals saw the development towards criticality for a pure hydrocarbon.

Redlich and Kwong extended the vdW concept to mixtures, and Soave introduced a corrective term, expressed through the acentric factor, to better describe how the saturation point of a hydrocarbon component evolves with temperature.
Figure 2 shows the phase envelope of a reservoir fluid with iso-volume (quality) lines. The quality lines are bound to meet at the critical point, and the location of the critical point exerts much influence on the phase amounts, properties, and compositions also at pressures and temperatures far from the critical point.

Figure 2 Phase envelope of a petroleum reservoir fluid with critical point (CP) and iso-volume (quality) lines.

Given that the location of the critical point affects the phase behavior of a reservoir fluid throughout the gas and liquid regions, and that the critical point is the basis of the cubic equations, one may wonder why the critical point of a reservoir fluid is not given importance in equation of state (EoS) modeling. The focus is instead on matching PVT data (CME, CVD, Differential Liberation, etc.) measured at the reservoir temperature. A likely explanation is that it can be difficult to measure the critical point of a reservoir fluid. For oils, the critical temperature is higher than the reservoir temperature. For gas condensates it is lower and can be well below 0°C. Also, it counts that the PVT studies that are standard today were defined at a time when it was not possible to simulate the critical point of a multicomponent mixture. Calculation of the critical point of a multicomponent mixture and flash calculations in the near-critical region only became possible with Professor Michael Michelsen’s pioneering work within phase equilibrium algorithms in the early 1980s [1].
A swelling experiment stands out among PVT experiments. It is performed at the reservoir temperature and starts with a measurement of the saturation point of the reservoir oil. Gas is added in steps, and after each gas addition, the saturation pressure is measured. It is further recorded when the saturation point changes from a bubble point to a dew point. Between the last bubble point and the first dew point is a composition that is critical at the saturation pressure. If the equation of state parameters are tuned to match that this composition is critical, it allows the critical point of the reservoir oil to be determined as is illustrated in Figure 3. This is done using the same EoS model to simulate the critical point of the fluid after removing the added gas. The components in the added gas have well-defined equation of state parameters, and the assumption is that these components are correctly described both in the critical fluid and in the reservoir fluid before gas is added.

Figure 3 Procedure used to determine the critical point of a reservoir oil.

Swelling experiments are quite costly and will rarely be conducted unless gas injection is considered as an increased recovery technique. Fortunately, sufficient swelling data has been published to allow correlations to be developed for predicting how the critical temperature and pressure of a reservoir oil evolve with the C7+/C6- molar ratio. This development is shown graphically in Figure 4 and is valid for reservoir fluids for which at least 10 mol% of the hydrocarbons are C7+ components. Reservoir fluids are not random mixtures but have a certain pattern that is the result of chemical reaction equilibria. It is for example well known that the logarithm of the mole percentage of a C7+ component develops linearly with its carbon number. This pattern brought about by chemical reactions that have taken place over thousands of years is the reason it is possible to develop simple correlations as those visualized in Figure 4.

Figure 4 Relations between critical temperature (left-hand) and critical pressure (right hand) and the molar ratio C7+/C6- for a reservoir oil composition.

The EoS modeling procedure, utilizing the found relationship between the critical point and the C7+/C6- molar ratio, is as follows for reservoir fluids for which at least 10 mol% of the hydrocarbons are C7+ components [2].


    1. Make a copy of the fluid and remove inorganics (N2, CO2 and H2S).
    2. Calculate the molar C7+/C6- ratio for the fluid from 1.
    3. Read off from Figure 4 the critical temperature and pressure for the fluid from 1.
    4. Tune the properties of the C7+ pseudo-components to match the measured saturation pressure of the reservoir fluid and the critical point of the reservoir fluid freed of inorganics.
    5. Use the resulting EoS model for the reservoir fluid. It is applicable at both reservoir and process conditions as well as when gas injection is used as EOR technique.

A paper at ADIPEC October 2-5, 2023 [3] presents a similar procedure applicable to gas condensates.


[1] Michelsen, M.L., Calculation of phase envelopes and critical points for multicomponent mixtures, Fluid Phase Equilibria 4, 1980, 1-10.

[2] Pedersen, K.S., Shaikh, J.A. and Christensen, P.L., Importance of critical point for the phase behavior of a reservoir fluid, Fluid Phase Equilibria 573, 2023.

[3] Pedersen, K.S., Christensen, P.L. and Shaikh, J.A., Use of critical point in equation of state modeling for reservoir fluids, SPE-216776-MS, ADIPEC, Abu Dhabi, October 2-5, 2023.

CO2 – A Spacious Waste Product

Underground storage of CO2 is seen as one of the options to stop the increase in CO2 concentration in the atmosphere caused by the combustion of gas and oil. Some challenges are associated with such disposal:

  1. Exhaustion gas is not pure CO2. Before disposal it must be cleaned for nitrogen and other gases.
  2. The weight amount of CO2 produced is significantly higher than that of the gas or oil burned.
  3. For each energy unit produced by burning gas or oil, 30% of that energy is required to store the produced CO2 (Celia et al. 2015).
  4. The required storage capacity far exceeds the volume the oil or gas occupied in the reservoir.
  5. There could be unintended environmental consequences of largescale CO2 concentrations in the underground.

The chemical reaction for burning of methane (CH4) is:
CH4 + 2O2 -> CO2 + 2H2O

Methane has a molecular weight of 16, while CO2 has a molecular weight of 44. That means for each burned methane (CH4) molecule, 2.75 times as high a weight amount of CO2 is produced.
Table 1 shows a typical reservoir oil composition. As is detailed in the table, burning 1 mole (=107.96 g) of oil will produce 344.18 g CO2. The weight amount of CO2 produced when burning the oil is in other words 344.18/107.96 = 3.19 times higher than the weight amount of the reservoir oil.








Mass (g)

per mole Oil

Mass (g) Carbon

per mole Oil

Mass (g) produced CO2

per mole Oil

N2 0.56 28.01 0.16 0.00 0.00
CO2 3.55 44.01 1.56 0.43 1.56
C1 45.33 16.04 7.27 5.44 19.94
C2 5.48 30.07 1.65 1.31 4.82
C3 3.70 44.10 1.63 1.33 4.88
iC4 0.70 58.12 0.41 0.34 1.23
nC4 1.65 58.12 0.96 0.79 2.90
iC5 0.73 72.15 0.53 0.44 1.61
nC5 0.87 72.15 0.63 0.52 1.91
C6 1.33 86.18 1.15 0.96 3.51
C7+ 36.11 254.86 92.03 82.31 301.80
Total 107.96 93.87 344.18
Table 1 Oil composition that has a saturation pressure of 268 bar at the reservoir temperature of 93°C. The reservoir pressure is 300 bar.

Atmospheric air supplies the oxygen (O2) for the combustion of gas and oil. It contains approximately 21% O2. Of the rest, 78% is nitrogen (N2), which component is unaffected by the combustion. Before starting disposal of CO2 in the underground, CO2 must be separated from N2 and other gases. This can be done using an amine absorption process as sketched in Figure 1. CO2 is absorbed when the combustion gas contacts the amine solution, while N2 and other gases are discharged at the top. The absorbed CO2 is separated from the amine solution in a heater.

Figure 1 Amine absorption unit for separating CO2 from other gases contained in combustion gas.

The oil composition in Table 1 has a density of 718 kg/m3 at reservoir conditions. With a 3.19 times mass increase (see above), the waste amount of CO2 produced when burning 1 reservoir cubic meter of oil is 718 x 3.19 kg = 2,290 kg of CO2.

Assume that 40% of the oil is produced by natural depletion. That is 287.2 kg per initial reservoir cubic meter of oil. Further assume for simplicity that the produced oil composition is identical to that in Table 1. With this assumption the total composition of the fluid remaining in the reservoir (60% of the initial oil in place) will also be identical to that of the oil in Table 1, but the average density will be 1/0.6 = 1.67 times lower than before production started (i.e. 718/1.67 = 478.7 kg/m3). This has made the reservoir pressure decrease from 300 bar to 93.6 bar (found by a V/T flash) and the reservoir fluid has split into two phases (48.9 volume% gas and 51.1 volume% oil).

Again, using the weight increase factor of 3.19 for oil -> CO2, the produced weight amount of CO2 per initial reservoir cubic meter oil will be 287.2 x 3.19 = 916.2 kg CO2.

Figure 2 shows how much the reservoir pressure would increase with each percent of the produced CO2 injected in the reservoir. The initial reservoir pressure of 300 bar is reached when around 28% of the produced CO2 is injected. This means that other storage options are needed for 72% of the CO2 produced.

Figure 2 Reservoir pressure as a function of percent of the CO2 produced by combustion of the oil in Table 1 injected in the reservoir.
As illustrated in Figure 3, deep saline reservoirs could be a supplement to depleted gas and oil reservoirs. Such reservoirs are present in large numbers worldwide and have sufficient storage capacity to consume all the CO2 produced by combustion of gas and oil. Despite an apparent immense potential, CO2 injection in saline aquifers has so far been limited to pilot scale tests and most studies on the storage of CO2 in saline aquifers are of a theoretical nature. A likely reason is that saline aquifers, unlike oil and gas reservoirs, have not proven their ability to encapsulate gas for thousands of years.
Figure 3 Deep saline aquifers as a source of CO2 storage capacity beyond that of depleted oil reservoirs.

CO2 injected into an aquifer will only dissolve in the saline water to a limited extent. Most CO2 will be present as a free CO2 phase containing small amounts of dissolved water originating from the aquifer. CO2 has a critical point of 31°C and 73.8 bar. In aquifers suitable for storage of CO2, both temperature and pressure will exceed the values at the critical point of CO2, and the free CO2 will be in a supercritical state.
Figure 4 shows what volume the CO2 produced by burning one reservoir cubic meter of the oil in Table 1 will occupy in an aquifer. At all conditions it will require a volume that is more than twice the volume of the oil at reservoir conditions.

Figure 4 Cubic meter of produced pure CO2 per reservoir m3 of oil as a function of pressure at various temperatures.

The theory states that the injected CO2 will displace the water in the aquifer until the amount of water in the displaced areas reaches the irreducible water saturation. It is unclear to what extent this theory is backed up by experimental studies. Depending on the CO2 injection rate, the displacement could be accompanied by a pressure increase that might cause cracking with subsequent release of CO2 into the atmosphere. Considering the enormous amounts of CO2 that potentially need to be stored, such releases of CO2 could have severe environmental consequences.

Celia, M. A., Bachu, S., Nordbotten, J. M., and Bandilla, K. W., Status of CO2 storage in deep saline aquifers with emphasis on modeling approaches and practical simulations, Water Resour. Res. 51, 6846–6892, 2015.

The PVT Modeling Discipline

PVT modeling of reservoir fluid samples is the link between a PVT lab and the simulation software used in reservoir, flow and process simulation studies. As sketched in Figure 1, the PVT lab measures a series of fluid property data. A PVT model is derived from the PVT data that can be exported to compositional and black oil simulators.

Figure 1 PVT modeling, the link between a PVT lab and reservoir, flow and process simulators.
PVT modeling is also called EoS modeling. EoS stands for equation of state, which is an equation connecting fluid composition, pressure (P), volume (V) and temperature (T). The standard in the oil and gas industry is to use a cubic equation, most often either the Soave-Redlich-Kwong or the Peng-Robinson equation with volume correction (SRK-Peneloux or PR-Peneloux). The equations are called cubic because the molar volume is expressed as a 3rd degree polynomial.
To make use of a cubic equation of state, each component must be assigned a critical temperature, a critical pressure, an acentric factor, and a volume shift parameter. In addition, each component pair must be assigned a binary interaction parameter. This is done through fluid characterization. The term C7+ characterization is used because the critical properties of the components from C7 and above vary between reservoir fluids. The optimum critical properties of the C7+ components must therefore be found by regression to experimental PVT data. The term common EoS is used when the same EoS model is used for multiple fluid samples. A field wide EoS model is a common EoS model applicable for a whole field.
Figure 2 shows the phase envelope of a heavy gas condensate with quality lines calculated using a cubic equation of state. It illustrates that the application of cubic equations is not limited to single phases. Cubic equations can also be used to calculate the number of phases and the amounts and compositions of each phase. Thermodynamic properties like Joule-Thomson coefficients and sound velocities may also be derived from a cubic equation of state.
Figure 2 Phase envelope for heavy gas condensate with quality lines for 99% (dashed), 90% (dotted) and 70% (dashed-dotted) liquid/vapor volume.
Until around 1990 PVT modeling was essentially limited to gas and oil. Since then, several subsea pipelines have been built for transportation of unprocessed well streams. At seabed conditions, solid phases can precipitate and possibly cause plugging of the pipeline. This led to the emergence of a flow assurance discipline whose task is to keep the fluid in a pipeline flowing and manage any solids precipitation through controlled shutdowns. Gas hydrates consist of water lattices stabilized by gas molecules and can form when a gas or an oil mixture carrying water is transported in a pipeline at temperatures below 30 °C. When a fluid is in the hydrate PT-region, hydrate inhibitors like MEG and MeOH must be added to lower the hydrate formation temperature to below the ambient temperature.
Wax may precipitate and deposit in pipelines transporting untreated gas condensates or oils at temperatures below 60 °C. The wax formed from a reservoir fluid consists of heavy paraffins that are kept in solution at the reservoir temperature but may solidify in production wells and subsea pipelines where the temperature is lower.
Production of reservoir fluids containing asphaltenes can be problematic. Asphaltene precipitation can occur in the reservoir when the pressure drops as production takes place or if gas is injected for Enhanced Oil Recovery (EOR) purposes. Figure 3 shows a typical phase diagram for an oil containing asphaltenes. Asphaltene precipitation occurs in a pressure range around the saturation pressure and has its maximum at the saturation pressure.
Figure 3 Asphaltene phase diagram for an oil showing upper asphaltene curve (full drawn line), saturation pressure (dashed line) and lower asphaltene curve (dashed-dotted line). The solid black dots are critical points.

A reservoir fluid composition changes with depth. Gravity segregation causes high molecular weight components seek towards the bottom and lighter components rise to the top. This component segregation is strengthened by a vertical temperature gradient, the effect of which can be described using irreversible thermodynamics. Models for simulating the compositional variation with depth are only applicable to petroleum reservoirs in communication that will allow the molecules to move freely up and down. If a fluid communication study cannot describe the compositional variation with depth, the field will have faults or compartmentalization hindering a free movement of molecules.

Kapexy Aps is specialized in PVT modeling and offers as an additional service to train clients in the EoS modeling discipline. This can be done through regular PVT simulation courses or by engaging customer engineers in EoS modeling projects under Kapexy’s supervision.

Reservoirs with a Critical Zone

The classical picture of a fluid column with a gas cap on top of an oil zone is one where the shift from oil to gas takes place at a gas-oil contact (GOC) at which the saturation pressure equals the reservoir pressure. This situation is illustrated in Figure 1. Right at the gas-oil contact the situation is the same as it would be in a separator operating at the P & T at the GOC. As is the case with a separator gas and a separator oil, the gas and oil in equilibrium at the GOC have different GOR’s, phase densities, etc., as is illustrated in Figure 2.

Figure 1 Variation in reservoir pressure and saturation pressure in a reservoir with a Gas-Oil-Contact (GOC)
Figure 2 Variation in GOR and fluid density in a reservoir with a Gas-Oil-Contact (GOC). The dashed lines mark the shift in fluid properties at the GOC.
Figure 3 shows a depth gradient plot that qualitatively looks like the one in Figure 1, but the saturation pressure never reaches the reservoir pressure. This is characteristic for a fluid column, where the fluid type does not change from oil to gas through a gas-oil contact but through a critical point. The fluid composition at the tip of the saturation point curve is critical, i.e. the fluid has a critical temperature equal to the reservoir temperature and a critical pressure equal to the fluid saturation pressure. At shallower depths, the critical temperature is lower than the reservoir temperature while deeper in the reservoir the critical temperature is higher than the reservoir temperature. The fluid below the critical zone will accordingly be classified as an oil and the fluid above the critical zone as a gas.
Figure 3 Variation in reservoir pressure and saturation pressure in a reservoir with a critical zone.

As can be seen from Figure 4 the GOR and fluid density develop continuously with depth unlike what is seen in Figure 2 for a reservoir with a GOC.

Figure 4 Variation in GOR and fluid density in a reservoir with a critical zone./h6>
The difference between a fluid column with a gas-oil contact and one with a critical zone is clear from the above plots, but in practice it is not always obvious from samples taken at different depths whether a fluid column belongs to one or the other type. It is often assumed that in a fluid column with an oil sample at one depth and a gas sample at shallower depth, there must be a classical gas-oil contact as in Figure 1, but as illustrated by Figure 3, this is not always the case.