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.

New Book

Technical notes on Kapexy’s website usually address a specific technical issue. This note is an exception, by presenting the 3rd edition of the book on Phase Equilibria of Petroleum Reservoir Fluids written by Karen Schou Pedersen, Peter Lindskou Christensen, and Jawad Azeem Shaikh. Together the three authors have more than 100 years of practical and theoretical experience in this subject. The book covers a wide range of experimental techniques and simulation methods in its seventeen chapters. Below is a brief introduction to each chapter.

1 Petroleum Reservoir Fluids

The constituents of petroleum reservoir fluids are introduced. Reservoir fluids consist primarily of hydrocarbons ranging from methane with a single carbon atom to hydrocarbon compounds with more than a hundred carbon atoms. Reservoir fluids may also contain nitrogen, carbon dioxide and hydrogen sulfide. The difference in phase behavior between pure hydrocarbons and hydrocarbon mixtures is explained. There are different reservoir fluid types ranging from natural gases dominated by lighter hydrocarbons to heavy oils dominated by components with more than ten carbon atoms. Examples of each fluid type are shown. The most used terms to describe the phase behavior of reservoir fluids, such as critical pressure and temperature, acentric factor, dew point, and phase envelope, are explained.

2 Sampling, Quality Control, and Compositional Analyses

To carry out simulations of phase equilibria and physical properties for a reservoir fluid, it is necessary to have a representative sample and a compositional analysis of the fluid. The most used sampling techniques are presented as well as methods to ensure that the samples are representative of the reservoir fluid. It is explained how gas and liquids can be analyzed by gas chromatography and how a more elaborate liquid analysis can be established by a true boiling point analysis. Through calculation examples, it is explained how reservoir fluid compositions are established, based on compositional analyses of gas and liquid samples from a flashes of reservoir fluid or separator samples to standard conditions.

3 PVT Experiments

The PVT experiments the oil industry has adopted as a standard are presented. They cover the experiments carried out on the reservoir fluid (constant mass expansion, differential liberation, constant volume depletion and separator experiments) as well as experiments carried out on the reservoir fluid with added gas (swelling, equilibrium contact, multi-contact, slim tube, and gas revaporization). The latter experiments are primarily carried out for fluids from reservoirs, for which it may be relevant to carry out gas injection to increase the recovery. Examples are given of experimental data for each type of PVT study. The material balance tests carried out for studies where material is removed are presented and it is outlined what equipment and experimental technique to apply to measure gas Z-factors accurately.

4 Equations of State

Cubic equations of state remain a standard for PVT simulations in the oil and gas industry. These equations date back to the van der Waals equation presented in 1873. Currently the most used cubic equations are the Soave-Redlich-Kwong and Peng-Robinson equations. Both are to be used with a volume correction to simulate accurate liquid densities. Non-cubic equations may be used for specialized purposes. The PC-SAFT equation was developed for polymers but is also applicable to oil mixtures. The GERG-2008 equation was developed to provide more accurate simulation results for natural gas mixtures than cubic equations and can be used for mixtures with hydrocarbons up to C10. Very accurate property simulations for pure CO2 can be achieved with the Span-Wagner equation.

5 C7+ Characterization

Petroleum reservoir fluids contain thousands of different components, and it is impossible to analyze all of them. The components lighter than C7 can be quantitatively identified while the fractions C7 and heavier are divided into boiling point cuts where each cut may contain several components. Today’s compositional analyses most often stop with a C36+ fraction containing C36 and heavier. The plus fraction may have components as heavy as C200. To perform equation of state calculations, the plus fraction must be split into carbon number fractions and equation of state parameters assigned to each fraction (Tc, Pc and acentric factor) using correlations in molecular weight and density. Some fractions must be lumped together into pseudo-components to have a manageable number of components to work with in the subsequent PVT simulations. The term C7+ characterization is used for the described preparation of a reservoir fluid for equation of state calculations.

6 Flash and Phase Envelope Calculations

A flash algorithm is needed to make use of an equation of state to predict the conditions at which a fluid splits into two or more phases and the quantities and compositions of each phase. The equations that define a flash problem are presented, as well as the methods for determining phase quantities and compositions at thermodynamic equilibrium. Also covered are the techniques for handling aqueous and pure solid phases in flash calculations. The techniques for determining a gas-liquid phase envelope are outlined as well as criteria for distinguishing between a gas and a liquid phase in the supercritical region.

7 PVT Simulation

Simulation of experimental PVT data is an important part of equation of state modeling. If the simulation results do not agree well with the experimental data, it signals that something is wrong with the fluid characterization. Examples of simulation results are presented for the PVT experiments covered in Chapter 3. It is shown that an inaccurate plus molecular weight can degrade PVTsim simulation results and how this can be corrected for. Z-factor simulation results for a natural gas are shown with various equations of state including the GERG-2008 equation and compared with experimental data. Simulation results are shown for the concentration of mercury that can occur in a natural gas in contact with free mercury.

8 Thermal Properties

Enthalpy and entropy are explained based on the considerations that were behind the definition of these properties. They have a contribution from intermolecular interactions and another from the intramolecular energy possessed by the individual molecules. The former contribution can be calculated from an equation of state, while the latter one must be calculated empirically. It is explained how a well test can be used to determine the Joule-Thomson coefficient of a reservoir fluid if the reservoir temperature is known, and how the reservoir temperature can be determined if it is uncertain, but the Joule-Thomson coefficient is known. Simulated gas phase Joule-Thomson coefficients are compared with experimental data. Heat capacity and velocity of sound are also introduced.

9 Regression to Experimental PVT Data

Since it is not possible to make a complete component analysis for reservoir fluids, there is always an uncertainty regarding the composition of a such fluid. When reservoir fluid phase behavior is to be modeled with an equation of state, this uncertainty is eliminated by tuning to measured PVT data. This tuning must be carried out in such way that it is ensured that not only the measured PVT data is matched, but also that the model parameters are valid at other conditions and if gas is added to the reservoir fluid with the aim of achieving an enhanced recovery. The importance of matching the critical point of the fluid is emphasized.

10 Transport Properties

The transport properties, viscosity, thermal conductivity, interfacial tension, and diffusion coefficients are covered. In connection with reservoir simulation studies, it is especially the viscosity that is of interest, while all the mentioned transport properties are important in simulation of pipeline transport. For viscosity and thermal conductivity, the most reliable models are based on the corresponding states principle. Also presented is the LBC viscosity model, which has gained widespread use by being simple and easy to tune on. The experimental technique for measuring gas-oil interfacial tension is presented with correlations for calculating the interfacial tension. Transport property data are shown with corresponding simulation results.

11 Wax Formation

Heavy paraffinic compounds contained in reservoir fluids may precipitate as a solid wax phase if the fluid is cooled. Wax precipitation in a pipeline transporting an oil or a gas condensate will increase the viscosity of the liquid phase, and a wax layer may build up on the inside of the pipeline. Data is presented for wax precipitation from both stable oils and live oils. Modeling of wax precipitation from a reservoir fluid requires division of the C7+ components into potentially wax forming and non-wax forming compounds. The wax forming compounds must be assigned a melting temperature and a heat of fusion (melting) to represent the phase transition from liquid to wax. The amount of precipitated wax can be reduced by adding wax inhibitors, the most common of which are presented.

12 Asphaltenes

Asphaltene precipitation from reservoir oils may possibly occur in a pressure interval around the bubble point pressure. The precipitate is a highly viscous and sticky material that may cause deposition problems in production wells and pipelines. Asphaltene precipitation is increased if gas is added. Since experimental asphaltene studies are quite expensive, it may be attractive to use a screening method to clarify whether a reservoir fluid is at risk of causing asphaltene problems. Since paraffinic components are poor solvents for asphaltenes, paraffinic reservoir fluids are the most problematic even if the asphaltene content is low. With an appropriate choice of critical properties and binary interaction parameters for the asphaltene fraction, asphaltene precipitation can be modeled with a cubic equation of state.

13 Gas Hydrates

When transporting reservoir fluids carrying water at temperatures below 35°C, there is a risk of gas hydrates forming. These are solid structures consisting of water lattices stabilized by gas molecules. The physical appearance resembles that of snow and ice. Formation of gas hydrates may lead to plugging of pipes and process equipment. There are accurate models for predicting the pressure and temperature conditions at which gas hydrates can form. If pipeline transport takes place under conditions where hydrates can form, it is common practice to add a hydrate inhibitor. The most used are methanol and mono ethylene glycol. Salt is often contained in the formation water produced with a reservoir fluid and will also act as inhibitors.

14 Compositional Variations with Depth

The composition changes with the depth in a petroleum reservoir. The concentration of heavy components increases with depth. This is partly due to the action of gravity and partly to the vertical temperature gradient that exists in most petroleum reservoirs. Both effects will increase the compositional gradient and can be modeled by coupling transport of heat and mass using the concept of irreversible thermodynamics. For highly viscous fields, there is a need for a viscosity correction. In a gas zone, an increased content of heavy components will make the saturation pressure increase with depth. If the saturation pressure and reservoir pressure coincide, there will be a gas-oil contact, where the fluid composition changes discontinuously from gas to oil. If the saturation pressure remains lower than the reservoir pressure, the fluid type may instead change continuously from gas to oil by passing through a critical point.

15 Minimum Miscibility Pressure

Gas injection is an effective technique for obtaining an enhanced recovery from an oil field. The gas can be a hydrocarbon gas or CO2. Gas injection is most effective with a miscible displacement where the gas does not bypass the oil to create a gas breakthrough. A miscible displacement is achieved by a series of contacts between gas and oil, where the two phases exchange components to eventually become identical at a critical point. The lowest pressure for which a miscible displacement can be achieved is called the minimum miscibility pressure or simply the MMP. The MMP can be calculated analytically by a tie-line method, or it can be calculated by simulating the slim tube experiment used to experimentally determine the MMP.

16 Formation Water and Hydrate Inhibitors

Well streams often carry water from an underlying water zone, which calls for models that can simulate the mutual solubility of the water and hydrocarbon phases and the properties of the water phase. Due to strong intermolecular interactions, water cannot be handled using a cubic equation of state with classical mixing rules. The cubic equation must either use an advanced mixing rule as proposed by Huron and Vidal or have an additional association term (Cubic Plus Association) to represent the mutual solubility of water and hydrocarbons. The produced water phase will often contain salt, and if the well stream is to be transported in a pipeline, addition of a hydrate inhibitor may be needed. Suitable models to deal with these challenges are presented, as well as models for simulating the viscosity of water-oil emulsions.

17 Scale Precipitation

Produced well streams often carry formation water with dissolved salts from an underlying water zone. The solubility of some salts in water will be so low that they under certain conditions they will precipitate as a solid salt. Salt deposition is often referred to as scaling and is a potential problem in pipelines that transport unprocessed well streams carrying formation water. In the reservoir, scale precipitation can be seen when seawater is injected with the purpose of achieving an enhanced recovery. The solubility of a given salt can be derived from its solubility product. When more salts are present, their interaction will affect the solubility of the individual salts. This can be modeled using Pitzer’s activity coefficient model.

The Critical Point of a Reservoir Fluid – A Key Parameter in EoS Modeling

Summary
The phase behavior of a pure hydrocarbon is throughout the gas and liquid region essentially determined by the critical temperature and pressure of the component. Two recent Kapexy publications [1,2] show that the critical point also for a reservoir fluid exerts a large influence on the phase behavior of the fluid in the whole gas and liquid region. The critical point is so decisive for the behavior of a reservoir fluid that, in addition to the critical point, only a measured saturation point is needed to develop a reliable equation of state model. A measured critical point is rarely available for reservoir fluids, but the critical point of an oil can be calculated from the composition of the fluid. The same applies to the critical point of the C7+ fraction of a gas condensate. By utilizing this knowledge, the time spent developing equation of state models can be significantly reduced and performed with far less measured data than is standard today. There is the additional advantage that equation of state modeling can be performed as soon as a compositional analysis is available and does not have to await the full PVT study.

Theory
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”. This is a consequence of the vdW equation relating 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.

Today the industry standard cubic equations are the volume corrected Soave-Redlich-Kwong and Peng-Robinson equations. Unlike the van der Waals equation they can handle mixtures and therefore enable simulation of the critical point of a petroleum reservoir fluid.
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 assigned 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 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 multicomponent mixtures 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 [3].

EoS modeling consists of representing the C7+ fraction of a reservoir fluid as an appropriate number of pseudo-components and assigning values of Tc, Pc and acentric factor to each of the C7+ components. Petroleum reservoir fluids are not random mixtures. The logarithm of the mole percentages of the C7+ components develop linearly with carbon number. This pattern is the result of chemical reactions that have taken place over thousands of years. The critical temperature of the components contained in the C7+ fraction increases with carbon number and the critical pressure decreases. As illustrated in Figure 3, EoS modeling can therefore be simplified to rotating the curves representing the standard development of Tc and Pc with carbon number around a fixed value of C7 until the target PVT data is matched.

Figure 3 Development of Tc and Pc with carbon number for C7+ fractions. The full drawn lines show the default developments. The dashed lines show the variation accepted during EoS model development.

Gas Condensates
Those involved in equation of state (EoS) modeling for gas condensates will be familiar with the situation where the saturation point of the reservoir fluid is easily matched but the liquid dropout curves are not. The problem is exemplified in the left-hand side of Figure 4, which shows the experimental liquid dropout curve for a gas condensate as well as the liquid dropout curves simulated with three different EoS models, all of which match the saturation pressure. With EoS_1, the simulated liquid dropout curve is too flat. A perfect match is seen with EoS_2, while with EoS_3 the saturation pressure is simulated to be a bubble point instead of a dew point. The reason the liquid dropout curves differ is to be found in different simulated critical points. As can be seen from the phase envelope plots on the right-hand side of Figure 4, with EoS_1, the fluid is simulated to have a critical temperature much lower than the reservoir temperature. With EoS_2, the simulated critical temperature is still lower than the reservoir temperature, but not by much. Finally, the simulated critical temperature with EoS_3 is higher than the reservoir temperature. The simulated saturation point at the reservoir temperature is a bubble point and the fluid would erroneously be classified as an oil.

Figure 4 The left-hand side shows experimental and simulated liquid dropout data for a gas condensate fluid. The simulated liquid dropout curves are for three different EoS models. The right-hand side shows phase envelopes and critical points simulated using each of the three EoS-models.

Kapexy has performed an analysis of a large number of gas condensate EoS models, all of which provided a good match of liquid dropout data measured in constant mass expansion and constant volume depletion experiments [2]. As illustrated in Figure 5, the critical temperature and critical pressure of the C7+ fraction were found to increase with the average molecular weight.

Figure 5 Simulated phase envelopes for the C7+ fractions of two gas condensates exemplifying the trend that the critical temperature and the critical pressure increase with average molecular weight of the C7+ fraction.

Correlations were developed for predicting the critical point of the C7+ fraction of a gas condensate from its average molecular weight [2]. These correlations are graphically illustrated in Figure 6.

Figure 6 Critical temperature and pressure of the C7+ fraction of a gas condensate as a function of its average molecular weight.

For any gas condensate fluid, it is now possible from Figure 6 to read off the critical temperature and the critical pressure of the C7+ fraction based on its average molecular weight. If a measured saturation point exists for the entire fluid, the information in Figure 7 is available. Subsequently, the Tc and Pc curves in Figure 3 are rotated around the values for C7 until the simulation results agree with the data in Figure 7. The result can be as shown in Table 1 and as exemplified for this fluid in Figure 8, this will normally give a good agreement with the measured liquid dropout curves.

Figure 7 Data points deciding the phase behavior of the gas condensate reservoir fluid in Table 1.
Table 1 Gas condensate reservoir fluid for which the C7+ fraction has been characterized to match data in Figure 7. Experimental and simulated liquid dropout curves can be seen from Figure 8.
Figure 8 Experimental and simulated CME and CVD liquid dropout curves for the gas condensate mixture in Table 1, which has an average C7+ molecular weight of 165.

Oil Mixture
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 9. This is done using the same EoS model to simulate the critical point of the fluid after having removed 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 composition with gas added and in the reservoir fluid before adding any gas.

Figure 9 How 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- hydrocarbon molar ratio. This development is shown graphically in Figure 10 and is valid for reservoir fluids for which at least 10 mol% of the hydrocarbons are C 7+ components.

Figure 10 Relations between critical temperature (left-hand) and critical pressure (right-hand) and the molar ratio of C7+/C6- hydrocarbons for a reservoir oil composition.

The EoS modeling procedure, utilizing the found relationship between the critical point and the C7+/C6- hydrocarbon molar ratio, is as follows for reservoir fluids for which at least 10 mol% of the hydrocarbons are C7+ components [1].

  1. Make a copy of the fluid and remove inorganics (N2, CO2 and H2S).
  2. Calculate the molar C7+/C6- hydrocarbon ratio for the fluid from 1.
  3. Read off from Figure 10 the critical temperature and pressure for the fluid from 1.
  4. Rotate the Tc and Pc curves in Figure 3 to match the measured saturation pressure of the reservoir fluid and the critical point from 3. 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 an EOR technique.

References

[1] 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.

[2] 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, Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, October 2-5, 2023.

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

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.

 

Component

 

Mol%

 

Molecular

Weight

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.

Reference
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.