Oil and dissolved gas volume at reservoir conditions divided by oil volume at standard conditions. Since most measurements of oil and gas production are made at the surface, and since the fluid flow takes place in the formation, volume factors are needed to convert measured surface volumes to reservoir conditions. Oil formation volume factors are almost always greater than 1.0 because the oil in the formation usually contains dissolved gas that comes out of solution in the wellbore with dropping pressure.
Oil Formation Volume Factor (Bo)
Oil formation volume factor is defined as the ratio of the volume of oil at reservoir (in-situ) conditions to that at stock tank (surface) conditions. This factor, is used to convert the flow rate of oil (at stock tank conditions) to reservoir conditions. It is defined as:
In pressure transient analysis the flow rate used in the calculations is defined assuming reservoir conditions. Since the oil flow rate is generally measured at the surface, in stock tank barrels, this rate must be converted to reservoir conditions by multiplying the surface rate by the oil formation volume factor.
Below the bubble point pressure, the oil formation volume factor increases with pressure. This is because more gas goes into solution as the pressure is increased causing the oil to swell. Above the bubble point pressure, the oil formation volume factor decreases as the pressure is increased, because there is no more gas available to go into solution and the oil is compressed.
The value of the oil formation volume factor is generally between 1 and 2 Rbbl / stbbl (R m3 / st m3). It is readily obtained from laboratory PVT measurements or may be calculated from correlations such as Vasquez and Beggs. It is recommended that the value be evaluated at reservoir conditions at the average reservoir pressure at the time of the test.
Note that when calculating the oil formation volume factor from correlations, the solution gas oil ratio (Rs) has a significant effect on the value.
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Oil in place is the total hydrocarbon content of an oil reservoir and is often abbreviated STOOIP, which stands for Stock Tank Original Oil In Place, or STOIIP for Stock Tank Oil Initially In Place, referring to the oil in place before the commencement of production. In this case, stock tank refers to the storage vessel (often purely notional) containing the oil after production.
Oil in place must not be confused with oil reserves, that are the technically and economically recoverable portion of oil volume in the reservoir. Current recovery factors for oil fields around the world typically range between 10 and 60 percent; some are over 80 percent. The wide variance is due largely to the diversity of fluid and reservoir characteristics for different deposits.
Accurate calculation of the value of STOIIP requires knowledge of:
volume of rock containing oil (Bulk Rock Volume, in the USA this is usually in acre-feet)
percentage porosity of the rock in the reservoir
percentage water content of that porosity
amount of shrinkage that the oil undergoes when brought to the Earth's surface
and is achieved using the formula
= STOIIP (barrels)
= Bulk (rock) volume (acre-feet or cubic metres)
= Fluid-filled porosity of the rock (fraction)
= Water saturation - water-filled portion of this porosity (fraction)
= Formation volume factor (dimensionless factor for the change in volume between reservoir and standard conditions at surface)
Gas saturation is traditionally omitted from this equation.
The constant value 7758 converts acre-feet to stock tank barrels. An acre of reservoir 1 foot thick would contain 7758 barrels of oil in the limiting case of 100% porosity, zero water saturation and no oil shrinkage. If the metric system is being used, a conversion factor of 6.289808 can be used to convert cubic metres to stock tank barrels. A 1 cubic metre container would hold 6.289808 barrels of oil.
When oil is produced, the high reservoir temperature and pressure decreases to surface conditions and gas bubbles out of the oil. As the gas bubbles out of the oil, the volume of the oil decreases. Stabilized oil under surface conditions (either 60 F and 14.7 psi or 15 C and 101.325 kPa) is called stock tank oil. Oil reserves are calculated in terms of stock tank oil volumes rather than reservoir oil volumes. Oil formation volume factor ( Bo ) can be defined as ratio of Volume at reservoir condition to Volume at the surface condition (at 60F and 14.7psi). It usually varies from 1.0 to 1.7. A formation volume factor of 1.4 is characteristic of high-shrinkage oil and 1.2 of low-shrinkage oil
Due to the dramatically different conditions prevailing at the reservoir when compared to the conditions at the surface, we do not expect that 1 barrel of fluid at reservoir conditions could contain the same amount of matter as 1 barrel of fluid at surface conditions. Volumetric factors were introduced in petroleum and natural gas calculations in order to readily relate the volume of fluids that are obtained at the surface (stock tank) to the volume that the fluid actually occupied when it was compressed in the reservoir.
For example, the volume that a live oil occupies at the reservoir is more than the volume of oil that leaves the stock tank at the surface. This may be counter-intuitive. However, this is a result of the evolution of gas from oil as pressure decreases from reservoir pressure to surface pressure. If an oil had no gas in solution (i.e., a dead oil), the volume that it would occupy at reservoir conditions is less than the volume that it occupies at the surface. In this case, only liquid compressibility plays a role in the change of volume.
The formation volume factor of a natural gas (Bg) relates the volume of 1 lbmol of gas at reservoir conditions to the volume of the same lbmol of gas at standard conditions, as follows:
Those volumes are, evidently, the specific molar volumes of the gas at the given conditions. The reciprocal of the specific molar volume is the molar density, and thus, Equation (18.5) could be written:
Introducing the definition for densities in terms of compressibility factor,
Therefore, recalling that ,
Gas formation volume factors can be also expressed in terms of [RB/SCF]. In such a case, 1 RB = 5.615 RCF and we write:
The formation volume factor of an oil or condensate (Bo) relates the volume of 1 lbmol of liquid at reservoir conditions to the volume of that liquid once it has gone through the surface separation facility.
The total volume occupied by 1 lbmol of liquid at reservoir conditions (Vo)res can be calculated through the compressibility factor of that liquid, as follows:
where n = 1 lbmol,(18.11)
Upon separation, some gas is going to be taken out of the liquid stream feeding the surface facility. Let us call “nst” the moles of liquid leaving the stock tank per mole of feed entering the separation facility. The volume that 1 lbmol of reservoir liquid is going to occupy after going through the separation facility is given by:
Here we assume that the last stage of separation, the stock tank, operates at standard conditions. Introducing Equations (18.12) and (18.11) into (18.10), we end up with:
Please notice that (Zo)sc — unlike Zsc for a gas — is never equal to one. Oil formation volume factor can be also seen as the volume of reservoir fluid required to produce one barrel of oil in the stock tank.
Natural gas below the earth faces different conditions from gas at the surface. Underground, in "reservoir conditions," temperature and pressure compress the gas, reducing its volume. The formation volume factor relates the gas's volume at these conditions with its volume at standard conditions, which are 520 degrees Rankine and 14.65 pounds per square inch of pressure. To calculate the formation volume factor, you need to know the gas's compressibility factor and its temperature and pressure at reservoir conditions.
Gas Formation Volume Factor (Bg)
The gas formation volume factor, defined below, is a function of the fluid composition and the pressure/temperature ratio between reservoir (in-situ) and standard conditions (14.65 psia and 519.67 °R or 60°F):
It is a very strong function of pressure, and a weak function of temperature and gas composition.
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A gas can be defined as a homogenous fluid of low density and low viscosity, which has neither independent shape nor volume. It expands to completely fill the vessel in which it is contained. The properties of gases differ from liquids mainly because the molecules in gases are much further apart than liquids. The ideal gas law states:
This equation has limited practical value since no known gas behaves as an ideal gas. However, this equation does describe the behavior of most real gases at low pressures and it serves as a starting point to develop equations of states for real gases at elevated pressures. Furthermore, the behaviors of most real gases do not deviate drastically from the behavior predicted by this equation. By inserting a correction factor (Z) into the ideal gas equation, real gas behavior can be accurately predicted.
The correction factor is called the gas compressibility factor; the deviation from ideal gas behavior.
Gas gravity is the molar mass (molecular weight) of the natural gas divided by the molar mass of air (28.94 kg/kmol). It ranges from 0.55 for dry sweet gas to approximately 1.5 for wet sour gas. Petroleum gases typically have a gravity of about 0.65.
The gas gravity affects the calculations of gas viscosity, compressibility, compressibility factor, and solution gas-oil-ratio.
The gas compressibility factor of a natural gas is a measure of its deviation from ideal gas behavior. The gas compressibility factor is the ratio of the volume actually occupied by a gas at a given pressure and temperature to the volume the gas would occupy at the same pressure and temperature if it behaved like an ideal gas.
The gas compressibility factor is usually between 0.8 and 1.2, but it can be as low as 0.3 and as high as 2.0. It is used in the calculation of gas pseudo-pressures, and in converting gas volumes and rates from standard conditions to reservoir conditions (and vice-versa). It is sometimes called the super-compressibility factor, and is often confused with the term ‘compressibility’ (which is the change in volume per unit change in pressure). The gas compressibility factor directly affects the gas compressibility.
The compressibility of a substance is the change in volume per unit change in pressure. The gas compressibility should not be confused with the gas compressibility factor. The gas compressibility is a very strong function of pressure and increases as the pressure decreases. Mathematically, it can be expressed as:
Where p is the specified pressure and Z is the gas compressibility factor at that pressure. Thus, the magnitude of gas compressibility is of the order of 1/p.
The gas formation volume factor is the gas volume at reservoir conditions divided by gas volume at standard conditions. It is used to convert surface measured volumes to reservoir conditions. Defined below, it is a function of the fluid composition and the pressure/temperature ratio between reservoir (in-situ) and standard conditions (14.65 psia and 519.67 °R or 60 °F):
It is a very strong function of pressure, and a weak function of temperature and gas composition.
Gas viscosity is a measure of the resistance to flow exerted by the gas and is given in units of centipoises (cp). Higher values indicate more resistance to flow. For gas, the viscosity increases with increasing temperature and pressure. As pressure decreases, gas viscosity decreases. The molecules are simply further apart at lower pressure and move past each other more easily.
Experimental determination of gas viscosity is difficult. Usually it is not measured but is obtained from correlations, which include corrections for H2S, CO2, and N2. Gas viscosity is used in numerous equations, most notably in the definitions of pseudo-pressure and pseudo-time. Typically, gas viscosity is in the range of 0.015 to 0.03 cp or 15 to 30 micro-Pa-s.
Gases can be converted to liquids by compressing the gas at a suitable temperature. As the temperature increases, the kinetic energies of the particles that make up the gas also increase, and the gases become more difficult to liquefy. The critical temperature of a substance is the temperature at and above which vapor of the substance cannot be liquefied, no matter how much pressure is applied. For example, the critical temperature of water is 374°C and carbon dioxide is 31.2°C.
Critical temperature represents the temperature above which distinct liquid and gas phases do not exist. As the critical temperature is approached, the properties of the gas and liquid phases become the same, resulting in one phase known as supercritical fluid. The critical temperature value is used in the definition of reduced temperature (Tr = T / Tc) which in turn is used directly in correlations or equations of state to determine various PVT properties of natural gases (e.g. viscosity, compressibility, gas compressibility factor, etc.).
The critical pressure of a substance is the pressure required to liquefy a gas at its critical temperature. For example, the critical pressure of water is 217.7 atm and carbon dioxide is 73.0 atm.
Critical pressure represents the pressure above which distinct liquid and gas phases do not exist. As the critical pressure is approached, the properties of the gas and liquid phases become the same, resulting in one phase known as supercritical fluid. The critical pressure value is used in the definition of reduced pressure (pr = p / pc) which in turn is used directly in correlations or equations of state to determine various PVT properties of natural gases (e.g. viscosity, compressibility, gas compressibility factor etc.).
There are three main sources for developing key oil properties. These are:
Subsurface sampling of the produced fluid at reservoir conditions. This is the best method since the complex mixtures of hydrocarbons make each oil unique. The individual properties can then be determined empirically in a laboratory.
Surface sampling at a separator where the rate of flow for each fluid, gas and liquids, is measured along with their respective compositions. These fluids are then recombined in the laboratory at reservoir conditions, and the resulting fluid is used to empirically determine key oil properties.
Correlations are often used when only key parameters, such as the density of the produced oil and the volume of solution-gas evolved, are known. Correlations should be used only after being proved/tuned with laboratory measurements for subsurface samples of analogous oils.
Oil gravity relates the density of oil to that of the density of water. The oil gravity has a very strong effect on the calculated oil viscosity and solution gas-oil ratio. It has an indirect effect on the oil compressibility and the oil formation volume factor, since these variables are affected by the solution gas-oil ratio.
The American Petroleum Institute (API) developed a specific gravity scale that measures the relative density of various petroleum liquids. API gravity is gradated in degrees on a hydrometer instrument and was designed so that most values would fall between 10° and 70° API.
Usually the oil gravity is readily known. It ranges from 45 °API (light oil) through 20 °API (medium density) to 10 °API (heavy oil). The conversion from API gravity (oil field units) to relative gravity (relative to water) is:
The conversion of oil relative gravity to oil density is:
ρw ≈ 62.37 lb∙m / ft3 or 1000 kg / m3
Oil formation volume factor (FVF) is defined as the ratio of the volume of oil and dissolved gas at reservoir (in-situ) conditions to the volume of oil at stock tank (surface) conditions. Since most measurements of oil and gas production are made at the surface, and the fluid flow takes place in the formation, volume factors are needed to convert measured surface volumes to reservoir conditions. It is defined as:
Oil formation volume factor is influenced by two main factors. The dominant factor is solution gas. As pressure increases, the amount of solution gas that the oil can dissolve increases such that the oil swells, and so the formation volume factor exceeds 1.0. Once there is no remaining free gas available to dissolve in the oil, further increases in pressure result in decline in formation volume factor due to the second influencing factor – the compressibility of oil. As shown in the diagram below, oil formation volume factor is dominated by swelling below the bubble point pressure (due to dissolved gas), and by compressibility above the bubble point pressure (since all available gas is now dissolved).
Shrinkage is the inverse of the formation volume factor for oil, and represents the difference between the volume of oil in the reservoir and its volume when produced to the surface (standard pressure and temperature. The value of shrinkage is generally between 0.5 and 1. The change in volume is due to solution gas coming out of the oil as the pressure decreases.
The compressibility of any fluid is defined as the relative change in fluid volume per unit change in pressure. This is usually expressed as volume change per unit pressure. Oil compressibility is a source of energy for fluid flow in a reservoir. In an undersaturated reservoir it is a dominant drive mechanism, but for a saturated reservoir it is overshadowed by gas compressibility effects due to the evolution of dissolved gas. Oil compressibility is a component of total compressibility, which is used in the determination of skin, dimensionless time, and material balance.
Oil compressibility, when plotted versus pressure, shows a significant discontinuity at the bubble point pressure. Above this pressure (undersaturated condition), the oil is a single phase liquid (consisting of oil and dissolved gas). The compressibility of this liquid can be measured in the laboratory, and it is a weak function of pressure. At and below the bubble point pressure (saturated condition), gas comes out of solution causing a sharp increase in compressibility which causes the discontinuity shown in the plot. Once below the bubble point, oil compressibility becomes a much stronger function of pressure.
The solution gas-oil ratio is the amount of gas dissolved in the oil at any pressure. It increases approximately linearly with pressure and is a function of the oil and gas composition. A heavy oil contains less dissolved gas than a light oil. In general, the solution gas-oil ratio varies from 0 (dead oil) to approximately 2000 scf/bbl (very light oil). The solution gas-oil ratio increases with pressure until the bubble point pressure is reached, after which it is a constant, and the oil is said to be undersaturated.
The solution gas-oil ratio is a significant component of the PVT correlations. It has a very significant influence on the oil formation volume factor, the oil viscosity, and the oil compressibility.
Oil viscosity is a measure of the resistance to flow exerted by the oil, and is given in units of centipoises (cP). Higher values indicate greater resistance to flow. For oil, the viscosity decreases with increasing temperature and pressure (up to the bubble point). Above the bubble point pressure, oil viscosity increases minimally with increasing pressure as shown below. It is a very strong function of reservoir temperature, oil gravity, and solution gas-oil ratio.
The oil viscosity is measured as a function of pressure in most PVT laboratory measurements. Occasionally, a routine oil analysis report will quote the oil viscosity (and the kinematic viscosity). These measurements are at stock tank conditions and should not be used as the in-situ oil viscosity. Dead-oil viscosity is defined as the viscosity of crude oil at atmospheric pressure (no gas in solution) and system temperature. There are several correlations available for estimating oil viscosity at reservoir conditions but great care must be taken since they are very sensitive to the oil gravity and solution gas-oil ratio inputs. The oil viscosity at reservoir conditions can vary from 10000 cP for a heavy oil to less than 1 cP for a light oil.
The bubble point pressure is defined as the pressure at which the first bubble of gas comes out of solution. At this point, we can say the oil is saturated - it cannot hold anymore gas. Above this pressure the oil is undersaturated, and the oil acts as a single phase liquid. At and below this pressure the oil is saturated, and any lowering of the pressure causes gas to be liberated resulting in two phase flow.
Estimating properties of reservoir waters is important for reservoir engineering calculations, specifically for those with water influx. Also, water is often a very important liquid component of an oil and gas production system. The physical properties of water play an important role in multi-phase flow calculations.
Because water composition is only generally affected by dissolved solids, correlating water properties is relatively simple. Also, changes in the physical properties of water as function of temperature and pressure are relatively small and usually can be predicted.
Water specific gravity is defined as the density of the water divided by the density of water at standard conditions (62.3 lb / ft3). Water contained in a reservoir is saline and usually has a specific gravity greater than 1.0. Water specific gravity has no effect on calculated properties such as water compressibility, formation volume factor, and viscosity. It is used, however, in the wellbore pressure drop calculations when converting pressures from wellhead to sandface.
Salinity represents the amount of dissolved salts, usually expressed as the number of clorine ions in a fixed volume of water, measured in parts per million (ppm).
Water viscosity is a measure of the resistance to flow exerted by the water. Higher values indicate more resistance to flow. For water, the viscosity decreases with increasing temperature and increases with increasing pressure. Water viscosity is a very weak function of pressure. Water at room temperature is approximately equal to 1 cP. In a reservoir it is typically between 0.5 to 1 cP. This is due to the higher temperature, salinity, and the solution gas content of the water.
The compressibility of any substance is the change in volume per unit volume per unit change in pressure. Water compressibility is a source of energy for fluid flow in a reservoir, but it is only significant when there is no free gas present in the reservoir. The value of water compressibility can be obtained from laboratory PVT measurements or determined from correlations. The magnitude is approximately between 1.0 x 10-6 and 9.0 x 10-6psi-1. It is a weak function of pressure, temperature, and salinity.
Water formation volume factor is defined as the ratio of the volume of water at reservoir (in-situ) conditions to that at stock tank (surface) conditions. This factor is used to convert the flow rate of water (at stock tank conditions) to reservoir conditions.
Water formation volume factor can be measured in the laboratory or determined from correlations. In most situations, water formation volume factor is very close to one, and so most practitioners tend to set it to one. It is a very weak function of pressure, temperature, and salinity.
The solution gas/water ratio is the amount of gas dissolved in the water. It increases approximately linearly with pressure and is a function of the water and gas composition. Quantitatively, the solubility of gas in water is considerably less than that of gas in oil.
A wet gas is any gas with a small amount of liquid present. The term "wet gas" has been used to describe a range of conditions ranging from a humid gas which is gas saturated with liquid vapour to a multiphase flow with a 90% volume of gas. There has been some debate as to its actual definition but there is currently no fully defined quantitative definition of a wet gas flow that is universally accepted.
Wet gas is a particularly important concept in the field of flow measurement, as the varying densities of the constituent material present a significant problem.
A typical example of wet gas flows are in the production of natural gas in the oil and gas industry. Natural gas is a mixture of hydrocarbon compounds with quantities of various non hydrocarbons. This exists in either a gaseous or liquid phase or in solution with crude oil in porous rock formations. The amount of hydrocarbons present in the liquid phase of the wet gas extracted depends on the reservoir temperature and pressure conditions, which change over time as the gas and liquid are removed. Changes in the liquid and gas content also occur when a wet gas is transported from a reservoir at high temperature and pressure to the surface where it experiences a lower temperature and pressure. The presence and changeability of this wet gas can cause problems and errors in the ability to accurately meter the gas phase flowrate.
The components that make up natural gas in Pennsylvania can vary based on the “thermal maturity” of the gas, which depends on how much temperature and pressure the geologic formation experienced over time. Natural gas is known as being dry or wet, with dry gas being more thermally mature and consisting primarily of methane, whereas wet gas is less thermally mature and may contain “natural gas liquids” including ethane, butane, propane, and pentane. These natural gas liquids need to be separated from the methane to ensure the natural gas sent to consumers has a consistent BTU content. Wet gas is currently considered to be more valuable in the marketplace as the natural gas liquids have inherent value as a commodity. In the Marcellus Shale, the natural gas varies from wet in the western portion of the state and to dry in the northeast as shown on the map.
wet gas, natural gas that contains an appreciable proportion of hydrocarbon compounds heavier than methane (e.g., ethane, propane, and butane). The mixture may be gaseous or both liquid and gaseous in the reservoir; the heavier hydrocarbons are condensable when brought to the surface and are frequently separated as natural gas liquids (NGLs). Alternatively, the propane and other lighter compounds may be marketed as liquefied petroleum gas (LPG), and heavier hydrocarbons may be made into gasoline (petrol).
Wet gases usually are characterized by the volume or weight of the condensables contained in a given volume of total gas produced. This figure, computed for volumes at 15 °C (59 °F) and 750 mm of mercury, is usually expressed either in gallons per 1,000 cubic feet or in grams per cubic metre. In the United States, for a gas to be classified as wet, it must contain more than 0.1 gallon of condensables per 1,000 cubic feet of gas.
The compressibility factor
(Z), also known as the compression factor, is a useful
thermodynamic property for modifying the ideal
gas law to account for the real
In general, deviation from ideal behavior becomes more significant
the closer a gas is to a phase change, the lower the temperature or
the larger the pressure. Compressibility factor values are usually
obtained by calculation from equations
of state (EOS), such as the virial
equation which take compound specific empirical
constants as input. For a gas that is a mixture of two or more pure
gases (air or natural gas, for example), a gas
composition is required before compressibility
can be calculated.
Alternatively, the compressibility factor for specific gases can be read from generalized compressibility charts that plot as a function of pressure at constant temperature.
The compressibility factor is defined as
where is the molar volume, is the molar volume of the corresponding ideal gas, is the pressure, is the temperature, and is the gas constant. For engineering applications, it is frequently expressed as
where is the density of the gas and is the specific gas constant, being the molar mass.
For an ideal gas the compressibility factor is per definition. In many real world applications requirements for accuracy demand that deviations from ideal gas behaviour, i.e., real gas behaviour, is taken into account. The value of generally increases with pressure and decreases with temperature. At high pressures molecules are colliding more often. This allows repulsive forces between molecules to have a noticeable effect, making the molar volume of the real gas () greater than the molar volume of the corresponding ideal gas (), which causes to exceed one. When pressures are lower, the molecules are free to move. In this case attractive forces dominate, making . The closer the gas is to its critical point or its boiling point, the more deviates from the ideal case.
Generalized compressibility factor diagram.
The unique relationship between the compressibility factor and the reduced temperature, , and the reduced pressure, , was first recognized by Johannes Diderik van der Waals in 1873 and is known as the two-parameter principle of corresponding states. The principle of corresponding states expresses the generalization that the properties of a gas which are dependent on intermolecular forces are related to the critical properties of the gas in a universal way. That provides a most important basis for developing correlations of molecular properties.
As for the compressibility of gases, the principle of corresponding states indicates that any pure gas at the same reduced temperature, , and reduced pressure, , should have the same compressibility factor.
The reduced temperature and pressure are defined by
Here and are known as the critical temperature and critical pressure of a gas. They are characteristics of each specific gas with being the temperature above which it is not possible to liquify a given gas and is the minimum pressure required to liquify a given gas at its critical temperature. Together they define the critical point of a fluid above which distinct liquid and gas phases of a given fluid do not exist.
The pressure-volume-temperature (PVT) data for real gases varies from one pure gas to another. However, when the compressibility factors of various single-component gases are graphed versus pressure along with temperature isotherms many of the graphs exhibit similar isotherm shapes.
In order to obtain a generalized graph that can be used for many different gases, the reduced pressure and temperature, and , are used to normalize the compressibility factor data. Figure 2 is an example of a generalized compressibility factor graph derived from hundreds of experimental PVT data points of 10 pure gases, namely methane, ethane, ethylene, propane, n-butane, i-pentane, n-hexane, nitrogen, carbon dioxide and steam.
There are more detailed generalized compressibility factor graphs based on as many as 25 or more different pure gases, such as the Nelson-Obert graphs. Such graphs are said to have an accuracy within 1-2 percent for values greater than 0.6 and within 4-6 percent for values of 0.3-0.6.
The generalized compressibility factor graphs may be considerably in error for strongly polar gases which are gases for which the centers of positive and negative charge do not coincide. In such cases the estimate for may be in error by as much as 15-20 percent.
The quantum gases hydrogen, helium, and neon do not conform to the corresponding-states behavior and the reduced pressure and temperature for those three gases should be redefined in the following manner to improve the accuracy of predicting their compressibility factors when using the generalized graphs:
where the temperatures are in kelvin and the pressures are in atmospheres. [4
PVm = RT
And the non ideal corrected is
PVm = ZRT
In the above P = Pressure , Vm is volume (molar volume of gas) Z = the compressibility factor , R = the universal constand and T is for temperature.
In conclusion of the above we can say that Z = PVm / RT which is the most commonly used EOS (Equation of State)
The compressibility factor of a natural gas is a measure of its deviation from ideal gas behavior. Its value is usually between 0.8 and 1.2, but it can be as low as 0.3 and as high as 2.0. It is used in the calculation of gas pseudo-pressures (y), and in converting gas volumes and rates from standard conditions to reservoir conditions (and vice-versa). It is sometimes called the super-compressibility factor, and is often confused with the term "compressibility" (which is the change in volume per unit volume per unit change in pressure). The gas compressibility factor directly affects the gas compressibility (cg).
Compressibility factor of natural gases is necessary in many petroleum engineering calculations. Some of these calculations are: evaluation of newly discovered formation, pressure drop from flow of gas through pipe, pressure gradient in gas wells, gas metering, gas compression, and processing. Typically, the gas compressibility factor is measured by laboratory experiments. These experiments are expensive and time consuming. Occasionally, experimental data became unavailable and the gas compressibility factor is estimated from correlations using gas composition or gas gravity.
This paper presents new methods for calculating the gas compressibility factors for the gas condensates at any temperature and pressure. The method is based on compositional analysis of 1200 compositions of gas condensates collected worldwide. When gas composition is known, this study presents a simple mixing rule to calculate the pseudo-critical properties of the gas condensate. The new mixing rule accounts for the presence of the heptane plus fraction. In case gas composition is unavailable, the study presents new gas gravity correlation to estimate pseudo-critical properties of the gas condensate. The study also presents evaluation of eight methods to characterized the plus fraction, three widely used mixing rules, and six methods to calculate the gas compressibility factor. Thus, this study presents evaluation of one-hundred forty-four possible methods of calculating the gas compressibility factor for gas condensates. Accuracy of the new mixing rule and the gas gravity correlation has been compared to other published methods. The comparison indicates that the proposed methods are consistent and provide accurate results.
Knowledge of gas compressibility factor for gas condensates is necessary in petroleum engineering calculations. Compressibility factors are used in material-balance equations to estimate initial gas in place. It is also used in calculations of gas flow through porous media, gas pressure gradient in tubing and pipe lines, gas metering, and gas compression. Typically the gas compressibility factor, Z-factor, is determined experimentally as a part of any standard PVT report. Occasionally, PVT reports are not available and compositional data or gas gravity is used to estimated Z-factor from correlations.
Standing and Katz1 (1942) presented a generalized compressibility factor chart. The chart represents compressibility factors of sweet and dry natural gas as a function of pseudo-reduced pressure (Ppr) and temperature and (Tpr). This chart is generally reliable for sweet natural gases with minor amounts of non-hydrocarbons. It is one of the most widely accepted correlations in the oil and gas industry. Standing and Katz (SK) chart was developed using data for binary mixtures of methane with propane, ethane, butane, and natural gases having a wide range of composition2. None of the gas mixtures had molecular weight in excess of 40. For low molecular weight gases, it was found that the Z-factor estimated from SK chart has error in the order of 2 to 3%. However, for gas mixtures whose components differ greatly in molecular weight from 40, the SK chart provides inaccurate Z-factors.
Gas compressibility factors normally are used when a reservoir fluid-depletion study is not available. This practice is acceptable for retrograde gases if the gas condensate is lean; however, if the gas is rich, the reserves may be seriously underestimated if the two-phase compressibility factor is not used. The compressibility factor chart (SK) is applicable to most gases encountered in petroleum reservoirs and provides satisfactory prediction for all engineering computations. The calculated volumetric behavior of gases containing only minor amounts of non-hydrocarbon can be accurate within 97%.