Bubble-point

The bubble point measurement is recognized as an ASTM procedure (F316-80 [26] and E128-61 [27]). This technique allows the determination of pore diameters and the presence of defects in the membrane. Bubble point is based on Jurin s law. If a porous membrane is impregnated with a liquid (e.g., water, alcohol) each pore has a meniscus of condensate at the gas-liquid interface which opposes the flux of gas. To unblock the pores a pressure Ap must be applied. According to the Jurin s law, the smaller the pores, the higher the pressure required 

In this method a wetting liquid is chosen to obtain a cos 0 = 1. The requisite properties of the liquid used are that  

The bubble point technique is thus a very convenient test to visualize the location of possible defects. In the presence of cracks, for instance, the first bubbles are located on the defects and the bubbles do not appear uniformly on the surface of the support. 

If one independent variable is the temperature or pressure and the only product is a saturated liquid (i.e., the other independent variable is the vapor fraction set at the zero limit), then the operation is a bubble point flash. The dependent variables are the pressure or temperature, the heat duty, and the liquid and vapor compositions. Since the liquid is the only product, its composition is identical to the feed composition. The vapor composition refers to the composition of a vapor at equilibrium with the liquid. Although its rate is zero, its composition is determinable and is equal to the composition of the first vapor bubble resulting from infinitesimal vaporization. Bubble points are not feasible at all temperatures and pressures. As discussed in 

Our work as process engineers and operators is based on three principles  

The purpose of this chapter is to explain what is meant by the terms bubble point and dew point, and how we can use these ideas to improve the operation of the distillation tower. To begin, we will derive the bubble-point equation, from the basic statement of vapor-liquid equilibrium  

We really should use mole fraction, and not concentration, in our description of y and x, but for our work, we will just say that the term concentration refers to the percent of a component that the operator would see in the gas-chromatographic (GC) results, as reported by the lab. The equilibrium constant, assuming the ideal-gas law applies, is defined as 

PT = total pressure we are working at, in psia (psia = psig + 14.7) 

If you do not recall the meanings of mole fraction or the ideal-gas law, don t worry—it is not necessary to recall these in order to understand bubble points, or dew points. Substituting Eq. (9.2) in Eq. (9.1), we obtain 

The total pressure over an equilibrium solution is, by definition, the sum of the partial pressures of the components involved  

Consider first the case of the B.P. pressure calculation the temperature and liquid phase mole fractions are given, and we want to calculate the total pressure and vapor phase composition of the equilibrium system. To this purpose, we will assume that  

Second virial coefficients, B,. and B,y, are available, or can be estimated from some empirical correlation, typically that of Tsonopoulosor that of Hayden and O Connell. 

Values for the Poynting effect can be determined from available or estimated liquid molar volume data. 

Parameter values for an expression describing the vapor pressure of all components involved, such as the Antoine equation, are available. 

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For the special case of a bubble-point calculation (incipient vaporization), a is 0 (also Q = 0) and Equation (7-13) becomes... 

The Newton-Raphson approach, being essentially a point-slope method, converges most rapidly for near linear objective functions. Thus it is helpful to note that tends to vary as 1/P and as exp(l/T). For bubble-point-temperature calculation, we can define an objective function... 

For bubble-point and dew-point pressure calculations, the appropriate forms are, respectively ... 

Convergence is usually accomplished in 2 to 4 iterations. For example, an average of 2.6 iterations was required for 9 bubble-point-temperature calculations over the complete composition range for the azeotropic system ehtanol-ethyl acetate. Standard initial estimates were used. Figure 1 shows results for the incipient vapor-phase compositions together with the experimental data of Murti and van Winkle (1958). For this case, calculated bubble-point temperatures were never more than 0.4 K from observed values. 

The computer subroutines for calculation of vapor-liquid equilibrium separations, including determination of bubble-point and dew-point temperatures and pressures, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements for these subroutines are given in Appendix J their execution times are strongly dependent on the separations being calculated but can be estimated (CDC 6400) from the times given for the thermodynamic subroutines they call (essentially all computation effort is in these thermodynamic subroutines). 

ERF error flag, integer variable normally zero ERF= 1 indicates parameters are not available for one or more binary pairs in the mixture ERF = 2 indicates no solution was obtained ERF = 3 or 4 indicates the specified flash temperature is less than the bubble-point temperature or greater than the dew-point temperature respectively ERF = 5 indicates bad input arguments. 

BUDET calculates the bubble-point temperature or dew-point temperature for a mixture of N components (N < 20) at specified pressure and liquid or vapor composition. The subroutine also furnishes the composition of the incipient vapor or liquid and the vaporization equilibrium ratios. 

Bubble-point temperature or dew-point temperatures are calculated iteratively by applying the Newton-Raphson iteration to the objective functions given by Equations (7-23) or (7-24) respectively. 

Bubble-point and dew-point pressures are calculated using a first-order iteration procedure described by the footnote to Equation (7-25). 

The last design variable which needs to be fixed before the design can proceed, but which is of lesser importance, is feed condition. Subcooled feed (i.e., below bubble point)... 

Both the reboiling and condensing processes normally take place over a range of temperature. Practical considerations, however, usually dictate that the heat to the reboiler must be supplied at a temperature above the dew point of the vapor leaving the reboiler and that the heat removed in the condenser must be removed at a temperature lower than the bubble point of the liquid. Hence, in preliminary design at least, both reboiling and condensing can be assumed to take place at constant temperatures. ... 

The saturation pressure, P, is different from the bubble point pressure (see. Vidal, 1973) and has no physical reality it merely serves as an intermediate calculation. 

For mixtures, the calculation is more complex because it is necessary to determine the bubble point pressure by calculating the partial fugacities of the components in the two phases at equilibrium. 

Once the bubble point is reached (at point B), the first bubble of ethane vapour is released. From point B to C liquid and gas co-exist in the cell, and the pressure is maintained constant as more of the liquid changes to the gaseous state. The system exhibits infinite compressibility until the last drop of liquid is left In the cell (point C), which is the dew point. Below the dew point pressure only gas remains in the cell, and as pressure is reduced below the dew point, the volume increase is determined by the compressibility of the gas. The gas compressibility is much greater than the liquid compressibility, and hence the change of volume for a given reduction in pressure (the... 

The experiment could be repeated at a number of different temperatures and initial pressures to determine the shape of the two-phase envelope defined by the bubble point line and the dew point line. These two lines meet at the critical point, where it is no longer possible to distinguish between a compressed gas and a liquid. 

It is important to remember the significance of the bubble point line, the dew point line, and the two phase region, within which gas and liquid exist in equilibrium. 

When the two components are mixed together (say in a mixture of 10% ethane, 90% n-heptane) the bubble point curve and the dew point curve no longer coincide, and a two-phase envelope appears. Within this two-phase region, a mixture of liquid and gas exist, with both components being present in each phase in proportions dictated by the exact temperature and pressure, i.e. the composition of the liquid and gas phases within the two-phase envelope are not constant. The mixture has its own critical point C g. 

For both volatile oil and blaok oil the initial reservoir temperature is below the critical point, and the fluid is therefore a liquid in the reservoir. As the pressure drops the bubble point is eventually reached, and the first bubble of gas is released from the liquid. The composition of this gas will be made up of the more volatile components of the mixture. Both volatile oils and black oils will liberate gas in the separators, whose conditions of pressure and temperature are well inside the two-phase envelope. 

A volatile oil contains a relatively large fraction of lighter and intermediate oomponents which vaporise easily. With a small drop in pressure below the bubble point, the relative amount of liquid to gas in the two-phase mixture drops rapidly, as shown in the phase diagram by the wide spacing of the iso-vol lines. At reservoir pressures below the bubble point, gas is released In the reservoir, and Is known as solution gas, since above the bubble point this gas was contained in solution. Some of this liberated gas will flow towards the producing wells, while some will remain in the reservoir and migrate towards the crest of the structure to form a secondary gas cap. 

Black oils are a common category of reservoir fluids, and are similar to volatile oils in behaviour, except that they contain a lower fraction of volatile components and therefore require a much larger pressure drop below the bubble point before significant volumes of gas are released from solution. This is reflected by the position of the iso-vol lines in the phase diagram, where the lines of low liquid percentage are grouped around the dew point line. 

When the pressure of a volatile oil or black oil reservoir is above the bubble point, we refer to the oil as undersaturated. When the pressure is at the bubble point we refer to it as saturated oil, since if any more gas were added to the system it could not be dissolved in the oil. The bubble point is therefore the saturation pressure for the reservoir fluid. 

An oil reservoir which exists at initial conditions with an overlying gas cap must by definition be at the bubble point pressure at the interface between the gas and the oil, the gas-oil-contact (GOC). Gas existing in an initial gas cap is called free gas, while the gas in solution in the oil is called dissolved or solution gas. 

The value of the compresjiibility of oil is a function of the amount of dissolved gas, but is in the order of 10 x 10" psi" By comparison, typical water and gas compressibilities are 4x10" psi" and 500 x 10" psi" respectively. Above the bubble point in an oil reservoir the compressibility of the oil is a major determinant of how the pressure declines for a given change in volume (brought about by a withdrawal of reservoir fluid during production). 

Unlike gases, liquid viscosity decreases as temperature increases, as the molecules move further apart and decrease their internal friction. Like gases, oil viscosity increases as the pressure increases, at least above the bubble point. Below the bubble point, when the solution gas is liberated, oil viscosity increases because the lighter oil components of the oil (which lower the viscosity of oil) are the ones which transfer to the gas phase. 

Assuming an initial reservoir pressure above the bubble point (undersaturated reservoir oil), only one phase exists in the reservoir. The volume of oil (rm or rb) at reservoir conditions of temperature and pressure is calculated from the mapping techniques discussed in Section 5.4. 

As the reservoir pressure drops from the initial reservoir pressure towards the bubble point pressure (PJ, the oil expands slightly according to its compressibility. However, once the pressure of the oil drops below the bubble point, gas is liberated from the oil, and the remaining oil occupies a smaller volume. The gas dissolved in the oil is called the solution gas, and the ratio of the volume gas dissolved per volume of oil is called the solution gas oil ratio (Rg, measured in scf/stb of sm /stm ). Above the bubble point, Rg is constant and is known as the initial solution gas oil ratio (Rgj), but as the pressure falls below the bubble point and solution gas is liberated, Rg decreases. The volume of gas liberated is (Rg - Rg) scf/stb. 

If the reservoir pressure remains above the bubble point then any gas liberated from the oil must be released in the tubing and the separators, and will therefore appear at the surface. In this case the producing gas oil ratio (Rp) will be equal to R. i.e. every stock tank barrel of oil produced liberates Rs scf of gas af surface. 

If, however, the reservoir pressure drops below the bubble point, then gas will be liberated in the reservoir. This liberated gas may flow either towards the producing wells under the hydrodynamic force imposed by the lower pressure at the well, or it may migrate... 

The collection of representative reservoir fluid samples is important in order to establish the PVT properties - phase envelope, bubble point, Rg, B, and the physical properties - composition, density, viscosity. These values are used to determine the initial volumes of fluid in place in stock tank volumes, the flow properties of the fluid both in the reservoir and through the surface facilities, and to identify any components which may require special treatment, such as sulphur compounds. 

Fluid samples may be collected downhole at near-reservoir conditions, or at surface. Subsurface samples are more expensive to collect, since they require downhole sampling tools, but are more likely to capture a representative sample, since they are targeted at collecting a single phase fluid. A surface sample is inevitably a two phase sample which requires recombining to recreate the reservoir fluid. Both sampling techniques face the same problem of trying to capture a representative sample (i.e. the correct proportion of gas to oil) when the pressure falls below the bubble point. 

Sampling saturated reservoirs with this technique requires special care to attempt to obtain a representative sample, and in any case when the flowing bottom hole pressure is lower than the bubble point, the validity of the sample remains doubtful. Multiple subsurface samples are usually taken by running sample bombs in tandem or performing repeat runs. The samples are checked for consistency by measuring their bubble point pressure at surface temperature. Samples whose bubble point lie within 2% of each other may be sent to the laboratory for PVT analysis. 

The oil and gas samples are taken from the appropriate flowlines of the same separator, whose pressure, temperature and flowrate must be carefully recorded to allow the recombination ratios to be calculated. In addition the pressure and temperature of the stock tank must be recorded to be able to later calculate the shrinkage of oil from the point at which it is sampled and the stock tank. The oil and gas samples are sent separately to the laboratory where they are recombined before PVT analysis is performed. A quality check on the sampling technique is that the bubble point of the recombined sample at the temperature of the separator from which the samples were taken should be equal to the separator pressure. 

Below is a typical oil PVT table which is the result of PVT analysis, and which would be used by the reservoir engineer in calculation of reservoir fluid properties with pressure. The initial reservoir pressure is 6000 psia, and the bubble point pressure of the oil Is 980 psia. 

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

Solution gas drive occurs in a reservoir which contains no initial gas cap or underlying active aquifer to support the pressure and therefore oil is produced by the driving force due to the expansion of oil and connate water, plus any compaction drive.. The contribution to drive energy from compaction and connate water is small, so the oil compressibility initially dominates the drive energy. Because the oil compressibility itself is low, pressure drops rapidly as production takes place, until the pressure reaches the bubble point. 

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