Bubble-point procedure

The measurement of equivalent pore size by a bubble point procedure is perhaps the most well known and involves inunersing the fabric in a suitable wetting fluid and then measuring the air pressure that is necessary to create a bubble on the surface. The pore size can be calculated from the relationship r= 2 Tx lOVoPg, where r is the pore radius (pm), T is the surface tension of the fluid (mNm" ), o is the density of water at the temperature of test (gcm" ), P is the bubble pressure (nunH O) andg=981cms . ... 

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

The calculation for a point on the flash curve that is intermediate between the bubble point and the dew point is referred to as an isothermal-flash calculation because To is specified. Except for an ideal binary mixture, procedures for calculating an isothermal flash are iterative. A popular method is the following due to Rachford and Rice [I. Pet. Technol, 4(10), sec. 1, p. 19, and sec. 2, p. 3 (October 1952)]. The component mole balance (FZi = Vy, + LXi), phase-distribution relation (K = yJXi), and total mole balance (F = V + L) can be combined to give... 

A computer solution was obtained as follows. The only initial assumptions are a condenser outlet temperature of 65 F and a bottoms-prodiict temperature of 165 F, The bubble-point temperature of the feed is computed as 123,5 F, In the initiahzation procedure, the constants A and B in (13-106) for inner-loop calcu-... 

Membrane Characterization The two important characteristics of a UF membrane are its permeability and its retention characteristics. Ultrafiltration membranes contain pores too small to be tested by bubble point. Direc t microscopic observation of the surface is difficult and unreliable. The pores, especially the smaller ones, usually close when samples are dried for the electron microscope. Critical-point drying of a membrane (replacing the water with a flmd which can be removed at its critical point) is utihzed even though this procedure has complications of its own it has been used to produce a Few good pictures. 

As discussed by Franks (1972), in order to solve this system of equations, a value of temperature T must be found to satisfy the condition that the difference term 6 = P - Zpj is very small, i.e., that the equilibrium condition is satisfied. This is known as a bubble point calculation. The above system of defining equations, however represent, an implicit algebraic loop and the trial and error solution procedure can be very time consuming, especially when incorporated into a dynamic simulation program. 

The calculation of y and P in Equation 14.16a is achieved by bubble point pressure-type calculations whereas that of x and y in Equation 14.16b is by isothermal-isobaric //cm-/(-type calculations. These calculations have to be performed during each iteration of the minimization procedure using the current estimates of the parameters. Given that both the bubble point and the flash calculations are iterative in nature the overall computational requirements are significant. Furthermore, convergence problems in the thermodynamic calculations could also be encountered when the parameter values are away from their optimal values. 

To estimate the stage, and the condenser and reboiler temperatures, procedures are required for calculating dew and bubble points. By definition, a saturated liquid is at its bubble point (any rise in temperature will cause a bubble of vapour to form), and a saturated vapour is at its dew point (any drop in temperature will cause a drop of liquid to form). 

The following equations were used to calculate the bubble point in our reconciliation procedure ... 

A procedure is presented for correlating the effect of non-volatile salts on the vapor-liquid equilibrium properties of binary solvents. The procedure is based on estimating the influence of salt concentration on the infinite dilution activity coefficients of both components in a pseudo-binary solution. The procedure is tested on experimental data for five different salts in methanol-water solutions. With this technique and Wilson parameters determined from the infinite dilution activity coefficients, precise estimates of bubble point temperatures and vapor phase compositions may be obtained over a range of salt and solvent compositions. 

Now we will examine the methods of estimating the density of a reservoir liquid at reservoir conditions. First, we will consider liquids at their bubble points or liquids in contact with gas in either case, we will call these saturated liquids. The first step in the calculation procedure is to determine the density of the liquid at standard condition. The next step is to adjust this density to reser >oir conditions. 

The calculation of liquid density at pressures above the bubble point is a two-step procedure. First, the density at the bubble point must be computed using one of the methods previously described. Then this density must be adjusted to take into account the compression due to the increase in pressure from bubble-point pressure to the pressure of interest. 

The normal procedure for estimating formation volume factor at pressures above the bubble point is first to estimate the factor at bubble-point pressure and reservoir temperature using one of the methods just described. Then, adjust the factor to higher pressure through the use of the coefficient of isothermal compressibility. The equation used for this adjustment follows directly from the definition of the compressibility coefficient at pressures above the bubble point. 

Calculate the formation volume factor of the oil described in Exercise 11-13 at its bubble point of 1763 psia and 250°F. Use the procedure of Example 11-9. 

Step 5 Calculate the density of the reservoir liquid at reservoir conditions using the feed stream composition from Step 1, reservoir temperature, and bubble-point pressure. The procedure is described in Chapter 11. 

The bubble point test is simple, quick and reliable and is by far the most widely used method of characterizing microfiltration membranes. The membrane is first wetted with a suitable liquid, usually water for hydrophilic membranes and methanol for hydrophobic membranes. The membrane is then placed in a holder with a layer of liquid on the top surface. Air is fed to the bottom of the membrane, and the pressure is slowly increased until the first continuous string of air bubbles at the membrane surface is observed. This pressure is called the bubble point pressure and is a characteristic measure of the diameter of the largest pore in the membrane. Obtaining reliable and consistent results with the bubble point test requires care. It is essential, for example, that the membrane be completely wetted with the test liquid this may be difficult to determine. Because this test is so widely used by microfiltration membrane manufacturers, a great deal of work has been devoted to developing a reliable test procedure to address this and other issues. The use of this test is reviewed in Meltzer s book [3],... 

Bubble points for gas-liquid equilibrium were measured at constant temperature by observing the pressure at which the equilibrium gas phase disappeared upon injection of small amounts of solvent into the view cell. The equilibrium composition of the liquid phase was obtained from the known composition in the cell. Other pressures and corresponding compositions at this temperature were obtained by repeating the procedure for different porphyrin loadings. 

Since pf is a function of temperature, the dewpoint and bubble-point temperatures for an ideal vapor or liquid mixture can be determined as a function of the total pressure tr from Eq. (9) or (10), respectively. An analogous procedure can be used for real mixtures, but the nonidealities of the liquid and vapor phases must be accounted for. 

Bubble Point tests are usually carried out to characterize a membrane or porous material consistency or quality they are also a common procedure to determine the maximum pore size. 

Analogous with the procedure presented before, reactive distillation tines can be obtained by computing a series of dew and bubble points incorporating a chemical equilibrium term, as follows ... 

Compositions for the stripping section are found by the same procedure, but beginning with the reboiler and calculating up to the feed. With these compositions, the temperatures are updated, usually by a crial-and-error bubble-point technique. With the new temperatures,... 

Solution The given pressure lies between the dew- and bubble-point pressures established for this system in Example 14.3. The system therefore surely consists of two phases. The procedure is to find by trial that value of V for which Eq. (10.30) is satisfied. We recall that there is always a trivial solution for V = 1. The results of several trials are shown in the following table. The columns headed y, give values of the terms in the sum of Eq. (10.30), because each such term is in fact a y, value, as shown by Eq. (10.29). 

Related Calculations. The convergence-pressure K -value charts provide a useful andrapid graphical approach for phase-equilibrium calculations. The Natural Gas Processors Suppliers Association has published a very extensive set of charts showing the vapor-liquid equilibrium K values of each of the components methane to n-decane as functions of pressure, temperature, and convergence pressure. These charts are widely used in the petroleum industry. The procedure shown in this illustration can be used to perform similar calculations. See Examples 3.10 and 3.11 for straightforward calculation of dew points and bubble points, respectively. 

When the vapor phase is ideal, the Kt are independent of the vapor composition. In such a case, the procedure for bubble-point determination is to (1) guess a temperature (2) calculate the K, which equal Yiff/P, where yt is the activity coefficient of the ith component in the liquid phase, f is the fugacity of pure liquid i at system temperature and pressure, and P is the system pressure and (3) check if the preceding bubble-point equation is satisfied. If it is not, repeat the procedure with a different guess. 

Repeat the trial-and-error procedure until the bubble-point temperature is found. Asa second guess, try 67°C. Assume that because the temperature difference is small, the activity coefficients remain the same as in step 1. At 67°C, the vapor pressures are 478 and 205 mmHg. Then, Kt = 0.9746 and K2 = 0.8344, as found by the procedure outlined in the previous step. Then K X + K2x2 = 0.9466. Since this sum is less than 1, the assumed temperature is too low. 

The solution of the equations listed in Table 3.3.1 requires an iterative procedure. Thus, it is good strategy to examine the variables to determine if there are limits on their values. For example, the mole fractions of the components will vary from zero to one. This fact greatly simplifies the solution procedure. Also, the final flash temperature will lie somewhere between the bubble and dew-point temperatures. The bubble-point temperature is that temperature at which the first... 

To obtain the composition of the top and bottom products, first calculate the relative volatility of each component using the conditions of the feed as a first guess. The relative volatility depends on temperature and pressure. The bubble point of the feed at 400 psia (27.6 bar) and at the feed composition, calculated using ASPEN [57], is 86.5 °F (130 °C). The K-values of the feed are listed in Table 6.7.1. Bubble and dew points could also be calculated using K-values from the DePriester charts [31] and by using the calculation procedures given in Chapter 3. Next, calculate the relative volatility of the feed stream, defined by Equation 6.27.18, for each component relative to the heavy key component. 

The next step in the procedure is to calculate the optimum or operating reflux ratio. First, calculate the minimum reflux ratio using the Underwood equations, Equations 6.27.3 and 2.27.4. For the calculation use the geometric average volatility of each component listed in Table 6.27.3. Because flie feed is at its bubble point, q = 1. Thus, Equations 6.27.3 and 6.27.4 becomes... 

Calculations Assuming Ideal Solution Behavior for Multicomponent Systems. The oaloulation of the bubble-point pressure and the composition of the vapor at the bubble point for an ideal solution consisting of more than two components involves no new principles or procedures. If Raoult s Law is applicable the partial pressure of each component in the vapor can be calculated and their sum is equal to the bubble-point pressure. Stated mathematically... 

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