Water balance calculation example

Reservoir pressure is measured in selected wells using either permanent or nonpermanent bottom hole pressure gauges or wireline tools in new wells (RFT, MDT, see Section 5.3.5) to determine the profile of the pressure depletion in the reservoir. The pressures indicate the continuity of the reservoir, and the connectivity of sand layers and are used in material balance calculations and in the reservoir simulation model to confirm the volume of the fluids in the reservoir and the natural influx of water from the aquifer. The following example shows an RFT pressure plot from a development well in a field which has been producing for some time. 

This example illustrates the use of liquid-liquid phase equilibria in material balance calculations. The condensate stream from the condenser described in Example 4.2 is fed to a decanter to separate the condensed water and dichloroethane (EDC). Calculate the decanter outlet stream compositions. 

A very similar process is used to calculate evapotranspiration in a hydrological catchment with well-defined hydrogeological conditions. Viewed over longer intervals (one or more years), 55 = 0 can be assumed. 7=0 can also be assumed because the area is hydrogeologically verified. Thus, it is easy to calculate evapotranspiration by carefully measuring the areal precipitation (cf. Precipitation ) and runoff. Care must be taken to ensure that all errors in the calculation of individual components of the water balance equation are reflected in the result, for example evapotranspiration. 

We can perform approximate material balance calculations to see what happens to the process if we were to recycle the distillate and process it with the feed. We model each separator as a set of constant split factors for each species. For example, we see that 97.94% of the pentane, 35.00% of the acetone, and none of the methanol leave in the top stream from the extractor. Water enters as the extraction agent and also as a small part of the feed 0.63% of the total water entering leaves with this top stream. We capture these results in the first three rows of numbers in Table X. We denote molar flow for species k in stream j leaving unit i by and the fraction of the flow of species k in the feed to unit / leaving in stream / by... 

Note that the charge imbalances calculated from Equation (5.1) are stoichiometric charge imbalances, which are based on the assumption that all measured elemental concentrations appear as charged ionic species, for example that all aluminum in the solution is Al3+ all the calcium is Ca2+ and so on. This stoichiometric charge-balance calculation tends to work well as a screen for checking the quality of dilute groundwater and surface water analyses, which are largely uncomplexed (see Hem, 1985). 

Example 2.1. One hundred milliliters of water was measured 10 times in a 100 ml volumetric flask, a 250 ml graduated cylinder, and a 150 ml graduated Erlenmeyer flask—Table E2.1. Each flask was washed, dried then weighed on a balance with a resolution of 0.01 g. The flask was filled with deionized/distilled water so that the bottom of the meniscus barely touched the top of the graduation mark. Water along the tube neck was then wiped with a paper towel to remove any water drops. Calculate the mean and standard deviation for the flasks and the graduated cylinder. 

Example 6.5 Calculating Internal Water Balance Given a net drag coefficient of 0.1, determine the molar rate of water accumulation at the catalyst layer that must be removed to prevent flooding. 

Different surfactants are usually characterised by the solubility behaviour of their hydrophilic and hydrophobic molecule fraction in polar solvents, expressed by the HLB-value (hydrophilic-lipophilic-balance) of the surfactant. The HLB-value of a specific surfactant is often listed by the producer or can be easily calculated from listed increments [67]. If the water in a microemulsion contains electrolytes, the solubility of the surfactant in the water changes. It can be increased or decreased, depending on the kind of electrolyte [68,69]. The effect of electrolytes is explained by the HSAB principle (hard-soft-acid-base). For example, salts of hard acids and hard bases reduce the solubility of the surfactant in water. The solubility is increased by salts of soft acids and hard bases or by salts of hard acids and soft bases. Correspondingly, the solubility of the surfactant in water is increased by sodium alkyl sulfonates and decreased by sodium chloride or sodium sulfate. In the meantime, the physical interactions of the surfactant molecules and other components in microemulsions is well understood and the HSAB-principle was verified. The salts in water mainly influence the curvature of the surfactant film in a microemulsion. The curvature of the surfactant film can be expressed, analogous to the HLB-value, by the packing parameter Sp. The packing parameter is the ratio between the hydrophilic and lipophilic surfactant molecule part [70] ... 

In the foregoing treatment of the water molecule, which we shall use as an example, each of the two bond orbitals of the oxygen atom has been calculated to have 6 percent s character and 94 percent p character. Each of the two unshared-pair orbitals then has 44 percent s character and 56 percent p character. The maxima for the unshared-pair orbitals lie in directions making an angle of 142° with one another and such that their resultant is opposed to that for the two bond orbitals, which have their maxima at 93.5° with one another. The component for the four unshared-pair electrons is determined by the direction cosine —0.34, and that of the two bonding electrons of the oxygen atom by the direction cosine 0.68 hence the contribution of the four unshared-pair electrons to the dipole moment is just balanced by that of the two bonding electrons.18... 

Normally full valence MCSCF calculations (choosing all valence orbitals as active) represent a balanced treatment of correlation. However this is not always the case, especially not in systems containing lone-pair electrons. For example, a full valence MCSCF calculation for the water molecule yields less accurate values for the bond distance, the bond angle, and the dipole and quadrupole moment than an SCF calculation. The reason is that there are only two orbitals available for correlating the eight valence electrons (the 4ax and the 2b2 orbitals). Thus correlation is only introduced into the lone-pair orbital... 

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