Pressure drop form compressible fluid

Note that while the fluid density may be a function of the pressure in the bed in a compressible flow, the superficial mass velocity is constant. The Ergun equation in the form given in eq. (3.450) is more convenient when analyzing the effects of pressure drop in the fluid density. 

A program for hydraulic calculations, hydraulics.exe, has been developed to estimate pressure drop for noncompressible fluids, compressible fluids, and two-phase fluids. The main form has been divided into a number of frames for input and results. Calculations can be performed using either SI or English units (SI unit by default). The units are fixed ones, and the program does not allow for change of individual units. 

Permeability is normally determined using linear flow in the incompressible or compressible form, depending on whether a liquid or gas is used as the flowing fluid. The volumetric flowrate Q (or Q ,) is determined at several pressure drops. Q (or Q ,) is plotted versus the average pressure p . The slope of this line will yield the fluid conductivity K or, if the fluid density and viscosity are known, it provides the intrinsic permeability k. For gases, the fluid conductivity depends on pressure, so that... 

Eqs. (3.448) and (3.449) assume constant fluid density, in other words, diey hold for incompressible flow. However, in compressible flow, die density of the fluid is a function of the pressure drop (see Section 5.3.4). Then, we have to use the differential forms of... 

A loss mechanism similar in form to thermal expansion losses arises when there is a difference between the compressibility of the drop and the supervening fluid. Once more the drop expands and contracts relative to the fluid, re-radiating energy, but this time as a direct consequence of the fluctuating pressure field. 

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