Ratio of pressure gradient

One of the most important functions in the description of fluidization is the drag function which measures the ratio of pressure gradient to gas volume flux. The definition of this drag function is discussed in (14) through recourse to the correlation of Richardson (22). 

The preceding equation shows that the ratio of pressure gradient is equivalent to the mobility ratio in this case, being the same as the well-known concept of mobility ratio. 

Thus, the units of this effective viscosity are centipoises (Pa-s). The effective viscosity is not the actual viscosity of any real fluid, it is the viscosity of a virtual fluid simulating the combined flow of C02 and surfactant—brine through reservoir rock. The effective viscosity is a number that can be used in Darcy s law, along with the absolute permeability of the rock, to give the ratio of pressure gradient to superficial flow rate. In particular, the effective viscosity defined previously is not to be used with any assumed value of the relative permeability of dense C02 in the rock. As will be seen, experiments show that this effective viscosity is not constant, but changes in value as a number of other parameters of the flow are varied. 

Foam Effectiveness in Porous Media. No generally accepted correlations exist between foam characteristics measured outside the porous medium and foam effectiveness as a gas mobility-reducing agent in porous media. The performance of the nine surfactants that passed the solubility criteria was therefore evaluated in porous media under typical reservoir conditions. The results of such an evaluation can be expressed in several ways. One of the simplest measures of foam effectiveness, and arguably the most straightforward one, is the mobility-reduction factor (MRF). The MRF is defined as the ratio of pressure gradients across a... 

Fig. 15. Relative permeabilities of wetting phase and ratio of pressure gradient at and behind the flood front vs. fraction of residual nonwetting phase displaced.

Also in this equation the effects of drag flow and pressure flow can be separated the drag flow is proportional to the rotational speed of the screws, and the pressure flow is proportional to the ratio of pressure gradient and viscosity. 

While our derivation is focused on ratios of pressure gradients, in clinical cardiology, only LVP is routinely measured. Since the LVP and LAP contours are similar hut phase lagged [11], a symmetry argument may he applied to define an LVP-hased (LAP-independent) equivalent to the PPGR. Thus, we define a clinically applicable version of the PPGR, the PRR, as the ratio of pressure drop between mitral valve opening and minimum pressure to the pressure rise between minimum pressure and diastasis ... 

The pressure flow factors describe how the surface roughness would affect the lubricant flow driven by the pressure gradient. It is defined as the ratio of pressure flow in an... 

We note that if the pressure gradient is positive (pressure rises in the direction of flow), the pressure-flow term is negative and Q < Qd, whereas if pressure drops in the direction of flow, <2 > Qd- The ratio of pressure to drag flow is obtained from Eq. 6.3-19... 

For the conditions given in Example 3, what weir height would be necessary to reduce the dimensionless ratio of liquid gradient/pressure-drop head caused by bubble-cap assemblies to the recommended maximum value of 0.4 ... 

The shock wave usually has a pressure gradient across it such that the ratio of pressures pi/p2 2. 

It follows from (7.94) that the ratio of flow rates with and without account taken of the pressure gradient does not depend on the capillary radius, even though it was shown earlier that it is proportional to a. This outcome leads to the conclusion that at large values of Xo/a, application of electric field is not a preferable choice as compared to application of pressure gradient, even in the case of very small capillaries. 

The effects of pipe curvature and inclination, geometrical and physical parameters of capsules on capsule threshold velocity, cq)sule/liquid velocity ratio and pressure gradient were evaluated. Experimental errors were influenced by the used experimental loop and equipment. The errors were generally in rank of 2% for flow rate measmements, for pressure gradient in rank of 3%, reproducibility of carried out experiments was satisfactory. 

The mass flow rate ratio also depends on the magnitude of pressure gradient. The increase in mass flow rate due to slip reduces with increase in the pressure gradient value. 

Parameter inference. The forward model or theory relates the input properties and geometry to the instrument response. In the simplest case the theory will predict the response as a simple function of the input, such that the inverse formula, stating the input parameter as a function of the response can be obtained analytically. An example is calculating the resistance of a conductor as the ratio of potential gradient to electric current, or permeability as the ratio of fluid flux to pressure gradient. In a more complicated case there may be several parameters such as the radii of the different zones of mud invasion. When there are just a few parameters it may be possible to infer the parameters from one or more instrument responses using a least squares procedure. This is an application of the usual methods of the theory of measurement as reviewed in Section 5. 

Specifications of pressure gradients on surfaces of constant z are thereby replaced by equivalent gradients of on constant pressure surfaces. The first law of thermodynamics, Eq. (9.2.14), can be easily transformed, while the transformation of the continuity equation is straightforward but tedious. Neither derivation will be repeated here the interested reader is referred to the discussion given by Haltiner dlliams (1980). Applying this transformation to Eqs. (9.2.10)-(9.2.14) along with the small aspect ratio approximations discussed above, we obtain... 

Figure 4-325a shows a plot of overburden pressure gradient versus depth for typical soft (1) and hard (2) provinces. Figure 4-325b gives similar data for Poisson s ratio. 

Hottman and Johnson developed an empirical correlation to relate the ratio of resisitivities to the pore pressure gradient. In 1972, Eaton developed an empirical relationship that he modified in 1975 to the following [122] ... 

Compute the fracturation pressure gradient and fracturation pressure at 8,460 ft assuming a Poisson ratio of 0.4. 

Crude oil is pumped from a terminal to a refinery through a foot diameter pipeline. As a result of frictional heating, the temperature of the oil is 20 deg K higher at the refinery end than at the terminal end of the pipe and the viscosity has fallen to one half its original value. What is the ratio of the pressure gradient in the pipeline at the refinery end to that at the terminal end ... 

It was found that the pressure gradient and flow friction in micro-channels were higher than that predicted by the conventional laminar flow theory. In a low Re range, the measured pressure gradient increased linearly with Re. For Re > 500, the slope of the /(c-Re relationship increases with Re. The ratio C was about 1.3 for micro-channels of hydraulic diameter 51.3-64.9pm and 1.15-1.18 for microchannels of hydraulic diameter 114.5-168.9pm. It was also found that the ratio of C depends on the Reynolds number. 

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