Total pressure gradient

Total pressure drop for horizontal gas/solid flow includes acceleration effects at the entrance to the pipe and fric tional effects beyond the entrance region. A great number of correlations for pressure gradient are available, none of which is applicable to all flow regimes. Govier and Aziz review many of these and provide recommendations on when to use them. 

Example 3 Calculation of TG Method The TG method will he demonstrated hy using the same example problem that was used above for the approximate methods. The example column was analyzed previously and found to have C -I- 2N + 9 design variables. The specifications to be used in this example were also hstedat that time and included the total number of stages (N = 10), the feed-plate location (M = 5), the reflux temperature (corresponding to saturated liquid), the distillate rate (D = 48.9), and the top vapor rate (V = 175). As before, the pressure is uniform at 827 kPa (120 psia), but a pressure gradient could be easily handled if desired. 

Subsurface Fluid Pressure (Pore Pressure Gradient). The total overburden pressure is derived from the weight of the materials and fluids that lie above any particular depth level in the earth. Of interest to the petroleum industry are the sedimentary rocks derived from deposits in water, particularly, in seawater. Such sedimentary rocks contain rock particle grains and saline water within the pore spaces. Total theoretical maximum overburden pressure, P (Ib/ft-), is... 

The average specific gravity of minerals in the earth s crust is taken to be 2.7. The average specific gravity of saltwater is taken to be 1.07. If the average sedimentary rock porosity is assumed to be 10%, then the total theoretical maximum overburden pressure gradient (lb/fp)/ft becomes... 

The rock fracture pressure gradient at depth can be approximated by using Equation 2-174 and the variable Poisson s ratios versus depth data (Figure 2-58) and the variable total overburden stress gradients versus depth data (Figure 2-59). 

A knowledge of hold-up is particularly important for vertical flow since the hydrostatic pressure gradient, which is frequently the major component of the total pressure gradient, is directly proportional to liquid hold-up. However, in slug flow, the situation is complicated by the fact that any liquid which is in the form of an annular film surrounding the gas slug does not contribute to the hydrostatic pressure 14. ... 

The total pressure gradient in a horizontal pipe, (-d/Ypp/d/), consists of two components which represent the frictional and the acceleration pressure gradients respectively. 

Notes CO cardiac output VR venous return HR heart rate SV stroke volume EDV end-diastolic volume ESV end-systolic volume O blood flow AP pressure gradient R resistance r vessel radius P systolic pressure Piiastoik- diastolic pressure MAP mean arterial pressure TPR total peripheral resistance, P venous pressure Era- right atrial pressure Rv venous resistance. 

A pipeline has been proposed to transport a coal slurry 1200 mi from Wyoming to Texas, at a rate of 50 million tons/yr, through a 36 in. diameter pipeline. The coal slurry has the properties of a Bingham plastic, with a yield stress of 150dyn/cm2, a limiting viscosity of 40 cP, and an SG of 1.5. You must conduct a lab experiment in which the measured pressure gradient can be used to determine the total pressure drop in the pipeline. 

Consider a pool of water in the bed of your pickup truck. If you accelerate from rest, the water will slosh toward the rear, and you want to know how fast you can accelerate (ax) without spilling the water out of the back of the truck (see Fig. 4-4). That is, you must determine the slope (tan ) of the water surface as a function of the rate of acceleration (ax). Now at any point within the liquid there is a vertical pressure gradient due to gravity [Eq. (4-5)] and a horizontal pressure gradient due to the acceleration ax [Eq. (4-23)]. Thus at any location within the liquid the total differential pressure... 

In Section II.B of Chapter 3, the tube flow viscometer was described in which the viscosity of any fluid with unknown viscous properties could be determined from measurements of the total pressure gradient (— A4>/L) and the volumetric flow rate (Q) in a tube of known dimensions. The viscosity is given by... 

Finding the pressure drop corresponding to a total mass flux Gm from this equation requires a stepwise procedure using physical property data from which the densities of both the gas phase and the mixture can be determined as a function of pressure. For example, if the upstream pressure P and the mass flux Gm are known, the equation is used to evaluate the pressure gradient at point 1 and hence the change in pressure AP over a finite length AL, and hence the pressure Px+i = Px — AP. The densities are then determined at pressure P1+i. And the process is repeated at successive increments until the end of the pipe is reached. 

The presence of slip also means that the acceleration term in the general governing equation [Eq. (15-45)] cannot be evaluated in the same manner as the one for homogeneous flow conditions. When the acceleration term is expanded to account for the difference in phase velocities, the momentum equation, when solved for the total pressure gradient, becomes... 

Example 15-2 Estimate the pressure gradient (in psi/ft) for a two-phase mixture of air and water entering a horizontal 6 in. sch 40 pipe at a total mass flow rate of 6500 lbm/min at 150 psia, 60°F, with a quality (a) of 0.1 lbm air/lbm water. Compare your answers using the (a) omega (b) Lockhart-... 

The acceleration component to the total pressure gradient, from Eqs. (15-48), (15-50), and (15-53) should also be included for cases (b) and (c) but is negligible in these cases. 

Natural gas (methane) and 40° API crude oil are being pumped through a 6 in. sch 40 pipeline at 80°F. The mixture enters the pipe at 500 psia, a total rate of 6000 lbm/min, and 6% quality. What is the total pressure gradient in the pipe at... 

Gas diffusion in the nano-porous hydrophobic material under partial pressure gradient and at constant total pressure is theoretically and experimentally investigated. The dusty-gas model is used in which the porous media is presented as a system of hard spherical particles, uniformly distributed in the space. These particles are accepted as gas molecules with infinitely big mass. In the case of gas transport of two-component gas mixture (i = 1,2) the effective diffusion coefficient (Dj)eff of each of the... 

Draft Tube Pressure Drop. The pressure drop across the draft tube, AP2 3, is usually similar to that across the downcomer, APj 4, in magnitude. Thus, for a practical design basis, the total pressure drop across the draft tube and across the downcomer can be assumed to be equal. In most operating conditions, the pressure drop at the bottom section of the draft tube has a steep pressure gradient due primarily to acceleration of the solid particles from essentially zero vertical velocity. The acceleration term is especially significant when the solid circulation rate is high or when the draft tube is short. 

The terms represent the contributions from the total pressure gradient, the frictional drag of the pipe wall and the hydrostatic head of the two-phase mixture. 

Equation 7.10 shows that the total pressure gradient comprises three components that are due to fluid friction, the rate of change of momentum and the static head. The momentum term is usually called the accelerative component. Thus... 

Again, the three components of the total pressure gradient, friction, acceleration and the static head, are clear. 

The total pressure gradient is implicit because it appears in the accelerative term as well as on the left of the equation. Rewriting equation 7.64 to provide the total pressure gradient explicitly gives... 

This calculation with five increments gives the total pressure drop over the 1.3 m of the tube as 0.273 bar compared with the estimate of 0.320 bar found using the exit value of the pressure gradient. The error in making this simplification compared with the value using five increments is 17 per... 

---