Pete 314 1.1 PETE 314 — Transport Processes in Petroleum Production Fluid Mechanics: fluid statics; stress and strain, mass, energy, momentum balances; friction losses, turbulent flow, Reynolds Number (Moody diagram); Newtonian/Non- Newtonian fluids; flow in porous media (Darcy's law and Non-Darcy flow). Other transport phenomena: Heat conduction in solids; Heat convection in fluids. Diffusion of substances. (Fluid mechanics revisited: Transport of momentum.) Flow and heat transfer processes in reservoirs and wells. Pumps, compressors, heat exchangers.
Transcript
Pete 314 1.1
PETE 314 — Transport Processes in Petroleum Production
Fluid Mechanics: fluid statics; stress and strain, mass, energy, momentum balances; friction losses, turbulent flow, Reynolds Number (Moody diagram); Newtonian/Non-Newtonian fluids; flow in porous media (Darcy's law and Non-Darcy flow).
Other transport phenomena: Heat conduction in solids; Heat convection in fluids. Diffusion of substances. (Fluid mechanics revisited: Transport of momentum.)
Flow and heat transfer processes in reservoirs and wells. Pumps, compressors, heat exchangers.
Pete 314 1.2
Introduction to Fluid Mechanics
Fluid Mechanics is concerned with the behavior
of fluids at rest (statics) and in motion
(dynamics)
Distinction between solids and fluids:
• A solid is “hard” and not easily deformed. A fluid is
“soft” and deforms easily.
• Fluid is a substance that alters its shape in response
to shear force however small and deforms
continuously while acted on.
• Fluids tend to take the shape and form of the
container.
Pete 314 1.3
Some applications of fluid mechanics
1. Hydraulics: the flow of water in rivers, pipes, canals, pumps, turbines.2. Aerodynamics: the flow of air around airplanes, rockets, projectiles.3. Meteorology: the flow of the atmosphere.4. Particle dynamics: the flow of fluids around particles, the interaction
of particles and fluids (i.e., dust settling, slurries, pneumatic transport, fluidized beds, air pollutant particles, corpuscles in our blood).
5. Hydrology: the flow of water and water-borne pollutants in the ground.
6. Reservoir engineering: the flow of oil, gas, and water in petroleum reservoirs.
8. Combinations of fluid flow: with chemical reactions in combustion, with electromagnetic phenomena in magnetohydrodynamics, with mass transport in distillation or drying.
2. The first law of thermodynamics (the principle of the conservation of energy).
3. The second law of thermodynamics.
4. Newton’s second law of motion, which may be summarized in the form F = ma.
Each of these four ideas is a generalization of experimental data. None of them can be deduced from the others or from any other prior principle. Rather, they stand on their ability to predict correctly the results of any experiment ever run to test them.
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Stresses (Force normalized by area)
Tensile Compressive Shear
Unit of stress:
1 Pa = 1 N/m2
1 psi = 1 lbf/in2
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Reminder: Units of force and Newton’s 2nd Law F = m · a
SI system: Base dimensions are Length, Time, Mass, Temperature
A Newton is the force which when applied to a mass of 1 kg produces an acceleration of 1 m/s2.
Newton is a derived unit: 1N = (1kg).(1m/s2)
BG system: Base dimensions are Length, Force, Time, Temperature
A slug is the mass which produces an acceleration of 1 ft/s2 when a force of 1lb is applied on it:
Slug is a derived unit: 1slug=(1lb) (s2)/ (ft) = 32.174 lbm
EE system: Base dimensions are Length, Time, Mass, Force and Temperature
The pound-force (lbf) is defined as the force which accelerates
1pound-mass (lbm) with 32.174 ft/s2.
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Reminder: Dimensional homogeneity
All theoretically derived equations are dimensionally homogeneous:
dimensions of the left side of the equation must be the same as those
on the right side.
All equations must use consistent units: each term must have the same
units. Answers will be incorrect if the units in the equation are not
consistent. In strict SI system there is no need for conversions
In English system calculations we often need:
In Pete we use an even less coherent “system” of units, so we need
more conversion factors. For instance
2sN
mkg 11
ft
in1441
2
2
22/sft 25,037
Btu/lbm1
ft lbm 32.2
s lbf1
s lbf
ft slug1
s lbf
ft lbm 32.21
2
22
kJ 4.18
kcal
J 4.18
cal
J 1055
Btu
lbfft 778
Btu1
md
ft10 1.06
md
m10 9.871
2-142-16
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Flow
Continuous deformation Change of velocity of particles with respect to location If all particles move with the same velocity, there is no flow
(example: translation or rotation)
water
Movement but not flow! Movement but not flow!
From our point of view these are related to fluid statics!
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Description & Classification of Fluid Motions
Viscous and Inviscid Flows Laminar and Turbulent Flows Compressible and Incompressible Flows Internal and External Flows
Internal Flows• Flows completely bounded by solid surfaces.
Examples: Flow in ducts and vessels; flow in pumps, fans, and compressors.• Open-channel flow
The internal flow of liquids in which the ducts does not flow full.
Examples: Flow in rivers, irrigation ditches, and aqueducts.
External Flows • Flow over bodies immersed in an unbounded fluid.
Examples: Flow over a submerged submarine, flow over an airplane, and flow over a gulf ball, etc.
Pete 314 1.10
Fluid types: Gas vs liquid
If the fluid is a gas: it will expand readily, filling all the space vacated by the piston; gases can expand without limit to occupy space made available to them.
If the fluid is a liquid: as the piston is raised, the liquid can expand only a small amount, and then it can expand no more. What fills the space between the piston and the liquid? Part of the liquid must turn into a gas by boiling, and this gas expands to fill the vacant space. (When the molecules separate more than this distance, they cease behaving as a liquid and behave as a gas)
Because of their closer molecular spacing, liquids normally have higher densities, viscosities, refractive indices, etc., than gases. This frequently leads to quite different behaviors of liquids and gases.
Pete 314 1.11
Properties of Fluids
Fundamental approach: Study the behavior of individual molecules when trying to describe the behavior of fluids
Engineering approach: Characterization of the behavior by considering the average, or macroscopic, value of the quantity of interest, where the average is evaluated over a small volume containing a large number of molecules• Treat the fluid as a continuum: Assume that all the fluid
characteristics vary continuously throughout the fluid
Pete 314 1.12
Measures of Fluid Mass and Weight
Density of a fluid, (rho), is the amount of mass per unit volume of a substance: = m / Vo
For liquids, weak function of temperature and pressure For gases: strong function of T and P
from ideal gas law: = P M R T)
where R = universal gas constant, M = molecular mass (In strict SI the unit of molecular mass is kg/mol)
In strict SI the gas constant “is really constant” :
In the English system :
)T,P(
R mol-lb
Btu 1.987
R mol-lb
ftpsi 10.73R
oo
3
K mols
mkg 8.314
K mol
mN 8.314
K mol
J 8.314
K mol
mPa 8.314R
2
3
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Density V
m
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Specific gravity
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Viscosity (resistance to flow)
Shear stress
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Newtonian vs non-Newtonian rheology )( f
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s ft
lbm 106.72 cP 1
s Pa 0.001 cP 1s cm
g 0.01 cP 1
4-
cP 0100s m
kg 1 s Pa 1
Units of viscosity
The viscosity is the slope of the line of shear stress versus shear rate so its SI unit is 1 Pa / (1/s) = 1 Pa · s
The customary unit of viscosity is the poise , however it is too large a unit for most common fluids.
By sheer coincidence the viscosity of pure water at about is 0.01 poise; for that reason the common unit of viscosity in the US is the centipoise.
Pete 314 1.20
Kinematic viscosity
Exercise: What is the kinematic viscosity of air in strict SI ?
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Surface tension
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Units
1 N/m = 1 kg / s2
(lbf/in)
dyne/cm
1 dyne/cm = 0.001 N/m
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Exercise: Water at normal conditions has approx 73 dyne/cm. What would be the required mass in the previous example if the fluid were water?
Pete 314 1.24
Pressure: compressive force divided by areaOrdinary fluids cannot permanently
resist shear forces, so the water begins to flow and finally flows away.
If we really wanted to squeeze the water, we would put it in some container that would prevent its flowing out to the side.
The pressure at a point in a fluid at rest is the same in all directions.
The usual definition of pressure in a solid is as follows: Pressure at a point is the average of the compressive stresses measured in three perpendicular directions.
22
2
2 sm
kg 1
ms
mkg
1 m
N1 Pa 1
ft
lbf144
in
lbf1 psi 1
22
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Absolute and gauge pressure
-7.25 psig
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2
2
s
m 3.43
kgsm
kg
4.56
15.46
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Problems
Calculate the density of drilling mud that is 50 wt. % water, 50 wt. % BaSO4 (barite). Use SGbarite = 4.49.
Why are specific gravities most often referred to the density of water at 4 oC instead of 0 oC?
How many U.S. gallons are there in a cubic mile? The total proven oil reserves of the U.S. are roughly 30 x 109 bbl.
How many cubic miles is this? What is the density of Hg in strict SI units? Estimate your mass, height, average body radius. Approximating your
body as a cylinder, calculate your volume. Then calculate your density from the above obtained variables. Now compare the obtained density to any other information you might have (e.g. is it easy to swim?)
Pete 314 1.28
6.
2 cm3 gray fluid is poured into one tube of an U-tube of diameter 0.5 cm. The difference of the two levels becomes 5 cm. Find the Specific Gravity of the gray fluid. Hint: First find l from the volume of the gray fluid
2 cm3
l A
B C
D
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(1 atm = 101,325 Pa)
7.
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8. (Example 1.2.)Concentric-cylinder (“cup and bob”, e.g.
Fann or Brookfield) viscometer also called a Couette viscometer. An inner cylinder (the bob) rotates inside a stationary outer cylinder (the cup). The shaft that drives the bob is instrumented to record both the angular velocity and the applied torque. What is the shear rate and the shear stress?
Hint: Consider this viscometer as simply the device in Fig. 1.4, wrapped around a cylinder.
D1= 25.15 mm D2= 27.62 mm L = 92.27 mmRotation rate: N = 10 rpmObserved torque: Γ = 5×10-6 N·m (book error)
Pa 0545.0m
N0545.0
m)1027.92(m)1015.25(
)2 /m1015.25/(m N 105/
s
166.10
0
s
m1013.17
m101.23550
233
36
1
1
1311
312
LD
r
A
F
Δr
VNDV
)D(D.Δr
(not exact)
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1. Fluid mechanics is the study of forces and motions in fluids.2. Fluids are substances that move continually when subjected to a shear force as
long as the force is applied. Solids are substances that deform slightly when subjected to a shear force and then stop moving and permanently resist the force. (There are, however, intermediate types of substances.)
3. Fluid mechanics is based on the principle of the conservation of matter, the first two laws of thermodynamics, Newton’s laws of motion, and careful experiments.
4. Gases have weak intermolecular attractions and expand without limit. Liquids have much stronger intermolecular attractions and can expand very little. With increasing temperature and pressure, the differences between liquids and gases gradually disappear.
5. Density is mass per unit volume. Specific gravity of liquids is density / (density of water at ). Specific gravity of gases is density / (density of air at the same T and P).
6. Viscosity is a measure of a fluid’s resistance to flow. Most simple fluids are represented well by Newton’s law of viscosity. The exceptions (non-Newtonian fluids) are generally complex mixtures, some of which are of great practical significance. Kinematic viscosity is viscosity divided by density.
7. Surface tension is a measure of a liquid’s tendency to take a spherical shape, caused by the mutual attraction of the liquid’s molecules.
8. Pressure is compressive force divided by area. It is the same in all directions for a fluid at rest and practically the same in all directions for most moving fluids.
9. Much of fluid mechanics can be based either on force and momentum, or on energy. We base most of fluid mechanics on energy.
