Pumping applications in petroleum con't

Sucker rod pump
An artificial-lift pumping system using a surface power source to drive a downhole pump assembly. A beam and crank assembly creates reciprocating motion in a sucker-rod string that connects to the downhole pump assembly. The pump contains a plunger and valve assembly to convert the reciprocating motion to vertical fluid movement.

 

EXPLANATION OF HOW IT WORKS/ IS USED:

Figure B: Operational Detail of Sucker Rod Pump Here the plunger is shown at its lowest position. The pitman arm and the crank are in-line. The maximum pumping angle, denoted as theta in the calculations, is shown. L is the stroke length. After one stroke, the plunger moves upward by one stroke length and the walking beam pivots. The crank also rotates counterclockwise. At the end of the upstroke the pitman arm, the crank, and the walking beam are in-line.

For name and location of parts, see Figure A.

1. A motor supplies power to a gear box. A gearbox reduces the angular velocity and increases the torque relative to this input.
2. As shown in Figure B, (the crank turns counterclockwise) and lifts the counterweight. Since the crank is connected to the walking beam via the pitman arm, the beam pivots and submerges the plunger. Figure B also shows the horsehead at its lowest position. This marks the end of the down stroke. Note that the crank and the pitman arm are in-line at this position.
3. The upstroke raises the horsehead and the plunger, along with the fluid being pumped. The upstroke begins at the point shown in Figure B. At the end of the upstroke, all joints are in-line. This geometric constraint determines the length of the pitman arn.

Figures C(a) and C(b) show the plunger and ball valves in more detail. These valves are opened by fluid flow alone. On the upstroke, the riding valve is closed and the standing valve is open. Fluid above and within the plunger is lifted out of the casing while more fluid is pumped into the well. On the down stroke, the riding valve is opened and the standing valve is closed. Fluid flows into the plunger and no fluid is allowed to leave the well.

Hydraulic pump

A hydraulic ram or impulse pump is a device which uses the energy of fallingwater to lift a lesser amount of water to a higher elevation than the source.See Figure 1.  There are only two moving parts, thus there is littleto wear out.  Hydraulic rams are relatively economical to purchaseand install.  One can be built with detailed plans and if properlyinstalled, they will give many trouble-free years of service with no pumpingcosts.  For these reasons, the hydraulic ram is an attractive solutionwhere a large gravity flow exists.  A ram should be considered whenthere is a source that can provide at least seven times more water thanthe ram is to pump and the water is, or can be made, free of trash andsand.  There must be a site for the ram at least 0.5m below the watersource and water must be needed at a level higher than the source

 A Jet Pump

A Jet Pump is a type of impeller-diffuser pump that is used to draw water from wells into residences. It can be used for both shallow (25 feet or less) and deep wells (up to about 200 feet.)
Shown here is the underwater part of a deep well jet pump. Above the surface is a standard impeller-diffuser type pump. The output of the diffuser is split, and half to three-fourths of the water is sent back down the well through the Pressure Pipe (shown on the right here).
At the end of the pressure pipe the water is accelerated through a cone-shaped nozzle at the end of the pressure pipe, shown here within a red cutaway section. Then the water goes through a Venturi in the Suction Pipe (the pipe on the left).
The venturi has two parts: the Venturi Throat, which is the pinched section of the suction tube; and above that is the venturi itself which is the part where the tube widens and connects to the suction pipe.
The venturi speeds up the water causing a pressure drop which sucks in more water through the intake at the very base of the unit. The water goes up the Suction Pipe and through the impeller -- most of it for another trip around to the venturi.
Advantages
•  Increasing the speed before the onset of cavitation, because of the raised internal dynamic pressure
•  High power density (with respect to volume) of both the propulsor and the prime mover (because a smaller, higher-speed unit can be used)
•  Protection of the rotating element, making operation safer around swimmers and aquatic life
•  Improved shallow-water operations, because only the inlet needs to be submerged
•  Increased maneuverability, by adding a steerable nozzle to create vectored thrust
Disadvantages
•  Can be less efficient than a propeller at low speed
•  More expensive
•  Higher weight in the boat because of entrained water
•  Will not perform well if the boat is heavier than the jet is sized to propel
•  Can suffer more easily from cavitation than a conventional propeller

 

Pumping applications in petroleum

Pumping application in petroleum

Types of pumps in petroleum:-

1-ELECTRO SUBMERSIBLE OIL PUMP (esp.)

2-sucker rod pump.

3-hydraulic pump.

4- JET PUMP .

5- Progressive Cavity Pumps

 

 

ELECTRO SUBMERSIBLE OIL PUMP (esp.)

Electrosumergible pumping system (BES) is an artificial lift system that uses electrical energy converted into mechanical energy to lift a column of fluid from a given level to the surface, discharging at a given pressure. As in all cases when you want to design an artificial lift system, you should remember:
“Not always the cheapest is the most convenient”
“Not always the most expensive is the best solution”
Electrosumergible pumping has proven to be an artificial system of efficient and economical production. In the petroleum industry, compared with other artificial production systems has advantages and disadvantages, because for various reasons may not always be the best, well that is a candidate to produce artificially pumping electrosumergible must have characteristics that do not affect its operation relationships such as high gas / oil, high temperatures, the presence of sand in the produced fluids, which are factors with undesirable influences on the efficiency of the rig.
Among the features of the system are its ability to produce large amounts of fluid from different depths under a wide variety of conditions particularly well and is distinguished by the engine is directly coupled to the pump at the bottom of the well. The electric pump assembly works on a wide range of depths and volumes, their application is particularly successful when conditions are conducive to producing high volumes of liquids with low gas-oil ratio.
Description of pumping electrosumergible
A typical unit consists electrosumergible pump at the bottom of the pot for the following components: electric motor, protector, inlet section, electric submersible pumps and cable driver. The external parts are: head, cable surface. Control panel, transformer.
Key Components of a Pumping System electrosumergible:
1. Engine
2. Bomba (Stages, consisting of impeller and diffuser each)
3. Cable
4. Cable Restraint Suncho
5. Gas Separator
6. Section Sealant
7. Pressure Sensor Fund
8. Transformer (surface)
9. Variable Control
Team electrosumergible oil
Motor left) and pump (right)
Key features of a pumping system electrosumergible
It is necessary to bear in mind the conditions that tend to limit the use of this system:
1. It is not advisable to use this system in high regard GLR wells.
2. It is not advisable to use this system in wells under P. I. and low pressure.
3. It is essential for the design, knowing the bubble pressure of the reservoir will drain the well and the current pressure in the reservoir.
4. The importance of the latter is that it is not pumping a single phase (liquid) two-phase (gas + liquid), because the equation changes Productivity Index as the case, hence why it is necessary know the pressure of the reservoir and its value against its bubble pressure.
5. The mechanical conditions of the well may be another limiting factor so it is necessary to know the characteristics of the completion (diameter of the casing and the open intervals to production).
6. Another factor to consider is certainly the water cut, like most artificial lift systems, it is designed for incompressible fluids, and oil as we know it is understandable, even more so when accompanied by gas.
7. It must also consider the type of reservoir fluid and its characteristics (high viscosity of the fluid is a limiting factor, and in some cases, unconsolidated reservoirs, the fluids produced are accompanied by sand grains and in others are inlaid upon entering the facility, damaging parts)
Steps to design a pumping installation electrosumergible:
Collection of information from the well:
* Diameter, grade and weight of the liners.
* Perforated intervals.
* Estimated depth of the pump.
* Pressure: static and flowing to the midpoint of perforations.
Reservoir Data:
* Bubble Pressure
Production Data:
* Estimated Regime
*% Water
* G.L.R.
* Level Static
* Level Dynamic
Fluid Characteristics:
Oil Specific Gravity
Water Specific Gravity
Oil Viscosity
Additional considerations to take into account:
* Production of Fine
* Corrosion
* Scale
Emulsions *
* Presence of Sales
* Presence of H2S
* High Temperature
Main equations that facilitate the design of an artificial lift system by pumping electrosumergible (BES)
Productivity Index equation (when the pressure is greater than the bubble pressure, flow of a single phase):
Productivity Index equation (when the pressure is less than the bubble pressure, or two-phase flow equation Vogel)
Where:
Qmax: Maximum flow at zero pressure
PWF: Background Fluent pressure (referring to the vertical midpoint of the perforations)
Pr: Pressure from the reservoir to a given flow
q: flow regime PWF pressure
The level (height) of the fluid dynamic pump is calculated considering the pressure from the pump location (usually 100 ‘over the top of the perforations), and finally the submergence of the reservoir pressure at that depth.
The total height is the sum of the heights (pressures) represented by the frictional pressure loss in the tubing and the discharge pressure and the dynamic height, according to the following equation:
Overall height (Ht = Heat). It is the sheepdog that the pump must overcome.
Where:
Ht: Height
Hd: Height of discharge
Hs: Suction Head
Depth of Discharge. It is the algebraic sum of static discharge height and height due to friction losses in the system:
Where:
Hed: Height static discharge (pressure difference between the level of submergence and unloading, feet)
HFD: Height equivalent losses due to friction
Ps: discharge pressure in the separator (feet)
Suction Head. It is the algebraic sum of the static head plus friction losses in the suction of the pump:
Where:
Hes: Pump Vertical Depth (feet)
Hf: Height equivalent to the friction loss (0 feet)
Prs: Pressure from the reservoir to the depth of suction (ft)
To apply the equations is necessary first to determine the optimal value of q from the Vogel equation, the curve plotting the values of the regime (q) vs, dynamic height.
Once found the corresponding height value and the graph will pump performance is selected and the height and the corresponding power per stage, dividing the value of Ht between the height value found, you get the number of stages, then the latter value multiplied by the power (hp) is the total power of the engine brake.
Determination of Dynamic Level:
* Calculate the distance between the midpoint and the top of the holes (vertical)
* There is the algebraic sum of the level of submergence of the pump (1000 ‘) the pressure at the midpoint of the perforations and the distance from the pump at the same point (all in feet)
* Replaced the value found above and the other values in the equation and is the total charge flow regime selected.

to be con't

Hydraulics –Surge and Swab Pressures

•Swabbing
–When the drillstring is picked up to make a connection or trip out of the well, the mud in the annulus must fall to replace the volume of pipe pulled from the well.
–The hydrostatic pressure is momentarily reduced while the mud is falling in the annulus.
•Surging
–When the drillstring or casing is lowered or run into the well, mud is displaced from the well.
–The frictional pressure losses from the flow of mud in the annulus as it is displaced by the pipe causes pressures in excess of the hydrostatic pressure of the column of mud in the wellbore.
•Swab and surge pressures are related to the mud’s rheological properties:
–The mud’s gel strengths
–The speed at which the pipe is pulled from, or run into, the well
–The annular dimensions
–The length of drillstring in the well
•The rheological properties affect swab and surge pressures in the same manner as they affect annular pressure losses.
•Increases in either the plastic viscosity or the yield point will increase the swab and surge pressures.
•Since the maximum (not average) swab and surge pressures must be less than the pressures needed to swab the well in or break the formation down, swab and surge pressures must be calculated for the maximum drill string velocity when tripping.
•This is generally calculated as one-and-one-half times the average drill string velocity.
VMaxDrillstring(ft/min per stand) =(1.5 x stand length (ft) x 60 sec)/(min seconds per stand)
•The annular velocity must be calculated for each annular space.
•These annular velocities should be substituted into the API equations for the annular pressure losses for each interval.
•The swab and surge pressures are then calculated in the same manner as the ECD.
AVSwab-Surge(ft/min) =(VMaxDrillstring(ft/min) x drillstring displacement (bbl/ft))/(annular capacity (bbl/ft))
•The object of calculating swab and surge pressures is to determine safe pulling and running speeds and minimized trip times.
•This is done by changing the maximum or minimum time per stand and recalculating the swab and surge pressures until times per stand are found where the swab and surge pressures plus the hydrostatic pressure is approximately equal to the formation pressure and fracture pressure.
•This time per stand is only relevant for the present length of drillstring in the well.
•As pipe is removed from the hole, the drillstring length decreases and the bottom hole assembly will be pulled into large diameter casing.
•This will make it possible to pull each stand faster without risk of swabbing in the well.
•When tripping in to the well, the length of drillstring will be increasing and the annular spaces will decrease as the BHA is run into smaller diameters.
•This will require that the running time per stand be increased to avoid fracturing the formation.
•The swab and surge pressures should be calculated at either 500-or 1,000-ft intervals.
•Slip Velocity
–Free settling occurs when a single particle falls through a fluid without interference from other particles or container walls
•For Slip velocity we use stokes law
VS=( gC x DS*2(rS-rL))/(46.3μ)
–VS= Slip or settling velocity (ft/sec)
–gC= Gravitational constant (ft/sec2)
–DS= Diameter of the solid (ft)
–rS= Density of solid (lb/ft3)
–rL= Density of liquid (lb/ft3)
–μ= Viscosity of liquid (cP)
•This equation is a mathematical expression of events commonly observed:
–The larger the difference between the density of the cutting and the density of the liquid the faster the solid will settle.
–The larger the particle is the faster it settles
–The lower the liquid’s viscosity (1/μ), the faster the settling rate.

Hydraulics –ECD-Bit Hydraulics

•Equivalent circulating density (ECD)

–The pressure on a formation while circulating is equal to the total annular circulating pressure losses from the point of interest to the bell nipple, plus the hydrostatic pressure of the mud.
–This force is expressed as the density of mud that would exert a hydrostatic pressure equivalent to this pressure.
Formula for ECD
ECD (lb/gal) = Pa(psi)/ 0.052 x TVD (ft)
•Excessive ECD may cause losses by exceeding fracture gradient on a well
.•It is important to optimize rheological properties to avoid excessive ECD.

Bit Hydraulics

•In addition to bit pressure loss, several other hydraulics calculations are used to optimize the drilling performance.
•These include hydraulic horsepower, impact force and jet velocity calculations.
•Hydraulic Horsepower (hhp)
–The recommended hydraulic horsepower (hhp) range for most rock bits is 2.5 to 5.0 Horsepower per Square Inch (HSI) of bit area.
–Low hydraulic horsepower at the bit can result in low penetration rates and poor bit performance.
•Hydraulic Horsepower (hhp)
–The bit hydraulic horsepower cannot exceed the total system hydraulic horsepower.
hhpb= QPBit/1,740
–Q = Flow rate (gpm)
–PBit= Bit pressure loss (psi)
•Hydraulic Horsepower (hhp)
–Hydraulic Horsepower per square inch
HSI = 1.27 x hhpb/Bit Size*2
–Bit Size = Bit diameter (in.)
–System Hydraulic HorsepowerhhpSystem= PTotalQ1,714
–PTotal= Total system pressure losses (psi)

Nozzle Velocity

–Although more than one nozzle size may be run in a bit, the nozzle velocity will be the same for all of the nozzles.
–Nozzle velocities of 250 to 450 ft/sec are recommended for most bits.
–Nozzle velocities in excess of 450 ft/sec may erode the cutting structure of the bit.
•Nozzle Velocity
Vn(ft/sec) = 417.2 x Q/(Dn1*2+ Dn2*2+ Dn3*2+ …)
–Q = Flow rate (gpm)
–Dn= Nozzle diameter (32nds in.)
–Q = Flow rate (gpm)
•Percent pressure drop at the bi
t–It is generally desired to have 50 to 65% of surface pressure used across the bit.
%PBit= PBit x 100/PTotal
•Hydraulic impact force (IF)
IF (lb) = Vn x Qr/1,930
–Vn= Nozzle velocity (ft/sec)
–Q = Flow rate (gpm)
–r = Density (lb/gal)
–Impact force per inch squaredIF (psi) = 1.27 x IF (lb)/Bit Size*2

Hydraulics –Pressure losses

•The circulating system of a drilling well is made up of a number of components or intervals, each with a specific pressure drop.
•The sum of these interval pressure drops is equal to the total system pressure loss or the measured standpipe pressure.
•The total pressure loss for this system can described mathematically as:
PTotal= PSurf Equip+ PDrillstring+ PBit+ PAnnulus
•Surface pressure losses include losses between the standpipe pressure gauge and the drill pipe.
–This includes the standpipe, kellyhose, swivel, and kellyor top drive.
–To calculate the pressure loss in the surface connections, use the API pipe formula for pressure loss in the drill pipe.
•Top Drive Surface connections
–There is no current standard case for top drive units.
–The surface connections of most of these units consist of an 86-ft standpipe and 86 ft of hose with either a 3.0-or 3.8-in. ID. In addition, there is an “S”pipe that is different on almost every rig.
•Drill String Pressure losses
–The pressure loss in the drillstring is equal to the sum of the pressure losses in all of the drillstring intervals, including drill pipe, drill collars, mud motors, MWD/LWD/PWD or any other downhole tools.
•Friction Factor
–Before calculating the pressure loss, the Fanning friction factor (fp) is calculated next with different equations being used for laminar and turbulent flow.
–This friction factor is an indication of the resistance to fluid flow at the pipe wall.
–The friction factor in these calculations assumes a similar roughness for all tubulars.
•Formulas for friction Factor–If the Reynolds number is less than or equal to 2,100:
fp= 16/NRep
–If the Reynolds number is greater than or equal to 2,100
fp=((log n + 3.93)/50)/NRep((1.75 –log n)/7)
•Pipe Interval Pressure loss
–Drillstring (including drill collars) intervals are determined by the ID of the pipe.
–The length of an interval is the length of pipe that has the same internal diameter.
–The following equation is used to calculate the pressure loss for each drillstring interval.
•Formula for Pipe Pressure loss
•Pp(psi) =( fp x Vp*2 x r x L)/(92,916 x D)
•Vp= Velocity (ft/min)
•D = ID pipe (in.)
•r = Density (lb/gal)
•L = Length (ft)
•Pressure loss for motors and tools
–If the drillstring contains a downhole motor; an MWD, LWD or PWD tool; a turbine or a thruster, their pressure losses must be included in the system pressure losses when calculating the system’s hydraulics.
–These pressure losses can significantly change the pressure available at the bit, as well as bypass flow around the bit.
–The pressure loss through MWD and LWD tools varies widely with mud weight, mud properties, flow rate, tool design, tool size and the data transmission rate.
–Some manufacturers publish pressure losses for their tools but these pressure losses can be conservative, because they are usually determined with water.
–The pressure loss across motors and turbines cannot be accurately determined by formula, but, again, this pressure loss data is available from the suppliers.
–Regular nozzle type bit
Pbit= 156rQ*2/(Dn1*2+ Dn2*2+ Dn3*2+ …)*2
–Diamond type coring bitPbit= rQ*2/10,858(TFA)*2
–r = Density (lb/gal)
–Q = Flow ratio (gpm)
•Pressure loss in the annulus
–The total annular pressure loss is the sum of all of the annular interval pressure losses.
–Annular intervals are divided by each change in hydraulic diameter.
–A change in drillstring outside diameter and/or a change in casing, liner or open hole inside diameter would result in a hydraulic diameter change.
–As with the drillstring pressure loss equations, the friction factor must first be determined before calculating the pressure loss for each annular section.
–The pressure loss for each interval must be calculated separately and added together for the total annular pressure loss.
This equation is used to calculate the individual interval pressure losses.
Pa(psi) =( fa xVa x 2r x Lm)/((92,916 x D2)-D1)
–Va= Velocity (ft/min)
–D2= ID hole or casing (in.)
–D1= OD Drill pipe or collars (in.)
–r = Density (lb/gal)
–Lm= Length (ft)
-fa as before


–TFA = Total Flow Area (in.2)

Hydraulics

•Once the rheological properties for a fluid have been determined and modeled to predict flow behavior, hydraulics calculations are made to determine what effect this particular fluid will have on system pressures.
•The critical pressures are total system pressure (pump pressure), pressure loss across the bit and annular pressure loss (converted to ECD)
•Many wells are drilled under pressure limitations imposed by the drilling rig and associated equipment.
–The pressure ratings of the pump liners and surface equipment and the number of mud pumps available limit the circulating system to a maximum allowable circulating pressure.
•It is imperative to optimize drilling fluid hydraulics by controlling the rheological properties of the drilling fluid to avoid reaching this theoretical limit.
–This is especially true in extended-reach drilling.
•Fluids in laminar flow “act”differently than fluids in turbulent flow.
–These differences make it necessary to use different equations to determine the pressure losses in laminar and turbulent flow.
–Different equations are also required to calculate the pressure losses in the annulus and drillstring because of different geometries.
•The first step in hydraulics calculations is to determine which stage of flow is occurring in each geometric interval of the well.
•The velocity of the fluid in each of these intervals can be determined with the following equations.

Bulk Velocity

•Average bulk velocity in pipe (Vp):
Vp (ft/min) = 24.48 x Q (gpm)/(D)*2(in.)
•Average bulk velocity in annulus:Va (ft/min) =24.48 x Q (gpm)/ ((D2)*2–(D1)*2)(in.)

–V = Velocity (ft/min)
–Q = Flow ratio (gpm)
–D = Diameter (in.)

Reynolds Number

•The Reynolds number (NRe) is a dimensionless number that is used to determine whether a fluid is in laminar or turbulent flow.
–A Reynolds number less than or equal to 2,100 indicates laminar flow.
–A Reynolds number greater than 2,100 indicates turbulent flow.
–Earlier API hydraulics bulletins and many hydraulics programs that predate the current API hydraulics bulletin define laminar and turbulent flow differently.
•The general formula for Reynolds number is:
NRe= V Dr/μ
V = Velocity
D = Diameter
r = Density
μ= Viscosity
•The Reynolds number for inside the pipe is:
NRep= 15.467 x Vp x D x r/μep
•The Reynolds number for the annulus is:
NRea= 15.467x Va x (D2-D1) x r/μea
•D = ID drill pipe or drill collars
•D2= ID hole or casing
•D1= OD drill pipe or drill collars
•μep= Effective viscosity (cP) pipe
•μea= Effective viscosity (cP) annulus

Critical Velocity

•The critical velocity is used to describe the velocity where the transition occurs from laminar to turbulent flow.
•Flow in the drill pipe is generally turbulent.
•The equations for critical velocity in the pipe and in the annulus are listed below.
•Critical Pipe Velocity Vcp(ft/min)= ((38727 x Kp)/r)*(1/(2-n)) x ((1.6/D)x((3n+1)/4n)* (n(2-n))
•Critical Pipe Flow rate Qca(gpm)= VcpD*2/24.51
•Critical Annular Velocity Vca(ft/min)= ((25818 x Ka)/r)*(1/(2-n)) x ((2.4/(D2-D1))x((3n+1)/4n) *(n(2-n))
•Critical Annular Flow rate Qca(gpm)= Vca(D2-D1)*2/24.51

Rheology

•Fluid types
–There are two basic types of fluids, Newtonian and non-Newtonian.
–Rheological and hydraulic models have been developed to characterize the flow behavior of these two types of fluids.
•Newtonian fluids have a constant viscosity at a given temperature and pressure condition. Common Newtonian fluids include:
–Diesel
–Water
–Glycerin
–Clear brines
•Non-Newtonian fluids have viscosities that depend on measured shear rates for a given temperature and pressure condition. Examples of non-Newtonian fluids include:
–Most drilling fluids
–Cement

Rheological models

•Rheological models help predict fluid behavior across a wide range of shear rates.
•Most drilling fluids are non-Newtonian, pseudoplasticfluids.
•The most important rheological models that pertain to them are the:
–Bingham model
–Power law model
–Yield-power law or modified power law

•The Bingham model describes laminar flow using the following equation:
t = YP + (PV ×y)
–Where
–t is the measured shear stress in lb/100 ft2
–YP is the yield point in lb/100 ft2
–PV is the plastic viscosity in cP
–y is the shear rate in sec-1
•Current API guidelines require the calculation of YP and PV using the following equations:
•PV = 600rpm–300rpm
•YP = 300rpm–PV
•The power law model describes fluid rheological behavior using the following equation:
t = K ×(y)to the power n
•This model describes the rheological behavior of polymer-based drilling fluids that do not exhibit yield stress (i.e., viscosifiedclear brines).
•Some fluids viscosifiedwith biopolymers can also be described by power-law behavior.
•The general equations for calculating a fluid's flow index and consistency index are:
n =( log(t2/t1))/(log(y2/y1))
K = (t2)/(y2to the power n)
t is the calculated shear stress in lb/100 ft2
•t2is the shear stress at higher shear rate (600 rpm)
•t1is the shear stress at lower shear rate (300 rpm)
•n is the flow index
•y is the shear rate in sec-1
•y2is the higher shear rate (600)
•y1is the lower shear rate (300)
•K is the consistency index
•Because most drilling fluids exhibit yield stress, the Yield-power law [YPL]) model describes the rheological behavior of drilling muds more accurately than any other model.
•The YPL model uses the following equation to describe fluid behavior:
t = t0+ (K ×y)to the power n
–Where
–t is the measured shear stress in lb/100 ft2
–t0is the fluid's yield stress (shear stress at zero shear 0 rate) in lb/100 ft2
–K is the fluid's consistency index in cPor lb/100 ft2secn
–n is the fluid's flow index
–y is the shear rate in sec-1
•K and n values in the YPL model are calculated differently than their counterparts in the power law model.
•The YPL model reduces to the Bingham model when n = 1 and it reduces to the power law model when t0= 0.
•An obvious advantage the YPL model has over the power law model is that, from a set of data input, only one value for n and K are calculated.
–Note: The YPL model requires:
•A computer algorithm to obtain solutions.
•A minimum of three shear-stress/shear-rate measurements for solution. Model accuracy is improved with additional data input.