Hydraulics v2 1

DRILLING FLUID HYDRAULICS

Version 2.1 January 2001

Dave Hawker

Corporate Mission To be a worldwide leader in providing drilling and geological monitoring solutions to the oil and gas

industry, by utilizing innovative technologies and delivering exceptional customer service.

DATALOG DRILLING FLUID HYDRAULICS MANUAL, Version 2.1, issued January 2001


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CONTENTS

1 FUNCTIONS OF THE DRILLING FLUID...................................................................................................... 3 1.1 LUBRICATION AND COOLING OF THE BIT AND DRILLSTRING ............................................................................ 3 1.2 REMOVAL OF DRILLED CUTTINGS FROM THE ANNULUS AND BIT..................................................................... 4 1.3 CONTROL OF SUBSURFACE FORMATION PRESSURES........................................................................................ 5 1.4 BOTTOM HOLE CLEANING................................................................................................................................. 6 1.5 TRANSMIT HYDRAULIC HORSEPOWER TO THE BIT........................................................................................... 6 1.6 SUPPORT THE WEIGHT OF THE DRILLSTRING.................................................................................................... 6 1.7 FORMATION STABILITY .................................................................................................................................... 6 1.8 FORMATION EVALUATION................................................................................................................................ 7

2 TYPES OF DRILLING MUD............................................................................................................................. 8 2.1 WATER BASED MUDS ...................................................................................................................................... 8 2.2 OIL BASED MUDS .......................................................................................................................................... 10 2.3 SYNTHETIC MUDS.......................................................................................................................................... 11 2.4 COMMON MUD ADDITIVES ............................................................................................................................ 12

3 RHEOLOGY DEFINITIONS........................................................................................................................... 14 3.1 SHEAR RATE AND SHEAR STRESS .................................................................................................................. 14 3.2 FLUID VISCOSITY ........................................................................................................................................... 15 3.3 PLASTIC VISCOSITY AND YIELD POINT........................................................................................................... 16 3.4 GEL STRENGTH .............................................................................................................................................. 16

4 FLUID BEHAVIORAL MODELS................................................................................................................... 17 4.1 NEWTONIAN FLUIDS....................................................................................................................................... 17 4.2 BINGHAM PLASTIC MODEL ............................................................................................................................ 18 4.3 POWER LAW MODEL...................................................................................................................................... 19 4.4 THE MODIFIED POWER LAW .......................................................................................................................... 21 4.5 RHEOGRAM SUMMARY OF THE DRILLING FLUID MODELS.............................................................................. 22 4.6 MODEL EFFECTS ON VISCOUS FLOW.............................................................................................................. 23

5 LAMINAR, TURBULENT AND TRANSITIONAL FLOW PATTERNS ................................................... 24 5.1 LAMINAR FLOW ............................................................................................................................................. 24 5.2 TURBULENT FLOW......................................................................................................................................... 24 5.3 TRANSITIONAL FLOW..................................................................................................................................... 25 5.4 DETERMINATION OF FLOW TYPE.................................................................................................................... 25

5.4.1 Derivation of Effective Viscosity ............................................................................................................ 26 5.4.2 Determination of the Reynolds Number ................................................................................................. 27 5.4.3 Determination of Average Annular Velocity.......................................................................................... 27 5.4.4 Use of the Reynolds Number in determining Flow Type........................................................................ 28 5.4.5 Determination of Critical Velocity......................................................................................................... 28

6 DETERMINATION OF SYSTEM PRESSURE LOSSES ............................................................................. 30 6.1 FANNING FRICTION FACTOR........................................................................................................................... 30 6.2 DRILLSTRING PRESSURE LOSSES.................................................................................................................... 32 6.3 ANNULAR PRESSURE LOSSES......................................................................................................................... 33 6.4 BIT PRESSURE LOSS....................................................................................................................................... 34 6.5 SURFACE PRESSURE LOSSES.......................................................................................................................... 35

7 OTHER HYDRAULIC CALCULATIONS..................................................................................................... 36 7.1 CUTTINGS SLIP VELOCITY.............................................................................................................................. 36 7.2 PARTICLE REYNOLDS NUMBER...................................................................................................................... 37



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7.3 NOZZLE VELOCITY......................................................................................................................................... 38 8 HYDRAULICS OPTIMIZATION ................................................................................................................... 40

8.1 BIT HYDRAULIC HORSEPOWER ...................................................................................................................... 40 8.2 HYDRAULIC IMPACT FORCE........................................................................................................................... 40 8.3 HYDRAULIC OPTIMIZATION............................................................................................................................ 41 8.4 USE OF THE QLOG HYDRAULICS PROGRAMS................................................................................................. 42

9 EQUIVALENT CIRCULATING DENSITY................................................................................................... 45

10 SWAB AND SURGE PRESSURES................................................................................................................ 48 10.1 SURGE PRESSURES....................................................................................................................................... 48 10.2 SWAB PRESSURES ........................................................................................................................................ 49 10.3 CALCULATION OF SURGE AND SWAB PRESSURES......................................................................................... 50 10.4 USE OF THE QLOG SWAB AND SURGE PROGRAM....................................................................................... 51

APPENDIX - ANSWERS TO TRAINING EXERCISES.................................................................................. 53



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1 FUNCTIONS OF THE DRILLING FLUID The importance of the drilling mud in the drilling of a well cannot be over emphasized. It has a critical bearing on all aspects of the operation. Not only does it act as a transporting medium for cuttings and gas, enabling us to see at surface what is happening downhole, but the properties of the mud will determine how effective the drilling is; how well the hole and formations are protected, and how well subsurface pressure are controlled. The principle roles of the mud are: - • Lubrication and cooling of the drill bit and the drillstring • Removal of drilled cuttings from the annulus • Bottom hole cleaning • Control of subsurface formation pressures • Transmit hydraulic horsepower to the bit • Help support the weight of the drillstring • Aid formation stability • Aid in formation evaluation • Protect formation productivity 1.1 Lubrication and Cooling of the Bit and Drillstring The drilling action and rotation of the drillstring produces a lot of heat, at the bit and throughout the drillstring, due to friction. The drilling fluid helps, not only to keep the bit/string cool through lubrication, but also to absorb the heat that is generated and release it, to a degree, as it returns to surface and cools. The mud has to cool the bit and lubricate the teeth to allow for effective drilling and to minimize damage and wear. The mud lubricates the drillstring by reducing friction between the string and the borehole wall - this is often achieved by using additives such as bentonite, polymers, graphite or oil. Optimum lubrication is provided by oil emulsion mud systems, coupled with various emulsifying agents. High drilling torque can be a serious problem in directional drilling, especially in areas of hard, abrasive formations and lubricity is a very important function of the mud. Extra steps may be taken, such as the addition of glycol or even tiny beads, to gain maximum lubrication. Lubrication is important to maximize drilling efficiency and directional control, and to keep drilling torque and the risk of pipe fatigue and twist-off to a minimum.



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1.2 Removal of Drilled Cuttings from the Annulus and Bit This is a very important role of the mud. Cuttings need to be removed from the annulus for a number of reasons: -

• to prevent loading of the annulus • to keep annular pressure to a minimum • to allow for free movement and rotation of the drillstring • so that the cuttings reach the surface in such a condition that they can be evaluated by a

geologist to accurately interpret the downhole geology This principle is not only determined by the physical properties of the mud but by the type of flow pattern present in the annulus. The cuttings need to be removed effectively, but damage and erosion to the cuttings has to be avoided. The removal of cuttings is primarily dependent on the annular velocity, the fluid density, the yield point and gel strength of the mud. Other factors also come into play, such as hole inclination, pipe rotation, and of course, the size, density and even shape, of the drilled cuttings. The typical density of drilled cuttings is obviously greater than the mud density. It is therefore normal for a degree of cuttings slip, where, especially when the mud is motionless, cuttings will sink, or slip through the mud. This can have the effect that the time that cuttings arrive at surface does not correlate with the correct drilled depth and with lagged parameters such as gas. This phenomenon is especially important during periods of no circulation such as a trip, when cuttings will sink and build up at the bottom of the hole (hole fill). Mud properties, such as viscosity and gel strength, have to be such so as to minimize this. The drilling fluid is then termed thixotropic, in that it possesses gelling properties. When circulating, thixotropic fluids are liquid, allowing them to transport the drilled cuttings to surface. When there is no circulation, the drilling fluid will gel, or thicken, in order to suspend the cuttings and prevent them from falling and settling around the bit at the bottom of the hole. The degree of cuttings slip will also be affected by the annular velocities: - If annular velocities are reduced for any reason (eg pump volume, large hole section, downhole conditions), mud properties would have to be changed to compensate for an increased degree of slip. If the cuttings content does build up in the annulus, higher annular velocities or changes to yield may be the solution. A common practice, especially in shallow, large hole diameter sections, is to sweep the hole with a high viscosity pill of mud. This has the advantage of maintaining good hole cleaning without having to change the properties of the “active” mud system.



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1.3 Control of Subsurface Formation Pressures Minimum mudweight is optimum for faster drilling rates and to minimize the risk of damaging formations and losing circulation. However, in conventional drilling the mud also has to have a sufficient density that will exert enough downhole pressure to protect the well against subsurface formation pressures. The pressure exerted at the bottom of the hole, due to the weight of the static vertical column of mud, is known as the Mud Hydrostatic Pressure. If the mud hydrostatic pressure is equal to the formation pressure, the well is said to be at balance. If the mud hydrostatic pressure is less than the formation pressure, the well is said to be underbalanced and therefore subject to the influx, or flow, of formation fluid into the annulus (kick). If the mud hydrostatic pressure is greater than the formation pressure, the well is said to be overbalanced and therefore protected against influxes of formation fluid into the wellbore. If the overbalance is too great, however, there is the possibility of a number of different problems. Fluids will naturally tend to flow in directions of decreasing pressure. In an overbalanced well, it is therefore normal for the drilling fluid to flow into, or invade, permeable formation. Such invasion, or even the flushing of formations prior to drilling, may prevent effective formation evaluation or ultimately lead to permanent damage to the formation (ie blocking of pore spaces and pore throats, restricting permeability). Too great an overbalance may also lead to the fracturing of weaker or unconsolidated formations. This will lead to drilling problems associated with the formation falling, or sloughing, into the annulus, but more importantly, may lead to the drilling fluid flowing freely into the formation. Such lost circulation can lead to the mud level dropping in the annulus and therefore a reduction in the mud hydrostatic pressure. This can result in other permeable formations becoming underbalanced. The well is then subject to the most dangerous situation possible, known as a blowout, where formation fluids are flowing freely into one part of the well and circulation is being lost to another part of the well. PHYD = ρρρρ x TVD x 0.052 where ρ = mud density (ppg) PHYD = psi TVD = feet PHYD = ρρρρ x TVD x 0.433 where ρ = SG PHYD = psi TVD = feet PHYD = ρρρρ x TVD x 0.00981 where ρ = kg/m3 PHYD = Kpa TVD = m



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1.4 Bottom hole cleaning This is a very important role of the mud, but one that is very difficult to achieve in practice. The jetting action of the mud exiting the bit nozzles has to provide sufficient velocity and cross flow across the rock face to effectively remove cuttings from around the bit as rock is newly penetrated. This would prevent cuttings from building up around the bit and teeth (bit balling), prevent excessive grinding of the cuttings and clear them on their way up the annulus, and maximize the drilling efficiency. Many variables play a part in the efficiency of bottom hole cleaning, including bit weight and rotation speed, bit type, flow rate, jet velocity, differential pressure, nozzle size, location and distance from rock face, solids volume etc. 1.5 Transmit Hydraulic Horsepower to the Bit Effectively, the drilling fluid transmits the HHP, delivered by the rig pumps, to the drill bit. The circulation rate of the drilling fluid should be such that optimum power can be used to clean the face of the hole ahead of the bit and allow for optimum drilling efficiency. The amount of HHP expended at the bit determines the degree to which hydraulics are optimized, whether for bottom hole cleaning or for laminar flow in the annulus. 1.6 Support the Weight of the Drillstring The blocks, suspended from the derrick, must support the increasing weight of the drillstring as greater depths are reached. Through displacement, the drillstring is buoyed up by the drilling fluid. This effectively reduces the total weight that the surface equipment must support. 1.7 Formation Stability Wellbore stability is obviously paramount for a successful operation. A clean and stable hole will allow for: -

• Optimum drill rates • Uninhibited string rotation • Minimal risk of stuck pipe • Minimal loading of the annulus, allowing good hole cleaning and lower circulating pressures • Ability to run wireline tools and casing strings to the bottom of the hole

The drilling fluid must therefore be able to: -

• prevent erosion or collapse of the wellbore; • prevent formation pressures causing formation caving • prevent swelling and sloughing of shales (oil based mud preferred, water based muds would have

to be treated with Ca/K/Asphalt compounds); • prevent the ‘dissolving’ of salt sections (use salt saturated or oil based mud to prevent taking the

salt into solution.



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1.8 Formation Evaluation This really, is the reason for drilling wells, to encounter and evaluate potential reservoir zones. However, wells are often drilled with attention completely focussed on drill rates and costs, and often, programs are implemented that have a detrimental effect on formation evaluation. One of the principle problems has been the use of hydrocarbon based additives in the drilling fluids which complicate and interfere with cuttings analysis. Cuttings Analysis Naturally, it is important to obtain the best possible cuttings for geological analysis. The mud viscosity determines how effectively the cuttings are held by the mud and lifted from the hole. The type of flow will determine the degree of erosion and structural alteration of the cuttings, thus smooth laminar flow is preferred to chaotic turbulent flow. Oil base muds typically produce excellent quality of cuttings, especially within argillaceous lithologies where water base systems can react with the clay minerals. Wireline Logs and Production Tests With a normally overbalanced wellbore, water base fluids will naturally invade permeable formations. This displaces formation fluids away from the wellbore, leaving a mixture of formation fluid and mud filtrate. This type of water invasion can affect the accuracy of wireline log analysis, especially resistivity measurement of the formation fluid, and sidewall cores, making hydrocarbon identification and reservoir evaluation very difficult. To minimize fluid invasion, a filter cake is allowed to build up on the wall of the borehole. This occurs when invasion is taking place and mud solids (either added to the drilling fluid, or present from drilled formation particles) are left behind on the borehole wall. When sufficiently thick, an impermeable layer prevents further invasion. Should mud invasion be too severe, not only may wireline analysis be lost, but the formation may become permanently damaged. In other words, pore throats and permeability may be blocked by the mud filtrate, which would prevent gaining flow results from tests such as RFT or DST’s. Normal build up of filter cake is normally sufficient to avoid excessive invasion, but this may be less effective in deviated/horizontal wells where movement of the drillstring along the underside of the wellbore can remove any cake that has been deposited. Oil base mud removes the risk of invasion in most situations, since it is immiscible with water and therefore unable to mix with formation fluids. Drilling with underbalanced drilling fluids also removes the risk of mud invasion, since the formation pressure exceeds that of the wellbore, preventing any fluid movement in that direction.



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2 TYPES OF DRILLING MUD This manual provides a brief summary of conventional drilling fluids used in balanced drilling applications. Broadly, they can be grouped into the following categories: - Water Based including gel and polymer muds Oil Based, including Invert Emulsions Synthetic or Mineral oils (World Oil, June 2000, is the main source of this classification) 2.1 Water Based Muds Non-Dispersed Using clear or native water, these systems include spud muds, natural muds and other lightly treated systems. They are typically used for shallow wells or top hole sections. No thinners or dispersants are added to disperse drilled solids and clay particles. Rather, the water is allowed to react with formations containing shales/clays so that the mud will build up solids content and density naturally. Dispersed These mud systems are typically used at greater depths where higher densities are required or problematic hole conditions require specialized treatment. The mud system will be dispersed with specific additives to provide specific properties to the mud system. Lignosulphates/lignites/tannins These are effective deflocculants and filtrate reducers, providing high

density muds with a tolerance to high temperatures and solids contamination.

Potassium bearing chemicals Provide greater shale inhibition Calcium Muds Calcium (or magnesium) addition to freshwater drilling muds reduces, or inhibits, the swelling and hydration of clays and shales. High levels of dissolved calcium are used to minimize sloughing shale and hole enlargement. Calcium treated muds are also good for drilling gypsum/anhydrite lithologies because they resist contamination. However, at higher temperatures, they are susceptible to gelling and solidifying.



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Polymer Muds Typically, long chain polymers (e.g. acrylamide, cellulose) are used in mud systems to provide a number of advantages: -

• Encapsulate drill solids to prevent dispersion • Coat shales for inhibition and prevention of sloughing • Increase viscosity • Reduce fluid loss (filtration)

KCl/NaCl muds Inhibited salts such as these provide greater shale stability. Low Solids These include systems where solids are strictly controlled, typically with total solids volume between 6 and 10% and clay volume less than 3%. They typically use polymer additives as a viscosifier and are non-dispersed. This type of system is used to significantly improve penetration rates. Saltwater Saturated Salt Chloride concentration around 190,000 mg/l. Used to drill salt formations to prevent dissolving. Saltwater Chloride concentration between 10,000 and 190,000 mg/l. Muds are prepared from either fresh or brine water and salts added to the desired level of concentration. KCl would typically used when shale inhibition is required. Additives such as starch would also be added to increase viscosity and improve hole cleaning.



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2.2 Oil Based Muds Oil Based Muds These systems are used when high levels of fluid stability and inhibition are required. They have many advantages, such as: -

• Inhibition to reduce problems caused by swelling or sloughing shales. • Provides good lubricity and reduces torque and drag and risk of sticking. • Stable at high temperatures. • Preserves natural permeability, not damaging hydrocarbon zones through invasion.

Due to these characteristics, typically these mud systems provide faster drilling rates. This helps to offset the higher cost of oil based systems, but a number of disadvantages remain: -

• Environmental concerns • Flammability • Solids removal due to high PV (need good equipment as with polymer muds. • Problems for interpretation of log information • Cost

Oil based muds contain only oil in the liquid phase, and although they may pick up formation water, no additional water or brine is added. To provide viscosity to oil based muds, gelling agents or emulsifiers have to be added. Alkalinity can be improved by adding lime, organic materials or soaps. Invert Emulsion Muds These are water-in-oil emulsions; typically with base oil or diesel as the continuous phase, and up to 50% brine in the emulsifier phase. Calcium chloride brine is a common emulsifier used in these systems. Emulsion Muds With these fluids, water provides the major continuous phase, with oil now constituting the dispersed phase (normally 5 - 10%). With water being the main phase, costs are reduced and environmental concerns are minimized. But adding the oil provides the advantages associated with oil base systems, such as increased ROP, reduced filter loss, improved lubrication, reduced drag and torque.



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2.3 Synthetic Muds One of the big disadvantages of oil based muds, despite all of the drilling and formation advantages provided, is the hazard it represents to the environment and to those personnel that come into contact with the mud. For this reason, synthetic oils (and mineral oils) have gained in their use. They provide much of the performance advantages of hydrocarbon oil systems but have none of the associated environmental concerns. Common systems are esters, ethers, and poly or isomerized alpha olefins. These are environmentally friendly and biodegradable and can be discharged safely offshore.



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2.4 Common Mud Additives

TYPE PURPOSE AGENTS Alkalines To control acidity and alkalinity Lime, caustic soda, soda ash,

bicarbonate of soda

Corrosion Inhibition Prevent corrosion pH control Neutralize hazardous, acid, gases such as hydrogen sulphide Prevent scale from forming in the drilling fluid

Amine- or phosphate-based products are commonly used

Defoamers Reduce foaming action, especially in brackish or saltwater muds

Emulsifiers To create a heterogeneous mixture of two insoluble liquids

Oil based muds – fatty acids, amine-based chemicals Water based muds – detergents, soaps, organic acids

Filtrate or Water Loss Additives to reduce water loss, the tendency of the liquid phase to pass through the filter cake into the formation.

Bentonite clay, lignite, polyacrylate, pregelatinized starch.

Flocculants Increase viscosity Improve hole cleaning De-water or clarify low-solids fluids. Particles in suspension will group into bunches or “flocs”, causing solids to settle out.

Salt, hydrated lime, gypsum, soda ash, bicarbonate of soda, polymers

Lubricants To reduce friction, thereby reducing torque and drag

Oils, synthetic liquids, graphite, glycol or surfactants

Pipe-freeing agents To reduce friction and increase lubricity at the point where the pipe is stuck.

Detergents, soaps, oils, surfactants

Shale inhibition To reduce shale hydration when drilling water sensitive shales, thereby preventing excessive wellbore enlargement and heaving or caving of the shale.

Soluble calcium or potassium, inorganic salts, organic compounds.

Surfactants Surface active agents; reduce tension between contacting surfaces such as water/oil, water/solid, water/air etc.

Emulsifiers, de-emulsifiers, wetting agents, flocculants or de-flocculents, depending on the surfaces involved.



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Temperature stability Increase rheological and filtration stability in fluids exposed to high temperatures.

Acrylic or sulphenated polymers, lignite, lignosulphate, tannin

Thinners, Dispersants These modify the relationship between viscosity and solids volume, reducing gel strength and increasing the “pumpability” of a fluid. A thinner, more specifically, acts as a deflocculent to reduce attraction of clay particles which causes high viscosity and gel strength.

Tannins, lignite and lignosulphates, polyphosphates

Viscosifiers Increase viscosity, providing better solid suspension and hole cleaning.

Bentonite, CMC, attapulgite clays and polymers

Weighting agents To provide necessary density to control formation pressures, provide hole stability and to prevent u-tubing when pulling the drillpipe

Barite, lead compounds, iron oxides, calcium carbonate



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3 RHEOLOGY DEFINITIONS The majority of hydraulic parameters are, first of all, dependent on what type of fluid the drilling mud is and therefore which model is used for the calculations. The categories are determined by the fluid behaviour when it is subjected to an applied force (shear stress). Precisely, in terms of fluid behaviour, we are concerned with: - • At what point of applied shear stress is movement initiated in the fluid? • Once movement has been initiated, what is the nature of the fluid movement (Shear Rate)? 3.1 Shear Rate and Shear Stress In a simple flow, the Shear Rate is the change in fluid velocity divided by the width of the channel through which the fluid is moving. Shear Rate (γγγγ) = v2 - v1 h

= sec-1 At wellsite, the Shear Rate is determined by the rotational speed of the Fann Viscometer in which the tests are conducted. Thus, Shear Stress is recorded at rotational speeds of 600 (shear rate = 1022 sec-1), 300 (shear rate = 511 sec-1), 200, 100, 6 and 3 rpm. Shear Stress is the force per unit area required to move a fluid at a given shear rate.

Shear Stress (ττττ) = F/A = lb. ft or lb. ft or dynes in2 100ft2 cm2

v2

v1

h

AreaForce



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The shear stresses recorded for each of the shear rates at the different rotational speeds of the viscometer can then be plotted to produce an overall behaviour profile across the ‘rheological spectrum’.

3.2 Fluid Viscosity Mathematically, viscosity is determined by dividing a fluid’s shear stress by the corresponding shear rate. Fluid Viscosity (µµµµ) = Shear Stress = dynes/cm2 = poise Shear Rate sec-1 1 poise = 100 centipoise (cP) 1 lb. ft. sec = 47886 cP ft2 Viscosity controls the magnitude of shear stress which develops as one layer of fluid slides over another. It is a measure of the friction between fluid layers, providing a scale for describing fluid thickness. It will decrease with temperature. In simple terms, it describes the thickness of the mud when it is in motion. Funnel Viscosity This is a direct measurement from the Funnel (as opposed to Fann) viscometer and is measured in secs/qt. Generally, it is used at wellsite for immediate measurements, and is simply the length of time it takes for one quart of fluid to pass through the funnel. Funnel viscosity is not regarded as being applicable to the analysis of circulating performance. One final determination is Apparent Viscosity, simply θ600/2

100 200 300 400 500 600 Shear Rate, RPM

Shear Stress,

Lb/100ft2



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3.3 Plastic Viscosity and Yield Point For a Bingham Fluid (see next section), Plastic Viscosity (PV) is the amount of shear stress, in excess of the yield stress, that will induce a unit rate of shear. More simply, it is the relationship between shear stress and shear rate during fluid movement. It is the slope of the straight line that passes through θ600 and θ300 (the stresses caused by rotational speeds of 600 and 300 rpm). The Yield Point (YP), or yield stress, of a fluid is a measure of the attractive forces between mud particles resulting from the presence of +ve and -ve charges on the particle surfaces. It is a measure of the forces that cause mud to gel once it is motionless and it determines the carrying, or holding, capacity of the mud. In other words, it is the strength of the fluid capable of supporting a certain particle weight or size. Normal unit of measurement is Imperial lb or Metric: dynes / cm2 100ft2

3.4 Gel Strength Gel Strength is the ability of the mud to develop and retain a gel structure. It is analogous to shear strength and defines the ability of the mud to hold solids in suspension. More simply, it describes the thickness of a mud that has been motionless for a period of time (unlike viscosity which describes the mud thickness when in motion). It is a measure of the thickening property of a fluid and is a function of time. Measurements are therefore conducted after periods of 10 seconds and 10 minutes. Normal units of measurement lb 100ft2

With the duration of a drilling operation, i.e. the ‘age’ of a drilling fluid, viscosity and gel strengths will both tend to increase as a result of the introduction of solids into the mud system. More fluid can be added to compensate for this, or surface removal of mud solids can be achieved through passing the drilling mud through centrifuges.



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4 FLUID BEHAVIORAL MODELS 4.1 Newtonian Fluids A Newtonian fluid will begin to move, or deform, the instant that a force, or shear stress, is applied. Once this movement has been initiated, the degree of movement thereafter is proportional to the stress applied. i.e. A linear relationship exists between Shear Stress (τ) and Shear Rate (γ). For a Newtonian Fluid, therefore: ττττ = µµµµ γγγγ where µ = viscosity Most drilling fluids and cement slurries, however, exhibit non-Newtonian behaviour where the laminar flow relationship between shear stress and shear rate is non-linear. These fluids also require a certain amount of shear stress to initiate flow and thereafter, require additional stress to be applied as the shear rate increases. The level of shear stress required to initiate fluid flow is known as the fluid’s Yield Point. Two main models have been used as a standard in the oil industry: - 1. The Bingham Plastic Model 2. The Power Law Model In recent years, it is generally accepted that both models have merit but that the Power Law Model is more applicable to the majority of fluids. A third, widely used, model has been developed, being a combination of both previous models. This model is known as the Modified Power Law (also known as the Yield Power Law or Herschel-Bulkley Model).

τ

γ

gradient = µ



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4.2 Bingham Plastic Model This model predicts that fluid movement will take place only after a minimum value of Shear Stress has been applied. This minimum value is the Yield Point of the fluid. Once movement has been initiated, the relationship between ττττ and γγγγ is linear (ie Newtonian), with the constant being called the Plastic Viscosity (PV). PV is dependant on both temperature and pressure. For Bingham Fluids τ = YP + γ.PV PV = θθθθ600 - θθθθ300 YP = θθθθ300 - PV = ττττ0 The Bingham Plastic Model represents, fairly well, the behaviour exhibited by fluids such as bentonite slurries, class G cements and low gravity oils. A typical Bingham fluid will have high viscosity but no gel strength. For more complex fluids, however, the Bingham model is subject to error. Whereas the Bingham model simulates fluid behaviour in the high shear rate range (300 to 600 rpm), it is generally inaccurate in the low shear range. Shear stresses measured at high shear rates are usually poor indicators of fluid behaviour at low shear rates, the area of interest for simulating annular flow behaviour. Subject to this error, the calculated Yield Point will tend to result in calculated pressure losses and equivalent circulating densities that are larger than those actually observed.

γγγγ (rpm)

Dial Reading

gradient = PV

YP

θ300

θ600



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4.3 Power Law Model The Power Law Model assumes that fluid movement will be initiated immediately that any shield stress is applied. The model then predicts that, once movement is initiated, fluids will exhibit a non-linear relationship between τ and γ and introduces two ‘index’ values in order to determine the relationship. When the log of stress and strain is plotted: - For Power Law Fluids ττττ = K (γγγγ)n where K = consistency index n = flow behaviour index Determination of ‘n’ and ‘K’:- n = 3.32 log θθθθ600 θθθθ300 K = 1.067 θθθθ300 (lb/100ft2) OR K = 5.11 θθθθ300 (dynes/cm2) (511)n (511)n

γ (rpm)

Dial Reading

θ600 θ300

300 600

log ττττ

1 10 100 1000 log γγγγ

gradient = n 100

10

K



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The Power Law rheological model better fits the behaviour of most fluids, especially polymer based fluids, than the Bingham Plastic Model. Fluids that follow this model have no shear stress when the shear rate is zero. The draw back here, is that most fluids have a yield stress but this cannot be accounted for in this model. Similar to the Bingham Plastic model, but to a lesser degree, the Power Law model accurately predicts fluid behaviour at high shear rates but shows a degree of error at the lower shear rates. The result of this is that annular pressure losses and ECD’s are ‘under-predicted’ by this model’s calculations. In many cases, however, the Power Law Model does closely approximate fluid properties even when calculated from the high shear rate values. Different values of ‘n’ are possible, depending on which shear stress/rate pairings are used in the calculation. Thus, this model can be applied by using data from a range of annular shear rates, providing a better accuracy in predicting drilling fluid performance. Calculation of ‘n and K’ at other shear rates: - With θθθθ200 and θθθθ100 With θθθθ6 and θθθθ3 n = 3.32 log θ200/θ100 n = 3.32 log θ6/θ3 K = θ100 / (170.3)n K = θ3 / (5.11)n In the extreme case, when n=1, the fluid will become a Newtonian fluid ie τ = Kγ where K will be equal to viscosity µ. When to use the low shear rate pairing (6 and 3 rpm)? • to more accurately describe the suspension and hole cleaning potential of a fluid • in large diameter holes • in horizontal drilling applications



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4.4 The Modified Power Law This model combines the theoretical and practical aspects of the Bingham Plastic and the Power Law models. In this model, the ‘n and K’ values are similar to those derived by the Power Law model. The model assumes that fluids will require a certain amount of applied stress before movement will take place and, for these fluids having a yield stress, the calculated values of ‘n and K’ will be different. For Modified Power Law Fluids ττττ = ττττ0 + K (γγγγ)n where K = consistency index n = flow behaviour index The value τ0 is the fluid’s yield point at zero shear rate and, in theory, is identical to the Bingham Plastic yield point, though it’s calculated value is different. When n = 1, the model becomes the Bingham Plastic Model τ0 = 0, the model becomes the Power Law model The model works well for both water based and oil based drilling muds because both exhibit shear thinning behaviour and have a shear stress at zero shear rate. The problem with the model is that the determination of n, K and τ0 is very complex.

τ0 (yield point or yield stress)

Shear Rate

Shear Stress



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4.5 Rheogram Summary of the Drilling Fluid Models NOTE, in order for the QLOG system to accurately calculate realtime hydraulics, the Shear Rate values need to be updated regularly in the Equipment Table. The data can be entered in any of the 3 standard shear rate pairings i.e. θ600 and θ300 θ200 and θ100 θ6 and θ3 The industry normal is to use the 600/300 pairing but as was seen in this manual, there are applications when the 6/3 pairing can be more meaningful. Ideally, if there is a reason for using the 6/3 pairing, it should be discussed and confirmed with the drilling and mud engineers.

Newtonian

Power Law

Modified Power Bingham Plastic

Shear Rate

Shear Stress



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4.6 Model Effects on Viscous Flow Newtonian Fluids Laminar flow through pipe or annulus is characterized by a parabolic velocity profile, with the velocity approaching zero at the walls and being at a maximum in the centre of the flow. Non Newtonian Fluids For these fluids, the flow will not necessarily be parabolic. As the fluid becomes ‘increasingly’ non-Newtonian, the velocity profile will become increasingly flatter towards the centre. This is known as plugged flow. Using the Power Law as a basis, when ‘n’ is equal to one, the fluid is Newtonian and the velocity profile will indeed be parabolic. As the value of ‘n’ decreases, i.e. the fluid becomes increasingly non-Newtonian and the velocity profile will become increasingly flatter. In this flat part of the profile, the shear rate will be close to zero (i.e. very little movement between adjacent laminae). Fluids that exhibit a high viscosity in this near zero shear rate condition offer significant improvements in hole cleaning efficiency. Effect of ‘n’ on velocity profile

Low Shear Zone Areas of High Shear

n=1 n=0.6 n=0.2



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5 LAMINAR, TURBULENT and TRANSITIONAL FLOW PATTERNS The type of flow pattern is largely determined by the fluid velocity, the annular diameters and the characteristics of the mud. In general, the lower the fluid velocity and the greater the annular diameter, the more likely the flow is to be laminar. A turbulent flow pattern is more likely when the fluid velocity is high and when there is a small annular clearance i.e. around the drill collar section. 5.1 Laminar Flow A smooth flow pattern will be exhibited with fluid layers travelling in straight lines parallel to the axis. The velocity will increase towards the centre of the stream. Laminar flow will develop from low fluid velocities. There is only one directional component of fluid velocity and that is longitudinal. Shear resistance is caused by the sliding action of fluid layers only. 5.2 Turbulent Flow With turbulent flow, the flow pattern is random in both time and space, with chaotic and disordered motion of the fluid particles. This results in two-directional velocity components, longitudinal and transverse. With multi-directional and chaotic movement, and increased frictional; forces, shear resistances are far greater in turbulent flow than in laminar flow.



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Turbulent flow will develop at higher fluid velocities with the final velocity profile tending to be reasonably uniform despite the chaotic components. For this reason, turbulent flow is actually more effective in cuttings removal, but the disadvantages outweigh this advantage. Disadvantages: -

• erosion of cuttings, thereby destroying interpretative properties • the possibility of hole erosion • increased pressure losses due to higher frictional forces from the fluid movement, faster

velocities and more contact with the wall • removal of mud filter cake

Another advantage of turbulent flow comes during cementing operations, since the random flow helps to dislodge mud cake from the borehole walls. This will allow the cement to get a good contact on fresh surfaces and provide a good bond. 5.3 Transitional Flow In reality, there is not an instantaneous change from laminar to turbulent flow as fluid velocity increases. There will obviously be a transitional period where the flow changes from one to the other. This transitional flow will exhibit elements of both laminar and turbulent flow. 5.4 Determination of Flow Type It is very important that we are able to determine what type of flow pattern is present, not only because of the physical effects, but in order to calculate pressure losses in the string and the annulus, a very important part of hydraulic analysis. Fluid velocity and annular diameters are used to determine the type of flow, in conjunction with mud density and mud viscosity. These parameters are used to determine the Reynolds Number, a dimensionless number: Re = DVρρρρ where D = diameter µµµµe V = fluid velocity ρ = density µe = effective viscosity Notice that the effective viscosity is used in the determination of the Reynolds number, rather than the viscosity derived by surface measurements.



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5.4.1 Derivation of Effective Viscosity Bingham Fluid

µµµµe = PV + 300(Dh −−−− Dp) YP (imperial) v = PV + 2874 (Dh −−−− Dp) YP (metric) 48000 v

v = average annular velocity Dh/Dp = hole and pipe (outside) diameters Imperial units: µe = cP Metric: µe = cP v = ft/min v = m/sec D = inches D = mm YP = lb/100ft2 YP = dynes/cm2 PV = cP PV = cP Power Law Fluid µµµµe = [ (2.4 v) x (2n + 1) ] n x 200K (Dh−−−−Dp) (imperial) [ (Dh−−−−Dp) (3n) ] v = 1916K (Dh−−−−Dp) x [ (4000 v) x (2n + 1) ] n 4800v [ (Dh−−−−Dp) ( n ) ] (metric) = [ (200 v) x (2n + 1) ] n x 0.5K (Dh−−−−Dp) [ (Dh−−−−Dp) (3n) ] v (SI) Imperial: µe = cP Metric: µe = cP SI: µe = mPa.s v = ft/min v = m/sec v = m/min D = inches D = mm D = mm K = lb/100ft2 K = dynes/cm2 K = Poise



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5.4.2 Determination of the Reynolds Number Imperial Re = 15.47 Dvρρρρ D = diameter = inches µµµµe v = average velocity = ft/min ρ = mud density = ppg µe = effective visc = cP Metric Re = 1000 DVρρρρ D = mm µµµµe v = m/sec ρ = kg/litre µe = cP SI Re = DVρρρρ D = mm 60µµµµe v = m/min ρ = kg/m3

µe = mPa.s For Reynolds number inside the pipe, D = pipe internal diameter For Reynolds number in the annulus, D = hole diameter - pipe outside diameter Note that for fluid velocity, an average velocity is used in the determination of the Reynolds Number and Effective Viscosity. In reality, as we have seen, the velocity is least at the walls of the conduit, increasing to a maximum at the centre of the channel. The average fluid velocity (annular velocity or pipe velocity) is determined using the following formulae: 5.4.3 Determination of Average Annular Velocity v (ft/min) = 24.5 Q Q = flowrate (gpm) Dh

2 −−−− Dp2 Dh = hole diameter (in)

Dp = pipe outer diameter (in) v (ft/min) = 1030 Q Q = bbls/min Dh

2 −−−− Dp2 Diameters (in)

v (m/min) = 1273000 Q Q = m3/min Dh

2 −−−− Dp2 Diameters (mm)

These formulae can obviously be used to calculate the velocity of the mud within the drillstring. In this case, Dh

2 would be replaced by Di2, the inside diameter of the pipe, and ‘Dp’ would, in this case, be

equal to zero.



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5.4.4 Use of the Reynolds Number in determining Flow Type The value of the Reynolds number defines the transition between laminar and turbulent flow. Bingham Plastic The Critical Reynolds Number is 2100. If Re < Rec, then the flow is said to be laminar If Re > Rec, then the flow is said to be turbulent Power Law The Critical Reynolds Number is given by ‘3470 - 1370n’ If Re < 3470 - 1370n, the flow is laminar If Re > 4270 - 1370n, the flow is turbulent If 3470 - 1370n < Re < 4270 - 1370n, the flow is transitional 5.4.5 Determination of Critical Velocity The Critical Velocity is the fluid velocity (whether annular or pipe) at which the flow type becomes turbulent. In reality, at wellsite, the engineer is primarily concerned with the annular velocity since turbulent flow here has the associated problems of hole erosion, damage to cuttings and removal of filter cake. When analyzing annular velocity, the engineer will be looking for sufficient annular velocity to effectively lift and remove the cuttings, but within a laminar flow regime so that minimal damage is done. Many engineers will be happy with, even require, transitional or turbulent flow around the drill collar section. Here, the annular clearance is smallest so it is most important to keep the section clear of cuttings. For remaining annular sections, however, laminar flow will always be required to minimize hole damage and to keep pressure losses low. Bingham String Vc = 2.48 x ( PV + √√√√ (PV2 + 73.57.YP.Di

2.ρρρρ)) Di

ρρρρ Annular Vc = 3.04 x ( PV + √√√√ (PV2 + 40.05YP(Dh−−−−Dp)2ρρρρ )) (Dh−−−−Dp)ρρρρ



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Vc = critical velocity (m/min) Dh = hole diameter (mm) Dp = pipe outer diameter (mm) Di = pipe inner diameter (mm) ρ = mud density (kg/litre) PV = plastic viscosity YP = yield point Power Law 1 n String Vc = 0.6 [ (3470 −−−− 1370n)K ] 2−−−−n [ 3n + 1 ] 2−−−−n [ 1.27 ρρρρ ] [ 1.25 Di n ] 1 n Annular Vc = 0.6 [ (3470 −−−− 1370n)K ] 2−−−−n [ 2n + 1 ] 2−−−−n [ 2.05 ρρρρ ] [0.64 (Dh−−−−Dp)n ] The units are the same as above. n and K are the Power Law coefficients. Further equations to determine the Critical Annular Velocity: - 1 n Imperial Vc (ft/min) = [ 3.88 x 104K] 2 - n [ ( 2.4 ) (2n + 1) ] 2 - n

[ ρρρρ ] [ (Dh-Dp) ( 3n ) ] ρ = ppg D = inches K = lb / 100ft2 1 n SI Vc (m/min) = [ 9 x 104K] 2 - n [ ( 200 ) (2n + 1) ] 2 - n [ ρρρρ ] [ (Dh-Dp) ( 3n ) ] ρ = kg / m3 D = mm K = Poise



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6 DETERMINATION OF SYSTEM PRESSURE LOSSES To understand pressure distribution throughout the well, it can be considered as a closed system, with pressure losses occurring throughout the system : -

• as mud passes through the entire length of drillpipe • as mud passes through the bit • as mud flows back up through the annulus • as mud is pumped through surface lines eg standpipe, kelly hose, pumps

The total of all theses losses i.e. Total System Pressure Loss should be equal to the actual pressure measured on the standpipe and is therefore equal to the pressure that the pumps are operating at. This is a very important part of hydraulic evaluation. Obviously, the maximum pressure loss possible will be determined by the rating of the pumps and other surface equipment. This maximum is normally far in excess of the pressure loss that will be desired by the drilling engineer. The logging engineer’s task is normally to take given parameters from the drilling engineer, then select, for example, the correct nozzle sizes that will produce the desired system pressure loss. Pressure loss is largely dependant on the flowrate, mud density and rheology, the length of each section and the diameters of each pipe and annular section. Whether the flow is laminar or turbulent is also an important influence on the pressure loss - turbulent flow will produce larger pressure losses. 6.1 Fanning Friction Factor Frictional forces result whenever a fluid is moving, with fluid layers interacting against each other and against channel walls or other obstacles to flow. These forces have a large effect on the resultant pressure losses in a given annular or pipe section. The frictional forces present will be very different depending on whether the flow is laminar or turbulent: - • with laminar flow, the fluid movement is in one direction only - parallel to the conduit walls, with

velocity increasing towards the centre. Frictional forces will therefore only be present due to fluid ‘layers’ moving longitudinally against each other.

• with turbulent flow, fluid movement is much more complex and multi-directional, so that many more

frictional forces are present. For this reason, a coefficient called the Fanning Friction Factor is determined for each type of flow and whether we are dealing with pipe or annular pressure losses. The friction factor is determined from the Reynolds Number which has already been calculated for pipe or annular sections based on annular velocity, diameters, density and effective viscosity.



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Laminar Flow fann = 24 / Re Re = Annular Reynolds No. fpipe = 16 / Re Re = Pipe Reynolds No. Turbulent Flow fturb = a / Reb where Re = Reynolds number in the pipe or annulus a = log n + 3.93 50 b = 1.75 - log n 7 Transitional Flow fann = [ Re - c ] x [ ( a ) - (24) ] + 24 [ 800 ] [ (4270 - 1370n)b ( c ) ] c where Re = Annular Reynolds No. a = (log n + 3.93) / 50 b = (1.75 - log n) / 7 c = 3470 - 1370n fpipe = [ Re - c ] x [ ( a ) - (16) ] + 16 [ 800 ] [ (4270 - 1370n)b ( c ) ] c where Re = Pipe Reynolds No.

a, b, and c are as above When using the Power Law Model, the values of the Fanning Friction are substituted into equations in order to calculate pressure losses in the annulus or in the pipe. When calculating these pressure losses, each individual section has to be calculated separately, then totaled to give an overall pipe or annular pressure loss.



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6.2 Drillstring Pressure Losses Initial pump pressure is lost, through friction, as the mud is pumped through the drillstring. Losses will be greater in the lower drillstring sections where the inside diameter is smaller and mud velocity greater. Bingham For laminar flow, Ploss (KPa) = LQ PV + YP L 612.95 Di

4 13.26Di For turbulent flow, Ploss (KPa) = L ρρρρ0.8 Q1.8 PV0.2 901.63 Di

4.8 where L = length of section (m) Q = flowrate (litre/min) ρ = mud density (kg/litre) PV = plastic viscosity YP = yield point Di = pipe inner diameter (inch) Power Law Here, there is just one equation to be considered, since whether the flow is laminar or turbulent has already been accounted for by the Reynolds Number and the Fanning Friction Factor. SI Ploss (Kpa) = fp.v2.ρρρρ.L 1800 Di where fp = Friction Factor in the pipe v = Average velocity in the pipe (m/min) ρ = Mud density (kg/m3) Di = Pipe inner diameter (mm) L = Length of section (m) Imperial Ploss (psi) = fp.v2.ρρρρ.L 92870 Di where v = ft/min ρ = ppg Di = inches L = ft



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6.3 Annular Pressure Losses Frictional pressure losses occur as the mud returns up the annulus, but these are typically the smallest component of overall pressure loss in the system downhole. As with the drillstring losses, the pressure loss will be greater towards the bottom of the hole, around the drill collar section, where annular clearance (hole diameter minus outer pipe diameter) is least and annular velocity greatest. Bingham laminar flow, Ploss = L Q PV + YP L 408.63(Dh+Dp)(Dh−−−−Dp)3 13.26(Dh−−−−Dp) turbulent flow, Ploss = L ρρρρ0.8 Q1.8 PV0.2 706.96 (Dh+Dp)1.8(Dh−−−−Dp)3 The units are the same as those used in the drillstring pressure loss formula. Dh = hole diameter (inch) Dp = pipe outer diam (inch) Power Law SI Ploss (Kpa) = fa.v2.ρρρρ.L L = Length of section (m) 1800 (Dh - Dp) fa = Annular Friction Factor v = Average annular velocity (m/min) ρ = Mud density (kg/m3) Dh = Hole diameter (mm) Dp = Pipe outside diameter (mm) Imperial Ploss (psi) = fa.v2.ρρρρ.L 92870 (Dh - Dp) where v = ft/min ρ = ppg Dh = inches Dp = inches L = ft



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6.4 Bit Pressure Loss These are the system pressure losses that occur when the mud passes through the bit nozzles. Due to the very fast velocities involved and the small area of the nozzles, this will be the largest singular pressure loss throughout the entire system. SI Ploss (Kpa) = ρρρρ. Q2. 277778 (D1

2 + D22 +D3

2 +....)2

where ρ = mud density (kg/m3) Q = flow rate (m3/min) Dn = nozzle diameter (mm) Imperial Ploss (psi) = ρρρρ. Q2. 156 (D1

2 + D22 +D3

2 +....)2

where ρ = ppg Q = gpm Dn = 32nds inch Unfortunately, these equations (and the QLOG software) will not produce accurate calculations for diamond bit pressure losses. Eastman Christensen suggest the following calculations: - For Radial Flow, Ploss (bar) = 7.3188 ρρρρ0.61 Q TFA For Feeder Collector, Ploss (bar) = 24.738 ρρρρ0.34 Q1.47

TFA1.76 where ρ = mud density (kg/l) Q = flowrate (l/min) TFA = mm2 1 bar = 100KPa



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6.5 Surface Pressure Losses The calculation of pressure losses due to surface equipment is not as clear cut as previous calculated losses and will be dependant on the type of equipment present on the rig. i.e. type of pump, length of standpipe and surface lines, length of kelly etc One method of calculation is based on the Bingham Plastic Model for turbulent flow pressure losses. The main part of the equation, ρ0.8 Q1.8 PV0.2 is multiplied by a constant representing 4 rig types or classifications. Surface Ploss = E ρρρρ0.8 Q1.8 PV0.2 where Ploss = psi or KPa ρ = ppg or kg/litre Q = gpm or litre/min E is the constant representing the 4 rig surface equipment types. The rig type should be attainable from charts/tables kept on the rig. If not, the usual type and default is Type 4. Classification E Imperial Metric 1 2.5 x 10−4 8.8 x 10−6 2 9.6 x 10−5 3.3 x 10−6 3 5.3 x 10−5 1.8 x 10−6 4 4.2 x 10−5 1.4 x 10−6 In practice, this classification is generally not available at wellsite. For this reason, together with the fact that the method is based on a Bingham fluid, Datalog uses a different technique based on mud density and flowrate, together with a constant to represent different types of rig equipment. Hence: Surface Pressure Loss = 0.35 x Factor x Mud Density x Flowrate (Kpa) (kg/m3) (m3/min) Factor represents the value selected in the QLOG equipment table - the surface connection factor. This value can range from 0.2 to 0.5, with 0.5 being the normal default value.



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7 OTHER HYDRAULIC CALCULATIONS 7.1 Cuttings Slip Velocity Up to this point, the annular velocities that we have seen calculated only deal with the velocity of the fluid. Drilled cuttings are obviously going to be far heavier, typically, than the mud, so that there is always going to be a degree of ‘slip’, with the cuttings falling through the mud. How significant the degree of cuttings slip is going to be will be dependent on the relative densities, viscosity and ‘carrying’ potential of the mud, and particle size. Net Cuttings Velocity = annular velocity − cuttings slip velocity SI units Vs = 0.42 Dp (ρρρρp −−−− ρρρρ m)0.667 Dp = particle diameter (mm) ρρρρm

0.333 µµµµe0.333 ρp = particle density (kg/m3)

ρm = mud density (kg/m3) µe = effective mud viscosity (mPa.s) Vs = slip velocity (m/min) Imperial Vs = 175 Dp (ρρρρp −−−− ρρρρ m)0.667 Dp = inches ρρρρm

0.333 µµµµe0.333 ρp = ppg

ρm = ppg µe = cP Vs = ft/min Cuttings slip velocity, when the flow type is turbulent, will be clearly different from when the flow is laminar and constant forces are involved. With turbulent flow, whether the slip velocity is constant or not is dependant on the Reynolds Number determined for the cuttings. Cuttings Slip Velocity in Turbulent Flow SI units Vs (m/min) = 6.85 [ Dp (ρρρρp - ρρρρm) ] 0.5

[ 1.5ρρρρ ] Imperial Vs (ft/min) = 113.4 [ Dp (ρρρρp - ρρρρm) ] 0.5

[ 1.5ρρρρ ] Note that there are no velocity or viscosity inputs into this equation. It is, therefore, entirely dependent on the Particle Reynolds number as to whether the slip velocity will be constant.



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7.2 Particle Reynolds Number SI units Rep = 0.01686. ρρρρ. Vs. Dp where ρ = mud density (kg/m3) µµµµe Vs = slip velocity (m/min) Dp = particle diameter (mm) µe = effective viscosity (mPa.s) Imperial Rep = 15.47. ρρρρ. Vs. Dp where ρ = ppg µµµµe Vs = ft/min Dp = inches µe = cP If the Particle Reynolds Number > 2000, the particle will fall at the same rate i.e. cuttings slip velocity will be constant in turbulent flow In the determination of slip velocity, a Cuttings Re number is incorporated. So to, because of the different frictional forces present on the cuttings, is a friction or drag coefficient.



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7.3 Nozzle Velocity Vn (m/sec) = Q Q = flowrate (litre/min) 38.71A A = total flow area of nozzles (in2) Vn (ft/sec) = 0.32Q Q = gpm A A = in2 Nozzle conversion to Total Flow Area TFA (inch2) = 1/4ππππ (d1

2 + d22 + d3

2 ) = 1/4ππππ ΣΣΣΣ d2 ( 322 ) 1024 where d = nozzle size in 32nds of an inch Alternatively, the nozzle diameters, rather than TFA can be used: SI units Vn (m/sec) = 21220 Q where Q = m3/min ΣΣΣΣ Dn

2 Dn = mm Imperial Vn (ft/sec) = 418.3 Q where Q = gpm ΣΣΣΣ Dn

2 Dn = 32nds inch



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Exercise 1a Use of the Hydraulics Program Ensure that the user units are set to the correct units, following the unit types in the question. Use the following hole and pipe profiles and setups: 13 3/8” casing set at 500m, ID = 12.42” (315.5mm) 12 1/4” (311.2mm) hole drilled to a depth of 1500m 200m x 9 1/2” DC’s, OD 9.5” ID 3.0” (241.3/76.2mm) 100m x 8” DC’s OD 8.0” ID 3.0” (203.2/76.2mm) 300m x HWDP OD 5.0” ID 3.0” (127/76.2mm) DP OD 5.0” ID 4.28” (127/108.7mm) Jets 3 x 15 (3 x 11.9mm) MD 9.8ppg 100 SPM at flowrate 2.0 m3/min θ600 and θ300 60/35 Surface Conn Factor 0.5 (make sure you set this parameter in the QLOG equipment table) 1. What type of flow is present in each annular section? What is the Total System and Surface Pressure Loss? 2. Compare the surface pressure loss using a factor of 0.2 3. Using a SCF of 0.5, what flowrate is required to produce a system pressure of 2500psi? 4. What new jet sizes are required to reduce the pressure back to 2000psi? 5. What is the pressure if the mud weight is increased to 10.8ppg? 6. With a flowrate of 2.0 m3/min, what jet sizes are now required to give a system pressure of

around 2000psi? 7. Is the flow still laminar in all annular sections? 8. If transitional flow is acceptable around the 9 1/2” DC’s but not the 8” DC’s, what is the

maximum flowrate? 9. With this flowrate, how many jets may have washed out if a surface pressure drop to 1650psi has

been recorded?



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8 HYDRAULICS OPTIMIZATION 8.1 Bit Hydraulic Horsepower This is the power used by the jetting action of the bit, which has to balance maximum ROP and maximum jetting with effective hole cleaning. SI units Bit HP (KW) = Pb x Q x 0.01667 Q = flowrate (m3/min) Pb = bit pressure loss (KPa) Imperial Bit HP (HP) = Pb x Q Q = gpm 1714 Pb = psi The Total System Hydraulic Horsepower can be calculated by substituting the Total System Pressure Loss (in place of Bit Pressure Loss) into the same equation. 8.2 Hydraulic Impact Force This is the force exerted on the formation due to the fluid exiting the jets. Cleaning is by direct erosion on the bottom and by cross flow under the bit. Excessive hydraulic impact is a major cause of formation flushing, where permeable zones ahead of the bit can be swept clean of formation fluids. SI units Bit IF (newtons) = ρρρρ Q Vn ρ = mud density (kg/m3) 60 Q = flowrate (m3/min) Vn = nozzle velocity (m/sec) Imperial Bit IF (lbs) = ρρρρ Q Vn ρ = ppg 1932 Q = gpm Vn = ft/sec



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8.3 Hydraulic Optimization Hydraulics can be optimized in two ways: - 1) By optimising the Impact Force of the jets on the bottom of the hole. 2) By optimising the Hydraulic Power expended by the bit. The power expended (or used up) by the bit is a proportion of the total power available (HPt). This can be determined from the maximum pressure of the pumps: where max HPpump = HPt = Pmax Q 1714 Or, more typically, it can be determined on the basis of a desired maximum pump pressure together with a maximum flow rate that will give sufficient annular velocity for cuttings removal. Once the maximum power available to the system is known, hydraulic performance can be optimized in the following ways: - 1) Optimize Horsepower by setting the Bit HP to 65% of Total Available Power 2) Optimize Impact Force by setting the Bit HP to 48% of Total Available Power Impact Force relates directly to the erosional force of the drill fluid and is therefore good optimization for bottom hole cleaning. Hydraulic Horsepower optimization generally requires lower annular velocities so that flow type is more likely to be laminar. Since the hydraulic horsepower at the bit is dependent on jet velocity and therefore on the pressure loss at the bit, hydraulic performance in practice can simply be optimized by selecting jet sizes to give: Bit Pressure Loss = 65% System Pressure Loss



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8.4 Use of the QLOG hydraulics programs Current Profiles (onhyd) This is an optimization program that works based on realtime information such as pump output, mud density and pressure losses. These values can be changed should a change in parameters be the reason for running the optimization program. The minimum and maximum jet velocities are suggested values. The program can then be run to give you the parameters required for optimum hydraulics based on both Hydraulic Impact Force and Hydraulic Horsepower at the bit. New Profiles (offhyd) This program is offline so that you can input any hole and pipe profiles, mud parameters, flow rate and jet size and calculate the resulting hydraulic parameters such as pressure losses, flow types, annular velocities etc. This program would be used when pre-determining the correct parameters for a new hole section or bit run. By changing the inputs, you can attempt to optimize the hydraulics.



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Exercise 1b Optimizing Hydraulics Use the original profiles and set ups that were used in exercise 1a 1. What is the % Hydraulic Horsepower of the bit? 2. Using the following ranges and limitations, try to optimize the hydraulics whilst still retaining

laminar flows and good annular velocities for cuttings removals. Flowrate 1.8 to 2.2 m3/min Mud density 9.6 to 10.2 ppg Maximum System Pressure 2800 psi Minimum Jet sizes 3 x 10mm



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Exercise 1c Optimizing Hydraulics Use the following hole and pipe profiles and setups: 9 5/8” casing set at 2500m, ID 8.68” (220.4mm) 8 1/2” (215.9mm) hole drilled to 4000m 500m x 6 1/2” DC’s OD 6.5”, ID 2.88” (165.1/73.1mm) 400m x HWDP OD 5.0”, ID 3.0” (127/76.2mm) DP OD 5.0”, ID 4.28” (127/108.7mm) Flowrate 1.4 m3/min Mud density 10.5ppg Surface Conn Factor 0.5 θ600 and θ300 70/42 1. What jets would produce a system pressure of 2500 psi? With these setups, what are a) the flow types in each annular section b) the annular velocities in each section c) the % HP at the bit 2. With a flowrate of 1.6m3/min, what jets are required to give a system pressure of 2200psi ? What now are a) the flow types b) the annular velocities c) the % HP at bit 3. Using the following ranges and limits, attempt to optimize the hydraulics whilst retaining laminar

flows in each section and good annular velocities. Flowrate 1.3 to 1.6 m3/min Mud density 10.3 to 10.6 ppg Maximum system pressure 2850 psi



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9 Equivalent Circulating Density The pressure exerted at the bottom of the hole by the static column of mud is known as the Hydrostatic Pressure. PHYD = ρρρρ x TVD x 0.052 where ρ = mud density (ppg) PHYD = psi TVD = feet PHYD = ρρρρ x TVD x 0.433 where ρ = SG PHYD = psi TVD = feet PHYD = ρρρρ x TVD x 0.00981 where ρ = kg/m3 PHYD = Kpa TVD = m During circulation, the pressure exerted by the “dynamic” fluid column at the bottom of the hole increases (and also the equivalent pressure at any point in the annulus). This increase results from the frictional forces and annular pressure losses caused by the fluid movement. Knowing this pressure is extremely important during drilling, since the balancing pressure in the wellbore is changing from that simply calculated from the mud density. Higher circulating pressure will result in: -

• Greater overbalance in comparison to the formation pressure • Increased risk of formation flushing • More severe formation invasion • Increased risk of differential sticking • Greater load exerted on the surface equipment

The increased pressure is termed the Dynamic Pressure or Bottom Hole Circulating Pressure (BHCP). BHCP = PHYD + ∆∆∆∆ Pa where ∆ Pa is the sum of the annular pressure losses Since pressure exerted is a function of density and vertical height, the increased pressure means that, effectively, the ‘equivalent’ density of the mud will increase when the fluid is moving. This is termed the Equivalent Circulating Density.



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Examples to calculate the ECD are shown below: a. ECD = ρρρρ + ∆∆∆∆ Pa ECD = ppg EMW (equivalent mudweight) (0.052xTVD) ∆ Pa = psi TVD = feet ρ = ppg BHCP can therefore be expressed as “ECD x 0.052 x TVD” b. ECD = ρρρρ + ∆∆∆∆ Pa ECD = kg/m3 EMW 0.00981xTVD ∆ Pa = KPa TVD = m ρ = kg/m3 BHCP can therefore be expressed as “ECD x 0.00981 x TVD”



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Exercise 1d Equivalent Circulating Density For each of the following situations, calculate the mud density from the hydrostatic pressure acting at the depth shown. 1. TVD 3500ft Hydrostatic Pressure 1729psi 2. TVD 14000ft Hydrostatic Pressure 8010psi 3. TVD 3000m Hydrostatic Pressure 32373Kpa 4. TVD 1500m Hydrostatic Pressure 15,156Kpa 5. TVD 4000m Hydrostatic Pressure 9555psi For each of the following situations, calculate a) Hydrostatic Pressure b) Bottom Hole Circulating Pressure c) Equivalent Circulating Density 6. TVD 4000 ft Mud density 9.5ppg Annular Pressure Losses 250psi 7. TVD 3000m Mud density 1150 kg/m3 Annular Pressure Losses 3000 Kpa



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10 Swab and Surge Pressures Similar to the increase in bottom hole pressure when circulating (ECD), pressure changes are seen, as a result of induced mud movement and resulting frictional pressures, when pipe is run in, or pulled out, of the hole. 10.1 Surge Pressures Surge Pressures result when pipe is run into the hole. This causes an upward movement of the mud in the annulus as it is being displaced by the drillstring (as seen by the mud displaced at surface into the pit system), resulting in frictional pressure.

This frictional pressure causes an increase, or surge, in pressure when the pipe is being run into the hole. The size of the pressure increase is dependent on a number of factors, including the length of pipe, the pipe running speed, the annular clearance and whether the pipe is open or closed. In addition to the frictional pressure, which can be calculated, it is also reasonable to assume that fast downward movement of the pipe will cause a shock wave that will travel through the mud and be damaging to the wellbore. Surge pressures will certainly cause damage to formations, causing mud invasion of permeable formations, unstable hole conditions etc.

The real danger of surge pressure, however, is that if it is too excessive, it could exceed the fracture pressure of weaker or unconsolidated formations and cause breakdown. This would lead to lost circulation (mud being lost to the formation) at that zone. This in turn would lead to a drop in the mud level in the annulus, reducing the hydrostatic pressure throughout the wellbore. Ultimately then, with reduced pressure in the annulus, a permeable formation at another point in the wellbore may begin to flow. With lost circulation at one point and influx at another, we now have the beginnings of an underground blowout! It is a common misconception, that if the string is inside casing, then the open wellbore is safe from surge pressures. This is most definitely not the case! Whatever the depth of the bit during running in, the surge pressure caused by the mud movement to that depth, will also be acting at the bottom of the hole. Therefore, even if the string is inside casing, the resulting surge pressure, if large enough, could be causing breakdown of a formation in the open wellbore. This is extremely pertinent when the hole depth is not too far beyond the last casing point! Running casing is a particularly vulnerable time, for surge pressures, due to the small annular clearance and the fact that the casing is closed ended. For this reason, casing is always run at a slow speed, and mud displacements are very closely monitored.



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10.2 Swab Pressures Swab Pressures, again, result from the friction caused by the mud movement resulting from lifting the pipe out of the hole. The frictional pressure losses, with upward pipe movement, now result in an overall reduction in the mud hydrostatic pressure. The mud movement results principally from two processes: -

1. With slower pipe movement, an initial upward movement of the mud surrounding the pipe may result. Due to the mud’s viscosity, it can tend to “cling” to the pipe and be dragged upward with the pipe lift.

2. More importantly, as the pipe lift continues, and especially with

rapid pipe movement, a void space is left immediately beneath the bit and, naturally, mud from the annulus will fall to fill this void.

This frictional pressure loss causes a reduction in the mud hydrostatic pressure. If the pressure is reduced below the formation pore fluid pressure, then two things can result: -

1. With impermeable shale type formations, the underbalanced situation causes the formation to

fracture and cave at the borehole wall. This generates the familiar pressure cavings that can load the annulus and lead to pack off of the drill string.

2. With permeable formations, the situation is far more critical and, simply, the underbalanced situation

leads to the invasion of formation fluids, which may result in a kick. In addition to these frictional pressure losses, a piston type process can lead to further fluid influx from permeable formations. When full gauge tools such as stabilizers are pulled passed permeable formations, the lack of annular clearance can cause a syringe type effect, drawing fluids into the borehole. • More than 25% of blowouts result from reduced hydrostatic pressure caused by swabbing. • Beside the well safety aspect, invasion of fluids due to swabbing can lead to mud contamination and

necessitate the costly task of replacing the mud. • Pressure changes due to changing pipe direction, eg during connections, can be particularly

damaging to the well by causing sloughing shale, by forming bridges or ledges, and by causing hole fill requiring reaming.



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10.3 Calculation of Surge and Swab Pressures The same method is used to calculate the differential pressure caused by both surging and swabbing. To determine the new hydrostatic pressure, the differential pressure is either added or subtracted depending on whether surge or swab respectively. Firstly, the Fluid Velocity of the displaced mud caused by the pipe movement has to be calculated. For Closed Ended Pipe: Fluid Vel (ft/min) = [ 0.45 + Dp

2 ] x Vp Vp = pipe speed (ft/min) [ Dh

2 −−−− Dp2 ] Dh = hole diameter (in)

Dp = pipe outer diameter (in) Di = pipe inner diameter (in) For Open Ended Pipe: Fluid Vel (ft/min) = [ 0.45 + Dp

2 −−−− Di2 ] x Vp

[ Dh2 −−−− Dp

2 + Di2 ]

This fluid velocity then has to be converted to the equivalent flowrate by using the annular velocity equation, where: - fluid velocity (ft/min) = 24.5 Q where Q = gpm Dh

2 −−−− Dp2

The change in pressure is then calculated for each annular/pipe section using the Pressure Loss equations. This is calculated for both laminar and turbulent flow with the largest value being taken. The total swab or surge pressure acting on the bottom of the hole is the sum of all of the pressure losses for each annular/pipe section.



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10.4 Use of the QLOG Swab and Surge Program This program is used to determine the pressures induced by the defined maximum and minimum running speeds of the pipe. Thus, a safe speed can be deduced in order to avoid excessive pressures. Required information: - Bit depth and hole depth Taken from the realtime system, editable if required. Current surge/swab pressure Taken from current recorded pressures, editable if required. Current Flow In Taken from realtime system, editable if required. Use Current Profile i.e. current hole and pipe profiles, the user should select Y(es). Max/Min running speed Limits defined by the user. Negative values should be used in order to

calculate swab pressures. For example, for surge pressure, the minimum running speed may be 5m/min and the maximum 50m/min. For the same limits, the swab calculation requires the minimum to be set at -50m/min, and the maximum at -5m/min.

Current running speed Read from realtime system, editable if required. Once the data is entered correctly: - Press F7 to calculate the maximum and minimum pressures. Press F2 to print the data out. Press F8 to produce a plot. The plot will be pressure against running speed and will show the pressures against the max/min limits defined together with the current pressure/running speed situation.



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Exercise 1e Use of the Swab Surge program This program accesses information from the realtime system. Therefore: - Enter the hole and pipe profiles from Exercise 1c into the realtime files. Enter the following into equipment table a) Mud density override 9.3ppg b) θ600 and θ300 50/30 (NB for the purposes of this exercises, ensure that the mud density channel is not configured so that the over-ride facility in the equipment table can be used) Using maximum and minimum running speeds of 20 and 100 m/min, calculate the swab/surge pressures with the following bit depths: 1000m 2000m 3000m 3500m 3950m With an increased mudweight of 10.3ppg, calculate, for the same maximum and minimum running speeds, the swab/surge pressures at 3500 and 3950m.



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APPENDIX - Answers to Training Exercises



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Exercise 1a Use of Hydraulics Program 1. Laminar flow in all sections System pressure loss 2038 psi Surface pressure loss 59.6psi 2. 23.8 psi 3. 2.24 m3/min giving a pressure of 2498psi 4. 1 x 13mm, 2 x 14mm, giving a pressure of 1994psi 5. 2162psi 6. 1 x 12mm, 2 x 13mm, giving a pressure of 1983psi 7. Yes, flow is laminar in each section 8. 2.24 m3/min 9. 1 jet with 12mm jet washout, pressure would be 1658psi with 13mm jet washout, pressure would be 1671psi Exercise 1b Optimizing hydraulics 1. 46.2% HP at the bit 2. Two possible situations are: - a. Mud weight 9.9ppg Flowrate 2.0 m3/min Jets 2 x 10, 1 x 11 This gives 60.2% HHP at the bit 2771psi system pressure loss Laminar flow in all sections with good annular velocities b. Mud weight 10.15ppg Flowrate 1.9 m3/min Jets 3 x 10 This gives 63.9% HHP at the bit 2765psi system pressure loss Laminar flows, but lower annular velocities



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Exercise 1c Optimizing Hydraulics 1. 3 x 10mm jets, giving system pressure loss of 2523psi a) laminar in all sections b) 55 to 92 m/min c) 39.3 % 2. 3 x 14mm jets, giving system pressure loss of 2211psi a) transitional around collars, laminar in all other sections b) 63 to 105 m/min c) 15.3 % 3. With flowrate 1.3 m3/min system pressure loss of 2834psi mud weight 10.3 ppg % power at bit 52.2 % jets 2 x 9, 1 x 8mm Laminar flows in all sections Annular velocities 51 to 86 m/min With flowrate 1.34 m3/min System Ploss 2841 psi

mud weight 10.6 ppg % Bit HP 49.2 jets 3 x 9mm Laminar flows

Ann Velocity 51 – 86 m/min Note that in the second situation, the annular velocities are the same (which is the objective for the 65% optimization), yet we are closer to 48% and optimum bottom hole cleaning – this may be the preferred selection. Exercise 1d Equivalent Circulating Densities 1. 9.5 ppg 2. 11.0ppg 3. 1100 kg/m3 4. 1030 kg/m3 5. 14.0ppg 6. Phyd = 1976 psi BHCP = 2226 psi ECD = 10.7 ppg EMW 7. Phyd = 33844 Kpa BHCP = 36844 Kpa ECD = 1252 kg/m3 EMW



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Exercise 1e Swab/Surge Program at 1000m, min/max pressure = 35 + 211 psi at 2000m, 50 + 280 psi at 3000m, 69 + 388 psi at 3500m, 77 + 426 psi at 3950m. 85 + 461 psi With 10.3ppg mud weight: at 3500m, min/max pressure = 77 + 460 psi at 3950m, 85 + 497 psi

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Hydraulics v2 1