The methods for the calculations used herein take into account the effects of temperature and pressure on the rheology and density of the drilling fluid.. Drilling fluid rheology is impo
Flow regime principle
The behavior of a fluid is influenced by its flow regime, which significantly impacts its ability to perform essential functions Flow can be classified as either laminar or turbulent, depending on factors such as fluid velocity, channel size and shape, density, and viscosity Fluids transition between laminar and turbulent flow, exhibiting characteristics of both during this phase Understanding the flow regime is crucial for assessing fluid performance, especially in scenarios like drilling, where the rotation of the inner surface can induce turbulent instabilities across all flow rates.
In axial laminar flow, the fluid travels in smooth, parallel lines along the channel walls This type of flow typically occurs at low velocities or with viscous fluids As the velocity and viscosity of the fluid increase, the pressure needed to maintain the flow also rises.
In turbulent flow, the fluid exhibits swirling and eddying motions while predominantly moving forward, with spontaneous velocity fluctuations Factors such as wall roughness and changes in flow direction can intensify turbulence Typically, turbulent flow occurs at higher velocities or with fluids of low viscosity Additionally, the pressure needed to propel the fluid increases linearly with density and approximately with the square of the velocity, indicating that more pump pressure is necessary for turbulent flow compared to laminar flow.
The transition between axial laminar and turbulent flow is determined by the balance of viscous and inertial forces In laminar flow, viscous forces prevail, whereas in turbulent flow, inertial forces take precedence For Newtonian fluids, the relationship between viscous forces and flow rate is linear, while inertial forces increase with the square of the flow rate.
The Reynolds number (NRe) represents the ratio of inertial forces to viscous forces in fluid dynamics When consistent units are used, this dimensionless quantity is crucial for characterizing flow in a pipe, defined by the equation: \$NRe = \frac{\mu \rho}{\text{(appropriate units)}}\$.
N Re = dV (1) where d is the diameter of the flow channel;
V is the average flow velocity; ρ is the fluid density; μ is the fluid viscosity
In cases where flow occurs in an annulus, it is essential to adjust the flow channel diameter to \$d_{hyd} = d_h - d_p\$, which represents the difference between the outer diameter of the drill pipe and the inner diameter of the casing or open hole.
The flow of liquid in a flow channel can be classified as laminar, transitional, or turbulent, with the transition from laminar to transitional flow occurring at a critical velocity For standard drilling fluids, this transition typically happens within a Reynolds number range of 2,000 to 4,000.
Viscosity
Viscosity is defined as the ratio of shear stress to shear rate, with traditional units being dyne-s/cm², known as Poise (P) Due to the relatively high viscosity represented by 1 P for most fluids, the centiPoise (cP) is commonly used, where 1 cP equals one-hundredth of a poise or one milliPascal-second The relationship between viscosity (\( \mu \)), shear stress (\( \tau \)), and shear rate (\( \gamma \)) is expressed by the equation \( \mu = \frac{\tau}{\gamma} \).
Viscosity in most drilling fluids is not a constant and varies with shear rate To assess rate-dependent effects, shear stress measurements are taken at various shear rates These measurements allow for the calculation of rheological parameters and enable the plotting of viscosity against shear rate.
Effective viscosity refers to the viscosity measured or calculated at the shear rate relevant to the current flow conditions in the wellbore or drillpipe This term is specifically used to distinguish the viscosity discussed in this section from other viscosity definitions For viscosity measurements to be meaningful, it is essential to specify the shear rate.
Shear stress
Shear stress is defined as the force necessary to maintain a specific rate of fluid flow, quantified as a force per unit area For instance, in a parallel-plate scenario, applying a force of 1.0 dyne to each square centimeter of the top plate results in a shear stress of 1.0 dyne/cm² To prevent the bottom plate from moving, an equal force in the opposite direction is required, maintaining the same shear stress of 1.0 dyne/cm² throughout the fluid at any level.
A is the moving plate with a velocity of 1.0 cm/s
D is the velocity gradient, velocity divided by height, ΔV / h, 1.0 cm/s / 1 cm = 1 s -1
Figure 1—Parallel plates showing shear rate in fluid-filled gap as one plate slides past another 4.3.2 Shear stress τ is expressed mathematically as:
A is the surface area subjected to stress
In a pipe, the force that drives a liquid column is determined by multiplying the pressure at the end of the column by the cross-sectional area of that end.
= (4) where d is the diameter of pipe;
P is the pressure on end of liquid column
4.3.4 The area of the fluid surface in contact with the pipe wall over the length is given by: dL
A is the surface area of the fluid;
4.3.5 Thus, the shear stress at the pipe wall is expressed as:
4.3.6 In an annulus with inner and outer diameters known, the shear stress is expressed in the same manner:
(7) where dp is the outer diameter of pipe; dh is the diameter of hole
P dp dh L dp dh dp dh
Shear rate
Shear rate refers to the velocity gradient measured across the diameter of a pipe or annulus, indicating how one layer of fluid moves past another For instance, when two large parallel plates are separated by one centimeter and filled with fluid, if the bottom plate remains stationary while the top plate slides at a constant speed of 1 cm/s, different fluid velocities are observed The fluid layer adjacent to the bottom plate remains still, while the layer near the top plate approaches a velocity of nearly 1 cm/s, resulting in an average fluid velocity of 0.5 cm/s at the midpoint between the plates.
The velocity gradient represents the rate of change of velocity (\(\Delta V\)) with respect to the distance from the wall (\(h\)) In the scenario illustrated in Figure 1, the shear rate is calculated as \(dV/h\), which is measured in units of 1/time The standard unit for shear rate is the reciprocal second, commonly denoted as (1/s or s\(^{-1}\)).
This example pertains to Newtonian fluids, characterized by a constant shear rate However, this does not apply to circulating fluids In laminar flow within a pipe, the shear rate varies, being highest near the pipe wall While an average shear rate can be utilized for calculations, it is important to note that the shear rate is not uniform throughout the flow channel.
4.4.4 It is important to express the above concept mathematically so that models and calculations can be developed Shear rate (γ) is defined as: r
V Δ γ = Δ (10) where ΔV is the velocity change between fluid layers; Δr is the distance between fluid layers
4.4.5 In a pipe the shear rate at the pipe wall (γwp) for a Newtonian fluid can be expressed as a function of the average velocity (V) and the diameter of the pipe (d)
V =Q= (12) where γwp is the shear rate at pipe wall for a Newtonian fluid;
Q is the volumetric flow rate;
A is the surface area of cross section; d is the pipe diameter;
Vp is the average velocity in pipe
4.4.6 In an annulus of outside diameter (dh) and inside diameter (dp), the wall shear rate for a Newtonian fluid can be shown to be:
= − π (14) where γ wa is the shear rate at annulus wall for a Newtonian fluid;
Q is the volumetric flow rate; dp is the outer diameter of pipe; d h is the diameter of hole;
Va is the average velocity in annulus
4.4.7 Equations which correct the pipe and annulus shear rates for non-Newtonian behavior are given in
Relationship of shear stress and shear rate
Shear stress is defined as the force per unit area necessary to maintain fluid flow, while shear rate refers to the change in fluid velocity relative to the distance from the wall Viscosity represents the ratio of shear stress to shear rate, establishing a crucial mathematical relationship that characterizes the fluid's rheological model.
4.5.2 When a drill cutting particle settles in a drilling fluid, the fluid immediately surrounding the particle is subjected to a shear rate defined as settling shear rate γ s : dc
Vs is the average settling velocity (ft/s); dc is the equivalent particle diameter (in.)
The settling shear rate is used to calculate the viscosity of fluid experienced by the settling particle.
Fluid characterization
Fluids are categorized based on their rheological behavior into two main types: Newtonian and Non-Newtonian fluids Newtonian fluids maintain a constant viscosity regardless of changes in shear rate, while Non-Newtonian fluids exhibit a viscosity that varies with shear rate changes.
4.6.2 Temperature and pressure affect the viscosity of a fluid Therefore, to properly describe the drilling fluid flow, the test temperature and pressure must be specified
4.6.3 Some mathematical models used for hydraulic calculations are shown in this section.
Newtonian fluids
4.7.1 Fluids for which shear stress is directly proportional to shear rate are called Newtonian Water, glycerin, and light oil are examples of Newtonian fluids
4.7.2 A single viscosity measurement characterizes a Newtonian fluid at a specified temperature and pressure.
Non-Newtonian fluids
4.8.1 Fluids for which shear stress is not directly proportional to shear rate are called non-Newtonian Most drilling fluids are non Newtonian
4.8.1.1 Drilling fluids are shear thinning when they exhibit less viscosity at higher shear rates than at lower shear rates
4.8.1.2 There are some non-Newtonian fluids which exhibit dilatant behavior The viscosity of these fluids increases with increasing shear rate Dilatant behavior rarely occurs in drilling fluids
The difference between Newtonian and non-Newtonian fluids can be demonstrated using the API standard concentric-cylinder viscometer A fluid is classified as Newtonian if the reading at 600 r/min is double that at 300 r/min Conversely, if the 600 r/min reading is less than twice the 300 r/min reading, the fluid is identified as non-Newtonian and exhibits shear thinning behavior.
Pseudoplastic fluids are a type of shear thinning fluid that start to flow with the application of even the slightest shearing force or pressure As the shear rate increases, these fluids exhibit a continuous reduction in viscosity.
Shear thinning fluids, known as viscoplastic fluids, do not flow until a specific shear stress, called yield stress, is applied.
Fluids can display time-dependent behaviors, where viscosity varies over time under a constant shear rate until equilibrium is reached Thixotropic fluids are characterized by a reduction in viscosity over time, whereas rheopectic fluids show an increase in viscosity as time progresses.
Thixotropic fluids demonstrate gelation or gel strength development, where viscosity increases over time while the fluid is static To initiate flow, a sufficient force must be applied to overcome the gel strength.
The rheological characteristics of drilling fluids can range from an elastic, gelled solid to a purely viscous, Newtonian fluid Despite the complex flow behavior of circulating fluids, it is standard practice to describe their flow properties using straightforward rheological terms.
4.8.8 General statements regarding drilling fluids are usually subject to exceptions because of the extraordinary complexity of these fluids.
Rheological models
Rheological models play a crucial role in characterizing fluid flow, particularly in drilling fluids However, no single model can fully capture the rheological characteristics across all shear rates A comprehensive understanding of fluid performance requires both knowledge of these models and practical experience To visually represent a rheological model, a shear stress versus shear rate plot, known as a rheogram, is commonly utilized.
The Bingham Plastic Model describes fluids that exhibit a linear relationship between shear stress and shear rate after surpassing a specific shear stress threshold This model is characterized by two key parameters: plastic viscosity and yield point, which are determined at shear rates of 511 s\(^{-1}\) and 1022 s\(^{-1}\) It effectively represents fluids in the higher shear-rate range In a rheogram plotted on rectilinear coordinates, the Bingham plastic model appears as a straight line that intersects the zero shear-rate axis at a yield point greater than zero.
The Power Law model is essential for characterizing shear thinning or pseudoplastic drilling fluids, as it illustrates that the rheogram appears as a straight line on a log-log graph This linear representation indicates that true power law fluids do not possess a yield stress, as there is no intercept The model's two key constants, n and K, are usually derived from measurements taken at shear rates of 511 s\(^{-1}\).
The generalized power law is applicable when multiple shear-rate pairs are established within the relevant shear-rate range This methodology has been implemented in the latest editions of API 13D.
4.9.4 Herschel-Bulkley Model—Also called the “modified” power law and yield-pseudoplastic model, the
The Herschel-Bulkley model effectively characterizes the flow of pseudoplastic drilling fluids that necessitate a yield stress to commence flow In a rheogram, the relationship between shear stress minus yield stress and shear rate appears as a straight line on log-log coordinates This model is favored for its ability to describe the flow behavior of various drilling fluids, its incorporation of a yield stress value crucial for hydraulic considerations, and its inclusion of the Bingham plastic model and power law as specific cases.
The API Drilling Fluid Report records essential rheological parameters, specifically plastic viscosity and yield point, derived from the Bingham plastic model These parameters are crucial for calculating key metrics in various other rheological models.
4.9.6 The mathematical treatment of Herschel-Bulkley, Bingham plastic and power law fluids is described in
The flow characteristics of drilling fluids are influenced by the viscosity of the base fluid, the presence of solid particles, oil, or gases, the flow channel characteristics, and the volumetric flow rate Interactions between the continuous and discontinuous phases, whether chemical or physical, significantly impact the rheological parameters of the fluid Commonly used models, such as Bingham plastic and power law, provide indicators to guide fluid conditioning for achieving the desired rheological properties.
5 Determination of drilling fluid rheological parameters
Measurement of rheological parameters
The determination of drilling fluid rheological parameters is important in the calculation of circulating hydraulics, hole cleaning efficiency, and prediction of barite sag in oil wells
The Marsh funnel is a commonly used field instrument for measuring funnel viscosity, which is determined by the timed rate of flow, typically expressed in seconds per quart This conical funnel can hold 1.5 liters of drilling fluid and features an orifice at the bottom By adhering to standard procedures, the outflow time for one quart of fresh water at a temperature of 70 °F ± 5 °F is recorded.
Funnel viscosity, measured at (21 °C ± 2 °C) with a time of 26 s ± 0.5 s, is a quick and straightforward test routinely conducted on all liquid drilling fluid systems This test is essential for detecting changes in drilling fluid properties or conditions When variations in funnel viscosity are noted, further rheological testing with a concentric-cylinder viscometer is necessary to pinpoint the changes in fluid properties However, it is important to recognize that funnel viscosity provides only a one-point measurement and does not explain the reasons behind high or low viscosity Additionally, a single funnel viscosity measurement cannot be considered representative of all drilling fluids of the same type or density For detailed operating procedures, refer to API Recommended Practice 13B-1/ISO 10414-1.
Standard Procedure for Field Testing Water-Based Drilling Fluids, or Recommended Practice 13B-2/
ISO 10414-2, Recommended Practice Standard Procedure for Field Testing Oil-Based Drilling Fluids, sections entitled “Marsh Funnel”
Low-temperature, non-pressurized concentric-cylinder (Couette) viscometers are rotational instruments that utilize either an electric motor or a hand-crank to measure fluid viscosity These devices consist of two cylinders, with fluid contained in the annular space between them The outer sleeve, or rotor, rotates at a constant speed, creating torque on the inner cylinder, or bob, which is measured using a torsion spring A dial attached to the bob displays its deflection in degrees, allowing for the direct calculation of plastic viscosity and yield point at rotor speeds of 300 r/min and 600 r/min These viscometers are essential for testing drilling fluids and vary in terms of drive mechanisms, available speeds, readout methods, and measuring angles.
The rapid calculation of plastic viscosity and yield point can be achieved using readings at 300 r/min and 600 r/min, as outlined in Table 1, which presents two models along with their operating limits Detailed operating procedures for various models of concentric-cylinder viscometers are provided in API 13B-1/ISO 10414-1 and API 13B-2/ISO 10414-2 For instruments not covered by these standards, specific operating procedures can be obtained directly from the manufacturers.
Table 1—Low-temperature, non-pressurized concentric-cylinder viscometers
Model Drive Power Readout Rotor Speed r/min
High-temperature, pressurized instruments, specifically concentric-cylinder viscometers, are essential for measuring the flow properties of drilling fluids under elevated temperatures and pressures These instruments vary in their temperature and pressure limitations, with specific operating procedures provided by manufacturers The high-temperature, low-pressure viscometer operates up to 2,000 psi and 500 °F, utilizing nitrogen gas as the pressurizing medium It measures torque exerted on the inner cylinder, with variable rotor speeds from 1 r/min to 600 r/min and a viscosity range of 1 cP to 300,000 cP, all programmable within a temperature range of 0 °F to 500 °F, featuring a computer interface for real-time data display In contrast, the high-temperature, high-pressure viscometer operates at limits of 40,000 psi and 600 °F, using mineral oil as the pressurizing medium, and maintains the same geometry as atmospheric viscometers with variable rotor speeds.
The rotor operates at 600 r/min and features external flights to promote circulation Key parameters such as temperature, pressure, rotor speed, and shear stress are shown on digital readouts The system includes digital temperature control with ramp and soak capabilities, while a computer manages and displays all operational parameters digitally.
Rheological models
Determining the rheological parameters of drilling fluid is crucial for calculating circulating hydraulics, enhancing hole cleaning efficiency, and predicting barite sag in oil wells The Herschel-Bulkley (H-B) rheological model is recommended for both field and office applications.
Since 1926, this model has reliably simulated measured rheological data for both water-based and non-aqueous drilling fluids, establishing itself as the standard rheological model in the drilling industry for advanced engineering calculations.
This section discusses the operation of a concentric-cylinder viscometer, where a rotating outer cylinder applies shear to the fluid located between its inner wall and a central bob A diagram illustrating the viscometer's cylinder and bob is provided in Figure 2.
The R1B1 configuration in oilfield applications features a precisely controlled gap between the rotating cylinder and the bob, ensuring a uniform shear rate during operation With a rotor inner diameter of 3.683 cm and a bob diameter of 3.449 cm, the diameter ratio is maintained at 1.0678, adhering to international DIN standards.
The H-B model is defined by three key parameters, represented in the equation \$k \gamma^n \tau = \tau_y + 16\$, where \$n\$ denotes the flow index (dimensionless), \$k\$ signifies the consistency index (force/area times time), and \$\tau_y\$ represents the fluid yield stress (force/area).
The H-B governing equation simplifies to well-known rheological models under specific conditions When the yield stress \$\tau_y\$ matches the yield point and the flow index \$n = 1\$, it aligns with the Bingham plastic model Conversely, if the yield stress \$\tau_y = 0\$ (as seen in drilling fluids without yield stress), the H-B model transitions to the power law Thus, the H-B model serves as a comprehensive framework that encompasses Bingham plastic fluids, power law fluids, and other variations in between.
In the H-B model, the consistency parameter \( k \) is functionally similar to the plastic viscosity term in the Bingham plastic rheological model, though it typically has a different numerical value The \( \tau_y \) parameter reflects the suspension characteristics of drilling fluid and is analogous to the yield point in the Bingham plastic model, but it usually has a lower numerical value The true yield stress \( \tau_y \) can be estimated through field viscometer measurements or numerical techniques, both of which are detailed in this section.
In fluid rheology, particularly when using a standard oilfield viscometer, it is essential to apply specific instrument conversion factors for accurate calculations Shear stress, measured in lbf/100 ft², is calculated by multiplying the dial reading in degrees of deflection by 1.066, a correction often overlooked in basic calculations Additionally, shear rate, expressed in s⁻¹, is obtained by multiplying the rotor speed in revolutions per minute (r/min) by 1.703.
5.2.5 Solution methods for drilling fluid H-B parameters
Solving for drilling fluid H-B parameters using the measurement method [9] involves the following steps
5.2.5.1 Approximate the fluid yield stress, commonly known as the low-shear-rate yield point, by the following equation The τy value should be between zero and the Bingham yield point:
2θ3 θ τ y = − (18) a) Determine the fluid flow index value by:
3.32 600 n log 10 (19) b) Determine the fluid consistency index by:
5.2.5.2 For water-based drilling fluids containing large amounts of viscous polymers and hence have high θ600 values, the yield stress calculation in 5.2.5.1 can overstate values for τy
5.2.6 Solving for the H-B parameters using numerical techniques
To solve for the H-B parameters using numerical techniques, one must follow a series of steps First, perform a curve fit of the measured viscometer data, utilizing at least three shear stress/shear rate data pairs This numerical solution can be implemented in a spreadsheet Next, convert the shear stress dial readings to τi, measured in lbf/100 ft² Finally, make an initial guess for the value of n1, with a recommended starting point of n = 1, and calculate the results for each of the N data sets.
1) the corrected shear rates γi (not needed for guess of n=1),
3) the value for τy and k by:
4) the error in curve fitting by: a calculating the following
( Σ γ i n × ln ( ) γ i ) , ( Σ γ i 2n × ln ( ) γ i ) , ( Σ τ i × γ i n × ln ( ) γ i ) (23) b calculating the error Err by:
To refine the calculations, guess a second value of \( n \) and repeat the steps outlined in sections 5.2.6 a) to 5.2.6 d) If the error value \( Err \) is below the recommended threshold of 0.05, cease further calculations and utilize the last computed values for \( n \), \( k \), and \( \tau_y \) Conversely, if \( Err \) exceeds this acceptable limit, derive a new value for \( n_3 \) using a standard convergence method Additionally, if the calculated values of \( \tau_y \) fall below zero, it suggests difficulties in fitting the data In such cases, the user may opt for one of the following actions.
1) use another rheological model (Bingham plastic or power law) in the calculations, or
2) reset the value of τy to 0 or to a very small positive value such as 0.001 lbf/100 ft 2
It is essential to verify the accuracy of the values of n, k, and τy in predicting the measured dial readings, irrespective of the measurement technique or numerical calculation method employed.
To accurately analyze viscometer measurements, follow these steps: first, utilize the corrected shear rates (\(γ_i\)) along with the three calculated H-B parameters to compute the shear stress (\(τ\)) on the viscometer bob using the H-B model, expressed as \(τ = τ_y + k γ^n\) Next, convert the predicted shear stress values into dial reading units (° deflection) by dividing by 1.066 Finally, employ statistical methods to assess the fit between the measured and predicted data.
Assuming a high degree of fit between the measured and predicted dial readings, the calculated values of the
H-B parameters can be applied with confidence in hydraulics and hole-cleaning equations to calculate pressure losses and Equivalent Circulating Density (ECD)
In this Bulletin, certain calculations require parameters from the Bingham plastic and power law rheological models, with the calculation methods for these parameters following the guidelines published by the API.
5.2.9.2 Bingham plastic rheological model—This model uses the θ 600 and θ 300 viscometer dial reading to calculate two parameters:
Plastic viscosity (PV), in cP = θ600 - θ300 (25)
Yield point (YP), in lbf/100 ft 2 = θ 300 – PV (26)
The recent version of this Bulletin introduces a power law model that utilizes two sets of viscometer dial readings to determine the flow index \( n \) and consistency index \( k \) for both pipe and annular flow Unlike the conventional power law, which relies solely on data from higher shear rates, this model allows for the calculation of distinct values for \( n \) and \( k \), resulting in values that often differ significantly from those derived using the Herschel-Bulkley rheological model.
6 Prediction of downhole behaviour of drilling fluids
Principle
To accurately calculate the hydraulics of oil-well drilling fluids, it is essential to consider the downhole behavior of fluid properties, particularly when using oil-based and synthetic-based drilling fluids The prediction of downhole behavior in drilling fluids should focus on three principal areas.
Each of these areas is discussed in this section.
Circulating temperature predictions in oil-well drilling
Accurate prediction of the bottom hole circulating temperature (\$T_{bhc}\$) is essential during oil-well drilling for effective hydraulic and drilling fluid density modeling, particularly when utilizing invert emulsion and all-oil drilling fluids.
Predicting circulating temperatures in a wellbore is complex due to the numerous operational and physical parameters involved A simplified calculation method is introduced, requiring minimal input parameters while maintaining sufficient accuracy for temperature predictions This model, which can be easily implemented in a spreadsheet, yields reliable results for specific ranges of bottom hole static temperature (T bhs) and geothermal gradient.
6.2.2 Input parameters needed for the prediction of downhole circulating temperatures are as follows:
⎯ bottom hole static temperature (Tbhs) ,
⎯ for offshore wells, water depth (Dw); for land wells, Dw = 0,
⎯ surface temperature (T0) measured at a depth of 50 ft or approximated by the measured surface temperature
6.2.3 Temperature calculation methods for land and offshore wells are as follows a) For land wells having a known Tbhs, the Tbhc can be calculated using the following method [11]
Tbhc = -102.1 + [3 354 × tg] + [(1.342 – 22.28 × tg) × Tbhs] (32) b) For land wells having a known geothermal gradient, Tbhc can be calculated by the following
The equation for Tbhc is given by Tbhc = -102.1 + [3 354 × tg] + [(1.342 – 22.28 × tg) × Tbhs] For offshore wells with a known Tbhs, this method can be applied after adjusting the geothermal gradient for the water column tgw.
5) Calculate the geothermal gradient adjusted for water depth tgw (°F / 100 ft) by:
Tbhc = -102.1 + [3 354 × tgw] + [(1.342 – 22.28 × tgw) × Tbhs] (36) d) For offshore wells having a known geothermal gradient, the above equations can be used after adjusting for water depth
6.2.4 Construction of a static temperature profile for a well takes the following under consideration
Static well temperatures are determined using specific data points: the measured surface temperature is considered the static temperature at a depth of D tvd = 0 For offshore wells, it is essential to adjust the geothermal gradients to reflect the water depth Additionally, static temperatures within a seawater column can be predicted based on depth, particularly for water depths of 3000 feet or less.
Tml (°F) = 154.43 – 14.214 × ln (Dw) (39) for water depths > 3000 ft,
During the drilling of a well, estimates for the total bottom hole temperature (Tbhs) are derived from a known geothermal gradient, or conversely, the geothermal gradient is estimated based on a known Tbhs It is essential to collect multiple data points as functions of the drilling depth (Dtvd) throughout the drilling process.
A straight-line fit of the collected data points provides a predicted static temperature profile by depth These values, or their averages over a specified depth interval, can subsequently be used in models to predict the downhole static rheology and density of drilling fluids, as discussed later in this section.
6.2.5 Construction of a dynamic temperature profile for a well takes the following under consideration
6.2.5.1 Dynamic circulating temperatures for a well can be predicted in a similar manner to those used above in predicting static temperatures
6.2.5.2 Using the values for Tbhs and the geothermal gradients, the Tbhc for each of the points can be calculated using the equations in 6.2.3
The flowline temperature, denoted as Tfl, is regularly monitored and represents the dynamic circulating temperature at a depth of Dtvd = 0 This measurement is essential for calibrating the circulating temperature predictions derived from the equations outlined in section 6.2.3.
A straight-line fit of the collected data points provides a predicted dynamic temperature profile by depth These temperature values, or their averages over a specified depth interval, can subsequently be used in models to predict the downhole dynamic rheology and density of drilling fluids, as discussed later in this section.
Prediction of downhole rheology of oil-well drilling fluids
Accurate prediction of downhole rheology in drilling fluids is crucial for optimizing hydraulic and hole-cleaning capabilities Enhanced rheology predictions allow for more precise calculations of circulating pressure losses, surge and swab pressures, and hole-cleaning efficiencies, which is especially valuable in well sections with minimal differentials between pore pressures and formation fracture gradients For certain fluid types, such as oil-based or synthetic-based fluids, downhole rheological properties can differ significantly from surface measurements, limiting the effectiveness of hydraulics calculations based solely on surface rheology data.
When predicting downhole fluid density, it is essential to consider the impact of temperature and pressure on rheology The generalized effects of these factors on downhole rheological properties can be summarized when analyzed individually.
6.3.2.1 The effects of temperature usually serve to increase the viscosity of oil-well drilling fluids at low temperatures (