WO2001002832A1 - Modelling the rheological behaviour of drilling fluids as a function of pressure and temperature - Google Patents

Modelling the rheological behaviour of drilling fluids as a function of pressure and temperature Download PDF

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Publication number
WO2001002832A1
WO2001002832A1 PCT/EP2000/005512 EP0005512W WO0102832A1 WO 2001002832 A1 WO2001002832 A1 WO 2001002832A1 EP 0005512 W EP0005512 W EP 0005512W WO 0102832 A1 WO0102832 A1 WO 0102832A1
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pressure
temperature
equations
values
parameters
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PCT/EP2000/005512
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French (fr)
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Mickael Allouche
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Sofitech N.V.
Schlumberger Canada Limited
Compagnie Des Services Dowell Schlumberger
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Priority to AU55329/00A priority Critical patent/AU5532900A/en
Publication of WO2001002832A1 publication Critical patent/WO2001002832A1/en

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N11/00—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N11/00—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
    • G01N2011/0026—Investigating specific flow properties of non-Newtonian fluids

Definitions

  • the present invention relates to the field of petroleum service and supply industries, and in particular to the techniques used for predicting the behavior of drilling fluids.
  • a drilling fluid or mud is injected, whose main functions are to transport the cuttings from the bottom to the surface, to cool and lubricate the drill bit, to maintain the size of the hole by preventing phenomena in which its walls collapse or narrow, and to prevent the ingress of water, oil, or gas, with the hydrostatic pressure of the drilling mud balancing the pressure exerted by the fluids or gases in the formations.
  • a drilling mud is constituted by a liquid phase (water, brine, oil, water-in-oil emulsion, or oil-in-water emulsion) together with solids in suspension, and in particular cuttings.
  • a drilling mud contains additives which increase the viscosity of the mud and which thus give it good suspensive capacity to counter settling of the cuttings, and a weighting material, generally barium sulfate also known as barite, for the purpose of controlling its density.
  • the apparent viscosity of a fluid obeying the power law is thus infinite at zero shear rate and zero at very high shear rates (infinite shear rate).
  • the Herschel- Bulkley model assumes that plastic viscosity tends towards a non-zero value at high shear rates which appears to comply more closely with the principles of physics even if, in practice, the power law model is usually sufficient for describing the fluids used.
  • the three-parameter Herschel-Bulkley model provides better correlation with experimental rheograms for bentonite-free drilling muds.
  • the parameters n and k have not been given any physical interpretation such that there is no way of predicting their values under different conditions of temperature and pressure.
  • the methodology proposed by the present invention consists in estimating the apparent viscosity at a temperature T and a pressure P for three distinct shear rates, on the basis of an equation of the type:
  • the values of the parameters B and C depend on the shear rate, however this dependency is relatively weak.
  • the plastic viscosity of a bentonite-free mud can thus be estimated by using values for B and C as determined at a single shear rate, so that it suffices to measure viscosity at two different temperature and pressure pairs.
  • the experimental drilling mud was prepared using 390 grams (g) of a CONOCO LVT 200 type oil (density 820 kg/m 3 at 15°C), 12 g of and INTERDRILL EMUL HT type emulsifying agent, 2 g of a second emulsifying agent of the INTERDRILL LO-RM type, 14 g of a viscosity agent IDF TRUVIS HT, 8 g of lime, 32.8 g of calcium chloride (in an 86% solution), 81.8 g of water, and 467.8 g of barite.
  • INTERDRILL EMUL HT, INTERDRILL LO-RM, and IDF TRUVIS HT are additives available from Schlumberger Dowell.
  • the rheological measurements were obtained using a Huxley-Bertram rheometer comprising two concentric cylinders: rotation was applied to the outer cylinder and the torque required to compensate the shear due to the shear rate applied by the rotation was measured. It should be observed that the shear rate exerted in the mud is proportional
  • the experimental drilling fluid was tested at temperatures of 50°C, 93°C, 138°C, and 182°C, at pressures of 4.5 MPa, 69 MPa, 34.5 MPa, and 100 MPa, giving 16 series of measurements performed at 14 different shear rates lying in the range 5 s ' to 1000 s " .
  • the last step of validating the results is to compare the head losses calculated using the Herschel-Bulkley parameters predicted from the apparent viscosities in application of the invention with those obtained using parameters derived from measurements.
  • the calculations were performed for a flow in a tube having a diameter of 5 inches (12.7 cm) and for a tube having a diameter of 2 inches (5.08 cm), at various flow speeds.

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Abstract

The present invention provides a method of predicting the rheological behavior of a non-Newtonian fluid at a given temperature and pressure, leading to an estimate of the apparent viscosity at a temperature T and a pressure P for three distinct shear rates (a) and based on an equation (b), and on solving a set of three equations of the said type to determine values for the parameters of the Herschel-Bulkley model for the same conditions of temperature and pressure by solving the set of three equations (c) corresponding to these three shear rates (a).

Description

MODELLING THE RHEOLOGICAL BEHAVIOUR OF DRILLING FLUIDS AS A FUNCTION OF PRESSURE AND TEMPERATURE
The present invention relates to the field of petroleum service and supply industries, and in particular to the techniques used for predicting the behavior of drilling fluids.
To drill a well such as an oil well, a drilling fluid or mud is injected, whose main functions are to transport the cuttings from the bottom to the surface, to cool and lubricate the drill bit, to maintain the size of the hole by preventing phenomena in which its walls collapse or narrow, and to prevent the ingress of water, oil, or gas, with the hydrostatic pressure of the drilling mud balancing the pressure exerted by the fluids or gases in the formations.
A drilling mud is constituted by a liquid phase (water, brine, oil, water-in-oil emulsion, or oil-in-water emulsion) together with solids in suspension, and in particular cuttings. A large number of materials are used, but very generally, a drilling mud contains additives which increase the viscosity of the mud and which thus give it good suspensive capacity to counter settling of the cuttings, and a weighting material, generally barium sulfate also known as barite, for the purpose of controlling its density.
To be able to predict the behavior of such a fluid in a borehole, it is essential to calculate the flow conditions to which it will be subjected and also to calculate head losses as a function of the geometry of the well. The equations governing flow conditions are well known to the person skilled in the art and they rely on fluid rheology, i.e. on equations which describe the response of the fluid to an imposed stress, in particular equations relating the shear stress τ of the fluid to the shear rate exerted thereon.
In the case of so-called "Newtonian" fluids, e.g. water, the shear stress τ is proportional
to the shear rate /and to the viscosity η, defined by the ratio — being constant.
Y
Nevertheless, that simple model does not apply to most of the fluids used when making a well, and in particular it does not apply to any fluid charged with solids such as a drilling mud. For these so-called "non-Newtonian" fluids, apparent viscosity varies as a function of shear rate.
Several models have been developed to characterize this rheological behavior. In the
Bingham model, commonly used to model the rheology of cementing slurries or grouts, shear stress is represented by the equation τ = τy + μp . γ for τ ≥ τy in which μp is the plastic viscosity and τ is the shear threshold. In other words, when the Bingham model is applicable, the fluid flows only when subjected to some minimum shear rate, above which it has a response that varies linearly. The apparent viscosity of a Bingham fluid (defined as the ratio μ = — ) is thus infinite at zero shear rate and is equal to the
Y plastic viscosity at very high shear rates (infinite shear rate).
The so-called power law model is represented by the equation τ = k . χ" in which n is a dimensionless number and k is the consistency index proportional to the apparent viscosity of the fluid. The apparent viscosity of a fluid obeying the power law is thus infinite at zero shear rate and zero at very high shear rates (infinite shear rate).
Numerous other models have been proposed, and in particular the Herschel-Bulkley model which, so to speak, combines the above two models and is represented by the three-parameter equation τ = τy + k . γn . Unlike the power law model, the Herschel- Bulkley model assumes that plastic viscosity tends towards a non-zero value at high shear rates which appears to comply more closely with the principles of physics even if, in practice, the power law model is usually sufficient for describing the fluids used.
Nevertheless, of the three models mentioned, the three-parameter Herschel-Bulkley model provides better correlation with experimental rheograms for bentonite-free drilling muds. However, as yet, the parameters n and k have not been given any physical interpretation such that there is no way of predicting their values under different conditions of temperature and pressure.
As a result, it would be desirable to be able to have a model based on the Herschel- Bulkley model, but including variations of temperature and pressure so as to be able to satisfy the need expressed by the simulation industry, in particular to enable it to provide better modelling of the flow of drilling mud or other fluids used when making or treating oil wells or the like.
As already observed by Houwen and Geeham (Society of Petroleum Engineers, SPE 15416, October 1986), and as shown by Figures 1 to 3 accompanying the present application, the way in which the parameters of the Herschel-Bulkley model vary as a
* function of variations in temperature and in pressure cannot be represented by a simple polynomial or exponential function.
However, the above authors have shown that when the rheology of a fluid cannot be represented by the Bingham model, the plastic viscosity for a shear rate /can be predicted by means of an exponential function of the Arrhenius' equation type:
Figure imgf000004_0001
in which B and C are coefficients to be determined by experimental measurements.
The methodology proposed by the present invention consists in estimating the apparent viscosity at a temperature T and a pressure P for three distinct shear rates, on the basis of an equation of the type:
Figure imgf000004_0002
and in determining the values of the parameters in the Herschel-Bulkley model under the same conditions of temperature and pressure by solving the set of three equations corresponding to the three shear rates.
To estimate the apparent viscosity μ(T,P) at a given shear rate, values of μ are necessary for the three T,P pairs. These values can be obtained experimentally. Nevertheless, it is preferable not to use them directly but to use them for calculating the parameters of the Herschel-Bulkley model for these P,T pairs and subsequently to recalculate the viscosity γ values from the equation μ = — + k . χ"~l thereby making it possible in particular to
Ϋ solve the system of three-parameter equations associated with the Herschel-Bulkley model in simple manner, e.g. by selecting shear rates equal to 10 s" , 100 s" and 1000 s" , even though viscosity-measuring apparatuses do not generally enable such shear rates to be applied exactly insofar as shear rate is in fact the product of a number of rotations and a factor associated with the dimensions of the measurement cell.
It must be emphasized that the apparent viscosity of a Herschel-Bulkley fluid cannot be modelled accurately by means of an Arrhenius' type equation, since the difference
* between the predicted values and experimental values can be as much as 30%. The parameters of the Herschel-Bulkley model that result therefrom are thus themselves rather far from the real parameters, and differences of as much as 500% can arise for the values of k. Nevertheless, the rheograms predicted by the model proposed by the present invention for shear rates of less than 1000 s"1, are very close to experimental rheograms, so the model turns out to be entirely suitable for use in calculating head losses.
The values of the parameters B and C depend on the shear rate, however this dependency is relatively weak. In practice, the plastic viscosity of a bentonite-free mud can thus be estimated by using values for B and C as determined at a single shear rate, so that it suffices to measure viscosity at two different temperature and pressure pairs.
Other characteristics, advantages, and details of the invention appear from the additional description below, given with reference to an example of calculating Herschel-Bulkley parameters for a typical drilling mud.
The experimental drilling mud was prepared using 390 grams (g) of a CONOCO LVT 200 type oil (density 820 kg/m3 at 15°C), 12 g of and INTERDRILL EMUL HT type emulsifying agent, 2 g of a second emulsifying agent of the INTERDRILL LO-RM type, 14 g of a viscosity agent IDF TRUVIS HT, 8 g of lime, 32.8 g of calcium chloride (in an 86% solution), 81.8 g of water, and 467.8 g of barite. INTERDRILL EMUL HT, INTERDRILL LO-RM, and IDF TRUVIS HT are additives available from Schlumberger Dowell.
The rheological measurements were obtained using a Huxley-Bertram rheometer comprising two concentric cylinders: rotation was applied to the outer cylinder and the torque required to compensate the shear due to the shear rate applied by the rotation was measured. It should be observed that the shear rate exerted in the mud is proportional
to the speed of rotation Ω in a ratio = — — -Ω where s is the ratio between the radiμs s2 -\ of the outer cylinder and the radius of the inner cylinder. Under such conditions, and assuming that the fluid is incompressible and that the movement of the fluid is not turbulent, the shear stress exerted on the fluid is proportional to the measured torque.
The experimental drilling fluid was tested at temperatures of 50°C, 93°C, 138°C, and 182°C, at pressures of 4.5 MPa, 69 MPa, 34.5 MPa, and 100 MPa, giving 16 series of measurements performed at 14 different shear rates lying in the range 5 s' to 1000 s" .
These measurements have made it possible to calculate the Herschel-Bulkley numerical parameters as they appear in the table below which was used for plotting the curves of Figures 1 to 3.
Figure imgf000006_0001
From this table, it is possible to calculate the apparent viscosity μ in Pa.s, using the
equation μ = — + k . f~ , which for = 10 s' gives the following, for example. Ϋ
Figure imgf000006_0002
The same calculations were performed at shear rates equal to 100 s"1 and 1000 s"1. Using the method of least squares, the coefficients Bs and were finally determined for a shear rate ,. using the equation:
Figure imgf000007_0001
In the present case, and using T=50°C and P=4.5MPa as reference temperature and pressure, the following results were obtained:
Figure imgf000007_0003
It can be seen that B and C are relatively insensitive to variations in shear rate, such that to a first approximation, it is possible to use a mean value, such as B = 1000 Kelvin and C = 2 Kelvin/MPa.
For any temperature and pressure conditions, it is then possible to find the parameters of the Herschel-Bulkley model by solving the following system of equations:
Figure imgf000007_0002
By comparing the values calculated in this way with the experimental values, the following differences were observed (expressed as percentages):
Figure imgf000008_0001
It can be seen that the difference between the theoretical model and the experimental data rises to nearly 200% for the coefficient k. Nevertheless, the difference between the experimental rheograms and the calculated rheograms is very small as can be seen from Figure 4 where the continuous line represents the curve obtained from numerical values of the model (n=0.93, k=0.127 Pa.s", τy=7.06 Pa), and where the dashed line represents the curve obtained from experimental points represented by squares (n=0.77, k=0.374 Pa.sn, τy=5.83 Pa).
The last step of validating the results is to compare the head losses calculated using the Herschel-Bulkley parameters predicted from the apparent viscosities in application of the invention with those obtained using parameters derived from measurements. The calculations were performed for a flow in a tube having a diameter of 5 inches (12.7 cm) and for a tube having a diameter of 2 inches (5.08 cm), at various flow speeds.
Figure imgf000009_0001
It can be seen that for intermediate shear rates (in the range 300 s"'and 1000 s"1), the values predicted by the model do not differ from the real values by more than 10%. At very low shear rates (3 s" ), the difference between the predicted values and the real values can be as great as 25%; however this apparently large difference is of little importance, given the low head loss values induced by shear rates that are so low and also the poor accuracy of measurements performed with the rheometer at such shear rates.

Claims

1. A method of predicting the rheological behavior of a non-Newtonian fluid at a given temperature and pressure, leading to an estimate of the apparent viscosity at a temperature T and a pressure P for three distinct shear rates /. and based on an equation of the following type:
μ (T,P)
Figure imgf000010_0001
and on solving a set of three equations of the said type to determine values for the parameters of the Herschel-Bulkley model for the same conditions of temperature and pressure by solving the set of three equations μi.γi = τy + k . γ" corresponding to these three shear rates ,..
2. A method according to claim 1, in which the parameters B and C are determined from values of μ measured for three temperature and pressure pairs.
3. A method according to claim 1, characterized in that no account is taken of variation in B and C as a function of shear rate.
4. A method according to any preceding claim, characterized in that the equations are solved by the method of least squares.
PCT/EP2000/005512 1999-07-06 2000-06-15 Modelling the rheological behaviour of drilling fluids as a function of pressure and temperature WO2001002832A1 (en)

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Cited By (18)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2367843A (en) * 2000-10-11 2002-04-17 Smith International Modelling the dynamic behaviour of a complete drilling tool assembly
GB2378520A (en) * 2001-08-07 2003-02-12 Schlumberger Holdings Method for determining drilling fluid properties downhole during wellbore drilling
FR2831270A1 (en) * 2001-10-19 2003-04-25 Inst Francais Du Petrole Continuous measurement of drilling fluid rheological characteristics involves using adapted sensor on circulation pipe, to determine rheogram
US7380594B2 (en) 2002-11-26 2008-06-03 Shell Oil Company Method of installing a tubular assembly in a wellbore
US7899658B2 (en) 2000-10-11 2011-03-01 Smith International, Inc. Method for evaluating and improving drilling operations
CN102434119A (en) * 2011-09-20 2012-05-02 中国石油化工股份有限公司 Control method of Casson model drilling fluid rheological parameters
US8718993B2 (en) 2010-02-02 2014-05-06 Conocophillips Company Multilevel percolation aggregation solver for petroleum reservoir simulations
US9279314B2 (en) 2011-08-11 2016-03-08 Conocophillips Company Heat front capture in thermal recovery simulations of hydrocarbon reservoirs
WO2016099536A1 (en) * 2014-12-19 2016-06-23 Halliburton Energy Services, Inc. Methods for determining rheological quantities of a drilling fluid using apparent viscosity
WO2017039455A1 (en) * 2015-08-28 2017-03-09 Statoil Petroleum As Measurement of cedent properties
US10174569B2 (en) 2013-06-20 2019-01-08 Aspect International (2015) Private Limited NMR/MRI-based integrated system for analyzing and treating of a drilling mud for drilling mud recycling process and methods thereof
US10444170B2 (en) 2015-07-02 2019-10-15 Aspect Ai Ltd. System and method for analysis of fluids flowing in a conduit
US10598581B2 (en) 2013-11-06 2020-03-24 Aspect Imaging Ltd. Inline rheology/viscosity, density, and flow rate measurement
US10655996B2 (en) 2016-04-12 2020-05-19 Aspect Imaging Ltd. System and method for measuring velocity profiles
US10670574B2 (en) 2015-01-19 2020-06-02 Aspect International (2015) Private Limited NMR-based systems for crude oil enhancement and methods thereof
US10809338B2 (en) 2015-04-12 2020-10-20 Aspect Ai Ltd. System and method for NMR imaging of fluids in non-circular cross-sectional conduits
CN112727438A (en) * 2021-01-04 2021-04-30 西南石油大学 Annular pressure drop calculation method suitable for long open hole section of ultra-deep well
US11378506B2 (en) 2017-12-12 2022-07-05 Baker Hughes, A Ge Company, Llc Methods and systems for monitoring drilling fluid rheological characteristics

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FR2879282B1 (en) 2004-12-13 2007-02-09 Inst Francais Du Petrole METHOD FOR DETERMINING CONDITIONS FOR RESTORING PARAFFINIC CRUDE FLOWS
FR2968761B1 (en) * 2010-12-08 2012-12-14 IFP Energies Nouvelles METHOD FOR DETERMINING THE VISCOSITY OF HYDRATES SUSPENSION FORMED WITHIN EMULSION
CN108760576B (en) * 2018-05-30 2024-05-14 碎得机械(北京)有限公司 System and method for testing rheological property of dangerous waste conveyed by pipeline

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Cited By (28)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6785641B1 (en) 2000-10-11 2004-08-31 Smith International, Inc. Simulating the dynamic response of a drilling tool assembly and its application to drilling tool assembly design optimization and drilling performance optimization
GB2367843B (en) * 2000-10-11 2002-11-06 Smith International Simulating the dynamic response of a drilling tool assembly and its application to drilling tool assembly design optimization and drilling performance optimi
GB2367843A (en) * 2000-10-11 2002-04-17 Smith International Modelling the dynamic behaviour of a complete drilling tool assembly
US7899658B2 (en) 2000-10-11 2011-03-01 Smith International, Inc. Method for evaluating and improving drilling operations
US7139689B2 (en) 2000-10-11 2006-11-21 Smith International, Inc. Simulating the dynamic response of a drilling tool assembly and its application to drilling tool assembly design optimization and drilling performance optimization
GB2378520B (en) * 2001-08-07 2003-10-15 Schlumberger Holdings Method for determining drilling fluid properties downhole during wellbore drilling
US6659197B2 (en) 2001-08-07 2003-12-09 Schlumberger Technology Corporation Method for determining drilling fluid properties downhole during wellbore drilling
GB2378520A (en) * 2001-08-07 2003-02-12 Schlumberger Holdings Method for determining drilling fluid properties downhole during wellbore drilling
US6769295B2 (en) 2001-10-19 2004-08-03 Institut Francais Du Petrole Continuous measurement of the rheological characteristics of well fluids
FR2831270A1 (en) * 2001-10-19 2003-04-25 Inst Francais Du Petrole Continuous measurement of drilling fluid rheological characteristics involves using adapted sensor on circulation pipe, to determine rheogram
US7380594B2 (en) 2002-11-26 2008-06-03 Shell Oil Company Method of installing a tubular assembly in a wellbore
US8718993B2 (en) 2010-02-02 2014-05-06 Conocophillips Company Multilevel percolation aggregation solver for petroleum reservoir simulations
US9279314B2 (en) 2011-08-11 2016-03-08 Conocophillips Company Heat front capture in thermal recovery simulations of hydrocarbon reservoirs
CN102434119A (en) * 2011-09-20 2012-05-02 中国石油化工股份有限公司 Control method of Casson model drilling fluid rheological parameters
US10174569B2 (en) 2013-06-20 2019-01-08 Aspect International (2015) Private Limited NMR/MRI-based integrated system for analyzing and treating of a drilling mud for drilling mud recycling process and methods thereof
US10598581B2 (en) 2013-11-06 2020-03-24 Aspect Imaging Ltd. Inline rheology/viscosity, density, and flow rate measurement
WO2016099536A1 (en) * 2014-12-19 2016-06-23 Halliburton Energy Services, Inc. Methods for determining rheological quantities of a drilling fluid using apparent viscosity
AU2014413962B2 (en) * 2014-12-19 2018-05-10 Halliburton Energy Services, Inc. Methods for determining rheological quantities of a drilling fluid using apparent viscosity
US9568408B2 (en) 2014-12-19 2017-02-14 Halliburton Energy Services, Inc. Methods for determining rheological quantities of a drilling fluid using apparent viscosity
US10670574B2 (en) 2015-01-19 2020-06-02 Aspect International (2015) Private Limited NMR-based systems for crude oil enhancement and methods thereof
US10809338B2 (en) 2015-04-12 2020-10-20 Aspect Ai Ltd. System and method for NMR imaging of fluids in non-circular cross-sectional conduits
US10444170B2 (en) 2015-07-02 2019-10-15 Aspect Ai Ltd. System and method for analysis of fluids flowing in a conduit
WO2017039455A1 (en) * 2015-08-28 2017-03-09 Statoil Petroleum As Measurement of cedent properties
US11085287B2 (en) 2015-08-28 2021-08-10 Statoil Petroleum As Measurement of cement properties
US10655996B2 (en) 2016-04-12 2020-05-19 Aspect Imaging Ltd. System and method for measuring velocity profiles
US11378506B2 (en) 2017-12-12 2022-07-05 Baker Hughes, A Ge Company, Llc Methods and systems for monitoring drilling fluid rheological characteristics
CN112727438A (en) * 2021-01-04 2021-04-30 西南石油大学 Annular pressure drop calculation method suitable for long open hole section of ultra-deep well
CN112727438B (en) * 2021-01-04 2022-02-18 西南石油大学 Annular pressure drop calculation method suitable for long open hole section of ultra-deep well

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