Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 9, No. 2, 2024 

 

199 

Research	on	the	Error	Calibration	Method	of	
Rheological	Parameters	of	Rectangular	Tubular	
Viscometer	
Jianrui Song, He Zhang 

School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China 

 

Abstract: In order to solve the problem of high error in the process of measuring the rheology of drilling fluids by the common 
pipe flow method, an online measurement device for the rheology of drilling fluids with rectangular tubular drilling fluids was 
fabricated, and a calibration method for the measurement error of rheological parameters was proposed and corresponding 
experiments were carried out. By measuring the differential pressure value and flow, flow rate and other parameters when the 
drilling fluid flows through the measuring tube, upload them to the host computer for processing, use VMD to decompose the 
measured differential pressure data, remove the residual term, and then perform Hibert transform on each modal component to 
obtain its analytical signal, modulate the amplitude and phase of each analytical signal, and then reconstruct the signal to obtain 
the optimized differential data, and finally bring it into the constructed calibration model of the rheological parameter 
measurement error of drilling fluid to obtain the rheological parameters. The experimental results show that the proposed method 
can obtain more accurate rheological parameters of drilling fluid, improve the measurement accuracy of drilling fluid rheology 
parameters, so as to judge the downhole situation more accurately and ensure the personal safety of on-site staff. 

Keywords: Rheology; Rectangular tubes; In-line measurement; VMD; Viscosity. 
 

1. Introduction 
In petroleum engineering, the properties of the drilling 

fluid determine the success of the drilling of an oil and gas 
well. Drilling fluids has the function of transporting cuttings, 
transmitting signals and stabilizing the wellbore, and has an 
irreplaceable role in drilling. The rheology of drilling fluid 
refers to the flow and deformation of drilling fluid under the 
action of external force, which is usually described by the 
rheological curve of drilling fluid and rheological parameters 
such as plastic viscosity, apparent viscosity, and dynamic 
shear force. The control of rheological parameters of drilling 
fluid is of great significance for drilling hydraulic 
optimization and rock breaking, accurate control of downhole 
pressure and wellbore stability, and wellbore cleaning [1]. In 
recent years, the measurement of drilling fluid performance 
parameters has been highly valued by engineers, especially 
with the development of the oil drilling industry, drilling fluid 
to meet more and more functional requirements, how to 
accurately measure the rheology of drilling fluid is an 
important problem in practical engineering [2]. 

 At present, the instruments widely used for rheological 
measurement of drilling fluids mainly include martensitic 
viscometer and rotational viscometer. The marsh funnel can 
easily obtain results, is widely used in the drilling site, and is 
easy to operate. However, the marsh funnel can only measure 
the funnel viscosity value of the drilling fluid, and the 
measurement time is long, the measurement error is large, and 
the accuracy and timeliness are insufficient. The rotational 
viscometer is the most commonly used instrument to measure 
the viscosity of drilling fluid at the drilling site, but it cannot 
be measured in real time, there are manual operation errors, 
and there are no automatic conditions [3]. Huang YR 
proposed the principle and structure of a capillary slit 
rheometer that can be measured automatically and 
continuously, and realized high-precision automatic 

measurement [4]. Liu BS, Wang ZJ et al. proposed a double-
tube capillary measuring instrument, which realized the real-
time continuous measurement of drilling fluid under the 
action of multiple shear stresses [5]. Wu Z proposed a drilling 
fluid rheology measuring instrument based on capillary 
method, which realized the change of different flow rates of 
drilling fluid under the same flow rate, and effectively 
reduced the experimental labor intensity of field personnel [6]. 
Sun Haoyu, Zhou YJ et al. proposed an online monitoring 
device for the rheology of variable diameter special-shaped 
tubular drilling fluid, and proposed a three-temperature cubic 
function temperature pressure difference correction 
compensation model for the influence of temperature on the 
pressure difference, which improved the measurement 
accuracy [7], but this paper only considers the influence of 
temperature on the differential pressure measurement results, 
and ignores other influencing factors under actual conditions. 

For the existing on-line measurement device of drilling 
fluid rheology parameters, the measurement accuracy of the 
differential pressure data and flow velocity data at both ends 
of the measuring tube is very important for the calculation 
accuracy of the rheological parameters of water-based drilling 
fluid. Since the device needs to use pumping equipment to 
pump drilling fluid from the main line to the measuring line, 
the diaphragm pump is generally selected as the pumping 
equipment. Diaphragm pumps are reciprocating positive 
displacement pumps, and their reciprocating motion will 
cause the flow of water-based drilling fluid in the pipeline to 
change, that is, the fluid pulsation effect. The fluid pulsation 
effect will bring strong interference to the measurement of 
differential pressure signal, and seriously reduce the accuracy 
of the measurement of rheological parameters of water-based 
drilling fluids. Therefore, in this paper, the measurement error 
correction method of special-shaped tubular viscometer is 
studied to improve the calculation accuracy of the rheological 
parameters of water-based drilling fluids. 



 

200 

2. Measurement Principle of Drilling 
Fluid Rheology Tube Flow Method 
Section Headings 

2.1. Rheological model of drilling fluid 
The fluids mainly include Newtonian fluids and non-

Newtonian fluids, and the water-based drilling fluids used in 
the field are all non-Newtonian fluids, and the variation 
relationship between the shear stress and the shear rate 
calculated by the measurement of the drilling fluid can 
accurately describe the rheological properties of the drilling 
fluid [8], which can be represented by the rheological curve 
as shown in Figure 1: 

 

Figure 1. Fluid rheology curves 

 

Several rheological modes are commonly used in the 
drilling industry: Bingham mode, power law mode, Carson 
mode and H-B mode. 

1.Bingham mode 

The Bingham mode is primarily used to describe the flow 
state of a plastic fluid. In Bingham mode, there is a static shear 
force in the fluid, which can only change the fluid from rest 
to flow when the externally applied shear stress 𝜏 is greater 
than the limit of the static shear force. The Bingham model 
rheological equation is shown in the following equation (1): 

 
𝜏 𝜏 𝜂𝛾                      (1) 

 
where 𝜏  is the dynamic shear force, Pα; 𝛾 is the shear 

rate, 𝑠 ; 𝜂 is plastic viscosity, Pα∙s. 

2.Power-law mode 

The power-law mode is mainly used to describe the 
rheology of fluids at low shear rates. In power-law mode, 
there is no static shear force on the fluid, and any amount of 
shear stress will move the fluid in motion. In general, both 
pseudoplastic fluids and expansive fluids are suitable for 
power-law rheological modes, defined as pseudoplastic fluids 
when the fluidity index 𝑛 is less than 1 and expansive when 
the fluidity index n is greater than 1. The power-law mode 
rheological equation (2) shows: 

 

𝜏 𝐾𝛾                      (2) 
 

where 𝐾 is the consistency coefficient，𝑃𝛼 ∙ 𝑠; 𝑛 is the 
flow index. 

3.Carson mode 

The advantage of the Carson mode is that it can better 
describe the dynamic shear force and shear dilution behavior 
of the fluid, and compared with the Bingham rheological 
mode, the Carson mode has more advantages in low shear 
rates and medium shear rates, and is more commonly used in 
low shear rates and medium shear rates. The rheological 
equation for the Carson mode is shown in the following 
equation (3): 

 

𝜏 𝜏 𝜂 𝛾                      (3) 

 
where 𝜏  is the Carson yield value, 𝑃𝛼;𝜂  is the plastic 

viscosity of Carson, 𝑃𝛼. 

4.H-B mode  

The H-B mode mainly describes a pseudoplastic fluid that 
requires a certain dynamic shear force to be applied to the 
flow of the fluid [9]. The H-B mode is a composite of the 
above modes: when the hydrostatic shear force 𝜏  is 0 and 
the fluidity index 𝑛 is 1, the H-B mode is the same as the 
Newtonian model; When the hydrostatic shear force 𝜏  is 0 
and the fluidity index 𝑛 is not 1, the H-B mode is the same 
as the power-law mode. Compared with the appeal mode, the 
H-B model can better describe the rheological properties of 
the drilling fluid, especially at low shear rate, and the 
accuracy is higher than that of the above three rheological 
modes. The rheological equation for the H-B mode is shown 
in the following equation (4): 

 

𝜏 𝜏 𝐾𝛾                       (4) 
  
where 𝜏 is the shear stress, 𝑃𝛼; 𝜏  is the yield value, 𝑃𝛼; 

𝛾  is the shear rate, 𝑠  ; 𝐾  is the consistency coefficient, 
𝑃𝛼 ∙ 𝑠. 

2.2. Pipe flow pressure loss analysis 
When the incompressible homogeneous fluid passes 

through the thin tube with equal inner diameter placed 
horizontally at a constant velocity, the fluid is subjected to two 
forces: one is the force 𝐹 𝜋𝑟 ∆𝑝 acting on the pressure 
difference between the two ends of the thin tube on the 
cylindrical end face, and the other is the resistance 𝐹
𝜋𝜏 𝑑𝐿 on the cylindrical wall during the fluid flow. Due to 
the constant velocity of the fluid, the shear stress of the pipe 
wall can be obtained: 

 

𝜏
∆

                      (5) 

 
where 𝑟 is the radius of the pipe, ∆𝑝 is the pressure 

difference between the two ends of the measuring pipe, 
and 𝐿 is the length of the measuring tube. 

2.3. The principle of Poiseuille  
If the differential pressure of a measuring tube of length L 

is ΔP, the flow velocity at the distance from the center is: 

 

v r ΔP/4μL ∙ R r                (6) 



 

201 

where 𝜇 is dynamic viscosity; 

As can be seen from Figure 2: 

 

 
Figure 2. Schematic diagram of fluid pipeline flow 

 

At 𝑟 𝑅, the flow velocity is the smallest, and at 𝑟 0, 
the flow velocity is maximum [10]: 

 

𝜏 ∙                      (7) 

 

                        (8) 

 
Assuming that the no-slip condition at the pipe wall is valid, 

the following formula can be written: 

 

𝑄 𝑣 ∙ 2𝜋𝑟𝑑𝑟                 (9) 

 
Bringing the above equation v(r) into it, we get: 

 

𝑄
∙ ∙

                    (10) 

 

According to the flow calculation formula, 𝑄 ∙ 𝑉, 
then we can obtain: 

 

Δ𝑃                     (11) 

 
Substituting equation 11  into equation 8  yields: 

 

𝜏 𝜇                     (12) 

 
According to Newton's equations, since 𝜏 𝜇 , 

therefore, . 

For the non-Newtonian fluid of drilling fluid, it is assumed 
that 𝑦 𝑣, 𝑧 𝜋𝑟 ; Points are sorted out: 

 

𝑦𝑑𝑧 𝑦𝑧| 𝑧𝑑𝑦             (13) 

 
When 𝑟 𝑅 , flow velocity=0, the arrangement is as 

follows: 

𝑄 𝜋𝑟 𝑑𝑟            (14) 

 
For pipes, the shear stress at the pipe wall is 

𝛾 ∙            (15) 

 

Introducing a generalized fluidity index， . 

Finishing the above formula, you get: 

 

𝛾                     (16) 

 
where: 𝛾  is the shear rate of the pipe wall; 𝑣  is the 

velocity of the drilling fluid flowing through the measuring 
tube; 𝑅 is the inner diameter of the measuring tube, and 𝑁 is 
the generalized fluidity index, which can be obtained 

according to the ln𝜏 ln  curve. 

From the above formula, the shear stress and shear rate can 
be obtained respectively, the rheological curve can be plotted, 
and the rheological parameter values of the drilling fluid can 
be obtained. 

2.4. Rectangular tubes 
In the process of using the conventional tubular viscometer, 

it is found that due to the characteristics of the round tube 
itself, the measurement error caused by the change of inlet 
and outlet kinetic energy often occurs in the measurement 
process, resulting in the problem of low measurement 
accuracy. 

For the conventional round pipe, assuming that a pressure 
transmitter is horizontally installed at both ends of the straight 
pipe section of a measuring pipe with a diameter of D, and the 
distance between the two pressure transmitters is L, when the 
fluid with a volume flow rate of Q flows through the straight 
pipe section, a pressure loss will be generated between the 
two pressure transmitters, and its magnitude is ∆p, and its 
value can be known from Poiseuille law: 

 

∆𝑝                   (17) 

 
where μ is the dynamic viscosity. 

For Bingham fluid, the formula for pressure loss in 
Bingham fluid tube flow can be obtained: 

 

∆𝑝                 (18) 

 
where 𝜏  is the yield point. 

The dynamic viscosity μ obtained from the above equation 
(18) is: 

 

𝜇
∆

               (19) 

 
For the rectangular measuring tube, assuming that the 

width of the rectangular measuring tube is α, the height is h, 
and the α is much greater than h, a pressure transmitter is 
installed horizontally at both ends of the straight pipe section 
of the measuring tube, and the distance between the two is L, 
assuming that the fluid flow velocity is v and the pressure loss 
between the two pressure transmitters is ∆p, then the flow 
pressure consumption formula of the Bingham fluid 
rectangular pipe is as follows: 

 



 

202 

Δ𝑃                  (20) 

 
𝑄 𝛼ℎ𝑣                      (21) 

 
The dynamic viscosity μ obtained from the above equation 

(20) is: 

 

𝜇
∆

                   (22) 

 

3. Rectangular Tubular Viscometer 
Rheological Parameter Error 
Calibration Model 

3.1. Fluid pulsation 
In order to shorten the overall measurement cycle and 

realize the rapid measurement of the performance parameters 
of the drilling fluid, the diaphragm pump is generally used to 
pump the water-based drilling fluid into the measurement 
pipeline for measurement. If the diaphragm pump discharges 
the same fluid each time it does reciprocating work, it can be 
considered that the average flow rate of the pump is constant. 
However, in practice, due to the working principle of the 
diaphragm pump, its instantaneous flow rate is changing, and 
its flow state is mainly pulsating flow, which will bring strong 
interference to the measurement of differential pressure signal 
and seriously reduce the accuracy of the measurement of 
rheological parameters of water-based drilling fluid [11]. 

3.2. VMD 
The VMD algorithm is an adaptive and non-recursive 

signal decomposition mode, which can decompose a non-
stationary signal into k modal components with different 
bandwidths, and the algorithm is especially suitable for 
dealing with nonlinear non-stationary signals [12]. The VMD 
algorithm mainly includes the following steps: 

To decompose the initial signal into modal functions, it is 
necessary to ensure that the sum of the estimated bandwidths 
of each modal function is minimal, and the VMD-constrained 
variational model is as follows: 

 

 
𝑚𝑖𝑛

,
  ∑   ∥∥∂ 𝛿 𝑡 ∗ 𝑢 𝑡 𝑒 ∥∥

𝑠. 𝑡. ∑   𝑢 𝑓
    (23) 

 
where 𝑢 𝑢 , 𝑢 , . . . , 𝑢   is the function of each 

modality, and 𝜔 𝜔 , 𝜔 , . . . , 𝜔  is the center frequency 
of each mode. 

The two-time penalty factor α and the pull operator λ are 
introduced to convert the constrained variational model of the 
above formula into an unconstrained variational model, which 
can ensure the accuracy of the reconstructed signal and ensure 
the strictness of the constraints, and the expression is as 
follows: 

 𝐿 𝑢 , 𝜔 , 𝜆 𝛼 ∑   ∥
∥∂ 𝛿 𝑡 ∗

𝑢 𝑡 𝑒 ∥
∥ ∥∥𝑥 𝑡 ∑   𝑢 𝑡 ∥∥      (24) 

 

The saddle point is found by iteratively updating 
𝑢 , 𝜔 , 𝜆  by using ADMM: 

 𝑢 𝜔
∑              (25) 

 

In the same way, the iterative center frequency expression 
can be obtained: 

 

 𝜔
  | |

 | |
               (26) 

 

For the above iterative process, in order to obtain K modal 
component signals, the discriminant accuracy must meet the 
requirements. 

 

 ∑  
∥ ∥

∥ ∥
𝜀               (27) 

 

It is worth noting that the traditional VMD needs to 
artificially set the decomposition mode number k value, and 
a large k value will cause the VMD to over-decompose the 
original signal and interfere with the signal analysis. The 
small k value will cause some modal components with limited 
bandwidth to be unable to be completely decomposed, 
resulting in modal aliasing and excessive fluctuations of the 
decomposed low-frequency signal. 

The specific implementation process of VMD is as follows: 

1. Initialize the parameters 𝑢 , 𝜔 , 𝜆 , n=0; 

2. Execute a loop so that 𝑛 = 𝑛＋1, for ω>0, according to 
the above formula, update the values of 𝑢  and 𝜔 ; 

3. Update the value of the pull operator λ 

 𝜆 𝜔 ← 𝜆 𝜔 𝜏 𝑓 𝜔 ∑   𝑢 𝜔   

4.For the given accuracy convergence criterion ε, if the ε 
does not meet the above accuracy convergence requirements, 
go back to step 2; If the ε meets the above accuracy 
convergence requirements, the iteration is stopped. 

3.3. Rheological parameter error calibration 
model 

The measurement parameters of the differential pressure 
sensor on the measuring tube of the water-based drilling fluid 
rheology online monitoring device are affected by the fluid 
pulsation, and the α of the differential pressure sensor is a 
function of the error between the measured differential 
pressure value and the theoretical differential pressure value, 
and the error obeys the normal distribution of 𝜇 0, that is, 
𝑁 0, 𝜎 , and i The probability density function is shown in 
the following equation (28): 

 

 𝑓 𝑥
√

e                   (28) 

 

In each sampling period T, the differential pressure sensor 
decomposes the collected data through VMD to obtain a set 
of target state estimates relative to the current measurement 
management theory differential pressure parameters, and the 
likelihood function can be obtained as follows equation (29): 

 

 𝐿 𝜇, 𝜎 2𝜋𝜎 𝑒 ∑           (29) 

 



 

203 

By estimating the parameters of the probability density 
function, the corresponding likelihood value 𝑎   for each 
sample 𝑥  as follows equation (30) 

: 

 𝛼  
√ ∗ exp ∗              (30) 

 
By using the likelihood value, the weight ω of any of the 

differential pressure parameters in this group of sample values 
for the estimated theoretical differential pressure state is 𝜔  
as follows equation (31): 

 

 𝜔
∑                       (31) 

 

By analyzing the differential pressure parameters, the 
optimal differential pressure estimate of the measuring tube 
can be obtained 𝑥 𝑘  is as follows equation (32) 

: 

 𝑥 𝑘 ∑   𝛼 𝑥 𝑘                 (32) 
 

where 𝑥 𝑘  is the measured shear stress value at time k, 
and 𝑥 𝑘  is the optimal predicted output of the differential 
pressure signal. 

Through the accurate estimation of the differential pressure 
parameters, the shear stress and shear rate of the data drilling 
fluid are accurately calculated, the flow curve of the water-
based drilling fluid is accurately drawn, and the dynamic 
calibration of the rheological parameters of the drilling fluid 
is finally realized. 

4. Experiments and Data Analysis 

4.1. Protocol design 
In order to verify the accuracy of the rheological parameter 

error calibration method of the rectangular tubular viscometer 
proposed in this paper, the rheological parameter acquisition 
scheme of the rectangular tubular viscometer was designed, 
the experimental bench was built, and the experimental data 

were obtained, and the experimental verification method 
proposed in this paper could effectively calibrate the error. 

First of all, the electric diaphragm pump continuously 
pumps the drilling fluid from the mud storage tank to the 
experimental device, the drilling fluid passes through the 
damper, and then flows out through the mass flow meter, the 
mass flow meter measures the current drilling fluid 
temperature, density and mass flow data, and judges whether 
the current flow is stable through the measured data, and then 
the electric diaphragm pump is fed back to ensure that the 
current drilling fluid flow is constant. Then the drilling fluid 
passes through the rectangular measuring tube, and the flush 
membrane differential pressure sensor is installed on the 
measuring tube, and the differential pressure sensor is used to 
measure the differential pressure signal at both ends of the 
measuring tube, and the differential pressure signal is 
transmitted to the host computer, and the traditional six-speed 
measurement result is output, and the values of plastic 
viscosity, dynamic shear force, static shear force, consistency 
coefficient and fluidity index are obtained, and the drilling 
fluid returns to the drilling fluid tank at the same time to 
complete the cycle. 

4.2. Experimental bench construction 
The experimental measuring frame is mainly composed of 

a diaphragm pump, a damper, a mass flow meter, a 
rectangular measuring tube, a differential pressure sensor, and 
a slurry storage tank. The measuring tube is a rectangular tube 
of 10mm×30mm×2m and a wall thickness of 2mm. The 
diaphragm pump is used as a power source to continuously 
pump the drilling fluid from the mud storage tank to the 
experimental device; Dampers can physically reduce fluid 
pulsation [15]; The mass flow meter is responsible for the 
feedback control of the diaphragm pump to ensure that the 
current drilling fluid flow is constant; The differential 
pressure sensor uses a flush membrane differential pressure 
sensor to measure the differential pressure, and the measured 
raw differential pressure data is recorded in real time and 
transmitted to the host computer, and the working principle of 
the device is shown in the following figure 4: 

 

 
Figure 4. Diagram of the installation model 

 

The specific experimental setup is shown in the figure 5: 

 



 

204 

 
1-Diaphragm pumps; 2-shock absorber; 3-Mass flow 

meter; 

4-Differential pressure sensor; 5-Rectangular measuring 
tubes 

Figure 5. Actual drawing of the installation 

4.3. Rheological experiments and results 
analysis 

In the process of rheology experiment using the 
experimental platform built, it should be noted that in the 
measurement process, the measurement of each flow rate 
needs to be maintained for 3 minutes, which is to carry out 
the differential pressure measurement after the flow reaches 
stability, so that the measured differential pressure data is 
more stable, the measurement time is 15s, the average value 
of multiple sampling is taken, when the data acquisition under 
the quantity is completed, the flow rate is changed by the 
program control pump, and the flow rate of 1.3m/s, 0.6m/s, 
and 0.2m/s is measured in turn, and the process flow chart is 
as follows: 

 
Figure 6. Process flow diagram 

 

During the experiment, the flush membrane differential 
pressure sensor was used to collect the differential pressure 
data at both ends of the measuring tube, and the obtained 
differential pressure data was transmitted to the upper 
computer, and then the signal was decomposed and processed 
by VMD on the upper computer, and then the rheological 
parameters of the drilling fluid were calculated after 
reconstruction, and the decomposition process is as follows: 

 
Figure 7. VMD decomposition process 

 

The original and processed differential pressure signals are 
shown in the figure 8 below: 

 

 
Figure 8. VMD effect comparison chart 

 

As can be seen from Figure 8 above, the reconstructed 
signal is smoother than the original signal, which improves 
the quality of the signal. At the same time, the reconstructed 
signal is almost the same as the original signal, but the 
reconstructed signal is smoother, which indicates that the 
reconstructed signal does not affect the properties of the 
original signal, and almost all the characteristics of the 
original signal are retained. 

The differential pressure signal after VMD decomposition 
and reconstruction was brought into the constructed 
rheological parameter measurement and correction model of 
drilling fluid, and the shear stress and shear rate of the data 
drilling fluid were accurately calculated through the accurate 
estimation of the differential pressure parameters, and the 
flow curve of the water-based drilling fluid was accurately 
drawn, and finally the dynamic calibration of the rheological 
parameters of the drilling fluid was realized. 

4.4. Comparison of experimental results of 
25mPa.s bentonite drilling fluid 

25mPa.s bentonite drilling fluid was prepared, and the 
rheological parameters of the drilling fluid were measured by 
the developed drilling fluid rheology measurement device, the 
pressure difference signals at both ends of the measuring tube 
were collected, and the original data and the data calibrated 



 

205 

by the error correction method were brought into the drilling 
fluid rheological parameter model, and the test results of the 

two methods were compared, and the comparison of the 
results before and after the correction is shown in Table 1. 

 

Table 1. Comparison of results before and after correction 

 
parameter 

Apparent viscosity Plastic viscosity 

Before amendment After the correction Before amendment After the correction 
Standard value 25 25 23 23 
average value 22.46 23.74 21.37 22.51 
absolute error 2.54 1.26 1.63 0.49 
relative error 10.16% 5.04% 7.08% 2.13% 

 

As can be seen from Table 1 above, when the drilling fluid 
with a viscosity of 25mPa.s flows through the measuring 
device, the device can indeed determine the rheological 
parameters of the drilling fluid, and the correction method of 
the rheological parameters of the drilling fluid can indeed 
improve the accuracy of the measurement parameters. 

4.5. Comparison of experimental results of 
52mPa.s bentonite drilling fluid 

52mPa.s bentonite drilling fluid was prepared, and the 

rheological parameters of the drilling fluid were measured by 
the developed drilling fluid rheology measurement device, the 
pressure difference signals at both ends of the measuring tube 
were collected, and the original data and the data calibrated 
by the error correction method were brought into the drilling 
fluid rheological parameter model, and the test results of the 
two methods were compared, and the comparison of the 
results before and after the correction is shown in Table 2. 

 

Table 2. Comparison of results before and after correction 

 
parameter 

Apparent viscosity Plastic viscosity 

Before amendment After the 
correction 

Before amendment After the 
correction 

Standard value 52 52 39 39 
average value 55.37 53.03 42.46 40.96 
absolute error 3.37 1.30 3.46 1.96 
relative error 6.48% 2.5% 8.87% 5.02% 

 

As can be seen from Table 2 above, when the drilling fluid 
with a viscosity of 52mPa.s flows through the measuring 
device, the device can indeed determine the rheological 
parameters of the drilling fluid, and the correction method of 
the rheological parameters of the drilling fluid can indeed 
improve the accuracy of the measurement parameters. 

5. Summary 
Considering the problem of insufficient measurement 

accuracy of the rheological parameters of the drilling fluid in 
the field, the self-made on-line measurement device of the 
rheological parameters of the drilling fluid is used to measure 
the rheological parameters of the drilling fluid, and the 
problems of excessive error and insufficient accuracy caused 
by the influence of fluid pulsation of the measurement results 
of the device are studied, and the error calibration method of 
the rheological parameters is proposed. According to the 
measurement of the pressure difference value at both ends of 
the measuring tube, the original pressure difference signal is 
obtained, the signal is decomposed and reconstructed by 
VMD, and the optimized reconstruction signal is brought into 
the rheological parameter model, and finally the rheological 
parameters of drilling fluid are obtained. The experimental 
results show that the error correction method proposed in this 
paper can effectively improve the measurement accuracy of 
rheological parameters. 

References 
[1] Liu XL, You FC, Wu SZ, et al. Analysis of shale borehole 

instability mechanism and drilling fluid countermeasures [J]. 
Contemporary Chemical Industry, 2020, 49(01):129-133. 

[2] Mohamed A,Salehi S,Ahmed R. Significance and 
complications of drilling fluid rheology in geothermal drilling: 
A review[J]. GEOTHERMICS, JUN 2021, Vol. 93. 

[3] Zhao ZQ. Error analysis of rheological parameters of non-
Newtonian fluids measured by rotational viscometer [J]. 
Science and Technology Vision, 2013, (30): 297-298. 

[4] Huang YR.Measurement principle and application of capillary 
slit rheometer [J]. Acta Petrolei Sinica, 1994, (04):86-95. 

[5] Liu BS,WANG ZJ,MA YQ, et al.A new method for on-line 
detection of rheology of drilling fluids[J]. Drilling fluids and 
completion fluids, 2016,33(04):56-59. 

[6] Wu Z,Huang MJ, Liu XM, et al.Development of drilling fluid 
rheology measuring instrument[A]Proceedings of 2017 China 
Automation Conference and International Intelligent 
Manufacturing Innovation Conference [C]. Chinese 
Association of Automation, Jinan Municipal People's 
Government, Chinese Society of Automation, 2017:8. 

[7] SUN HY,ZHOU YJ,LIU HD. Research and application of on-
line monitoring device for rheology of variable diameter 
special-shaped tubular drilling fluid[J].Sino-foreign Energy, 
2019, 24(12): 49-54. 

[8] ZHOU XD. Rheological model research and calculation of 
drilling fluid[J].Chemical Design Communications, 2017, 
43(05): 236+243. 



 

206 

[9] ZHANG JK,LI GS,HUANG ZW, et al. Study on the flow 
characteristics of Heba fluid in vortex drill strings.Petroleum 
Drilling Techniques,2013,41(05):82-88. 

[10] XU YX. Derivation and experimental verification of Posuye's 
formula[J].Journal of Anqing Normal University(Natural 
Science Edition),2005,(04):56-57. 

[11] Lin JZ, Wang YY, Zhou SH, et al. Simulation and 
Experimental Analysis of Pressure Pulsation Characteristics of 
Pump Source Fluid[J]. APPLIED SCIENCES-BASEL, OCT 
2021, Vol. 11. 

[12] Gowri BG, Kumar SS,Mohan N, et al. A VMD Based 
Approach for Speech Enhancement[J]. ADVANCES IN 
SIGNAL PROCESSING AND INTELLIGENT 
RECOGNITION SYSTEMS (SIRS-2015), 2016, Vol.425, 
Page309-321. 

[13] Koegler AF, Haselmann D, Alt NSA, et al. Experimental 
Characterization of a Flow-through Pulsation Damper 
Regarding Pressure Pulsations and Vibrations [J]. CHEMICAL 
ENGINEERING & TECHNOLOGY. JAN 2017, Vol. 40, Page 
162-169.