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Study of the variation of drilling mud density with temperature, pressure, and circulation rate using artificial neural networks, statistical models, and empirical correlations






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Abstract

Well control is an important aspect of drilling operations because improper well control can result in kicks and blowouts with grave consequences. A successful well control requires a good understanding of the relationships between drilling mud pressure and formation pressure, as well as the variation of bottom hole pressure during drilling operations. As the hydrostatic pressure of the drilling mud column accounts for most of the pressure, a more accurate control of the changes of mud density will contribute to a more accurate bottom hole pressure modeling. Regarding the control of the mud density, a practical problem has existed so far in petroleum drilling: the mud density is determined at the surface condition, and its values vary along the depth of the well because of the changes of temperature and pressure, which consequently leads to an inaccuracy in mud density control in reality.


In order to reduce the inaccuracy in mud density control, this research aims to provide a reliable method to correctly predict the drilling mud’s density under specific conditions. Different artificial neural networks (ANN) were proposed to predict drilling mud density based on the value of mud density at surface conditions, circulation rate, bottomhole pressure, and temperature. This study then used statistical methods to compare the predicted results with results obtained from existing empirical correlations and from other researchers’ works to find out the most optimal artificial neural network which should consist of only one hidden layer. The main contributions of this research in comparison with existing papers are that: 1) Existing methods did not take into account the influence of circulation rate, therefore the real working conditions of the drilling mud were not represented entirely. Our research included the circulating rate in the ANN modeling and in the study of relative importance. The results indicated that the value of mud density at surface conditions had the greatest effect on the prediction results, and the influence of the circulating pump flow rate is small but should not be ignored; 2) Our research used different methods (ANN, Generalized Additive, Nonlinear Function) to predict the mud density in variation with temperature and pressure, which has never been approached in existing literature; 3) The sufficiency in the number of data was studied in this research, which has never been treated in previous studies. The Bootstrap method was used in this regard; 4) We remarked that the overfitting has not been treated properly in the existing literature review in this field, hence we included a thorough analysis of the overfitting in this paper.  Finally, the results of this paper can be useful in real life because it can help drillers to accurately predict the mud density under varied conditions of pressure and temperature, and therefore to increase the safety of the drilling operations.

Introduction

Ensuring safety is always the top priority in the oil and gas industry because accidents related to the petroleum sector often lead to loss of time, infrastructure, finance, and manpower. One of the accidents causing severe consequences is the loss of well control during the drilling process, specifically when the pressure in the wellbore is lower than the formation pressure. This scenario can happen if the mud density is not controlled adequately during the drilling operation due to the variation of pressure and temperature inside the wellbore, and consequently the mud density may be too low to maintain bottomhole pressure equal to formation pressure Cormack, 2017 1 . Therefore, being able to accurately calculate the mud density will help to assure a successful drilling operation. In order to achieve this objective, studying the influence of different factors affecting the density of the drilling fluid is extremely necessary.

In literature, there have been various studies relating to the prediction of drilling mud density at different conditions. It is well known that when bottomhole pressure increases, drilling mud density will increase since the drilling fluid volume is compressed, and conversely, when the bottom hole temperature increases, the drilling fluid volume expands leading to a decrease in its density, which is mentioned in Babu, 1996 2 ; Hussein and Amin, 2010 3 ; An et al., 2015 4 . McMordie et al., 1982 5 conducted an experimental research about the changes of drilling mud density with temperature (70-400 o F) and pressure (0-14000 psi). Similarly, Demirdal & Cunha, 2009 6 conducted experiments to study the variation of drilling mud density with the same range of pressure (0-14000 psi) but with a different range of temperature (25-175 o C). Zamora et al., 2013 7 also conducted experiments to study the volumetric behavior and the variation of density of base oils, brines, and drilling fluids with the range of temperature (36 o F–600 o F) and pressure (0-30000 psi). Some studies provided empirical correlations between mud density and pressure and temperature, such as Kemp, 1989 8 ; Peters et al., 1990 9 ; Isambourg et al., 1996 10 ; Zamora et al., 2000 11 ; Hemphill and Isambourg, 2005 12 ; and Peng et al., 2016 13 . egarding the application of machine learning in this field, some authors used Artificial Neural Network (Osman et al., 2003 14 ; Adesina 2015 15 , Okorie E. Agwu et al., 2020 16 ), while some others used different methods such as Fuzzy logic (Ahmadi et al., 2018 17 ), Support Vector Machine (Xu et al., 2014 18 ; Ahmadi, 2016 19 ; Kamari et al., 2017 20 ), Radial Basis Function Artificial Neural Network (Rahmati & Tatar, 2019 21 ), and Particle Swarm Optimization Artificial Neural Network (Ahmadi et al., 2018 17 ; Zhou et al., 2016 22 ). It is also worth mentioning the hydraulic model proposed by Charlez et al., 1998 23 to calculate downhole pressure and then to predict fluid downhole density. In brief, the common point of these studies is to predict drilling mud density at different bottomhole pressures and temperatures.

However, besides temperature and pressure, some other factors also affect the density of drilling fluid, such as the inclination angle of the well which was highlighted in the study of Tian et al., 2013 24 ; or the type of drilling fluid which was mentioned in the studies of Demirdal et al., 2007 25 and Demirdal & Cunha, 20096; and finally the circulation rate which was mentioned in the studies of Kårstad & Aadnøy, 1998 26 and Harris & Osisanya, 2005 27 . The study of Hemphill, 1996 28 investigated the effect of inclination angle and of cuttings on drilling fluid properties. Boatman, 1967 29 studied the influence of shale on drilling fluid density.

In reality, it is challenging to observe the changes in drilling fluid density because of costly specialized measuring equipment which must comply with well design requirements. Ombe et al., 2020 30 developed a specific measurement to achieve this task. Hoseinpour et al., 2022 31 combined well logging and geomechanical parameters to determine the mud window, but the authors could not predict the variation of the mud density in function of pressure, temperature, and some other factors.

In brief, the above literature review showed that developing a new method to accurately predict drilling mud density in the well under influence of various factors is necessary, which is the objective of our study. In this study, we resorted to not only machine learning methods but also empirical correlations as well as mathematical, and statistical methods.

Regarding the empirical correlations, Furbish, 1997 32 provided the following equation of state for liquid density:

(ppg) is predicted drilling mud density, is value of mud density at surface conditions, T and P are final temperature ( o F) and pressure (psi), T 0 and P 0 are standard temperature ( o F) and pressure (psi), α ( o F -1 ) is isobaric coefficient and β( o F -1 ) is isothermal compressibility. These coefficients were taken from the work of Zamora et al. (2000) wherein they used 0.0002546 và 2.823 × 10 -6 for α and β respectively for oil-based mud.

Another empirical correlation given by Hoberock et al., 1982 33 predicted oil-based mud density and water-based mud through the law of conservation of mass as detailed in the following:

is predicted drilling mud density, (ppg) is value of mud density at surface conditions, (ppg) is initial oil density, (ppg) is oil density in predicted drilling mud, (ppg) is water density in initial drilling mud, (ppg) is water density in predicted drilling mud, (%) is the percentage of oil volume in the drilling fluid, (%) is the percentage of water volume in the drilling fluid.

Kutasov, 1988 34 presented an empirical correlation to calculate drilling mud density:

(ppg) is the predicted drilling mud density, (ppg) is the drilling mud density at standard conditions. P 0 (psi) and T 0 ( o F) are standard pressure and temperature. P(psi) and T( o F) are the pressure and temperature at the predicted position. Kutasov evaluated α, β, , and with 5 drilling mud examples from McMordie et al., 1982 5 . Besides, Kutasov's correlation can be applied to oil-based mud and water-based mud. In our paper, the values of , and , which were taken from the work of Micah, 2011 35 , were 3.0997 × 10 -6 , 2.2139 × 10 -4 , and 5.0123 × 10 -7 , respectively.

Sorelle et al., 1982 36 focused on the changes in the volume of the components in drilling fluid caused by temperature and pressure, as being shown in the following formula:

(ppg) is the predicted drilling mud density, (ppg) is the value of mud density at surface conditions, (gal) is the change in oil volume, (gal) is the change in water volume, V(gal) is the total volume.

The literature review allowed us to see some possible contributions that we can bring to the research in this domain. Firstly, the study developed an artificial neural network modeling to predict drilling fluid density, combined with various mathematical, statistical (generalized additive model) and experimental models on the same dataset to provide a comprehensive and multidimensional understanding of the changes in drilling fluid density inside the wellbore. The simulation results were compared with actual data to verify the accuracy of the model.

Secondly, the number of features that our research used for the artificial neural network was greater than in previous studies. As mentioned above, previous papers considered mostly temperature and pressure as input features, while this study presented an artificial neural network modeling with inputs consisting of not only bottomhole temperature and pressure but initial drilling fluid density and circulation rate as well. Consequently, this paper conducted a study about the effect of various influencing factors mentioned above, besides pressure and temperature, on the drilling mud density .

Thirdy, this paper took into account the possible influence of the low number of input data used for ANN modeling. It is difficult to answer the question if a data set is enough for neural networks modeling because the conclusion depends on each particular case. Hence, in this study, we tried to answer this question by using the Bootstrap method to resample the data.

Finally, we remarked that the overfitting analysis was neglected in many previous researches as shown in the above literature review, we therefore included in this paper a thorough solution for the overfitting problem.

The findings of this study have the potential to be applied in real life because they help to improve the accuracy of the mud density’s determination, which in turn will improve the safety of the operations.

Methodology

Mathematical models

Regarding the mathematical models, we initially intended to use a linear function, which is easy to implement, to calculate the drilling mud density based on bottomhole pressure, bottomhole temperature and value of mud density at surface conditions. However, there are some assumptions that we must comply with which can be found in Dahraj & Bhutto, 2014 37 and Molnar, 2021 38 . The input data was collected from the works of McMordie et al., 1982 5 and Demirdal & Cunha, 2009 6 , which were summarized in Figure 1 . Figure 1 illustrates the variation of drilling mud density in function of temperature and pressure. The blue graph represents the temperature, the orange graph shows the pressure and the green one describes the value of mud density at surface conditions.

Figure 1 . The data collected from the works of McMordie et al. (1982) and Demirdal & Cunha (2009) were used in this research for the nonlinear function

Figure 1 The data collected from the works of McMordie et al. (1982) and Demirdal & Cunha (2009) were used in this research for the nonlinear function

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Figure 2 to Figure 4 showed that all the histograms of variables are not bell-shaped. Moreover, we also analyzed the distribution of residuals in Figure 5 . We observed that the distribution of residuals was not in shape with the red curve, which presented the normal distribution. Instead, the distribution was likely the fat-tailed distribution, which was not normal distribution, so the linear function was not suitable in this case. Consequently, we had to think about another method, which is the nonlinear function, to deal with the problem. This nonlinear function will also be used later to verify the results given by the artificial neural network modeling.

Figure 2 . Histogram of bottomhole pressure values (psi)

Figure 2 Histogram of bottomhole pressure values (psi)

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Figure 3 . Histogram of bottomhole temperature values (oF)

Figure 3 Histogram of bottomhole temperature values (oF)

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Figure 4 . Histogram of mud density at surface conditions (ppg)

Figure 4 Histogram of mud density at surface conditions (ppg)

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Figure 5 . Histogram of residuals

Figure 5 Histogram of residuals

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For the nonlinear function, the quadratic and cubic functions were tested, and we obtained that the correlation coefficient of the cubic function (0.9997) was higher than the one of the quadratic functions (0.9994). In reality, there may be other nonlinear functions with higher correlation coefficients, however, the more complex the function, the higher the risk of overfitting. The cubic function was therefore chosen for this study.

The nonlinear model was constructed by solving the linear least squares problems while using QR factorization which can be referred to the work of Golub & Loan, 1996 39 . The cubic function has the following form:

(ppg) the value of mud density at surface conditions, P and T are pressure (psi) and temperature ( o F) at the location of interest. The values from A to J were determined and listed in the following:

The nonlinear function presented a high coefficient of determination R 2 = 0.9994. Moreover, the value of mean square error was also accepted, with the MSE = 0.00971 for the nonlinear function (the caluclation of MSE is described in detail in the Appendix section). With input taken from Table 1, the calculated values of drilling mud density (ppg) from empirical correlations and nonlinear function are presented in Table 2.

Table 1 The input data which was used in this study for empirical correlations and nonlinear function

Table 2 showed that results obtained from the empirical correlations are close to results obtained from the nonlinear function. Hence, the nonlinear function can be used as an alternative method to predict the drilling fluid density in function of pressure and temperature. However, these methods do not take into account the influence of other factors such as the circulation rate. Hence, in the next section, an artificial neural network modeling will be presented.

Table 2 Drilling mud density (ppg) obtained from empirical correlations and the nonlinear functions using input data in Table 1

Machine learning model

Machine learning model

Machine learning model

Machine learning model

Machine learning model

Results and discussion

Since the authors wanted to present various models to predict drilling mud density, a generalized additive model (GAM) was built based on the input data in Figure 6 and evaluated using the same data from Table 1. A generalized additive model is a generalized linear model with a linear predictor involving a sum of smooth functions of covariates (Hastie and Tibshirani 1990 45 ). The GAMs can model non-Gaussian outcome variables, in terms of several predictor variables. The requirement of the generalized linear models that the relationships between the outcome and the predictors be linear was relinquished by Vanhove, 2014 46 . Instead, non-linear relationships can also be modeled with the form estimated from the data. This can be accomplished by fitting higher-order polynomial regressions on subsets of the data and adding the pieces together. The more subset regressions are fitted and connected together, the more wiggly the overall curve will be. Fitting too many subset regressions results in overwiggly curves that fit disproportionally much noise in the data (‘oversmoothing’). In order to prevent this, the algorithm can be furnished with a cross-validation procedure or a generalized (algebraic) approximation (Wood, 2006 47 ).

Whereas the additive model was estimated by penalized least squares, the GAM will be fitted by penalized likelihood maximization, and in practice this will be achieved by penalized iterative least squares. More specific details can be viewed in the paper of Wood, 2006 47 ; Zuur et al., 2009 48 ; Vanhove, 2014 46 . Table 4 will show the specific results of drilling mud density obtained from the generalized additive model.

To confirm the effect of circulation rate on the mud density and prove that the network obtained from this study can be applied, the results of drilling mud density obtained from ANN model and generalized additive model were compared with the results from the ANN model of Okorie E. Agwu et al., 2020 16 in Table 4.

Table 4 Drilling mud density (ppg) obtained from different artificial neural networks and the generalized additive model using the same input data in Table 1

The determination coefficient between the results obtained from our ANN model and input data is 0.9972, which is rather similar to the determination coefficient (0.9970) obtained from the ANN model of Okorie E. Agwu et al., 2020 16 . However, the mean square error of our network (0.01321) is lower than Okorie E. Agwu’s (0.04754). In addition, as mentioned above, the overfitting problem was included in our analysis, which was not done in Agwu et al., 2020 16 . We concluded that our ANN model provided a high value of coefficient of determination without encountering the overfitting problem. Moreover, the determination coefficient given by the generalized additive model is high (R 2 = 0.99865) while the mean square error is low (3.65 × 10 -6 ). Hence, our ANN model and generalized additive model can be used in real life applications.

Eventually, Table 6 showed that almost all of the methods were reliable. Only the calculated results given by Sorelle et al., 1982 36 gave a significant deviation compared to the input data, hence using the model of Sorelle is not highly recommended. Although the determination coefficient of our ANN model is lower than the one given by the generalized additive model, the ANN method can still be accepted because of its small mean square error (Table 5), and because it can include more influence factors in the input data than the other methods.

Figure 14 shows the predicted results obtained from different methods that were used in this study. The measured data in Figure 6 were the same data as the input data used in ANN modeling. Figure 14 allowed us to draw the same conclusions as mentioned in the previous paragraph.

Table 5 The results of drilling mud density (ppg) obtained from the optimized ANN, generalized additive model, and empirical correlations for the same input data from Table 1

Table 6 Comparison of correlation coefficients and errors given by different methods

Figure 14 . Graph shows results of drilling mud density (ppg) obtained from empirical correlations, nonlinear function, generalized additive model, and machine learning models

Figure 14 Graph shows results of drilling mud density (ppg) obtained from empirical correlations, nonlinear function, generalized additive model, and machine learning models

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Study of relative importance of different input parameters

Study of relative importance of different input parameters

Study of relative importance of different input parameters

Conclusions

This paper presented various methods (artificial neural network, generalized additive model, nonlinear function, empirical correlations) to predict drilling mud density in function of temperature, pressure, surface value of the drilling fluid, and circulation rate. The results lead to the following conclusions:

  • The Generalized Additive model and Artificial Neural Network have higher coefficient of determination R 2 and lower MSE than the other methods. However, it is recommended to use our optimized ANN method because we demonstrated that it did not have a problem of overfitting, while the Generalized Additive model presented a very low MSE, which should be used with caution.

  • The optimized ANN model consisted of only one hidden layer. In addition, the answer to the question if a data set is enough for neural networks modeling is not simple because it depends on each particular case. In this study, the Bootstrap method was used to resample the data and the conclusion was that the number of input data was enough to avoid the overfitting problem. Moreover, it is worthy to note that since there was often a lack of overfitting analysis in previous studies in literature review regarding this specific case, we solved this problem by conducting a thorough analysis of overfitting in this paper.

  • The nonlinear model is more appropriate than the linear model in this case based on the analysis of the histograms of different variables.

  • The empirical correlations presented higher deviation between predicted results and measured data, especially the correlation given by Sorelle et al. (1982).

  • The level of impact on drilling mud density is in the following order: value of mud density at surface conditions, bottomhole pressure, bottom hole temperature, and circulation rate.

ABBREVIATIONS

ANN: Artificial neural network

: Percentage of oil volume in the drilling fluid

: Percentage of water volume in the drilling fluid

GAM: Generalized additive model

MSE: Mean Squared Error

(psi): Standard pressure

(psi): Pressure at the predicted position

RMSE: Root Mean Squared Error

( o F): Standard temperature

( o F): Temperature at the predicted position

V (gal): Total volume

(gal): Difference in oil volume

(gal): Difference in water volume

: A true value of input data

: A maximum value of input data

: A minimum value of input data

: A dimensionless value of input data

: A true value of target data

: A dimensionless value of target data

(ppg): Value of mud density at surface conditions

(ppg): Predicted drilling mud density

(ppg): Initial oil density

(ppg): Oil density in predicted drilling mud

(ppg): Initial water density

(ppg): Water density in predicted drilling mud

CONFLICT OF INTEREST

The authors declare that there are no conflicts of interest in the publication of this article.

AUTHORS’ CONTRIBUTION

Pham Son Tung directed and supervised the development and completion of the research, as well as reviewed and revised the article.

Pham Thanh Nh a collected data, built the models, and drafted the manuscript.

APPENDIX

Mean Squared Error (MSE) is a formula for estimating the squared value of an error. The smaller the value of MSE, the more accurate the prediction is.

Root Mean Square Error (RMSE) is used to evaluate how well a model fits the data. When the value of RMSE is near 0, the model will be more accurate.

T-value is a measure that indicates the degree of influence of input factors on the results. The absolute value of the t-value indicates the greater the degree of influence. A negative t-value indicates an inverse relationship between the input factor and the result, and vice versa.

The correlation coefficient is a statistical parameter that measures the degree of fit between predicted and actual data of drilling fluid density.

N is the total number of observations, I is the index of I observation; X i * is the value of drilling mud density which is predicted from empirical correlations or machine learning models.

Pr (>|t|) is the p-value corresponding to the t-value. If the p-value is less than the statistical significance level α (usually 0.05), the factors associated with it will be statistically significant in the results, otherwise, it will be a random factor.

References

  1. Cormack D. An Introduction to Well Control Calculations for Drilling Operations. New York, USA; 2017. . ;:. Google Scholar
  2. Babu DR. Effects of P-ρ-T behavior of muds on static pressures during deep well drilling — part 2: static pressures. In: Paper (SPE27419) SPE drilling and completion, 1996; vol 11, no 2; 1996. . ;:. Google Scholar
  3. Hussein AMO, Amin RAM. Density measurement of vegetable and mineral based oil used in drilling fluids. In: Paper SPE 136974 presented at the 34th annual SPE international conference and exhibition held in Tinapa — Calabar, Nigeria. . ;:. Google Scholar
  4. An J, Lee K, Choe J. Well control simulation model of oil based muds for HPHT wells. In: Paper SPE 176093 presented at the SPE/IATMI Asia Pacific oil and gas conference and exhibition held in Nusa Dua, Bali, Indonesia; 2015. . ;:. Google Scholar
  5. McMordie Jr WC, Bland RG, Hauser JM. Effect of temperature and pressure on the density of drilling fluids. In: Paper SPE 11114 presented at the 57th annual Fall Technical Conference and Exhibition of the Society of Petroleum engineers of AIME held in New Orleans; 1982. . ;:. Google Scholar
  6. Demirdal B and Cunha JC. Olefin-based synthetic-drilling-fluids volumetric behavior under downhole conditions. SPE Drilling and Completion 24(2): 239–248; 2009. . ;:. Google Scholar
  7. Zamora M, Roy D, Slater K, Troncoso J. Study on the Volumetric Behavior of Base Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures. SPE Drilling & Completion 28 (3): 278–288; 2013. . ;:. Google Scholar
  8. Kemp NP, Thomas DC, Atkinso G, Atkinson BL. Density Modeling for Brines as a Function of Composition, Temperature, and Pressure. SPE Prod Eng 4: 394–400; 1989. . ;:. Google Scholar
  9. Peters EJ, Chenevert ME, Zhang C. A model for predicting the density of oil-based muds at high pressures and temperatures. In: Paper SPE-18036-PA, SPE Drilling Engineering, vol 5, no 2; 1990. . ;:. Google Scholar
  10. Isambourg P, Anfinsen BT, Marken C. Volumetric Behavior of Drilling Muds at High Pressure and High Temperature. Paper presented at the European Petroleum Conference, Milan, Italy; 1996. . ;:. Google Scholar
  11. Zamora M, Broussard PN, Stephens MP. The top 10 mud related concerns in deepwater drilling operations. In: Paper SPE 59019 presented at the SPE international petroleum conference and exhibition in Mexico, Villahermosa, Mexico; 2000. . ;:. Google Scholar
  12. Hemphill T, Isambourg P. New Model Predicts Oil, Synthetic Mud Densities. Oil & Gas Journal 103 (16): 56–58; 2005. . ;:. Google Scholar
  13. Peng Q, Fan H, Zhou H, Liu J, Kang B, Jiang W, Gao Y, Fu S. Drilling fluid density calculation model at high temperature high pressure. In: Paper OTC-26620-MS presented at the offshore technology conference Asia, Kuala Lumpur, Malaysia; 2016. . ;:. Google Scholar
  14. Osman EA, Aggour MA. Determination of Drilling Mud Density Change with Pressure and Temperature Made Simple and Accurate by ANN. In: Paper SPE 81422 presented at the SPE 13th middle east oil show and conference, Bahrain; 2003. . ;:. Google Scholar
  15. Adesina FAS, Abiodun A, Anthony A, Olugbenga F. Modelling the effect of temperature on environmentally safe oil based drilling mud using artificial neural network algorithm. Pet Coal J 57(1): 60–70; 2015. . ;:. Google Scholar
  16. Agwu Okorie E., Akpabio JU, Dosunmu A. Artificial neural network model for predicting the density of oil-based muds in high-temperature, high-pressure wells. J Petrol Explor Prod Technol 10: 1081–1095; 2020. . ;:. Google Scholar
  17. Ahmadi MA, Shadizadeh SR, Shah K, Bahadori A. An accurate model to predict drilling fluid density at wellbore conditions. Egypt J Pet 27(1): 1–10; 2018. . ;:. Google Scholar
  18. Xu S, Li J, Wu J, Rong K, Wang G. HTHP static mud density prediction model based on support vector machine. Drill Fluid Complet Fluid 31(3):28–31; 2014. . ;:. Google Scholar
  19. Ahmadi MA. Toward reliable model for prediction of drilling fluid density at wellbore conditions: a LSSVM model. Neurocomput J 211: 143–149; 2016. . ;:. Google Scholar
  20. Kamari A, Gharagheizi F, Shokrollahi A, Arabloo M, Mohammadi AH. Estimating the drilling fluid density in the mud technology: application in high temperature and high pressure petroleum wells. In: Mohammadi AH (ed) Heavy oil. New York, pp 285–295; 2017. . ;:. Google Scholar
  21. Rahmati AS, Tatar A. Application of radial basis function (RBF) neural networks to estimate oil field drilling fluid density at elevated pressures and temperatures. Oil Gas Sci Technol Rev IFP Energies Nouvelles; 2019. . ;:. Google Scholar
  22. Zhou H, Niu X, Fan H, Wang G. Effective calculation model of drilling fluids density and ESD for HTHP well while drilling. In: Paper IADC/SPE-180573-MS presented at the 2016 IADC/SPE Asia Pacific Drilling Technology Conference, Singapore; 2016. . ;:. Google Scholar
  23. Charlez PhA, Easton M, Morrice G, and P. Tardy. Validation of Advanced Hydraulic Modeling using PWD Data. Paper presented at the Offshore Technology Conference, Houston, Texas; 1998. . ;:. Google Scholar
  24. Li TT, Zhang M, Zhang HL, Tang LP. A new method to determine mud density in deflecting well. Advanced Materials Research (734–737): 1338–1342; 2013. . ;:. Google Scholar
  25. Demirdal B, Miska S, Takach N, Cunha JC (2007). Drilling Fluids Rheological and Volumetric Characterization Under Downhole Conditions. In: Paper SPE 108111 presented at the Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina; 2007. . ;:. Google Scholar
  26. Kårstad E and Aadnøy BS. Density Behavior of Drilling Fluids During High Pressure High Temperature Drilling Operations. Paper presented at the IADC/SPE Asia Pacific Drilling Technology, Jakarta, Indonesia; 1998. . ;:. Google Scholar
  27. Harris OO and Osisanya SO. Evaluation of Equivalent Circulating Density of Drilling Fluids under High-Pressure/High-Temperature Conditions. Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas; 2005. . ;:. Google Scholar
  28. Hemphill T. Prediction of Rheological Behavior of Ester-Based Drilling Fluids under Downhole Conditions. Paper presented at the International Petroleum Conference and Exhibition of Mexico, Villahermosa, Mexico; 1996. . ;:. Google Scholar
  29. Boatman WA. Measuring and Using Shale Density to Aid in Drilling Wells in High-Pressure Areas. J Pet Technol 19: 1423–1429; 1967. . ;:. Google Scholar
  30. Ombe EM, Elyas, OA., Qader TA, Mehdi M. Application of a real time mud density and rheology monitoring system to enhance drilling in high pressure high temperature gas wells with MPD systems. Paper presented at the International Petroleum Technology Conference, Dhahran, Kingdom of Saudi Arabia; 2020. . ;:. Google Scholar
  31. Hoseinpour M, Riahi MA. Determination of the mud weight window, optimum drilling trajectory, and wellbore stability using geomechanical parameters in one of the Iranian hydrocarbon reservoirs. J Petrol Explor Prod Technol 12: 63–82; 2022. . ;:. Google Scholar
  32. Furbish DJ. Fluid physics in geology: an introduction to fluid motions on earth’s surface and within its crusts. Oxford University Press, New York; 1997. . ;:. Google Scholar
  33. Hoberock LL, Thomas DC, Nickens HV. Here’s how compressibility and temperature affect bottom-hole mud pressure. Oil Gas J 80(12):159–164; 1982. . ;:. Google Scholar
  34. Kutasov IM. Empirical correlation determines downhole mud density. Oil Gas J 86:61–63; 1988. . ;:. Google Scholar
  35. Micah EM. Combined Effect of Rheological Model and Equivalent Diameter Definitions on Pressure Losses/Equivalent Circulating Density Estimation. Master Thesis, African University Of Science And Technology Abuja; 2011. . ;:. Google Scholar
  36. Sorelle RR, Jardiolin RA, Buckley P, Barrrios JR. Mathematical field model predicts downhole density changes in static drilling fluids. In: Paper SPE 11118 presented at SPE annual fall technical conference and exhibition, New Orleans, LA; 1982. . ;:. Google Scholar
  37. Dahraj NUH and Bhutto AA. Linear mathematical model developed using statistical methods to predict permeability from porosity. Society of Petroleum Engineers - PAPG/SPE Pakistan Section Annual Technical Conference; 2014. . ;:. Google Scholar
  38. Molnar C. Interpretable Machine Learning - A Guide for Making Black Box Models Explainable. ‎Independently published; 2021. . ;:. Google Scholar
  39. Golub GH, Loan CFV. Matrix computation, 3rd edn. Baltimore, USA; 1996. . ;:. Google Scholar
  40. Ghaffari A, Abdollahi H, Khoshayand MR, Bozchalooi IS., Dadgar A, Rafiee-Tehrani M. Performance comparison of neural network training algorithms in modeling of bimodal drug delivery. International Journal of Pharmaceutics, 327(1–2): 126–138; 2006. . ;:. Google Scholar
  41. Parrella F. Online support vector regression. A Thesis Presented for the Degree of Information Science, University of Genoa; 2007. . ;:. Google Scholar
  42. Mohaghegh S. Virtual-Intelligence Applications in Petroleum Engineering: Part 1 - Artificial Neural Networks. J Pet Technol 52: 64–73; 2000. . 2000;:. Google Scholar
  43. Horowitz J. Bootstrap. In: The New Palgrave Dictionary of Economics, 2nd edn. London, pp 1–7; 2020. . ;:. Google Scholar
  44. Uzair M, Jamil N. Effects of Hidden Layers on the Efficiency of Neural networks. Proceedings - 2020 23rd IEEE International Multi-Topic Conference, INMIC 2020, 1–6; 2020. . ;:. Google Scholar
  45. Hastie T, Tibshirani R. Generalized Additive Models, 1st edn. Suffolk, Great Britain; 1990. . ;:. Google Scholar
  46. Vanhove J. Receptive multilingualism across the lifespan Cognitive and linguistic factors in cognate guessing. Languages and Literatures/Multilingualism Research. PhD thesis. University of Fribourg; 2014. . ;:. Google Scholar
  47. Wood SN. Generalized additive models: An introduction with R, 2nd edn. Boca Raton, USA; 2006. . ;:. Google Scholar
  48. Zuur AF, Ieno EN, Walker NJ, Saveliev AA, Smith GM. Mixed effects models and extensions in ecology with R. New York; 2009. . ;:. Google Scholar


Author's Affiliation
Article Details

Issue: Vol 7 No 3 (2024)
Page No.: 2331-2352
Published: Dec 31, 2024
Section: Research article
DOI: https://doi.org/10.32508/stdjet.v7i3.1330

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Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Tùng, P., & Nhân, N. (2024). Study of the variation of drilling mud density with temperature, pressure, and circulation rate using artificial neural networks, statistical models, and empirical correlations. VNUHCM Journal of Engineering and Technology, 7(3), 2331-2352. https://doi.org/https://doi.org/10.32508/stdjet.v7i3.1330


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