Artificial neural network model for predicting the density of oil-based muds in high-temperature, high-pressure wells
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Abstract
In this paper, an artificial neural network model was developed to predict the downhole density of oil-based muds under high-temperature, high-pressure conditions. Six performance metrics, namely goodness of fit (R^{2}), mean square error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), sum of squares error (SSE) and root mean square error (RMSE), were used to assess the performance of the developed model. From the results, the model had an overall MSE of 0.000477 with an MAE of 0.017 and an R^{2} of 0.9999, MAPE of 0.127, RMSE of 0.022 and SSE of 0.056. All the model predictions were in excellent agreement with the measured results. Consequently, in assessing the generalization capability of the developed model for the oil-based mud, a new set of data that was not part of the training process of the model comprising 34 data points was used. In this regard, the model was able to predict 99% of the unfamiliar data with an MSE of 0.0159, MAE of 0.101, RMSE of 0.126, SSE of 0.54 and a MAPE of 0.7. In comparison with existing models, the ANN model developed in this study performed better. The sensitivity analysis performed shows that the initial mud density has the greatest impact on the final mud density downhole. This unique modelling technique and the model it evolved represents a huge step in the trajectory of achieving full automation of downhole mud density estimation. Furthermore, this method eliminates the need for surface measurement equipment, while at the same time, representing more accurately the downhole mud density at any given pressure and temperature.
Keywords
Artificial neural network Downhole mud density Drilling mud HTHPList of symbols
- AI
Artificial intelligence
- ANN
Artificial neural network
- ANN-PSO
Artificial neural network-particle swarm optimization hybrid
- ESD
Equivalent static density
- GA-FIS
Genetic algorithm fuzzy intelligent system
- GP
Genetic programming
- HTHP
High temperature high pressure
- lb/gal
Pounds per gallon
- MAE
Maximum absolute error
- MAPE
Mean absolute percentage error
- MSE
Mean square error
- MWD
Measurement while drilling
- OBM
Oil-based mud
- P
Pressure (psig)
- PSO-ANN
Particle swarm optimization artificial neural network
- R^{2}
Correlation coefficient
- RBF
Radial basis function
- RMSE
Root mean square error
- SBM
Synthetic-based mud
- SVM
Support vector machine
- SVR
Support vector regression
- T
Temperature (°F)
- \(\rho_{OBM}\)
Oil-based mud density
Introduction
Compositional and empirical models for predicting downhole mud density
References | Correlation developed |
---|---|
Hoberock et al. (1982) | \(\rho \left( {T,P} \right) = \frac{{\rho_{\text{o}} f_{\text{o}} + \rho_{\text{w}} f_{\text{w}} + \rho_{\text{s}} f_{\text{s}} + \rho_{\text{c}} f_{\text{c}} }}{{1 + f_{\text{o}} \left( {\frac{{\rho_{\text{o}} }}{{\rho_{{{\text{o}}i}} }} - 1} \right) + f_{w} \left( {\frac{{\rho_{\text{w}} }}{{\rho_{{{\text{w}}i}} }} - 1} \right)}}\) \(\rho \left( {T,P} \right)\) is the drilling fluid density at the temperature (T) and pressure (P) of interest. \(\rho_{{{\text{o}}i}} \;{\text{and}}\;\rho_{{{\text{w}}i}}\) is the oil and water density at T and P, respectively, \(\rho_{\text{o}} \;{\text{and}}\;\rho_{\text{w}}\) represent the oil and water density at T and P, respectively, \(f_{\text{o}} , f_{\text{w}} ,f_{\text{s}} , f_{\text{c}}\) represents volume fractions of oil, water solids and chemicals, respectively |
Sorelle et al. (1982) | \(\rho_{\text{w}} = 8.63186 - 3.31977*10^{ - 3} T + 2.3717*10^{ - 5}\, \left( {P - P_{\text{o}} } \right)\) \(\rho_{o} = 7.24032 - 2.84383*10^{ - 3} T + 2.7566*10^{ - 5}\, \left( {P - P_{o} } \right)\) \(\rho_{\text{o}} \;{\text{and}}\;\rho_{\text{w}}\) represent the oil and water density at temperature T and pressure P, respectively. Assumption: The wellbore temperature distribution is linear |
Politte (1985) | \(\rho_{O} \left( {P,T} \right) = C_{0} + C_{1} *PT + C_{2} P + C_{3} P^{2} + C_{4} T + C_{5} T^{2}\) where C_{0} = 0.8807, C_{1} = 1.5235 × 10^{−9}, C_{2} = 1.2806 × 10^{−6}, C_{3} = 1.0719 × 10^{−10}, C_{4} = − 0.00036, C_{5} = − 5.1670 × 10^{−8}; T is temperature in °F; P is pressure (psi) |
Kutasov (1988) | \(\rho_{\text{m}} = \rho_{\text{mo}} *e^{{a\left( {P - P_{\text{o}} } \right) - b\left( {T - T_{\text{o}} } \right) + c\left( {T - T_{\text{o}} } \right)^{2} }}\) P_{o}, T_{o} represent 1 atm and 15 °F, respectively, D is the surface mud density at standard temperature and pressure. a,b,c are the models empirical constants. T1 and P1 are surface temperature and pressure, respectively, \(\rho_{\text{m}}\) is mud density at standard rate, \(\rho_{\text{mo}}\) is mud density at HTHP conditions |
Kemp et al. (1989) | \(\rho = \frac{{\left( {1 + \mathop \sum \nolimits_{i} m_{i} M_{i} } \right)}}{{\left[ {\frac{1}{{\rho_{\text{w}} }} + \mathop \sum \nolimits_{i} m_{i} v_{i} } \right]}}\) where ρ = density, m_{i} = molality of the ith salt, M_{i} = molecular weight of the ith salt, ρ_{w} = density of pure water and v_{i} = apparent molal volume of the ith salt. Used for brine density determination only |
Peters et al. (1990) | \(\rho_{\text{m}} = \frac{{\rho_{{{\text{m}}1}} }}{{1 + V_{{f{\text{w}}1}} \left( {\frac{{\rho_{{{\text{w}}1}} }}{{\rho_{\text{w}} }} - 1} \right) + V_{{f{\text{h}}1}} \left( {\frac{{\rho_{{{\text{h}}1}} }}{{\rho_{\text{h}} }} - 1} \right)}}\) \(V_{{f{\text{w}}1}} \;{\text{and}}\;V_{{f{\text{h}}1}}\) are the fractional vols of water and hydrocarbon phases, respectively, while \(\rho_{\text{m}} \cdot \rho_{\text{w}} \;{\text{and}}\;\rho_{\text{h}}\) are the densities of water mud and the hydrocarbon phases |
Kårstad and Aadnøy (1998) | \(\rho = \rho_{0} e^{{\varGamma \left( {P,T} \right)}}\) \(\begin{aligned} \varGamma \left( {P,T} \right) & = \gamma_{P} \left( {P - P_{0} } \right) + \gamma_{PP} \left( {P - P_{0} } \right)^{2} + \gamma_{T} \left( {T - T_{0} } \right)+ \gamma_{TT} \left( {T - T_{0} } \right)^{2} + \gamma_{PT} \left( {P - P_{0} } \right)\left( {T - T_{0} } \right) \\ \end{aligned}\) The values of \(\gamma_{p} , \gamma_{pp} , \gamma_{T} , \gamma_{TT} \;{\text{and}}\;\gamma_{PT}\) are essentially unknown and must be determined for different muds |
Zamora et al. (2000) | \(SG_{o} = \left( {a_{o} T + b_{o} } \right) + \left( {a_{1} T + b_{1} } \right)P + \left( {a_{2} T + b_{2} } \right)P^{2}\) where a_{o} = − 3.8503 × 10^{−4}, b_{o} = 8.3847 × 10^{−1}, a_{1} = 1.5695 × 10^{−8}, b_{1} = 2.4817 × 10^{−6}, a_{2} = − 4.3373 × 10^{−13}, b_{2} = 6.5076 × 10^{−12} |
Hemphill and Isambourg (2005) | \(\rho = \left( {a_{1} + b_{1} P + c_{1} P^{2} } \right) + \left( {a_{2} + b_{2} P + c_{2} P^{2} } \right)T\) |
Demirdal et al. (2007) | \(\begin{aligned} \rho \left( {P,T} \right) & = \left( { - 5.357*{\text{e}}^{ - 06} T^{2} - 1.267{\text{e}}^{ - 03} T + 8.717} \right) \exp \left[ {\left( {9.452*{\text{e}}^{ - 11} T^{2} - 1.53{\text{e}}^{ - 8} T + 4.192{\text{e}}^{ - 6} } \right)*P} \right] \\ \end{aligned}\) |
Peng et al. (2016) | \(\rho \left( {T,P} \right) = \frac{{\rho \left( {T_{\text{o}} ,P_{\text{o}} } \right)}}{{\left( {1 + \beta_{p} \Delta T} \right)\left( {1 - \beta_{T} \Delta P} \right)}}\) where \(\beta_{P} , \beta_{T}\) are the isobaric expansivity and isothermal compressibility, respectively |
Summary of researches on mud density prediction using artificial intelligence
Authors | Type of study conducted | Method | Architecture | Input parameters | Output parameters |
---|---|---|---|---|---|
Osman and Aggour (2003) | Mud density of water-based mud (WBM) and oil-based mud (OBM) | ANN | 4-6-1 | Initial mud density at surface conditions, temperature, pressure, type of drilling fluid | Density |
Wang et al. (2012) | Predicting mud density at HTHP conditions | SVM (RBF) | Not applicable | Type of drilling fluid, initial surface density, temperature, pressure | Density |
Xu et al. (2014) | Predicting mud density at HTHP conditions | SVM | Not applicable | Not stated | Density |
Adesina et al. (2015) | Predicting downhole mud density of OBM | ANN | 1-10-1 | Temperature | Density |
Tatar et al. (2016) | Brine density prediction | Not stated | Not stated | Temperature, pressure and concentration | Brine density |
Ahmadi (2016) | Mud density prediction | Fuzzy logic | Not applicable | Initial mud density, pressure, temperature | Density |
Ahmadi (2016) | Predicting the rheology of WBM, OBM & gas muds | SVM | Not applicable | Initial mud density, pressure, temperature | Mud density |
Zhou et al. (2016) | HTHP drilling fluid density of WBM & OBM | ANN-PSO | 5-5-1 | Initial mud density, pressure, difference temperature difference, water volume fraction, oil volume fraction | Density |
Kamari et al. (2017) | Estimating drilling mud density | SVM | Not applicable | Initial density, pressure and temperature of OBM, WBM, Colloidal Gas Aphron (CGA) and synthetic drilling fluids | Density at pressure and temperature |
Tewari and Dwivedi (2017) | Estimating drilling mud density | ANN-SVM | 4-6-1 | Type of fluid and its density under normal surface condition, temperature and pressure | Density at pressure and temperature |
Ahmadi et al. (2018) | Prediction of mud density | PSO-ANN GA-FIS | Not stated | Initial mud density, pressure, temperature | Density |
Rahmati and Tatar (2019) | Prediction of mud density | RBF ANN | Not stated | Initial density, pressure and temperature of OBM, WBM, Colloidal Gas Aphron (CGA) and synthetic drilling fluids | Density at pressure and temperature |
Materials and methods
Database sources and range of input and output variables
Process input and output parameters of mud density and their values
Database parameter | Minimum | Maximum | Unit |
---|---|---|---|
Downhole pressure (P) | 0 | 14000 | Psig |
Downhole temperature (T) | 70 | 400 | °F |
Initial Mud density (\(\rho_{i}\)) | 11 | 18 | l b/gal |
Final mud density (\(\rho_{f}\)) | 9.59 | 18.46 | l b/gal |
Descriptive statistics of the input variables used in modelling downhole mud density
Parameter | Downhole pressure | Downhole temperature | Initial mud density |
---|---|---|---|
Mean | 4974.36 | 246.9 | 14.33 |
SD | 3663.57 | 111.328 | 2.879 |
Range | 14,000 | 330 | 7 |
Overview of artificial neural network
Implementation of the artificial neural network
Parameter settings for ANN model
Parameters | Values |
---|---|
Training data set | 71 (60% of dataset) |
Testing data set | 23 (20% of dataset) |
Validation data set | 23 (20% of dataset) |
Number of hidden layers | 1 |
Number of neurons in hidden layer | 1–20 |
Activation function (hidden layer) | Tansig |
Activation function (output layer) | Purelin |
Number of epochs | 1000 |
Learning rate | 0.70 |
Architecture selection | Trial-and-error |
Target goal mean square error | 10^{−5} |
Minimum performance gradient | 10^{−5} |
Performance of the ANN model
Weights and biases for ANN model in Eq. 2
Input layer weight matrix | Input layer bias vector | Hidden layer weight vector | Output layer bias vector | ||
---|---|---|---|---|---|
W_{ij} | |||||
j = 1 | j = 2 | j = 3 | b1 | W2 | b2 |
− 2.33494 | 1.6557 | 3.604944 | − 1.14224 | 0.013267 | − 0.2315 |
− 0.3625 | 0.213005 | 0.005013 | 0.917833 | 0.886391 | |
− 0.08568 | 0.077822 | − 0.23131 | 0.122961 | − 3.22244 | |
− 1.51904 | 0.682808 | − 6.73521 | − 3.54016 | − 0.08908 | |
0.577463 | 3.183481 | 0.379244 | 2.432787 | − 0.0119 |
Summary of ANN model performance
Training | Validation | Testing | |
---|---|---|---|
R^{2} | 0.99998 | 0.99994 | 0.99995 |
MSE | 0.0002849 | 0.0008419 | 0.000703 |
RMSE | 0.01687 | 0.029 | 0.0265 |
SSE | 0.0333 | 0.0985 | 0.0822 |
From Table 7, the assessment is based on the testing values only. Based on this, a combination of low MSE, SSE and RMSE values coupled with high R^{2} value (close to 1) makes the model a good one.
Relative importance of independent variables in the ANN model
Final connection weights
Downhole pressure | Downhole temperature | Initial mud density | Output | |
---|---|---|---|---|
Hidden layer 1 | − 2.33494 | 1.6557 | 3.604944 | 0.013267 |
Hidden layer 2 | − 0.3625 | 0.213005 | 0.005013 | 0.886391 |
Hidden layer 3 | − 0.08568 | 0.077822 | − 0.23131 | − 3.22244 |
Hidden layer 4 | − 1.51904 | 0.682808 | − 6.73521 | − 0.08908 |
Hidden layer 5 | 0.577463 | 3.183481 | 0.379244 | − 0.0119 |
Connection weights products, relative importance and rank of inputs
Downhole pressure | Downhole temperature | Initial mud density | |
---|---|---|---|
Hidden layer 1 | − 0.03098 | 0.021967 | 0.047828 |
Hidden layer 2 | − 0.32132 | 0.188806 | 0.004443 |
Hidden layer 3 | 0.276113 | − 0.25078 | 0.745372 |
Hidden layer 4 | 0.135323 | − 0.06083 | 0.600006 |
Hidden layer 5 | − 0.00687 | − 0.03788 | − 0.00451 |
Sum | 0.052269 | − 0.13872 | 1.393136 |
Rank | 3 | 2 | 1 |
Comparison of ANN model’s performance with existing AI models
Comparison of developed model with existing AI models
References | Method | Architecture | R^{2} | MSE | RMSE | SSE | MAPE | MAE |
---|---|---|---|---|---|---|---|---|
Osman and Aggour (2003) | ANN | 4-6-1 | 0.9998 | Not stated | 0.0056 | Not stated | 0.367 | Not stated |
Wang et al. (2012) | SVM (RBF) | Not applicable | 0.9994 | Not stated | 0.117 | Not stated | 0.872 | Not stated |
Xu et al. (2014) | SVM | Not applicable | Not stated | Not stated | Not stated | Not stated | Not stated | Not stated |
Adesina et al. (2015) | ANN | 1-10-1 | 0.99852 (Diesel OBM) 0.99414 (Jatropha OBM) 0.99675 (Canola OBM) | Not stated | Not stated | Not stated | Not stated | Not stated |
Tatar et al. (2016) | Not stated | Not stated | 0.999999 | Not stated | Not stated | Not stated | Not stated | Not stated |
Ahmadi (2016) | Fuzzy logic | Not applicable | 0.7237 | 69.0907 | Not stated | Not stated | Not stated | Not stated |
Ahmadi (2016) | SVM | Not applicable | 0.9999 | Not stated | Not stated | Not stated | Not stated | Not stated |
Zhou et al. (2016) | ANN-PSO | 5-5-1 | 0.9% (Max. rel. error) | Not stated | Not stated | Not stated | Not stated | 0.018 g/cm^{3} |
Kamari et al. (2017) | SVM | Not applicable | 0.999 | Not stated | Not stated | Not stated | Not stated | Not stated |
Tewari and Dwivedi (2017) | ANN-SVM | 4-6-1 | 0.9999 | Not stated | 0.00277 | Not stated | 0.2254 | Not stated |
Ahmadi et al. (2018) | PSO-ANN GA-FIS | Not applicable | 0.9964 0.9397 | 0.00014 0.091 | Not stated | Not stated | Not stated | Not stated |
This study | ANN | 3-5-1 | 0.9999 | 0.00048 | 0.022 | 0.056 | 0.127 | 0.017 |
According to Table 10, we find that the prediction accuracy is significantly different in various studies, and the model developed in this work is superior to all the other models. This is so because the model is not complex judging by the number of neurons in the hidden layer compared to the other models. Considering the results using the accuracy indicators, the ANN model developed in this study is found to be more appropriate for prediction of downhole mud density owing to its low MAE, MAPE and high R^{2} compared to the other models.
Comparison of the generalization capacity of the developed model with existing models
Generalization capacity assessment of various models used for predicting downhole density of oil-based muds
References | Correlation developed | R^{2} | MSE | MAE | RMSE | MAPE (%) |
---|---|---|---|---|---|---|
Sorelle et al. (1982) | \(\rho_{\text{o}} = 7.24032 - 2.84383*10^{ - 3} T + 2.7566*10^{ - 5} \left( {P - P_{\text{o}} } \right)\) | 0.0185 | 57.4 | 6.95 | 7.58 | 47.8 |
Hoberock et al. (1982) | \(\rho \left( {T,P} \right) = \frac{{\rho_{\text{o}} f_{\text{o}} + \rho_{\text{w}} f_{\text{w}} + \rho_{\text{s}} f_{\text{s}} + \rho_{\text{c}} f_{\text{c}} }}{{1 + f_{\text{o}} \left( {\frac{{\rho_{\text{o}} }}{{\rho_{{{\text{o}}i}} }} - 1} \right) + f_{w} \left( {\frac{{\rho_{\text{w}} }}{{\rho_{{{\text{w}}i}} }} - 1} \right)}}\) | 0.9999 | 0.0015 | 0.0339 | 0.0387 | 0.25 |
Politte (1985) | \(\rho_{O} \left( {P,T} \right) = C_{0} + C_{1} *PT + C_{2} P + C_{3} P^{2} + C_{4} T + C_{5} T^{2}\) | 0.0183 | 57.15 | 6.93 | 7.56 | 47.7 |
Kutasov (1988) | \(\rho_{\text{m}} = \rho_{\text{mo}} *{\text{e}}^{{a\left( {P - P_{\text{o}} } \right) - b\left( {T - T_{\text{o}} } \right) + c\left( {T - T_{\text{o}} } \right)^{2} }}\) | 0.9772 | 0.562 | 0.65 | 0.7496 | 4.973 |
EOS in Furbish (1997) | \(\rho = \rho_{\text{o}} \left[ {1 - \alpha \left( {T - T_{\text{o}} } \right) + \beta \left( {p - p_{\text{o}} } \right)} \right]\) | 0.9993 | 0.027 | 0.1392 | 0.164 | 0.96 |
Kårstad and Aadnøy(1998) | \(\rho = \rho_{0} {\text{e}}^{{\varGamma \left( {P,T} \right)}}\) | 0.9703 | 1.14 | 0.91 | 1.067 | 7.08 |
Zamora et al. (2000) | \({\text{SG}}_{\text{o}} = \left( {a_{\text{o}} T + b_{\text{o}} } \right) + \left( {a_{1} T + b_{1} } \right)P + \left( {a_{2} T + b_{2} } \right)P^{2}\) | 0.0186 | 60.48 | 7.17 | 7.77 | 49.5 |
Demirdal et al. (2007) | \(\begin{aligned} \rho \left( {P,T} \right) & = \left( { - 5.357*{\text{e}}^{ - 06} T^{2} - 1.267{\text{e}}^{ - 03} T + 8.717} \right) \\ & \quad \exp \left[ {\left( {9.452*{\text{e}}^{ - 11} T^{2} - 1.53{\text{e}}^{ - 8} T + 4.192{\text{e}}^{ - 6} } \right)*P} \right] \\ \end{aligned}\) | 0.0014 | 31.08 | 4.66 | 5.575 | 30.4 |
This study (ANN) | \(\rho_{\text{f}} = \mathop \sum \limits_{j = 1}^{5} \left\{ {{\text{purelin}}\left[ {{\text{LW}}_{j,1} \left( {\mathop \sum \limits_{i = 1}^{3} \mathop \sum \limits_{j = 1}^{5} {\text{tansig}}\left( {X_{i} *{\text{IW}}_{i,j} + b_{1} } \right)} \right)} \right] + b_{2} } \right\}\) | 0.9997 | 0.0159 | 0.1 | 0.126 | 0.7 |
Comparison of developed ANN model with an existing equation of state for liquid density prediction
Disparities between the developed ANN model and published ANN models
- 1.
The possibility to replicate and reproduce the results from published research is one of the major challenges in model development using artificial intelligence. This makes it rarely possible to re-implement AI models based on the information in the published research, let alone rerun the models because the details of the model and the simulation codes are either not presented in an understandable format or have not been made available. Beyond this, AI techniques such as ANN used in this work are more often than not tagged black box models. This work’s novelty lies in the fact that it has been able to illuminate the box such that the weights and biases that can be used for replicating the models have been presented. A close look at the ANN models by Osman and Aggour (2003), Adesina et al. (2015) and Rahmati and Tartar (2019) indicates that the vital details of the model which can make it replicable are not presented, hence limiting their application.
- 2.
The use of sensitivity analysis in this work has been able to make the AI model developed in this work explainable unlike the other ANN models in the literature
- 3.
There are huge concerns regarding the ability of an AI model to generalize to situations that were not represented in the data set used to train the model. To the best of my knowledge, the models in the literature were not tested for their generalization ability by using a new dataset, hence, it is difficult to ascertain how generalizable these models are in practice.
Design of a drilling process incorporating the developed ANN model for estimating downhole mud density
- (1)
The downhole sensors The sensors for the downhole temperature and pressure measurement would essentially be attached to the logging while drilling tools. The sensors should be of the differential pressure type and should be placed in the logging while drilling (LWD) tool. The basic sensing element should be designed to detect a difference in wellbore pressure and temperature as the depth of the well increases. In this way, the differential pressure transducer interrogates the readings and transmits it to the ANN model software installed in a computer. This enables the model to instantaneously process the readings and calculate the downhole density of the mud and transmit it to the surface panel at the drillers console. This process would save rig time and reduced the time spent on manually testing for the surface density of the mud in the mud tank which may not always represent the density of the mud downhole. It must be said, however, that the data from the sensors requires some cleansing, filtering or analysis; hence, bio-inspired algorithms would be developed for this purpose.
- (2)
The functionality of the developed ANN model in the design A software would be developed based on the ANN model and installed in a computer where the filtered data from the sensor would be passed. The constant in the model which is the initial density of the mud would be manually measured prior to the start of drilling and fed into the model. The downhole temperature and pressure at any given time and depth would be transmitted to the model and the downhole density calculated. Since the sensor data would be streamed and transmitted per unit time, the increase or decrease of the downhole mud density would be referenced to the initial mud density. The trend (either increase or decrease) would be shown graphically with respect to time and depth. If the density falls too low or gets too high, then an alarm would be triggered indicating a low or high mud density. This would be shown on the surface panel at the drillers console. This way, the downhole drilling fluid density that has taken into account the downhole temperature and pressure regimes in the wellbore would be monitored. When the need arises, measures to adjust the mud density would be done on the basis of this knowledge in order to assure safety and wellbore stability.
Practical implication of findings
Despite the fact that the Hoberock et al.’s model performs creditably well, one of the major drawbacks of the Hoberock et al.’s compositional model is that it requires long man hours to determine the volume fraction of oil, water, solids, chemicals, etc., required to perform the density computation. The procedure for carrying out a complete compositional analysis of mud is done using the mud retort test. Users complain the procedure is rigorous, lengthy and time consuming; with the test often taking more than an hour to complete (Salunda, online). However, with the ANN model, the man hours spent carrying out the compositional analysis can hopefully be reduced and reallocated to other high value-added tasks. Hence, the ANN model developed in this work is a valuable substitute for the Hoberock et al.’s model, especially when downhole mud density values are required in real time for critical decisions to be taken.
Conclusion
In this work, an artificial neural network model has been developed for the prediction of the downhole density of oil-based muds in wellbores. The objective of this work was to use a nature-inspired algorithm (ANN) to develop a robust and accurate model for the downhole density of oil-based muds that would be replicable and generalizable across new input datasets. The developed model in this work is robust and reliable due to its simplicity and accuracy for the application of interest. Beyond this, the model can be replicated unlike other AI models in the literature because the threshold weights and biases required for developing the model are provided. The prediction capability of the ANN model has been compared with the existing AI models as well as with other models for predicting OBM density. Based on the obtained results, the outputs of the developed ANN model are in good agreement with corresponding experimental data. In comparison with existing AI models, the developed ANN model gives more accurate estimations. Furthermore, the intelligent ANN model paves the way for rapid predictions of the downhole density of oil-based muds in HTHP wells unlike the time-consuming procedure associated with the Hoberock et al.’s model.
Recommendation
While the industry churns out exabytes of drilling data every nanosecond, and we wait patiently with enthusiasm for oil prices to rise and costs to fall, it is imperative that we use that space of time to leverage on the cost saving and value adding technology of AI to develop high-fidel models for predicting other mud related challenges that affect mud density such as barite sagging in oil-based muds.
Notes
Acknowledgements
The authors would like to appreciate the management of the University of Uyo for providing an enabling environment to carry out this research.
Funding
No funding was provided for this research by any individual or corporate organization.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
References
- Adesina FAS, Abiodun A, Anthony A, Olugbenga F (2015) Modelling the effect of temperature on environmentally safe oil based drilling mud using artificial neural network algorithm. Pet Coal J 57(1):60–70Google Scholar
- Ahad MM, Mahour B, Shahbazi K (2019) Application of machine learning and fuzzy logic in drilling and estimating rock and fluid properties. In: 5th International conference on applied research in electrical, mechanical and mechatronics engineeringGoogle Scholar
- Ahmadi MA (2016) Toward reliable model for prediction of drilling fluid density at wellbore conditions: a LSSVM model. Neurocomput J 211:143–149. https://doi.org/10.1016/j.neucom.2016.01.106 CrossRefGoogle Scholar
- Ahmadi MA, Shadizadeh SR, Shah K, Bahadori A (2018) An accurate model to predict drilling fluid density at wellbore conditions. Egypt J Pet 27(1):1–10. https://doi.org/10.1016/j.ejpe.2016.12.002 CrossRefGoogle Scholar
- Aird P (2019) Deepwater pressure management. In: Deepwater drilling: well planning, design, engineering, operations, and technology application, pp. 69–109. https://doi.org/10.1016/B978-0-08-102282-5.00003-X CrossRefGoogle Scholar
- Alexander DLJ, Tropsha A, Winkler DA (2015) Beware of R ^{2}: simple, unambiguous assessment of the prediction accuracy of QSAR and QSPR models. J Chem Inf Model 55(7):1316–1322CrossRefGoogle Scholar
- An J, Lee K, Choe J (2015) 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 from 20–22 October 2015. https://doi.org/10.2118/176093-MS
- Babu DR (1996) Effects of P-\(\rho\)-T behavior of muds on static pressures during deep well drilling—part 2: static pressures. In: Paper (SPE27419) SPE drilling and completion, vol 11, no 2. https://doi.org/10.2118/27419-PA CrossRefGoogle Scholar
- Bahiraei M, Heshmatian S, Moayedib H (2019) Artificial intelligence in the field of nanofluids: a review on applications and potential future directions. Powder Technol 353:276–301. https://doi.org/10.1016/j.powtec.2019.05.034 CrossRefGoogle Scholar
- Conn L, Roy S (2004) Fluid monitoring service raises bar in HTHP wells. Drill Contract 60:52–53Google Scholar
- 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 2007 SPE Latin American and Carribean petroleum engineering conference held in Buenos Aires, Argentina, 15–18 AprilGoogle Scholar
- Erge O, Ozbayoglu EM, Miska SZ, Yu M, Takach N, Saasen A, May R (2016) Equivalent circulating density modelling of yield power law fluids validated with CFD approach. J Pet Sci Eng 140:16–27CrossRefGoogle Scholar
- Fazeli H, Soleimani R, Ahmadi MA, Badrnezhad R, Mohammadi AH (2013) Experimental study and modelling of ultra-filtration of refinery effluents using a hybrid intelligent approach. J Energy Fuels 27(6):3523–3537CrossRefGoogle Scholar
- Furbish DJ (1997) Fluid physics in geology: an introduction to fluid motions on earth’s surface and within its crusts. Oxford University Press, New YorkGoogle Scholar
- Ghaffari A, Abdollahi H, Khoshayand MR, Soltani BI, Dadgar A, Rafiee-tehrani M (2006) Performance comparison of neural network training algorithms in modelling of bimodal drug delivery. Int J Pharm 327(1):126–138CrossRefGoogle Scholar
- Hemphill T, Isambourg P (2005) New model predicts oil, synthetic mud densities. Oil Gas J 103(16):56–58Google Scholar
- Hoberock LL, Thomas DC, Nickens HV (1982) Here’s how compressibility and temperature affect bottom-hole mud pressure. Oil Gas J 80(12):159–164Google Scholar
- Hussein AMO, Amin RAM (2010) 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, 31 July–7 August. http://dx.doi.org/10.2118/136974-MS
- Jorjani E, Chehreh CS, Mesroghli SH (2008) Application of artificial neural networks to predict chemical desulfurization of Tabas coal. J Fuel Technol 87(12):2727–2734CrossRefGoogle Scholar
- Kamari A, Gharagheizi F, Shokrollahi A, Arabloo M, Mohammadi AH (2017) Estimating the drilling fluid density in the mud technology: application in high temperature and high pressure petroleum wells. In: Mohammadi AH (ed) Heavy oil. Nova Science Publishers, Inc., Hauppauge, pp 285–295Google Scholar
- Kårstad E, Aadnøy BS (1998) Density behaviour of drilling fluids during high pressure high temperature drilling operations. In: Paper SPE 47806 presented at SPE/IADC Asia Pacific drilling technology conference, Jakarta, Indonesia, September 7–9, pp 227–237. http://dx.doi.org/10.2118/47806-MS
- Kemp NP, Thomas DC, Atkinson G, Atkinson BL (1989) Density modeling for brines as a function of composition, temperature, and pressure. SPE Prod Eng 4:394–400CrossRefGoogle Scholar
- Kronberger G (2010) Symbolic regression for knowledge discovery bloat, overfitting, and variable interaction networks. Ph.D. Dissertation. Technisch-Naturwissenschaftliche Fakultat, Johannes Kepler Universitat, AustriaGoogle Scholar
- Kutasov IM (1988) Empirical correlation determines downhole mud density. Oil Gas J 86:61–63Google Scholar
- Kutasov IM, Eppelbaum LV (2015). Wellbore and formation temperatures during drilling, cementing of casing and shut-in. In: Proceedings world geothermal congress 2015, Melbourne, Australia, 19–25 April 2015Google Scholar
- Lawson D, Marion G (2008) An introduction to mathematical modelling. https://people.maths.bris.ac.uk/~madjl/course_text.pdf. Accessed 10 June 2019
- McMordie Jr WC, Bland RG, Hauser JM (1982) 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 on September 26–29. http://dx.doi.org/10.2118/11114-MS
- Mekanik F, Imteaz M, Gato-Trinidad S, Elmahdi A (2013) Multiple regression and artificial neural network for long term rainfall forecasting using large scale climate modes. J Hydrol 503(2):11–21CrossRefGoogle Scholar
- Olden JD, Jackson DA (2002) Illuminating the “black box”: understanding variable contributions in artificial neural networks. J Ecol Model 154:135–150CrossRefGoogle Scholar
- Olden JD, Joy MK, Death RG (2004) An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data. J Ecol Model 178:389–397CrossRefGoogle Scholar
- Osman EA, Aggour MA (2003) 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. https://doi.org/10.2118/81422-MS
- Peng Q, Fan H, Zhou H, Liu J, Kang B, Jiang W, Gao Y, Fu S (2016) Drilling fluid density calculation model at high temperature high pressure. In: Paper OTC-26620-MS presented at the offshore technology conference Asia, 22–25 March, Kuala Lumpur, Malaysia, https://doi.org/10.4043/26620-MS
- Peters EJ, Chenevert ME, Zhang C (1990) 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. https://doi.org/10.2118/18036-PA CrossRefGoogle Scholar
- Politte MD (1985). Invert oil mud rheology as a function of temperature. In: Paper SPE 13458 presented at the SPE/IADC drilling conference, 5–8 March, New Orleans Louisiana. https://doi.org/10.2118/13458-MS
- Rahmati AS, Tatar A (2019) 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. https://doi.org/10.2516/ogst/2019021 CrossRefGoogle Scholar
- Salunda (online) Common problems with retort measurements. https://salunda.com/retort-measurements/. Accessed 07 May 2019
- Sidle B (2015) Flexible, single skin completion concept meets well integrity, zonal isolation needs. J Petrol Technol 67(11):32CrossRefGoogle Scholar
- Sorelle RR, Jardiolin RA, Buckley P, Barrrios JR (1982) 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, September 26–29. http://dx.doi.org/10.2118/11118-MS
- Tatar A, Halali MA, Mohammadi AH (2016) On the estimation of the density of brine with an extensive range of different salts compositions and concentrations. J Thermodyn Catal. https://doi.org/10.4172/2160-7544.1000167 CrossRefGoogle Scholar
- Tewari S, Dwivedi UD (2017) Development and testing of a NU-SVR based model for drilling mud density estimation of HPHT wells. In: Paper presented at the international conference on challenges and prospects of petroleum production and processing industriesGoogle Scholar
- Wang G, Pu XL, Tao HZ (2012) A support vector machine approach for the prediction of drilling fluid density at high temperature and high pressure. J Pet Sci Technol. https://doi.org/10.1080/10916466.2011.578095 CrossRefGoogle Scholar
- Watts MJ, Worner SP (2008) Using artificial neural networks to determine the relative contribution of abiotic factors influencing the establishment of insect pest species. J Ecol Inf 3:64–74CrossRefGoogle Scholar
- Xu S, Li J, Wu J, Rong K, Wang G (2014) HTHP static mud density prediction model based on support vector machine. Drill Fluid Complet Fluid 31(3):28–31Google Scholar
- Zamora M, Broussard PN, Stephens MP (2000) 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, 1–3 FebruaryGoogle Scholar
- Zhou H, Niu X, Fan H, Wang G (2016) 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. https://doi.org/10.2118/180573-MS
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