The oil and gas industry needs to reduce the operational cost, and to be able to operate safely and sustainably in remote, vulnerable and hazardous areas. Motivating factors include better planning of the well to be drilled, remote control of heavy machinery, removing personnel from hazardous areas, better understanding of the drilling process, and increasing safety for personnel and the environment. However the one important aspect of preventing developments in the drilling industry is that information from the downhole has been very limited. Limitations in the amount and quality of data from downhole adversely impact health, safety and the environment (HSE) and drilling efficiency. Today, information is available only from the near bit area of the drill string via mudpulse telemetry^{[1]}, which by its nature has several disadvantages, i.e., transmission rate as low as
Wired drill pipe (WDP) technology^{[24]} has been described as a gamechanger for the oil and gas industry. It has the ability to deliver highresolution data to the surface which can substantially improve realtime decision making, enable precise control of the drilling process by closing the control loop between surface and downhole equipment, and provide visibility of wellbore conditions along the drill string for drilling operations including tripping. The development of WDP technology has been motivated by the need to have more and better data from the near bit area and along the drill string in realtime. WDP technology has allowed sensors including temperature sensors, pressure sensors and many more to be discretely positioned along the drill string, presenting new opportunities for the direct measurement of drilling parameters, that were previously only discernible by semirealtime models, surface response characteristics, or were directly recorded to memory for subsequent post section analysis. The measurements provide a high frequency feedback to the realtime drilling models which help the drillers construct an overview of the downhole conditions. WDP has been field tested in more than
Nevertheless, one challenge raised with WDP is the data quality. Because of the nature of the sophisticated conditions in the wellbore, the sensors are inevitably exposed to the environmental effects like noises, tear and worn, possibility of sensor drifting, requirement of recalibration, transmission errors, etc. Data received from WDP are not necessarily always in good quality. It has been long recognized that poor data quality is hampering the attempts to make use of them in integrated planning, burden collaborative environments and the whole operation workflow. In light of this, many attempts have been made to reduce and eventually eliminate the effects of the poor quality data in order to achieve better decision making and more efficient drilling operations^{[913]}.
In this paper, an advanced technology, data validation and reconciliation (DVR)^{[14]}, has been applied to improve WDP data quality. In practice, the measurements (temperature, pressure, flow rate, stress, strain etc.) themselves are inevitably subjected to measurement errors, usually classified as random, systematic and gross. These errors often affect the results of the measurements. The data validation means improving the quality, achieved in particular by elimination of gross and compensation of systematic errors, and minimizing the influence of random errors. A fundamental method applied to the validation of data is their reconciliation to make them consistent to the mathematical models. Data reconciliation is usually performed by minimizing a leastsquares objective function subject to model equations, which come from maximum likelihood formulations and the assumption of normal error distributions. Such model equations range from simple material, component, and energy balances to full models involving all system variables and parameters. A more detailed background review on the DVR technique and its variants can be found from the recent work^{[15, 16]}. In this paper DVR has been applied to improve WDP data quality by using the data redundancy of the mathematical models (fluid density model, fluid temperature model and friction model) as the source of information to calibrate the measurement data (downhole pressure) and calculate the unmeasured drilling parameters (density, friction factor and heat transfer coefficient) simultaneously.
2 Wired drill pipe technologyUp to now and in a reasonably long period into the future, mud pulse telemetry (MPT) is and still will be the most commonly used technology in oil and gas industry. The advantages include low cost in design, production, commissioning and maintenance, and good adaptability to deep wells (up to
WDP technology has the ability to provide immediate access to the downhole measurements at a transmission rate of
The networked drill string data provided by WDP, together with advanced wellbore models can bring a lot of benefits to realtime drilling process^{[6, 10, 11, 1821]}. Most benefits are listed as below
1) Reinforce well control procedure (more information to detect kick volume, location, etc.)
2) Enhance managed pressure drilling operation
3) Strengthen equivalent circulation density management
4) Identify lost circulation or influx zone
5) Monitor annular pressure fluctuations
6) Monitor hole cleaning efficiency and hydraulics (for instance, cuttings loading distribution)
7) Detect drilling problems in early phase conditions, such as stuck pipe, pack off, washout, leakage, etc.
Three different placements of multiple WDP sensors during the deployments are summarized^{[20]}: sensors concentrated in the open hole, sensors biased towards the open hole with some coverage inside casing, and sensors spaced evenly along the drill string. The third placement has high capacity to monitor cutting solids movement along the whole annulus, to evaluate hole cleaning performance, to detect variations from the normal and indicate the location of events quickly.
Compared to MPT the most criticized feature of WDP is its cost during the life cycle. However we shall also see that WDP enables the next generation of downhole measurements which can reduce potential nonproductive time. In ^{[8]},
The performance of WDP can be summarized in the following three points^{[11]}:
1) Data transmission time. Compared with MPT, WDP has
2) Network maintenance. Compared with MPT, WDP has
3) Higher drilling performance.
So even though WDP requires a high cost for implementation, cost savings can be achieved in terms of shorter telemetry time, less maintenance, higher drilling performance, earlier and easier fault detections, better visibility and enhancement of automated drilling. Furthermore, a second generation of WDP with more stable, robust and reliable network system is developed^{[10]}. It is anticipated to further lower the investment cost and improve costeffective deployment. More practical developments related to optimal position of distributed sensors, improve level of accuracy and investigate possible drilling scenarios are next steps for consideration.
3 Mathematical models 3.1 Drilling fluid density modelDrilling fluid serves as the first line of providing hydrostatic pressure to prevent fluids in the formation from flowing into the wellbore, removing cuttings from the wellbore, suspending and releasing cuttings, cooling, lubricating and supporting the bit and drilling assembly and ensuring adequate formation evaluation, etc. Close monitoring of the properties of drilling fluid can help rigsite personnel make decisions, for instance, provide early warnings of some potential well control problems.
The density of drilling fluid determines the hydrostatic pressure and is the basis for controlling formation pressure. A too high mud density can lead to lost circulation and differential sticking, while a too low mud density can result in well cleaning problems, kick and wellbore instability. Continuous evaluation of the mud density, where the mud flows in the drill string and out in the annulus, is thereby of critical importance. The more the information of the mud density along the drill string, the better the drillers understand the downhole situation.
When drilling operation starts, the drilling fluid is subjected to increasing pressure and temperature. While the higher pressure increases the drilling fluid density, the increased temperature results in the mud density reduction. The accurate knowledge of the behavior of the drilling fluid density is necessary as the wellbore pressure and fluid temperature change along drillpipes. From Fig. 1, it is easily known that pressure and temperature have a major impact on the density. Neglecting the effect of temperature and pressure on fluid density especially for high pressure and high temperature (HPHT) wells, can yield wrong estimation of density, further in turn the erroneous bottom hole pressure estimation. The fluid density model may be written as, see^{[22]}
$ \begin{equation} \rho=\rho~(P, T) \end{equation} $  (1) 
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Fig. 1. Density as a function of pressure and temperature where the water based mud is used in Section 5 
where
$ \begin{equation} \rho=\rho_0+\frac{\rho_0}{\beta}(PP_0)\rho_0\alpha(TT_0)\label{density} \end{equation} $  (2) 
where
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Fig. 2. Illustrating the differences between the true density measurements and values calculated from the linearized density model 
While drilling with aerated fluids such as air, mist and/or foam, the density model can be expressed as^{[25]}
$ \begin{equation} \rho_f = \alpha_f\rho_g+(1\alpha_f)\rho \label{density_f} \end{equation} $  (3) 
where
$ \begin{equation} \rho_g = \frac{PM_g}{Z_gR_gT} \label{density_g} \end{equation} $  (4) 
where
$ \begin{align} \rho_f = &\frac{\alpha_fPM_g}{Z_gR_gT}+(1\alpha_f)(\rho_0+\frac{\rho_0}{\beta}(PP_0) \nonumber\\&\rho_0\alpha(TT_0)). \label{density_all} \end{align} $  (5) 
During conventional drilling, heat is transported from the formation up to the surface. Drilling fluid temperature information is essential for modeling and is significantly related to mud density, mud viscosity and other fluid parameters influenced by temperature. Knowledge of fluid temperature is important for prediction of the bottom hole pressure, cuttings transport, drillstring deformation and interpretation of well kicks as mud ballooning is caused by temperature^{[26]}. Hydrostatic pressure increases while cooling the circulating fluid^{[27]} as in this case liquid expands due to the increase of amount of applied heat. Thermal expansion of drilling fluid can be significant in HPHT wells and also in deepwater wells. Circulating fluid temperature depends on numbers of factors related to fluid properties, geology and other, for instance, well depth, circulation rate, formation properties, thermal properties, temperature distribution of the surrounding rocks, mud properties, inlet mud temperature, circulation time and geometry of wellbore and drillpipe etc. Temperature modelling is important and essential for real time operating and monitoring as it can help to detect problems during well operations and for better prediction of drilling fluid and cement behavior.
Most of the investigation methods for fluid temperature modelling in the wellbore are based on Ramey
$ \begin{equation} T_a(z, t)=\alpha_a{\rm e}^{\lambda_1z}+\beta_a{\rm e}^{\lambda_2z}+g_GzBg_G+T_{sf}\label{temperature} \end{equation} $  (6) 
where
$ \begin{align} \lambda_1&=\frac{1}{2A}(1\sqrt{1+\frac{4A}B}) \end{align} $  (7) 
$ \begin{align} \lambda_2&=\frac{1}{2A}(1+\sqrt{1+\frac{4A}B}) \end{align} $  (8) 
$ \begin{align} A&=\frac{\omega C_{fl}}{2\pi r_cU_a}\left(1+\frac{r_cU_af(t_D)}{k_f}\right)\label{f_tD} \end{align} $  (9) 
$ \begin{align} B&=\frac{\omega C_{fl}}{2\pi r_dU_a} \end{align} $  (10) 
$\begin{align} \alpha_a&=\frac{(T_{in}+Bg_GT_{sf})\lambda_2{\rm e}^{\lambda_2D}+g_G}{\lambda_1{\rm e}^{\lambda_1D}\lambda_2{\rm e}^{\lambda_2D}} \end{align} $  (11) 
$ \begin{align} \beta_a&=\frac{(T_{in}+Bg_GT_{sf})\lambda_1{\rm e}^{\lambda_1D}+g_G}{\lambda_1{\rm e}^{\lambda_1D}\lambda_2{\rm e}^{\lambda_2D}}. \end{align} $  (12) 
In (9),
$ \begin{align} f(t_D)=&(1.1281\sqrt{t_D})\times(10.3\sqrt{t_D}), \nonumber\\&\text{if}~~10^{10}\leq t_D \end{align} $  (13) 
$ \begin{align} f(t_D)=&(0.406\, 3+0.5\ln{t_D})\times(1+\frac{0.6}{t_D}), \nonumber\\&\text{if}~~ t_D>1.5 \end{align} $  (14) 
where the dimensionless time,
$ \begin{equation} t_D=\frac{\alpha_ht}{r_c^2}\times 3\, 600 \end{equation} $  (15) 
and the thermal diffusivity is defined as
$ \begin{equation} \alpha_h=\frac{k_f}{\rho_fC_f}. \end{equation} $  (16) 
Table 1 summarizes all parameters introduced in Section 3.2. Most parameters involved in (6) can be measured or calculated. However, determination of overall heat transfer coefficients is appreciably difficult. Lots of research work has been done in determining overall heat transfer coefficients over the past decades. Semiempirical works were published to estimate heat transfer coefficients in annuli in terms of different fluid regimes^{[32]}. In general, the overall heat transfer coefficients depend on the resistances to heat flow through the flowing fluid, tubing metal, casing metal and the cement, etc. It can be expressed as
$ \begin{equation} \frac1{U_a}=\frac{1}{h_d}+\frac{r_d}{k_p}\ln(\frac{r_{do}}{r_d})+\frac{r_{d}}{r_{do}}\frac1{h_a}.\label{ua} \end{equation} $  (17) 
To calculate
$ \begin{equation} h_d=0.023\frac{k}{2r_d}(N_{REp})^{\frac{4}{5}}(N_{Pr})^{\frac{2}{5}} \label{ha} \end{equation} $  (18) 
where the Rayleigh number is a dimensionless number associated with buoyancy driven flow which is affected by fluid viscosity, flow rate and density
$ \begin{equation} N_{REp}=\frac{2\omega}{r_d\mu}.\label{REp} \end{equation} $  (19) 
Prandtl number is defined as the ratio of momentum diffusivity to thermal diffusivity. That is, the Prandtl number is given as
$ \begin{equation} N_{Pr}=\frac{C_{fl}\mu}k. \end{equation} $  (20) 
From the above discussion, the overall heat transfer coefficients are influenced by many factors, such as flow regime, flow rate, fluid density, viscosity, thermal conductivity, geometry of wellbore and drillpipe, etc. Its calculation mainly relies upon empirical data and is with high uncertainty and inaccuracy. In this paper, the overall heat transfer coefficient can be extracted with the help of multiple WDP sensors and data reconciliation method. It is a crucial factor to determine the heat energy transmission in the wellbore, to calibrate fluid temperature, hydraulic, torque and drag and rate of penetration models, and in turn to evaluate solid transports and thermally induced stresses in the wellbore and to enhance drilling performance for realtime operation and improve well planning for design phase.
3.3 Drilling fluid friction modelDuring circulation of drilling fluids, the pressure in the wellbore consists of two components, the hydrostatic pressure and the dynamic fluid pressure loss. The hydrostatic pressure
$ \begin{equation} P_{h}=\rho gL\cos(I)\label{hy} \end{equation} $  (21) 
where all related parameters are given in Table 2. Frictional pressure loss is a function of several factors:
1) Fluid rheological behavior and properties (e.g., viscosity, density, etc.),
2) Flow regime (laminar, transitional or turbulent flow),
3) Flow rate,
4) Wellbore geometry and drill string configuration.
It is generally regarded that frictional pressure loss is directly proportional to its length, the fluid density, the fluid velocity squared and inversely proportional to the conduct diameter. It is calculated from the Fanning equation^{[34]}
$ \begin{equation} P_{Loss}=\frac{2 f\rho v^2L}{D}.\label{loss} \end{equation} $  (22) 
In general, the friction factor
$ \begin{equation} f=\frac{P_{Loss}D}{2\rho v^2 L}.\label{ff} \end{equation} $  (23) 
The Reynolds number
$ \begin{equation} Re=\frac{Dv\rho}{\mu}. \end{equation} $  (24) 
Generally, the flow regime of a liquid changes from laminar to turbulent at a fairly welldefined Reynolds number value^{[35]}. For flow of a Newtonian fluid, the flow is considered laminar if the Reynolds number is less than approximately
Various types of WDP sensors can be used and placed along the drill string, including pressure sensors, temperature sensors, inclinometers, bending/vibration and rotation sensors, flowrate sensors and many more. Among them, pressure and temperature sensors that measure rapidly changing conditions may be particularly valuable, since it can easily and precisely monitor the change of downhole situation, for instance, wellbore/formation stability, equivalent circulation density measurements, wash out etc. Placing multiple sensors along the drill string establishes distributed measurements which vary with time and depth.
In this paper, according to the location of the sensors positioned along the drill string, we consider the downhole network system by dividing the annulus between the drill string and the wall of the borehole into a number of control volumes or segments (
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Fig. 3. Illustration of annulus with 
Between one segment, the pressure difference
$ \begin{equation} P_{h(j)}=\rho_{(j)}gL_{(j)}{\rm cos}(I_{(j)}), \quad \forall j=1, \cdots, n_s1. \end{equation} $  (25) 
The pressure loss
$ \begin{equation} P_{Loss(j)}=\frac{2f_{(j)}\rho_{(j)}v_{(j)}^2}{D_{a(j)}} L_{(j)}, \quad \forall j=1, \cdots, n_s1 \end{equation} $  (26) 
where
$ \begin{align} &v_{(j)}=\frac{Q}{A_{(j)}} ~~ \text{with}~~ A_{(j)}=\frac\pi4(D_{W(j)}^2D_{D(j)}^2) \end{align} $  (27) 
$ \begin{align} &D_{a(j)}=D_{W(j)}D_{D(j)}. \end{align} $  (28) 
Therefore, the pressure
$ \begin{align} P_{(j+1)}=P_{(j)}+P_{h(j)}+P_{Loss(j)}, \quad\forall j=1, \cdots, n_s1. \label{pressure} \end{align} $  (29) 
To be able to understand the complicated downhole processes, a certain amount of data is necessary. Fast and accurate decision making is also built on availability of qualitative data. As is known that WDP has the ability to provide a big amount of data in realtime. However, it does not necessarily mean improved understanding of downhole processes or better decision making. When the volume of data is beyond some limit, it creates confusion for the observer and reduces quality of decision making dramatically; see the discussion in [7]. As a result, more efforts should be made to understand and interpret the received data such as data interpretation technique and some new tools to increase a variety of available sensors for accuracy, diversity and observability of WDP technique.
4.1 Mathematical formulationDVR is an advanced technology which uses process information and mathematical methods in order to automatically correct raw measurements, estimate model parameters/unmeasured variables in industrial processes. The use of DVR allows for extracting accurate and reliable information from raw measurement data and produces a consistent set of data representing the most likely process operation. The interest of applying DVR techniques has started from 1980
In the general case, not all variables of the process are measured. The estimates of unmeasured variables as well as model parameters are also obtained as part of the DVR problem. Data reconciliation can be formulated by a constrained weighted least squares optimization problem, where the measurement errors are minimized with process model constraints. Given
$ \begin{align} \min\limits_{y^*, x}J(x, y^*)&=\sum\limits_{i=1}^n(\frac{y_i^*y_i}{\sigma_i})^2\label{cost} \end{align} $  (30) 
$ \begin{align} &\text{subject to}\nonumber\\ &f_m(x, y^*)=0 \end{align} $  (31) 
$ g_m(x, y^*)\leq0 $  (32) 
where
Pressure
$ \begin{align} &\min\limits_{P^*_{(j)}, \rho_{(j)}, f_{(j)}, U_a}J(P^*_{(j)}, \rho_{(j)}, f_{(j)}, U_a)=\nonumber\\ &\qquad\qquad\qquad \sum\limits_{j=1}^{n_s}\left(\left(\frac{P^*_{(j)}P_{(j)}}{\sigma_{P, j}}\right)^2 +\left(\frac{T^*_{(j)}T_{(j)}}{\sigma_{T, j}}\right)^2\right)\label{cost1} \end{align} $  (33) 
subject to
$ \quad P^*_{(j+1)}=P^*_{(j)}+P_{h(j)}+P_{Loss(j)}, ~~\forall j=1, \cdots, n_s1 $  (34) 
$ \quad P_{h(j)}=\rho_{(j)}gL_{(j)}\cos(I_{(j)}), ~~\forall j=1, \cdots, n_s1 $  (35) 
$ P_{Loss(j)}=\frac{f_{(j)}\times\rho_{(j)}\times v_{(j)}^2}{D_{a(j)}}\times L_{(j)}, ~~\forall j=1, \cdots, n_s1 $  (36) 
$ \begin{align} & \rho_{(j)}=\rho_0+\frac{\rho_0}{\beta}(P^*_{(j)}P_0)\rho_0\alpha(T_{(j)}T_0), \nonumber\\ &~~~~~~~~~ \forall j=1, \cdots, n_s1 \end{align} $  (37) 
$ \begin{align} & T^*_{(j)}=\alpha_a{\rm e}^{\lambda_1z(j)}+\beta_a{\rm e}^{\lambda_2z(j)}+g_Gz(j)Bg_G+T_{sf}, \nonumber\\ &~~~~~~~~~ \forall j=1, \cdots, n_s1 \end{align} $  (38) 
$ P^*_{(j)}>0, ~~\forall j=1, \cdots, n_s $  (39) 
$ T^*_{(j)}>0, ~~\forall j=1, \cdots, n_s $  (40) 
$ f_l<f_{(j)}<f_u, ~~\forall j=1, \cdots, n_s1 $  (41) 
$ U_{a, l}<U_a<U_{a, u} $  (42) 
$ \rho_l<\rho_{(j)}<\rho_u, ~~\forall j=1, \cdots, n_s1 $  (43) 
where
In this paper, only the steadystate models (2), (6) and (29) are considered. The main consideration is to employ data reconciliation method on steadystate models to eliminate gross errors, to minimize random errors, to compensate systematic errors and calibrate mathematical steadystate models. Therefore, models calibration, data postanalysis and model verification are our main purpose. Recently, in papers ^{[58, 36]}, a low order dynamic hydraulic model introduced by Stamnes et al.^{[37]} is used for parameters estimation and controller design for managed pressure drilling operation using WDP technology. In their work, dynamic data reconciliation methods (moving horizon estimation or its combination with extended Kalman filter) are used to determine the dynamic parameters, such as fluid density, friction factor and gas influx flow rate etc. The optimal annulus friction factor and density are fed to the controller for realtime operations. To feed all the required information into the dynamic model for controller design to manipulate drilling operational parameters, the dynamic data reconciliation method^{[9]} is more advantageous. More discussions about benefits and challenges of dynamic reconciliation methods are summarized in [9].
5 Simulations and discussionsIn the case study we use the NPSOL sequential quadratic programming algorithm to solve the DVR problem (33)
The simulated well is a simple vertical well with an initial depth of
The flow rate is shown in Fig. 4. The well and mud data used in the case study are shown in Table 3. Density measurement with respect to pressure and temperature is shown in Fig. 1. The disturbed pressure and temperature values along drill string are shown in Figs. 5 and 6. Color versions of Figs. 5 and 6 are available online. Some observations are made:
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Fig. 4. Flow rate 
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Fig. 5. Distributed temperature measurements 
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Fig. 6. Distributed pressure measurements 
1) Due to assumed incompressible mud, the pressure in the annulus increases with the depth and the flow rate during drilling. In this case an increase of
2) From Fig. 6, in the first
In order to make
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Fig. 7. Distributed pressure calculations via DVR 
From Figs. 6 to 8, pressures
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Fig. 8. Comparison of measurements before and after correction 
As the part of the solution, the unmeasured density pressures
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Fig. 9. Distributed density calculations via DVR 
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Fig. 10. Distributed friction factor calculations via DVR 
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Fig. 11. Overall heat transfer coefficient calculations via DVR 
In Fig. 1, it shows that the density is increased by approximately 3 kg/m
This paper presents WDP data quality control issues. Some overall conclusions are summarized as below:
1) Through an optimization approach, model parameters are refined based upon additional data from sensors along the drill string, provided by the networked drill string.
2) Including all parameters essential to the well and drill string system results in accurately reproducing actual drilling parameters.
3) The framework is used with respect to the networked pressure and temperature measurements.
4) This approach allows for both improving measurements and monitoring the downhole conditions.
5) Conditions of sensor malfunction and misscalibration of a sensor could be distinguished.
6) This proposed method has the capacity of distinguishing a sensor defect from a kick or other unwanted events.
7 Future workThe procedure used in this paper to calibrate pressure at a given sensor could extend to detect a malfunctioning sensor. A similar approach can be used to detect slowly developing problems in the wellbore, such as bad hole cleaning. Extending this to a full system for fault detection and event identification is a priority to the authors.
AcknowledgementsThis work is supported by University of Stavanger, Norway. The authors wish to thank SINTEF, the Center for Integrated Operations in the Petroleum Industry and the management of National Oilwell Varco IntelliServ for their contribution and support in publishing this paper.
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