Real-time risk analysis method for diagnosis and warning of offshore downhole drilling incident

Journal of Loss Prevention in the Process Industries 62 (2019) 103933

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Real-time risk analysis method for diagnosis and warning of offshore downhole drilling incident

T

Shengnan Wua,∗, Laibin Zhanga, Jianchun Fana, Wenpei Zhenga, Yangfan Zhoua,b a b

College of Safety and Ocean Engineering, China University of Petroleum (Beijing), Beijing, China Beijing Municipal Institute of Labour Protection, Beijing, China

ARTICLE INFO

ABSTRACT

Keywords: Drilling incident diagnosis Risk warning Dynamic threshold Bayesian inference Probability analysis

Downhole drilling incidents in offshore oil and gas fields pose a threat to wellbore safety. Moreover, they are likely to develop into hazardous mishaps owing to delayed detection and false alarm. Real-time risk diagnosis and warning analysis are of substantial importance to gain time for reconstructing the wellbore pressure balance and thereby improve the well-control safety at an early stage. This paper presents a method for comprehensively analyzing the drilling parameters and data to estimate drilling downhole risk in real-time. The relative difference is introduced to capture dynamic characteristics for quantifying the trend evolution of the drilling data. The method involves models for determining the dynamic safety thresholds to diagnose downhole incidents. Further, it imparts the capability for preventing measurement errors and unapparent trends caused by ambiguous data. This approach is based on the Bayesian inference theory and incorporates the Gaussian rules to handle uncertainty issues and reduce false alarm rates. In contrast to previous works, the non-linear dependence of the drilling parameters is considered for the warning probability estimation. Case studies that were focused on lostcirculation incident for an offshore field well are used to illustrate the feasibility of the proposed method and to demonstrate that three alarm-levels based on risk propagation can be triggered rapidly for decision-making.

1. Introduction Offshore drilling activities have been challenging owing to the technological and operational complexities in conjunction with harsh ocean environment as well as the risk of delays (Sule et al., 2018). A major contributor to drilling delays is unforeseen abnormal downhole situation. In particular, for challenging drilling wells (e.g., narrow pressure margins at larger depths), downhole incidents such as mud loss to formation, influx of fluids from the formation to the wellbore, pipesticking, plugging of the drill bit, and drill string washout (Willersrud et al., 2015a; Wu et al., 2016) are of specific concern during the drilling process. The occurrence of these downhole incidents is likely to result in the loss of expensive productive time; moreover, a few of them are likely to develop into blowouts, particularly in an unbalanced regime. It is noteworthy that most wellbore incidents in the overbalanced regime do not result in a blowout. However, a few incidents such as differential pipe sticking and fractured formation may result in it if they culminate in an underbalanced scenario. Similar accidents exhibit the potential for causing severe casualties, environmental pollution, complete or partial loss of drilling facility and well integrity, as well as damage to reputation of corporations (Zhang et al., 2018a). Therefore, diagnosis of

∗

downhole incidents in real-time and prevention of false alarm can significantly contribute to the reconstruction of bottom hole pressure balance as well as reduction of the likelihood and impact of major accidents. Several studies have been conducted for detecting and diagnosing downhole incidents in drilling processes; they mainly used model-based leak or fault detection methods. Reitsma (2010) identified abnormal drilling events by inspecting the trends of annular discharge pressure and stand pipe pressure. A model related to gas kick detection and mitigation has been proposed on the basis of the switched control of the bottom hole pressure by manipulating the choke and back-pressure pump switches (Zhou et al., 2011). A model-based detection scheme for in-/out-flux quantification, localization, and mitigation, applying an adaptive observer has been presented (Hauge et al., 2013). An incident detection and isolation method based on residuals generated, using analytical redundancy relations was employed by Willersrud et al. (2015a); moreover, parameters have been estimated for diagnosing different drilling incidents (Willersrud et al., 2015b,c). However, to provide a reliable and early warning, it is necessary to conduct dynamic risk management and evaluate drilling downhole states in real-time. Numerous studies focusing on dynamic risk management by

Corresponding author. E-mail address: [email protected] (S. Wu).

https://doi.org/10.1016/j.jlp.2019.103933 Received 9 November 2018; Received in revised form 24 July 2019; Accepted 30 July 2019 Available online 31 July 2019 0950-4230/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Loss Prevention in the Process Industries 62 (2019) 103933

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integrating risk identification, assessment, prevention, and control related to offshore drilling have been reported (Abimbola et al., 2014; Adedigba et al., 2018; Paltrinieri and Khan, 2016; Paltrinieri et al., 2014). A dynamic risk method was tested and validated for kick detection and blowout prediction by Islam et al. (2017). Downhole monitoring techniques have been developed to observe deteriorating well conditions (Nayeem et al., 2016); moreover, mud logging warning signs have been applied (Ahmed et al., 2016) for early kick detection. The development of managed pressure drilling techniques has enabled an early kick detection method for decision-making (Karimi Vajargah and van Oort, 2015). Although advanced models have been developed, their complexity renders them impractical for real-time applications. Downhole incident alarm in real-time has been applied in the shale-gas well fracturing process through qualitative trend analysis (Zhang et al., 2018c). A real-time estimation technique coupled with a simplified transient two-phase model has also been presented for well control applications (Ambrus et al., 2016). The above-mentioned works have proposed several preliminary methods and provide effective knowledge for our work. However, a few challenges exist for their application in downhole abnormal situation analysis during offshore drilling phases: The main weakness is their incapability to perform real-time risk analysis with high accuracy. This is because of the high probability of delay in downhole detection caused by the flow variation of the fluid in a wellbore, which cannot be accurately reflected in real-time. Moreover, sensors with a slowly varying bias drift may give incorrect readings, or the collection of signals may be disturbed by noise. Conventional downhole abnormal incident detection relies only on the pit gain and the variations in the pump pressure as design approaches for process alarm; herein, any of them that exceed its predefined threshold activates the alarm. Similar methods are likely to result in a delayed alarm or false alarm; this renders it challenging for operators to assess the type of down-hole incident accurately and in a timely manner; thereby, the best opportunity to undertake corresponding measures to regulate them is likely to be lost. In addition, the non-consideration of the relationship between the cause of the downhole incidents and the characteristics of the data (e.g., high non-linearity and strong coupling) is also likely to increase the possibility of false alarm. Therefore, to improve the accuracy of down-hole incident diagnosis and reduce the rate of false alarm, a Bayesian-based artificial intelligence approach is proposed for real-time diagnosis and warning of downhole incidents during the offshore drilling process. In the related works on artificial intelligence techniques, substantial efforts have been undertaken for developing incident monitoring, diagnosis, and assessment in drilling areas (Guilherme et al., 2011; Morooka et al., 2001). Several typical approaches have been presented in the literature, such as neural networks (Behnoud far and Hosseini, 2017; Zhang et al., 2018b), support vector machines (Ebrahimi and Khamehchi, 2016), fuzzy approaches (Roisenberg et al., 2009), Bayesian approaches (Cai et al., 2014), and combinations of machine learning techniques (Ma, 2011). Bayesian networks (BNs) and dynamic BNs have been used to perform dynamic and quantitative risk analysis of offshore drilling operations by means of probability propagation (Abimbola et al., 2015; Bhandari et al., 2015; Khakzad et al., 2013; Zhang et al., 2018a). Among them, Abimbola et al. (2015) have, for example, proposed a BN-based risk model that considers potential scenarios for different pressure regimes. Object-oriented BNs integrated with the bow-tie model have been developed for quantitative risk analysis of drilling operations (Khakzad et al., 2013). Bhandari et al. (2015) applied a BN method to perform failure analysis of blowout events. However, few applications were devoted to the evaluation of the contribution of the process parameters and variables of oil and gas fields, particularly to integrate with multi-information in drilling downhole incident diagnosis and alarm. In addition, the uncertainty issues resulting from the inaccurate measurement and detection of downhole incidents are always omitted.

Therefore, this study presents a new framework for overcoming these limitations by applying the multi-information resulting from the parameters and their characteristics and by considering the effects of uncertainties for downhole drilling incident diagnosis and warning analysis. The main contributions of this study are as follows:

• Dynamic characteristics of the drilling process variables are cap• •

tured. Moreover, the dynamic upper and lower limits of safety thresholds are evaluated over time for diagnosing downhole drilling incidents in real-time. The detectability of minor variations in the process can be illustrated to reduce the measurement errors. The probability distribution in abnormal drilling states incorporating the Gaussian rules is estimated to handle the effects of uncertainty. The non-linear dependence of drilling parameters is considered for warning risk propagation. Multiple reliable variables are integrated for developing the risk warning model. The comprehensive risk index is introduced to reduce false alarm rates by using Bayesian inference and to trigger an early alarm for downhole drilling incidents.

The remaining paper is organized as follows: Section 2 presents a real-time risk diagnosis and warning framework for downhole incidents with the fundamental theory as well as detailed procedures, including the dynamic safety threshold construction and risk warning probability estimation. In Section 3, the proposed method is tested through a case study focused on lost circulation during drilling. Section 4 provides the conclusion and research perspectives of this study. 2. Proposed method In order to perform accurate and reliable real-time risk diagnosis and warning for downhole drilling incidents, a newly-proposed method based on Bayesian inference is specifically presented in this section. Trend analysis, dynamic threshold analysis, and probability-based warning are used to estimate the downhole drilling abnormal risk. The overall workflow is developed as shown in Fig. 1. 2.1. Downhole incident diagnosis Owing to the high risk and high cost of offshore drilling operations with high complexity and uncertainty, abnormal downhole incidents are a major concern. Similar incidents can be characterized by the variation trends of drilling process variables or parameters (Tang et al., 2019), which qualitatively describe the change behaviors (e.g. increasing, and decreasing) of real-time process-data over time. The drilling parameters that reflect the characteristics of the incidents are selected as the main abnormality parameters. In this section, a dynamic-safety-threshold-based model is introduced to diagnose the presence or absence of an abnormal event. The thresholds are obtained for the dynamic characteristics, guaranteeing the complete utilization of the monitoring data in the realization of real-time diagnosis. 2.1.1. Drilling process parameters Drilling process parameters (Nayeem et al., 2016) are mainly extracted from various sensors or measurement tools for real-time monitoring, to reflect the safety states of drilling operations. They are mainly divided into three categories: comprehensive logging parameters, drilling fluid parameters, and downhole pressure parameters (Fertl et al., 2002; Sun et al., 2018). A few drilling process parameters are listed in Table 1. Note that the abbreviation of the parameters is similar to those of field logging. Among these, MFO and MFI represent the mud flow out rate and the mud flow in rate, respectively; their variations provide the earliest indication of certain incidents (Speers and Gehrig, 1987). Mud flow out paddle (MFOP) is often used in the field, which is detected by the paddle type flow meter, indicating % of flow. This sensor provides an early warning of either a kick condition or 2

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Fig. 1. Overall workflow of downhole drilling incident diagnosis and warning.

a loss of circulation. For lost circulation, as the mud leaks into the formation, the mud return is significantly reduced; occasionally, no mud returns. For the kick, owing to the abnormally high pressure of the formation or the intrusion of fluid into the mud, the quantity of mud in the wellbore keeps increasing. Drilling parameters that characterize downhole accidents can be generally divided into primary warning parameters and secondary warning parameters. The former represents the early signs of potential occurrence of an incident, whereas the latter is the lagging changes in the wellbore. Based on field experience and available literature (Tang et al., 2019), the variation trends of process parameters contribute to effective warning of downhole incidents and further to the prevention of the occurrence and escalation of these incidents. The main drilling parameters are selected as the warning indicators for different drilling downhole incidents, and the variation trends of the warning indicators are analyzed. A few of them are listed in Table 2. As another example, the lost circulation of a well in the drilling process is characterized by a reduction in primary warning parameters such as MFO, SPP, MFI and TV and an increase in secondary warning ones such as KHL and ROP. For drilling engineering, the most commonly used parameters for abnormal warning are MFO and TV. Monitoring of MFO can be achieved earlier than online TV for early warning of an incident; however, online TV prevents the likelihood of missed alarm in monitoring. Therefore, warning in real-time for drilling incidents is generally combined with two or more parameters in field applications as well as downhole pressure difference assessment. The key to preventing offshore drilling downhole incidents is to capture the dynamic variation behaviors of these parameters accurately and in a timely manner.

Table 2 Tendency of drilling parameters related to drilling downhole incidents. Downhole anomalies

Kick

Lost circulation

Primary warning

Secondary warning

Parameters

Tendency

Parameters

Tendency

MFO TV ROP WOB SPP MFO TV SPP MFI

Increase Increase Increase Decrease Decrease Decrease Decrease Decrease Decrease

MFI TQ

Constant Constant

KHL ROP

Increase Increase

2.1.2. Characteristics and trend analysis The dynamic characteristics of the corresponding process parameters are of the highest concerns for downhole drilling incident diagnosis. The analysis of characteristic parameters contributes to the identification of the abnormal variation trends to ensure accurate downhole incident detection. The characteristic parameters are selected based on qualitative trend analysis using statistics such as mean (μ), relative difference (r), standard deviation (σ), gradient (v), and autocorrelation coefficient (ρ). The characteristic extraction interval is determined by the variation trend of various types of downhole drilling incidents. For lost circulation and well kick, it is necessary to analyze the trends and characteristics of the data over a period of time. For a downhole abnormal event such as an abrupt rupture or a puncture in the drilling tool, a marginal amount of data is required in a short time

Table 1 A few drilling process parameters. Drilling parameters

Abbreviation

Units

Drilling parameters

Abbreviation

Units

Stand pipe pressure Rate of penetration Weight on bit Torque

SPP ROP WOB TQ

MPa ft/h kN ft·lbf

Total volume of pit Mud flow out rate Mud flow in rate Hook Load

TV MFO MFI HKL

m3 m3/h m3/h kN

3

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Fig. 2. Risk warning model based on Bayesian inference. SI

={

m,

m 1,

, i,

, 1}.

(1)

Similarly, the dynamic characteristics in an LI can be obtained using this method. 2.1.3. Construction of dynamic safety threshold model The timeliness and accuracy of downhole abnormal incident diagnosis cannot be guaranteed only by assessing whether the anomalous change in the relevant drilling parameters exceeds the thresholds based on experience. Therefore, the dynamic-threshold-based model (Abid et al., 2009) is introduced to prevent this limitation and to remove the defects of different criteria owing to differences in geology and wellbore conditions. Such a method can calculate the dynamic safety thresholds of the drilling process parameters expressed by the actual well depth and geology conditions. A characteristic value of the parameter that is larger than the upper limit of the threshold or less than the lower limit of the threshold indicates the occurrence of downhole incidents. Therefore, a function of dynamic safety thresholds is proposed; moreover, the dynamic upper limit value (RDU ) and the dynamic lower limit value (RDL ) are expressed as

Fig. 3. Workflow of data preprocessing based on 3σ rules.

RDU =

for assessment. Therefore, according to the type of the downhole incident, the data window is categorized as either long-term or short-term one. The downhole risk detection should integrate characteristic parameters and extraction intervals into the downhole drilling abnormal diagnosis. In order to improve the reliability of downhole drilling risk identification, different characteristic parameter models can be assigned according to long-term and short-term data. The long-term data, denoted as LI, is divided into n short-term data (SI), i.e., LI = {SIn, SIn 1, , SIi, , SI1} . Each SI is divided into m intervals (IT), namely, SI = {ITm, ITm 1, , ITi, , IT1} . When the characteristic parameters in an ITi are expressed as (µi, ri, i, vi, i) , the dynamic characteristics in an SI, denoted as (µSI , rSI , SI , vSI , SI ), are expressed as

µSI = {µm , µm 1,

rSI = {rm, rm 1, m,

, ri,

, 1};

vSI = {vm, vm 1,

, vi,

, v1};

n i=1

R (ti )

n

1+

RU 100

(2)

1

RL 100

(3)

F(RDU ) = RDU

R (ti )

(4)

F(RDL) = R (ti )

RDL

(5)

If F(RDU ) < 0 , implying that the drilling process variable is higher in value than the dynamic upper limit, the drilling state is determined to be abnormal; if F(RDL) < 0 , implying that the drilling process variable is less in value than the dynamic lower limit, the drilling state is again determined to be abnormal.

, r1};

, i,

R ( ti )

n

where R (ti ) is the value of the drilling process variable at time ti , RU is the percentile value of the upper limit, and RL is the percentile value of the lower limit. The judgment function of the dynamic upper and lower limits of the dynamic safety thresholds is

, µ1};

m 1,

SI

={

, µi ,

RDL =

n i=1

4

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Fig. 4. Comparison of data preprocessing.

2.2. Risk warning model

and indicate the potential presence of an incident. The probability distribution presenting the abnormal event Ai under an indicator rk exceeding its threshold is defined as (Jaramillo et al., 2017)

In this section, a risk pre-warning model is proposed to overcome the additional limitation posed by false alarms caused by the thresholdbased algorithm in the assessment of downhole incidents in real-time. Therefore, a Bayesian-based probability analysis algorithm is introduced to quantify the diagnosis process and improve the warning accuracy.

P (Ai r k ) =

P (r k Ai ) P (Ai ) P (rk )

(6)

2.2.1. Bayesian inference

where A1, A2, ⋯, AN represent all the feasible states present in the system and P (Ai) is the prior distribution of Ai. Considering that a set of K indicators R = {r1, r2,⋯, rK} trigger their respective warnings, the probability distribution is expressed as

(1) Overview of Bayesian inference

P (Ai R) =

Bayesian inference (Cai et al., 2019), has been commonly applied by multiplying the prior by the likelihood function to obtain the posterior probability distribution, considering the uncertainty inherent in the data. Compared with other artificial intelligence methods, Bayesian reasoning exhibits the advantages of rapid parameter learning, which can effectively guarantee the objectivity and accuracy of the simulation with respect to the actual environment. It permits the update of random variables when new data is available, using a mathematical process (Liu and Callies, 2019). The process starts with a specified probability distribution. The prior distribution represents a population of feasible parameter values, which may be selected or estimated based on specified initial observations of the random variables and subjective knowledge. The posterior distribution is a compromise with reduced uncertainty, between the prior information and new information, after being integrated to update this prior distribution. If the system presents an abnormal state Ai, there should be at least one indicator rk that will cross a threshold value to trigger a warning

where P (R Ai ) represents the likelihood function of feasible states and the corresponding indicator. For the purposes of the proposed model in this paper, the Bayesian-based algorithm considers multiple types of states as well as several indicators. The likelihood functions are central to the Bayesian inference algorithm, which is expected to describe the probabilistic information about the indicators and to model uncertainties in combination with the evidence gathered. The parameters of the likelihood function may be treated in different ways, ranging from experimental tests or historical condition monitoring to maintenance data. Given the indicator rk and state Ai, the likelihood function is

P (R Ai ) P (Ai ) P (R )

(7)

K

P (R Ai ) =

P (rk Ai ) k=1

(8)

The maximum posterior hypothesis of the abnormal state Ai given R under the most probable hypothesis a ∈∅ can be expressed as 5

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Fig. 5. Variance trends of main process parameters MFOP, MFI, SPP, and TV.

Fig. 6. Relative differences of main process parameters MFOP, MFI, SPP, and TV.

6

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deviation of x. Then, the probability estimation process is to obtain the corresponding probability value by inputting the observation values of X under the condition of acquiring the mean and standard deviation. For a Bayesian application consisting of multiple real-valued random variables following a Gaussian distribution, the probability calculation process is complex and requires a high constraint. The twodimensional Gaussian distribution (Koljonen et al., 2007) is illustrated as an example with two expectation values (μ1, μ2), two standard deviations (σ1, σ2) and a correlation parameter (ρ); the cumulative distribution function of multiple variables is expressed as follows:

Table 3 Percentile values of partial drilling parameters. Parameters

Amplitude

Percentile values

Mean

Upper limit

Lower limit

MFOP MFI SPP TV

5 6 2 2

10% 5% 10% 4%

50 115 20 50

55 121 22 52

45 109 18 48

(Ai ) = argmax P (Ai R ) = argmax a

a

P (R Ai ) P (Ai ) = argmax P (R Ai ) P (Ai ) P (R ) a

(9)

F (X , Y ) =

2.2.2. Risk warning analysis

In general, when the detected variables are adequately large, it is effective to assume a normal distribution or lognormal distribution. The Gaussian rule (also known as normal distribution) (Liu et al., 2017) is a commonly used continuous variable distribution for estimating the probability; moreover, the multi-class statistical distributions are evolved from it. In similar models, the mean and standard deviation are also considered, and these parameters can be updated by new information with reduced uncertainty. For Bayesian application consisting of a single real-valued random variable X following a Gaussian distribution, the cumulative distribution function of X is expressed as

F (x ) =

f (x µ ,

2)

=

2 ) dt

f (x µ ,

1 2

2

= P (X

exp[ (x

x)

µ )2/2 2]

y

f (x , y µ , v ) dxdy = P (X , Y )

f (x , y µ , v ) = f (m µ , v ) 1 = exp (2 )2 det v

(1) Gaussian-based probability estimation

x

x

1 (m 2

T

µ) v

(12)

1

(m

µ)

(13)

where x and y represent the observed values of X and Y, µ is the expectation vector of m = (x , y ) , v is the covariance matrix (v =

2 1

1 2

1 2 2 2

), and

=

cov(X , Y ) 1 2

. The probability density function

of the multidimensional Gaussian distribution can be obtained by parameter estimation for the expectation vector and the covariance matrix. (2) Construction of risk warning model

(10)

The proposed model integrated with multiple information is aimed at optimizing the system design and at improving the accuracy of abnormal incident detection for decision-making. First, the data needs to be preprocessed to remove the coarse error points; secondly, the processed data is subjected to characteristic calculation for merging data and features by using weighting factors; finally, the decision is made (Fig. 2).

(11)

where f (x µ , is the probability density function, x represents the observed value of X, µ is the mean value of x, and is the standard 2)

Fig. 7. Dynamic-safety-threshold-based diagnosis for lost circulation. 7

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Fig. 8. Probability distribution under main process parameters MFO, MFI, SPP, and TV.

Fig. 9. CRI for lost circulation warning.

After the drilling parameter data is preprocessed, a weighted average method is used for risk warning by integrating weighting factors into multiple information (Ben Abdessalem et al., 2018). A similar method can prevent large errors caused by a single parameter-based drilling incident warning. Certain non-linearly distributed continuous variables may be approximately expressed as a superposition by introducing multiple distribution models to replace the single Gaussian distribution model. This implies that it can be linearly superimposed with a certain proportion through multiple Gaussian distributions. Let a variable be expressed as the weighted sum of m sub-Gaussian distributions with mean µm , standard deviation m , and weight m . The

Gaussian distribution for the non-linearly distributed variables is expressed as follows: M

G=

mN m=1

(R µm ,

m)

(14)

where m = 1. In this study, two types of states are used to describe the events in the drilling process: steady working state (W) and abnormal state (A). The probability satisfies P(W) = 1 P(A) . Therefore, the probability in the abnormal state given the process variable R is expressed as 8

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Fig. 10. Incident diagnosis using dynamic lower limit of TV with different percentile values.

Fig. 11. CRI of proposed method given abnormal drilling state following different rules.

P (A R ) =

P (R A ) P (A ) P (R A) P (A) + P (R W ) P (W )

3. Case study

(15)

In this section, the proposed method is applied to the lost circulation scenario of a field-well during drilling phases. When the drilling reached the well section at a depth of 9,383–9,410 ft, mud loss occurred under the equivalent circulating density of 15.6 ppg. The dynamic loss rate was approximately 10 bbl/h; it increased to over 50 bbl/h, and ultimately there was a complete loss without return. In this case, the data was recorded every 5 s, and tracks were derived from the selected drilling period from 20:20:07 to 22:34:57 on the day of the incident for incident diagnosis and warning in the early stage. The main drilling process parameters related to the lost circulation incident (including MFOP, MFI, SPP, and TV of the pit) are considered.

Assume that the working state and abnormal state of the drilling process given variable R follow Gaussian rules. According to Bayesian inference, if the variable R in the working state is distributed normally with mean μ and variance σ2, denoted as N(R|µ, 2) , and the R in the abnormal state follows Gaussian distribution with mean μ + jσ and variance σ2, denoted as N(R|µ + j , 2) , the risk probability of downhole drilling incidents given the variable R can be calculated based on Eq. (15). A comprehensive risk index (CRI) is introduced and calculated by assigning different weighting factors (w1, w2, ⋯, wk) to different variable probabilities. The CRI value is between zero and one, and it represents the different risk levels of downhole drilling incidents.

3.1. Trend analysis

K

CRI =

k P (A k=1

where

k

Rk )

Considering the influence factors such as sensors, its installation, and downhole operating conditions, there is likely to be a coarse error in data acquisition, i.e., severe deviations from most of them are likely. If the individual data with coarse error values may be outside the range

(16)

= 1. 9

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of normally acceptable fluctuation, or if that with coarse error values may be outside the range of abnormally unacceptable fluctuation, it will cause the phenomenon of false alarm or missing alarm. In order to satisfy the requirements of high-precision data processing and rapid calculation, a coarse error elimination algorithm based on 3σ rules is introduced. The data preprocessing workflow is shown in Fig. 3. Taking the data of MFOP as example, the data reprocessing result is shown in Fig. 4. In this case, when the sliding window length is set to 16 min, sections of the data with coarse errors can be successfully removed using the elimination algorithm based on 3σ rules. Fig. 5 shows the variance trends of the real-time data for four drilling process parameters. The solid blue, red, green and pink lines represent the original data. The black line (for MFOP) is the data smoothed by applying the Rloess method with spans of 5 min. It is observed that a similar tendency can be approximately divided into two stages: stable stage under normal conditions and varying stage under abnormal conditions. An apparent MFOP decrease could be observed at approximately 22:00; however, there is certain fluctuation in growth at another time. The abrupt decreases in MFI and SPP three times also increase the uncertainty of the incident occurrence. Note that the change in the TV of the pit first decreases and then increases gradually. During the drilling phases, there are certain fluctuations in the drilling data owing to downhole complexity and uncertainties. However, not all fluctuations are signs of downhole incidents. Therefore, in order to identify the local fluctuations from long-term variation trends of the process variables, the features of the data need to be calculated. The relative difference r represents the difference between the observed values and the steady state value; moreover, a similar characteristic is used to illustrate the trend of the drilling data. r can be expressed as

r=

n j

x (ti ) n j

these from the relative difference. Such diagnosis contributes to the analysis of the range of risk caused by lost circulation. Note that false alarm also ceases during diagnosis. For example, the alarm of the detected parameter MFOP will be triggered at approximately 20:56 using this algorithm; however, this result is not mentioned in the drilling report. 3.3. Risk warning analysis In order to reduce false alarm, the comprehensive risk for well lost circulation is evaluated in real-time. The probability distribution based on Gaussian probability theory, among the characteristic parameters following N(R|µ + 3 , 2) is calculated as shown in Fig. 8. It is evident that the probability in the MFOP increases from approximately zero to 99.9% at approximately 21:55; this may be regarded as a significant reference for risk warning. Meanwhile, those of the other parameters can be approximately estimated with the maximum value of 80%. Compared with the diagnosis results, the probability analysis provides engineers with additional information and prevents false alarm. By applying the prior probability distribution and likelihood function based on Bayesian inference, the posterior one for lost circulation is determined with the specified weight vectors m = {0.38, 0.18, 0.18, 0.26} . Using the proposed model, the probabilitybased risk warning for lost circulation is performed by integrating with multiple information, as shown in Fig. 9. The results reveal that three risk warning levels are specified, with the total probability attaining 0.3, 0.6, and 0.9, respectively. When the first alarm (level 1) is triggered at approximately 21:01, the causes and dynamic loss rate need to be verified without interrupting the drilling operations. The incident is detected when the total probability attains 0.6 at approximately 21:16, and an alarm should be started. The drilling system should be operated to examine the actual loss situation and then to take precautionary measures (e.g., plugging) in the early stage to prevent deterioration of the incident. When the third alarm with the probability of 0.9 is raised, the relevant emergency measures should be implemented in order to mitigate the accidents. The effect of real-time risk warning is significantly improved compared with the field detection at approximately 21:30–22:00. An early previous warning of lost circulation during the drilling operation will provide the premise and foundation for preventing and managing lost circulation.

x (t j )/ n

x (t j )/ n

(17)

Fig. 6 shows the variation trends of the relative difference for four drilling process parameters. A comparison of the real-time date of MFOP, MFI, SPP, and TV reveals two peak values for acquiring more accurate positioning information regarding lost circulation; these are likely to occur at approximately 21:22 and 21:56, based on relative difference. Note that the first peak for MFOP is not apparent whereas there is another peak at approximately 21:03 for TV. This implies that under the influence of different types of parameters and the quality of data, the occurrence time of lost circulation from TV is not consistent with that from the other parameters. Therefore, the integrated method is necessary to increase the reliability of the assessed results.

3.4. Discussion In the above method, two major factors can influence the diagnosis and warning results of downhole lost circulation: the percentile value of thresholds and the different distribution followed by abnormal states. Other factors such as weighting factors, sliding window size for data reprocessing, and data with different noise levels are out of the scope of this discussion owing to their negligible effects. It is important to note that the different well locations, the formation conditions, and the interference of operation procedure may affect the final diagnosis of drilling incidents. In particular, lost circulation is more likely caused by these special geological conditions or weak formations such as the very light gray and low-density limestone reservoir with narrow drilling fluid density window, as well as multiple pressure systems in the vertical direction. Therefore, this section only discusses the factors of a given well section. A low percentile value of the upper and lower limits of the thresholds results in early warning; however, it can also increase the risk of false alarm. A high value results in delayed detection and brings the risk of missed alarm. Using the dynamic lower limit of the parameter TV for assessing downhole incidents, the results are compared to investigate the influence of this factor with percentages of 1%, 2%, 4%, 8%, and 12% on the final diagnosis, as shown in Fig. 10. It is observed that the detection time is likely to be delayed by approximately 12 min with a higher percentage (12%), whereas a lower

3.2. Downhole incident diagnosis In order to improve the detection accuracy, a dynamic-safetythreshold-based model is introduced to diagnose the lost circulation incident in real-time. The thresholding model for applying different variables generally exhibits the limitation of the actual formation conditions and well structure; moreover, the percentile values of the drilling process parameters in the target well section are recommended based on field experience and statistics, as listed in Table 3. The values of the mean, the upper and lower limit values related to the four drilling process parameters are calculated by considering the percentage value under the steady drilling conditions, as listed in Table 3. Using Eqs. (2)–(5) mentioned in Section 2.1.3, the dynamic upper and lower limits of the safety thresholds are determined, and the assessment results are shown in Fig. 7. A trend analysis reveals an apparent decrease; the dynamic lower limits of the safety thresholds for the four parameters are used for incident diagnosis. Considering MFOP as an example, it is evident that F (MFOP-DL) < 0 indicates a likely risk of well lost-circulation. We also notice that the warning time using MFOP, MFI, SPP, and TV is different, and the results keep constant with 10

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percentage (1%) is likely to result in an earlier detection (approximately 4 min). The time delay or early detection is completely based on the percentages of the lower limit determined by the field conditions and on-site experience. For the cases in the result section, a universal percentage of 4% is suitable for applying TV. Note that the corresponding percentages can be updated given new observations and evidence in drilling. To test the effect of the different distributions followed by abnormal states on the model performance, several cases with different means (μ + 2σ, μ + 2.5σ, μ + 3σ, μ + 3.5σ, μ + 4σ) are assumed. A new distribution followed by abnormal states is established for risk warning analysis and is shown as in Fig. 11. Overall, when the warning time of different levels increases with distribution assuming the smaller mean, the algorithm provides a false alarm at approximately 20:50 for level 1. Similarly, whereas it decreases with distribution assuming the larger mean, the algorithm provides a delayed alarm for level 1. The effects of the first three distributions are not significant when the warning level 3 is triggered.

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4. Conclusion A new method has been developed in this study for downhole drilling incident diagnosis, as well as the risk warning in real-time. In the method, the dynamic characteristics are captured using the relative difference for trend analysis; moreover, the dynamic upper and lower limits of the safety thresholds are calculated to diagnose the drilling incidents in real-time. Furthermore, the risk probability distribution based on a Bayesian inference algorithm enables downhole incident warning at an early stage. The proposed method focused on field lost-circulation incident has been applied to a specific offshore drilling well and exhibited reliable performance. The trend analysis verifies the acquisition of more accurate positioning information on lost circulation. The combination of dynamic-threshold-based diagnosis and Bayesian estimation can effectively reduce false and missing alarm rates. The integration with multiple detection parameters can provide comprehensive warning levels as well as increase the reliability of the estimated probabilities, facilitating the timely mitigation of drilling downhole incidents. These results also indicate that the proposed method is a reasonable starting point in downhole diagnosis during the drilling process; furthermore, it can be integrated into a real-time monitoring and alarm device for field decision-making. Future work can be carried out in the following directions. This model can be developed using a fitting algorithm with high precision and low error characteristics for instantaneous prediction. It would also be more or less effective to consider the application of the model to other systems that emphasize timeliness, such as real-time production and overwork system. Acknowledgment This research is supported by Natural Science Foundation of China (No. 51809277), the Fundamental Research Funds for the Central Universities (No. 2462019BJRC006), China Postdoctoral Science Foundation (No. 2018M641599), and the 111 Project (No. B18054). The authors are grateful for the Editor and reviewers' helpful comments. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jlp.2019.103933. References Abid, M., Ding, S.X., Khan, A.Q., 2009. Dynamic threshold for fault detection in Lipschitz nonlinear systems. IFAC Proc. Vol. 42, 36–40.

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