WELLBORE STRING RUNNABILITY FOR DOWNHOLE OPERATIONS

Abstract

In some embodiments, a method comprises quantifying a condition of a wellbore into which a string is to be deployed, wherein quantifying the condition of the wellbore comprises, determining at least one geometrical parameter of the wellbore; and determining at least one mechanical parameter of the string that is caused by deploying the string downhole into the wellbore. The method also comprises determining a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

Description

BACKGROUND

During various stages of a wellbore, different types of strings may be needed downhole in the wellbore. Examples of such strings may include a drill string, a casing string, a wireline, a completion tubing, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure may be better understood by referencing the accompanying drawings.

FIG. 1 is an example chart of an overall string runnability in a wellbore, according to some embodiments.

FIG. 2 is a block diagram of an example data flowchart for determining string runnability in a wellbore, according to some embodiments.

FIG. 3 is an example Graphical User Interface (GUI) for monitoring string runnability in a wellbore, according to some embodiments.

FIG. 4 is an example chart of an overall condition of a tubing based on various factors, according to some embodiments.

FIG. 5 is a block diagram of a flowchart of example operations for determining an overall string runnability in a wellbore, according to some embodiments.

FIG. 6 is a block diagram of first example operations of a flowchart for estimation of a probability indicator between planned data, case-based data and real-time data, according to some embodiments.

FIG. 7 is a block diagram of second example operations of a flowchart for estimation of a probability indicator between planned data, case-based data and real-time data, according to some embodiments.

FIGS. 8A-8B are example graphical images charting depth versus a twist angle of a first wellbore and a second wellbore, respectively, according to some embodiments.

FIGS. 9A-9F are conceptual diagrams of different example configurations of strings positioned in wellbores, according to some embodiments.

FIGS. 10A-10D are conceptual diagrams of a wellbore with appearing and vanishing tortuosities, according to some embodiments.

FIG. 11 is a conceptual diagram of a stiff-string model, according to some embodiments.

FIG. 12 is a stiff-string model (for force balance at each node), according to some embodiments.

FIG. 13 is a graph that depicts a string and a through channel, according to some embodiments.

FIG. 14 is a conceptual diagram of an area of free tool passage for a straight tool, according to some embodiments.

FIGS. 15A-15C are conceptual diagrams of a string before and after loading into a wellbore, according to some embodiments.

FIG. 16 is a block diagram of a flowchart of example operations for comparing decomposed factors of a planned wellbore against the actual wellbore path in real-time, according to some embodiments.

FIG. 17 is a conceptual diagram of an example wellbore system, according to some embodiments.

FIG. 18 is a conceptual diagram of an example computer, according to some embodiments.

DESCRIPTION

The description that follows includes example systems, methods, techniques, and program flows that embody aspects of the disclosure. However, it is understood that this disclosure may be practiced without these specific details. In other instances, well-known instruction instances, protocols, structures, and techniques have not been shown in detail in order not to obfuscate the description.

Example embodiments relate to determining a wellbore string runnability (string runnability) for downhole operations. String runnability may be defined as the monitoring and forecasting of how well a string positioned in a wellbore can be run downhole during downhole operations. Examples of a string may include a drill string, casing string, production tubing, wireline, etc. Examples of downhole operations may include drilling, wireline, completion, production, etc. Also, the runnability of a string may be determined for one or more sections of a wellbore.

In some implementations, runnability of a string may be measured by the use of a comprehensive runnability index supported by real-time monitoring of multiple features with estimated indicators. The string runnability index may include combining at least one geometrical parameters of the wellbore with at least one mechanical parameter affected or influenced by operational parameters of downhole operations.

Thus, example embodiments may combine geometrical and mechanical calculations to provide an assessment of whether the string can be run without a short landing. Such an assessment may provide more opportunities for adjustments during different downhole operations (such as drilling). In general, the “smoothness” that connects the wellbore geometry and mechanical system may be related to the wellbore quality used to run the string. With real-time drilling parameters and complex equations, the runnability of the string may be assessed for a given size of a wellbore.

In some implementations, runnability metrics may be used to anticipate or diagnose other challenges such as complex stimulation work, artificial lift performance and possible well servicing complications that may arise because of unwanted curvature, wellbore torsion, wellbore drift, etc. Thus, example embodiments may predict the runnability of a string to the bottom of the wellbore while the wellbore is being drilled.

In some embodiments, any combination of wellbore tortuosity, wellbore torsion, wellbore profile energy, wellbore curvature passage through force, margin of slackoff force and overpull margin may support the evaluation of a proposed wellbore path to determine a string's runnability. Combining operational experience and trajectory metrics has proven to be effective in assessing operational risk for tasks like running a string in curve construction sections or to total depth on prolonged laterals. Example embodiments may include a mathematical formulation that considers flexural and torsional rigidities of a string to be positioned in the wellbore to estimate the mechanical tortuosity using the geometrical tortuosity. Additionally, the vanishing and appearing tortuosities may be determined as the wellbore is drilled and when the expected string is run down the wellbore.

Results have shown that this comprehensive methodology may provide a better understanding of the wellbore quantification than purely using the friction factor as the main parameter for quantifying the wellbore condition prior to running a string downhole. The mechanical loading of the string due to centralizers may also be considered for the expected running of the string downhole.

Also, example embodiments may address challenges related to aggregate calculations, such as overall cumulative curvature and cumulative dogleg severity. As further described below, the wellbore curvature and torsion along with the related mechanical forces may provide key insight and consideration for physics-based modeling of tension, compression, buckling, torque, stress and circulating pressure estimated while strings are running, rotating, and circulating. Example embodiments (detailed below) may include example calculations along with methods for evaluating these parameters. As further described below, the outcome of the operations described herein in real time while drilling the wellbore may provide the confidence of running the string to the target depth.

Example Operations

Analyzing the wellbore condition for running the casing string during drilling provides valuable remedial measures that can be taken ahead of time. Example embodiments may provide a composite index of the wellbore conditions that can be monitored during drilling. In some embodiments, analysis of the wellbore condition may be performed prior to running the string downhole in the wellbore.

FIG. 1 is an example chart of an overall string runnability in a wellbore, according to some embodiments. In FIG. 1, a chart 100 includes an overall string runnability-a comprehensive string runnability index monitor 102. The comprehensive string runnability index monitor 102 may include a drill string runnability during drilling (DRI) 106, a casing runnability for casing tripping operation (CRI) 104, and a completion and any other string (e.g., wireline) runnability for completion and any other string related operations (CompRI) 108.

Conventional approaches generally just rely on friction factor as the main parameter for quantifying a wellbore condition prior to running a string downhole. In contrast, example embodiments may provide a more comprehensive methodology that provides a better understanding of the wellbore quantification.

To illustrate, FIG. 2 is a block diagram of an example data flowchart for determining string runnability in a wellbore, according to some embodiments. A dataflow chart 200 of FIG. 2 includes a current depth 202 (within the wellbore where the string is to be run) that is input into a processor 201. Survey data 204 is measured for this current depth 202. The survey data 204 may be input into a coefficient calculation 208. Previous parameter values 204 and content database 210 may also be input into the coefficient calculation 208. The coefficient calculation 208 may then calculate and output a number of different coefficients (a Coefficient C₁ 212, a Coefficient C₂ 214, a Coefficient C₃ 216, a Coefficient C₄ 218, a Coefficient C₅ 220, a Coefficient C₆ 222, a Coefficient C₇ 224, a Coefficient C₈ 226, a Coefficient C_n 228, etc.). The different coefficients may include at least one geometrical parameter of the wellbore and at least one mechanical parameter of the string that is caused by deploying the string downhole into the wellbore. Examples of such coefficients are further described below. The number of coefficients may be combined to create a string runnability index 230 (which is also further described below). In some embodiments, the coefficients may be computed in real time as the well is drilled. For example, the string runnability index may be defined and calculated every N (e.g., 30) feet.

FIG. 3 is an example Graphical User Interface (GUI) for monitoring string runnability in a wellbore, according to some embodiments. A GUI 300 includes a graphic 302 of wellbore being drilled and depths in terms of feet of the wellbore. The GUI 300 also includes a table 304 for stuck pipe avoidance. The table 304 includes columns 310-322. The column 310 includes the depth of the wellbore. The column 312 includes the caving volume (inches (in)²/foot (ft)). The column 314 includes the maximum cutting bed height. The column 316 includes pack off actual 0%. The column 318 includes plan plug friction factor and actual plug friction factor. The column 320 includes differential trip in % and differential trip out %. The column 322 includes the casing runnability and project ahead. The GUI 300 also includes a GUI 306 that includes a display of the overall pack-off risk index.

FIG. 4 is an example chart of an overall condition of a tubing based on various factors, according to some embodiments. In FIG. 4, a chart 400 includes a number of factors that may be considered in accessing an overall condition 416 of a wellbore. In the chart 400, the number of factors that may affect the overall condition of the wellbore may include an optimum speed 402, an equivalent circulating density (ECD)/effective mud weight (EMW) 404 for the wellbore, a casing runnability index 406, a completions runnability index 408, a swab influx 410, a pore pressure 412, and a static drag 414.

The chart 400 also includes three circular regions defining the overall condition as good (a region 450), bad (a region 454), a transition between good and bad (a region 452). In this example, the overall condition 416 is at point 420 in the region 452. As shown, the overall condition 416 is most adversely affected by the optimum speed 402, the completions runnability index 408, and the pore pressure 412.

Example operations for determining different types of string runnability indices are now described. For example, with reference to the chart 400 of FIG. 4, example operations are now described to determine the casing runnability index 406 and/or the completions runnability index 408.

In particular, FIG. 5 is a block diagram of a flowchart of example operations for determining an overall string runnability in a wellbore, according to some embodiments. In FIG. 5, a flowchart 500 includes example operations that may be performed by hardware, firmware, software, or any combination thereof. For example, sensors positioned downhole and/or at a surface of a wellbore may perform measurements. An example system having such sensors is depicted in FIG. 17, which is further described below. Additionally, a processor positioned downhole and/or at the surface of the wellbore may perform at least some of these operations of the flowchart 500. An example computer having such a processor is depicted in FIG. 18, which is further described below. Operations of the flowchart 500 begin at block 502.

At block 502, a condition of a wellbore into which a string is to be deployed is quantified. For example, a processor may quantify a condition of a wellbore based on one or more measurements made by one or more sensors downhole and/or at the surface. In some implementations, quantifying the condition of the wellbore may include determining of at least one geometrical parameter of the wellbore. Examples of the geometrical parameters may include a curvature (dog leg) of a path of the wellbore, torsion of the wellbore, etc. In some implementations, quantifying the condition of the wellbore may include determining of at least one mechanical parameter that are influenced by operational parameters of an operation in the wellbore. For example, operations in the wellbore may include operations need to position a tubing in the wellbore. Examples of the mechanical parameters may include push force, maximum bending, maximum bending stress, fatigue ratio, etc. Quantifying the condition of the wellbore may be based on other factors. For example, in some implementations, quantifying the condition of the wellbore may be based on hydromechanical coupling (such as a friction factor calibration).

At block 504, a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore is determined. For example, a processor may determine a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore. For instance, the string runnability index (SRi) may be determined using Equation (Eq.) 1:

$\begin{array}{cc}\mathrm{SRi}=f_1\times f_2\times f_3\times f_4\times f_5\times f_6\times f_7\times f_8\times \dots & \left(\mathrm{Eq}.1\right)\end{array}$

• • where f₁, f₂ . . . are functional relationships that may dictate the string running difficulties. In some implementations, the SRi may be based on at least one geometrical parameter of the wellbore and at least one mechanical parameter that are influenced by operational parameters of a wellbore operation. Examples of a geometrical parameter may include wellbore curvature (e.g., dogleg), wellbore torsion, etc. Examples of a mechanical parameter may include push force needed to move the string into position in the wellbore, maximum bending of the string, maximum bending stress of the string, and a fatigue ratio of the string. In some implementations, the SRi may be based on hydromechanical coupling, such as friction factor calibration. A more detailed description of calculation of the SRi is set forth below.

At block 506, a determination is made of whether the string runnability index is less than or equal to a runnability threshold. For example, a processor may make this determination. In some implementations, the runnability threshold may be one. If the string runnability index is not less than or equal to the runnability threshold, operations of the flowchart 500 continue at block 508. Otherwise, operations of the flowchart 500 continue at block 510.

At block 508, a wellbore operation is performed to adjust the condition of the wellbore to lower the string runnability index. For example, a processor may send instructions to other devices to adjust the condition of the wellbore. Examples of such adjustments may include a reaming operation by a reamer to enlarge the diameter of the wellbore, altering a direction of a drilling operation to decrease an angle of a directional drilling operation, etc. Operations of the flowchart 500 return to block 502 to again quantify a condition of the wellbore.

At block 510, the string is deployed into the wellbore. For example, a processor may send instructions to other devices to deploy the string (such as a casing string, drill string, production string, etc.) into the wellbore. Operations of the flowchart 500 continue at block 512.

At block 512, a determination is made of whether to reassess the string runnability index. For example, a processor may make this determination. For instance, the string runnability index may be reassessed after a current segment of the string has been positioned in the wellbore, after the wellbore has been drilled a given depth since the last assessment, since expiration of a time period since the last assessment, etc. If a determination is made to reassess the string runnability index, operations of the flowchart 500 return to block 502 to again quantify a condition of the wellbore. Otherwise, operations of the flowchart 500 remain at block 512 to again make this determination.

String Runnability Index (SRi) Calculation

Example operations for calculating the string runnability index is now described. In some implementations, the SRi may be defined by Equation (2):

$\begin{array}{cc}\mathrm{SRi}={\int }_0^L\left(\mathrm{Geometrical}\mathrm{Parameters}\right)\times \left(\mathrm{Coupling}\right)\times \left(\mathrm{Mech}.\mathrm{Parameters}\right)& \left(\mathrm{Eq}.2\right)\end{array}$

• • where Geometrical Parameters are the geometrical parameters of path of the wellbore, Coupling is the hydromechanical coupling, and Mech. Parameters are the mechanical parameters that are influenced by the operational parameters.

The Geometrical Parameters may be defined by Equation (3):

$\begin{array}{cc}\mathrm{Geometrical}\mathrm{Parameters}={\left(\frac{k_a}{k_0}\right)}^{a_1}{\left(\frac{{\tau }_a}{{\tau }_0}\right)}^{a_2}{\left(\frac{t_{\mathrm{ta}}}{t_{t0}}\right)}^{a_3}& \left(\mathrm{Eq}.3\right)\end{array}$

• • where k is the wellbore curvature, t is torsion of the wellbore, and t is tortuosity.

The Coupling may be defined by Equation 4:

$\begin{array}{cc}\mathrm{Coupling}={\left(\frac{{\mu }_a}{{\mu }_0}\right)}^{a_4}& \left(\mathrm{Eq}.4\right)\end{array}$

• • where μ is the friction factor.

The Mechanical Parameters may be defined by Equation 5:

$\begin{array}{cc}\mathrm{Mechanical}\mathrm{Parameters}={\left(\frac{F_{\mathrm{push}}}{F_d}\right)}^{a_5}{\left(\frac{c_a}{c_0}\right)}^{a_6}{\left(\frac{{\sigma }_{\mathrm{vMa}}}{{\sigma }_{\mathrm{vMo}}}\right)}^{a_6}{\left(\frac{{\mathrm{BSMF}}_a}{{\mathrm{BSMF}}_0}\right)}^{a_7}{\left(\frac{{\mathrm{FR}}_a}{{\mathrm{FR}}_0}\right)}^{a_8}& \left(\mathrm{Eq}.5\right)\end{array}$

• • where F_push is the push force, σ is the stress, c is the maximum dogleg severity, BSMF is the Bending Stress Magnification Factor, and FR is the friction ratio.

In some implementations, the wellbore condition may be considered “very good running” for the string if SRi is less than or equal to 1, as defined by Equation 6:

$\begin{array}{cc}\mathrm{SRi}=\underset{0}{\overset{L}{\int }}{\left(\frac{K_a}{K_o}\right)}^{a_1}{\left(\frac{{\tau }_a}{{\tau }_o}\right)}^{a_2}{\left(\frac{K_{\mathrm{pa}}}{K_{\mathrm{wo}}}\right)}^{a_3}{\left(\frac{{\tau }_{\mathrm{pa}}}{{\tau }_{\mathrm{wo}}}\right)}^{a_4}{\left(\frac{{\mu }_a}{{\mu }_o}\right)}^{a_5}{\left(\frac{F_{\mathrm{push}}}{F_d}\right)}^{a_6}{\left(\frac{c_a}{c_o}\right)}^{a_7}{\left(\frac{{\mathrm{BSMF}}_a}{{\mathrm{BSMF}}_o}\right)}^{a_8}{\left(\frac{{\mathrm{FR}}_a}{{\mathrm{FR}}_o}\right)}^{a_9}\le 1& \left(\mathrm{Eq}.6\right)\end{array}$

In some implementations, the wellbore condition may be considered “good running” for the string if SRi is approximately equal to 1, as defined by Equation 7:

$\begin{array}{cc}\mathrm{SRi}=\underset{0}{\overset{L}{\int }}{\left(\frac{K_a}{K_o}\right)}^{a_1}{\left(\frac{{\tau }_a}{{\tau }_o}\right)}^{a_2}{\left(\frac{K_{\mathrm{pa}}}{K_{\mathrm{wo}}}\right)}^{a_3}{\left(\frac{{\tau }_{\mathrm{pa}}}{{\tau }_{\mathrm{wo}}}\right)}^{a_4}{\left(\frac{{\mu }_a}{{\mu }_o}\right)}^{a_5}{\left(\frac{F_{\mathrm{push}}}{F_d}\right)}^{a_6}{\left(\frac{c_a}{c_o}\right)}^{a_7}{\left(\frac{{\mathrm{BSMF}}_a}{{\mathrm{BSMF}}_o}\right)}^{a_8}{\left(\frac{{\mathrm{FR}}_a}{{\mathrm{FR}}_o}\right)}^{a_9}\approx 1& \left(\mathrm{Eq}.7\right)\end{array}$

In some implementations, the wellbore condition may be considered “poor running” for the string if SRi is greater than 1, as defined by Equation 8:

$\begin{array}{cc}\mathrm{SRi}=\underset{0}{\overset{L}{\int }}{\left(\frac{K_a}{K_o}\right)}^{a_1}{\left(\frac{{\tau }_a}{{\tau }_o}\right)}^{a_2}{\left(\frac{K_{\mathrm{pa}}}{K_{\mathrm{wo}}}\right)}^{a_3}{\left(\frac{{\tau }_{\mathrm{pa}}}{{\tau }_{\mathrm{wo}}}\right)}^{a_4}{\left(\frac{{\mu }_a}{{\mu }_o}\right)}^{a_5}{\left(\frac{F_{\mathrm{push}}}{F_d}\right)}^{a_6}{\left(\frac{c_a}{c_o}\right)}^{a_7}{\left(\frac{{\mathrm{BSMF}}_a}{{\mathrm{BSMF}}_o}\right)}^{a_8}{\left(\frac{{\mathrm{FR}}_a}{{\mathrm{FR}}_o}\right)}^{a_9}>1& \left(\mathrm{Eq}.8\right)\end{array}$

String Runnability-Uncertainty and Probability

In some implementations, various parameters may be assigned weightage and adjusted based on the uncertainty and the trend of the particular parameter and can be defined by Equation 9:

$\begin{array}{cc}\mathrm{SRi}=\underset{0}{\overset{L}{\int }}{\left(w_1\frac{K_a}{K_o}\right)}^{a_1}{\left(w_2\frac{{\tau }_a}{{\tau }_o}\right)}^{a_2}{\left(w_3\frac{t_a}{t_o}\right)}^{a_3}{\left(w_4\frac{{\mu }_a}{{\mu }_o}\right)}^{a_4}{\left(w_5\frac{F_{\mathrm{push}}}{F_d}\right)}^{a_5}{\left(w_6\frac{c_a}{c_o}\right)}^{a_6}{\left(w_7\frac{{\sigma }_{\mathrm{vMa}}}{{\sigma }_{\mathrm{vMo}}}\right)}^{a_7}{\left(w_8\frac{{\mathrm{BSMF}}_a}{{\mathrm{BSMF}}_o}\right)}^{a_8}{\left(w_9\frac{{\mathrm{FR}}_a}{{\mathrm{FR}}_o}\right)}^{a_9}\dots {\left(w_n\frac{F}{R_0}\right)}^{a_n}& \left(\mathrm{Eq}.9\right)\end{array}$

• • where (w₁ K_a/K_o)^a1(w₂ τ_a/τ_o)^a2(w₃ t_a/t_o)^a3 are weighted geometrical parameters,
  • where (w₄ μ_a/μ_o)^a4 is a weighted coupled parameter,
  • where (w₅ F_push/F_d)^a5(w₆ c_a/c_o)^a6 (w₇ σ_vMa/σ_vMo)^a7 (w₈ BSMF_a/BSMF_o)^a8 (w₉ FR_a/FR_o)^a9 are weighted mechanical parameters, and
  • where (w_nF/R_o)^an is any type of additional parameter.

The model weight (w_n) may be calculated using various methods. For example, the model weight (w_n) may be calculated using Bayesian model weights obtained from posterior model probabilities in real time, an exponential weight method, more complex functions model, etc.

In some implementations, the model weight (w_n) may be calculated is using the averaging scheme by assigning equal weight for all components (as set forth by Equation 10):

$\begin{array}{cc}\sum K_n=1\left(w_n\right)=1.& \left(\mathrm{Eq}.10\right)\end{array}$

In other words, w_n=1/N where N is the number of index parameters).

In some implementations, the relationship between model results and real-time results may be related based on Equation 11:

$\begin{array}{cc}f\left(x\right)=f\left(y\right)+\in \left(x\right)+\delta \left(x\right)& \left(\mathrm{Eq}.11\right)\end{array}$

• • where f(x) is the modeled calculated value,
  • where f(y) is the real-time value,
  • where ∈(x) is the adjusted value due to the variation and unknown influence of parameters that are not considered in the model, and
  • where δ(x) is the uncertainty of the real-time data. This uncertainty may be of different distribution but may be considered normal distribution of the input parameters for a fixed range of timescale.

In some implementations, the coefficient or the calibration factor for each parameter may be calculated using the Nash-Sutcliffe parameter using Equation 12:

$\begin{array}{cc}{a}_0=1-{\sum }_{n=1}^{\infty }\frac{❘C-A❘}{❘A-\stackrel{\bigvee }{A}❘}& \left(\mathrm{Eq}.12\right)\end{array}$

• • wherein C is a calculated value, A is actual real time data, and Ă is a mean of the real time data in the time series.

In some implementations, the values greater than zero are an illustration of better prediction of the mean observed data. The adjustment of the trend analysis and the probability may be estimated based on the below method. There may be three trends: 1) planned, 2) case based, and 3) real time (actual) value of data. It may be assumed that the planned trend is the correct trend, and the other two curves should follow the planned one trend:

	Planned	Cased-Based	Actual
	P1 →	C1	R1
	P2 →	C2	R2
	P3 →	C3	R3
	P4 →	C4	R4
	P5 →	C5	R5
	P6 →	C6	R6
	P7 →	C7	R7

FIG. 6 is a block diagram of first example operations of a flowchart for estimation of a probability indicator between planned data, case-based data and real-time data, according to some embodiments. In FIG. 6, a flowchart 600 includes example operations that may be performed by hardware, firmware, software, or any combination thereof. For example, a processor positioned downhole and/or at the surface of the wellbore may perform at least some of these operations of the flowchart 600. An example computer having such a processor is depicted in FIG. 18, which is further described below. Operations of the flowchart 600 begin at block 602.

At block 602, a window size for groups is selected. For example, the processor may perform this selection. For instance, the window size may be three so that each group may include three points in the series. To illustrate for the planned trend, a first window may include points (p1, p2, p3), a second window may include points (p4, p5, p6), etc.

At block 604, regression is applied to each group of the planned trend data to determine the slope between each point in each group. For example, the processor may perform this regression. For instance, for the group for the planned trend (p1, p2, p3), the slope S1 is determined between p1 and p2, and the slope S2 is determined between p2 and p3.

At block 606, the points of the cased based data and the real-time data for each group may be predicted based on determined slopes from each group of the planned trend data. For example, the processor may perform these operations. For instance, the predictions for the cased based data may be (pp1, pp3, pp3), and the predictions for the real-time data may be (rr1, rr2, rr3).

At block 608, an error is determined for case based data and real-time data based on a difference of prediction and actual data for each of the points of the case based data and real-time data. For example, the processor may perform this determination. For instance, the error for the case based data may be (e1, e2, e3). The error for the real-time data may be (ee1, ee2, ee3).

At block 610, the errors are summed pointwise. For example, the processor may perform this summation.

At block 612, a probability indicator is determined based on normalization of the summed errors point-wise value. For example, the processor may make this determination.

FIG. 7 is a block diagram of second example operations of a flowchart for estimation of a probability indicator between planned data, case-based data and real-time data, according to some embodiments. In FIG. 7, a flowchart 700 includes example operations that may be performed by hardware, firmware, software, or any combination thereof. For example, a processor positioned downhole and/or at the surface of the wellbore may perform at least some of these operations of the flowchart 700. An example computer having such a processor is depicted in FIG. 18, which is further described below. Operations of the flowchart 700 begin at block 702.

At block 702, a size of a sliding window is selected. For example, the processor may perform this selection.

At block 704, the sliding window is moved over the three trends (planned, case based, and real-time). For example, the processor may perform this operation. For instance, the size of the sliding window may be three. In this instance, for the planned trend, the groups may be (p1, p2, p3), (p2, p3, p4), (p3, p4, p5), etc.

At block 706, regression is applied over Y points in each cycle for the three trends to determine the slope between each point in each group. For example, the processor may perform this operation. For instance, in a first cycle for (p1, p2, p3), slope sp1 is determined between p1 and p2, and slope sp2 is determined between p2 and p3. In the first cycle for (c1, c2, c3), slope sc1 is determined between c1 and c2, and slope sc2 is determined between c2 and c3. In the first cycle for (r1, r2, r3), slope sr1 is determined between r1 and r2, and slope sr2 is determined between r2 and r3. Similarly, the processor may continue to move this sliding window down to further points to determine the slopes. Since all the curves should follow the same trends in normal, the slopes should be the same or substantially the same.

At block 708, errors are determined based on a deviation of slopes of case based data and real-time data with respect to the planned data. For example, the processor may perform this operation.

At block 710, a net error is determined based on a summation of the determined errors. For example, the processor may perform this operation.

At block 712, a probability indicator is determined based on normalization of the net error. For example, the processor may make this determination.

Wellbore Curvature

Wellbore curvature (k) may be a crucial indicator for (1) determining buildup rates on the bottomhole assembly (BHA), (2) comprehending a formation's deflection characteristics, and (3) assessing the effectiveness of a wellbore trajectory. The total trajectory of a drilled wellbore may be tracked using wellbore curvature. The forces acting on the running string that might cause deformation may be calculated.

Wellbore curvature may determine whether a string (e.g., the casing string, the drill string, the completion string, etc.) will trip. Wellbore curvature may also determine whether the string will be run properly and smoothly.

Accordingly, wellbore curvature may be important for safe, rapid, and effective drilling. To monitor and manage the running conditions of the strings, the wellbore curvature and torsion should be precisely computed. Wellbore curvature may be defined as the rate at which the tangent vector of the wellbore trajectory rotates with respect to the change in position along the curved length. Wellbore curvature may, thus, represent the extent of a wellbore trajectory's deviation from a straight line. Wellbore curvature shows the degree to which a wellbore trajectory bends. The wellbore curvature (k) at any point along the wellbore may be determined using Equation (13):

$\begin{array}{cc}k=\sqrt{k_{\propto }^2+k_{\varphi }^2{\sin }^2\alpha }& \left(\mathrm{Eq}.13\right)\end{array}$

• • where
  • a=Inclination angle, (°)
  • ϕ=Azimuth angle, (°)
  • k_α=Rate of inclination change (dropping off is a negative value), (°)/30 meters or (°)/100 feet)
  • k_ϕ=Rate of azimuth change (decreasing azimuth is a negative value), (°)/30 meters or (°)/100 feet)
  • k=Curvature of wellbore trajectory, (°)/30 meters or (°)/100 feet)

In some embodiments, Equation 13 may be used to calculate the curvature of the planned wellbore and compared against the actual wellbore.

Wellbore Torsion

In some implementations, another crucial element of the wellbore path or wellbore trajectory design may be wellbore turning which can be used to check the string runnability conditions. Drilling experience demonstrates that even when the wellbore curvature is minimal, during running operations, strings may still get either stuck or hard to push through. The weight provided to the drill bit during drilling is not always efficient (particularly when the rigidity and bend angle of a steerable motor are high). As a result, a downhole pipe string may twist as a result of a wellbore trajectory that is repeatedly turned, considerably increasing the drag and torque that is given to the string and leading to its deformation.

Wellbore torsion (τ) may be defined as the rate at which the wellbore trajectory's binormal vector spins in relation to a change in curved length. It shows the degree of borehole twisting. The wellbore torsion (τ) may be determined using Equation (14):

$\begin{array}{cc}\tau =\{\begin{array}{c}+❘b❘,\mathrm{if}b\mathrm{and}n\mathrm{are}\mathrm{in}\mathrm{the}\mathrm{opposite}\mathrm{direction}\\ -❘b❘,\mathrm{if}b\mathrm{and}n\mathrm{are}\mathrm{in}\mathrm{the}\mathrm{same}\mathrm{direction}\end{array}& \left(\mathrm{Eq}.14\right)\end{array}$

where

• • τ=torsion of the wellbore trajectory, (°)/30 meters (m), (°)/30 meters or (°)/100 feet)
  • b=unit binormal vector of wellbore trajectory
  • n=unit principal normal vector of wellbore trajectory

The wellbore torsion (τ) at any given point may be determined using Equation (15):

$\begin{array}{cc}\tau =\frac{K_{\alpha }{K}_{\varphi }-K_{\varphi }{K}_{\alpha }}{K^2}\sin \alpha +K_{\varphi }\left(1+\frac{K_{\alpha }^2}{K^2}\right)\cos \alpha & \left(\mathrm{Eq}.15\right)\end{array}$

The wellbore torsion (τ) for four different trajectories are defined by Equations (16), (17), (18), and (19):

$\begin{array}{cc}\tau =0,\mathrm{for}a\mathrm{spatial}-\mathrm{arc}\mathrm{trajectory}& \left(\mathrm{Eq}.16\right)\end{array}$ $\begin{array}{cc}\tau =K_{\varphi }\left(1+\frac{K_{\alpha }^2}{K^2}\right)\cos \alpha ,\mathrm{for}a\mathrm{natural}-\mathrm{curve}\mathrm{trajectory}& \left(\mathrm{Eq}.17\right)\end{array}$ $\begin{array}{cc}\tau =K_H\left(1+\frac{2K_V^2}{K^2}\right)\sin \alpha \cos \alpha ,\mathrm{for}a\mathrm{cylinder}-\mathrm{helix}\mathrm{trajectory}& \left(\mathrm{Eq}.18\right)\end{array}$ $\begin{array}{cc}\tau =K\frac{\sin \omega }{\tan \alpha }=K_{\varphi }\cos \alpha ,\mathrm{for}a\mathrm{constant}\mathrm{tool}-\mathrm{face}\mathrm{trajectory}& \left(\mathrm{Eq}.19\right)\end{array}$

Thus, wellbore torsion may determine whether the string will trip and whether one will be able to run the string properly and smoothly.

Wellbore Profile Energy

Less torque and drag during string running operation will be the outcome of reducing the overall energy of a space curve (i.e., condition wellbore trajectory of the wellbore drilled). This technique, which is defined for curves in space R3, may be straightforward, quick, and deterministic.

When the wellbore path is helical and changes azimuth and direction, conventional operations based on the inflection point will fail. The wellbore oscillation in this scenario won't be captured and quantified because the inflection point will remain constant. Additionally, the change azimuthally cannot be computed using a two-dimensional (2D) model with merely curvature. Better prediction is given by a three-dimensional (3D) comprehensive estimate that includes both curvature and torsion.

Instead of using the geometric meaning (based only on curvature and torsion), another mathematical criterion to quantify the running condition of the string may be based on the physical logic. The lowest energy curve may be a non-linear curve that simulates a narrow elastic beam and is distinguished by bending the least while traversing a specified set of locations in the wellbore. By contrasting the planned and actual well trajectories, it is thought to be a great criterion for the running of the strings during drilling itself. As a result, this technique describes the wellbore path's minimal energy (Samuel's criterion) with curvature and borehole torsion-Equation 20:

$\begin{array}{cc}{E}_s={\int }_0^l\left({k\left(x\right)}^2+{\tau \left(x\right)}^2\right)\mathrm{dx}& \left(\mathrm{Eq}.20\right)\end{array}$

In some implementations, the wellbore path's minimal energy may be further normalized to a standard wellbore course length between survey stations as defined by Equation 21:

$\begin{array}{cc}{E}_{{\left(\mathrm{abs}\right)}_n=\left(\frac{{\sum }_{i=1}^n\left(K_i^2+{\tau }_i^2\right)\Delta D_i}{D_n+\Delta D_n}\right)}& \left(\mathrm{Eq}.21\right)\end{array}$

• • where E₈ is the wellbore path's minimal energy and ΔD is the distance between the survey stations (in meters or feet).

In some implementations, a discrete string run index may be determined using a curvature and turning of a wellbore based on Equation 22:

$\begin{array}{cc}\mathrm{Discrete}\mathrm{String}\mathrm{Run}\mathrm{Index}=& \left(\mathrm{Eq}.22\right)\end{array}$ ${\tau }^2+K^2+\mu +\frac{\mathrm{EI}}{\Lambda }\left(\mathrm{or}\frac{\mathrm{AE}}{L}\mathrm{or}\frac{\mathrm{GJ}}{L}\left(\mathrm{spring}\mathrm{constant}\right)\right)$

For example, the discrete string run index may be calculated every N feet (e.g., every 30 feet).

To illustrate, FIGS. 8A-8B are example graphical images charting depth versus a twist angle of a first wellbore and a second wellbore, respectively, according to some embodiments. FIG. 8A is a graphical image 800 that depicts a change in a twist angle 804 over a depth 802 of the first wellbore. FIG. 8B is a graphical image 850 that depicts a change in a twist angle 854 over a depth 852 of the second wellbore. A twist angle may be based on a combination of the curvature and torsion of a wellbore. In these examples, a change in the twist angle 854 of FIG. 8B over the depth is greater than a change in the twist angle 804 over a similar depth.

Appearing and Vanishing Tortuosities

When the wellbore is planned, there may be numerous ways to calculate and use artificial undulation. The wellbore tortuosity changes after the wellbore is dug and before the wellbore is cased and cemented. However, conventional approaches continue using open hole surveys. FIGS. 9A-9F are conceptual diagrams of different example configurations of strings positioned in wellbores, according to some embodiments. FIG. 9A includes a string 904 positioned in a wellbore 902. FIG. 9B includes a string 906 positioned in a wellbore 908. FIG. 9C includes a string 910 positioned in a wellbore 912. FIG. 9D includes a string 914 positioned in a wellbore 916. FIG. 9E includes a string 918 positioned in a wellbore 920. FIG. 9F includes a string 922 positioned in a wellbore 924. This assumption is invalid to calculate and calibrate. This criterion is needed to correct the wellbore path conditions so that the string may be run under the modified conditions.

Alteration of survey may produce extra side force in the string. The amount of excess side force produced may depend on the degree of tortuosity, wellbore diameter, and string stiffness. The additional side force it causes may be extremely big and is not insignificant if the tortuosity is great enough. For getting the target to correctly estimate the side force caused by tortuosity, a stiff-string model may be used.

Vanishing Tortuosity

FIGS. 10A-10D are conceptual diagrams of a wellbore with appearing and vanishing tortuosities, according to some embodiments. FIG. 10A includes a wellbore 1000 that includes the original tortuosity of the openhole. FIG. 10B includes the wellbore 1000 at a next phase—wherein the original tortuosity vanishes as the casing is run and cemented resulting in a smooth wellbore (due to the stiffness of the casing that is run).

Appearing Tortuosity

FIG. 10C includes the wellbore 1000 at a next phase—wherein the original tortuosity of the openhole vanishes and new tortuosity appears as the casing is run and cemented resulting in undulated wellbore. This is due to the stiffness of the casing, buckling of the pipe and forces along the casings as they are run and cemented (as shown in FIG. 10C.

Appearing and Vanishing Tortuosity

FIG. 10D includes the wellbore 1000 at a next phase. This is a combination of the above resulting in the alteration of the openhole surveys. One of the reasons may be due to the top of the cement is not all the way to the top and sufficient to alter the position of the casing pipe above, immediately below the top of the cement and in the transition zone due to the pipe's torsional and flexural rigidity. This may result in 3D spiraling which can be seen in the rotation of the tangent-normal-binormal vectors.

Soft String and Stiff String

The overall string tripping operation may be made simpler by the torque-drag model formulation, which assumes that the string and wellbore have the same trajectory. It is presumed that contact is along the wellbore irrespective of the wellbore curvature.

It may be possible that this presumptive trajectory and the string's actual trajectory are one in the same. Unfortunately, the minimum curvature approach (which is the most widely used wellbore trajectory model) may result in the discontinuous bending moments at survey points. The stiff string model when using the bending stiffness may affect the torque and drag calculations as follows: (1) side forces, (2) stresses, and (3) positions of the string.

To illustrate, FIG. 11 is a conceptual diagram of a stiff-string model, according to some embodiments. A stiff-string model 1100 may be solved for each node in each of the two planes. For lateral motions away from a center of the wellbore, the XZ plane may be employed. For vertical movement, the YZ plane may be used. When the gaps (e.g., string/wall constraint) are solved, the solutions from these two planes come together.

For the stiff-string model 1100, angles in each plane may be measured counterclockwise around a centerline 1102. A positive moment will produce a positive angle. There may be concentrated forces at the survey locations as well as scattered loads between the survey points, depending on the continuity of the tangent and its derivatives.

The large-displacement beam-column formulation serves as the foundation for this derivation. The discontinuity in total force F in the string caused by pipe stiffness at a survey site may be calculated using Equation 23:

$\begin{array}{cc}\Delta \stackrel{\rightharpoonup }{F}=-\Delta \left\{\mathrm{EI}\left[{\overrightarrow{t}}^{″}+K^2\stackrel{\rightharpoonup }{t}\right]\right\}& \left(\mathrm{Eq}.23\right)\end{array}$

• • where E is Young's modulus; I is moment of inertia; t is the tangent vector; prime (″) indicates derivative with respect to measured depth; and K is the wellbore curvature.

The distributed contact force (F_n) due to string stiffness may be calculated using Equation 24:

$\begin{array}{cc}{F}_n=\mathrm{EI}\left[{\overrightarrow{t}}^{\mathrm{\prime \prime \prime }}+K^2{\overrightarrow{t}}^{\prime }-3\left({\overrightarrow{t}}^{\prime }*{\overrightarrow{t}}^{″}\right)\overrightarrow{t}\right]& \left(\mathrm{Eq}.24\right)\end{array}$

FIG. 12 is a stiff-string model (for force balance at each node), according to some embodiments. FIG. 12 includes a stiff-string model 1200.

FIG. 13 is a graph that depicts a string and a through channel, according to some embodiments. A graph 1300 includes an Xs axis 1302, a Ys axis 1304, and a Zs axis 1306. The graph 1300 includes a 3D through channel 1308 and a 3D deformed tool 1310.

Push Through Force

Calculation of tool passage force may also be critical in order to estimate the maximum string length when rigid string components are run inside a wellbore which are buckled also. Tool passage force for three-point contact for different inequality conditions may be summarized by Equations (25) and (26):

$\begin{array}{cc}\begin{array}{cc}{F}_{\mathrm{ct}}=\frac{96\mu \mathrm{EI}}{L^3}\left(r\left(1-\cos \frac{z_{p}l}{2}\right)-2r_c\right)& L_{\mathrm{ct}}>L>L_t\end{array}& \left(\mathrm{Eq}.25\right)\end{array}$ $\begin{array}{cc}{F}_{\mathrm{ct}}=\frac{96\mu \mathrm{EI}}{L_{\mathrm{ct}}^3}\left(r\left(1-\cos \frac{z_p{L}_{\mathrm{ct}}}{2}\right)-2r_c\right)+1.5\mu \mathrm{EI}\left(r-r_c\right)z_p^4\left(L-L_{\mathrm{tp}}\right)L>L_{\mathrm{ct}}& \left(\mathrm{Eq}.26\right)\end{array}$

• • where L_ct based on a three-point contact length may be computed by Equation 27:

$\begin{array}{cc}{L}_{\mathrm{ct}}=\frac{2}{z_p}\sqrt{39.64-\sqrt{{39.64}^2-45.3\left(\frac{r_c}{r}\right)}}& \left(\mathrm{Eq}.27\right)\end{array}$

where

• • E=Young's modulus, (pounds per square inch (psi))
  • I=moment of inertia-defined by Equation 28:

$\begin{array}{cc}I=\frac{\pi }{64}\left({\mathrm{OD}}^4-{\mathrm{ID}}^4\right)\mathrm{inches}{\left(\mathrm{in}\right)}^4& \left(\mathrm{Eq}.28\right)\end{array}$

• • where OD and ID are the outer diameter and inner diameter, respectively, of the tool, where L_t is the length of the tool (foot (ft)).

The push through force (F_push) may be computed by Equation 29:

$\begin{array}{cc}{F}_{\mathrm{push}}=\frac{96\mu \mathrm{EI}}{L^3}\left[r\left(1-\cos \frac{\beta L}{2}-2\delta \right)\right]& \left(\mathrm{Eq}.29\right)\end{array}$

• • where EI is the bending stiffness, μ is the friction factor, L is the length of the tool, β is the helix angle parameter, and δ is the string clearance (wellbore radius−string radius).

Conventional approaches to calculation of a string passage through a wellbore are based on planar curvature or planar curve assumptions. However, strings in wellbores (named as through-channel) involve 3-dimensional (3D) geometry and an arbitrary complicated 3D curve. However, a string (such as downhole tool, casing section, Bottom Hole Assembly (BHA), etc.) in the 3D curved through-channel may not always be straight. Example embodiments may build a 3D geometer model between an internal tool and external through-channel and analyze the tool clearance within the through-channel.

During modeling of the geometer model between tool and through-channel, the effects of the tool orientation and position in the through-channel, curved axial of tool, arbitrary 3-dimensional curved through-channel, etc. may be included. The maximum free passage tool length and free section area in the 3D channel may be calculated. Alternately, the 3D contact points between tool and through-channel for a given tool length and shape may be determined.

FIG. 13 is a graph of a string and through-channel, according to some embodiments. A graph 1300 includes coordinates (X_s 1302, Y_s 1304, and Z_s 1306). The graph 1300 includes a 3D through channel 1308 and a 3D deformed tool 1310. Equations of a through-channel based on the coordinates in FIG. 13 are defined by Equations 30:

$\begin{array}{cc}{x}_s-\mathrm{North}=f_{\mathrm{sx}}\left(\mathrm{md},\alpha ,\theta ,d_s\right)y_s-\mathrm{East}=f_{\mathrm{sy}}\left(\mathrm{md},\alpha ,\theta ,d_s\right)z_s-\mathrm{TVD}=f_{\mathrm{sz}}\left(\mathrm{md},\alpha ,\theta ,d_s\right){\alpha }_s-\mathrm{Inclination}=f_{s\alpha }\left(\mathrm{md}\right){\theta }_s-\mathrm{Azimuth}=f_{s\theta }\left(\mathrm{md}\right)D_s-\mathrm{Hole}\mathrm{Inner}\mathrm{Diameter}=f_{\mathrm{sd}}\left(\mathrm{md}\right)& \left(\mathrm{Eqs}.30\right)\end{array}$

Equations of the tool based on the coordinates in FIG. 13 are defined by Equations 31:

$\begin{array}{cc}{x}_s-\mathrm{North}=f_{\mathrm{sx}}\left(\mathrm{md},\alpha ,\theta ,d_s\right)y_s-\mathrm{East}=f_{\mathrm{sy}}\left(\mathrm{md},\alpha ,\theta ,d_s\right)z_s-\mathrm{TVD}=f_{\mathrm{sz}}\left(\mathrm{md},\alpha ,\theta ,d_s\right){\alpha }_s-\mathrm{Inclination}=f_{s\alpha }\left(\mathrm{md}\right){\theta }_s-\mathrm{Azimuth}=f_{s\theta }\left(\mathrm{md}\right)D_s-\mathrm{Hole}\mathrm{Inner}\mathrm{Diameter}=f_{\mathrm{sd}}\left(\mathrm{md}\right)& \left(\mathrm{Eqs}.31\right)\end{array}$

• • where md is measured depth. The ellipse equation of the outer side of a tool at given measured depth (md) is given by Equation 32:

$\begin{array}{cc}a\times x_t^2\times b\times y_t^2-2c\times x_t\times y_t\times -2e\times x_t-2h\times y_t+g=\frac{d_t^2}{4}& \left(\mathrm{Eq}.32\right)\end{array}$

• • where a=sin (θ_t)²,
  • where b=sin (α_t)²+cos (θ_t)²×cos (a_t)²
  • where c=sin (θ_t)×cos (θ_t)×cos (α_t)
  • where e=sin (θ_t)×cos (θ_t)×cos (α_t)×z_t
  • where h=sin (θt)²×cos (θ_t)×sin (α_t)×z_t
  • where g=(1+cos (θ_t)²)×sin (θ_t)×z_t²

The ellipse equation of the inner side of a through channel is given by Equation 33:

$\begin{array}{cc}{a}^{\prime }\times x_s^2+b^{\prime }\times y_s^2-2c^{\prime }\times x_s\times y_s-2e^{\prime }\times x_s-2h^{\prime }\times y_s+g^{\prime }=\frac{d_s^2}{4}& \left(\mathrm{Eq}.33\right)\end{array}$

• • where a′=sin(θ_s)²
  • where b′=sin (α_s)²+cos (θ_s)²×cos (α_s)²
  • where c′=sin (θ_s)×cos (θs)×cos (α_s)
  • where e′=sin (θ_s)×cos (θ_s)×cos (α_s)×z_s
  • where h′=sin (θ_s)²×cos (θ_s)×cos (α_s)×z_s
  • where g′=(1+cos (θ_t)²)×sin (θ_t)×z_s²

On the basis of these equations, the area of tool free passage may be calculated.

FIG. 14 is a diagram of an area of free tool passage for a straight tool, according to some embodiments. A diagram 1400 of FIG. 14 includes a bottom of section 1402, a top of section 1404, and an area of free tool passage 1406. If the axial line of a tool is a 3D curve, Equations 34-36 may be used to calculate the cross area between the tool and the through channel, contact points, and angles between the tool and the through channel:

$\begin{array}{cc}h\left(\beta ,\mathrm{md}\right)={\bigcup }_{\mathrm{md}=\mathrm{top}\mathrm{of}\mathrm{tool},\beta =0}^{\mathrm{md}=\mathrm{bottom}\mathrm{of}\mathrm{tool},\beta =360}{f}_c\left(x_t,y_t,z_t,x_s,y_s,z_s,\beta ,\mathrm{md}\right)& \left(\mathrm{Eq}.34\right)\end{array}$ $\begin{array}{cc}{h}_c\left(\mathrm{md}\right)=\underset{\beta =0\mathrm{to}360}{\max }h\left(\beta ,\mathrm{md}\right)& \left(\mathrm{Eq}.35\right)\end{array}$ $\begin{array}{cc}{\beta }_c\left(\mathrm{md}\right)=\beta \left\{h\left(\beta ,\mathrm{md}\right)=h_c\left(\mathrm{md}\right)\right\}& \left(\mathrm{Eq}.36\right)\end{array}$

• • where β is direction angle in the cross-section of the through-channel. Its value may be from 0 to 360 degrees.

where h(β, md) is the intersection location between the tool and the through-channel at md and β. If the tool is in the through-channel, h(β, md) is negative. If the tool is out of the through-channel, h(β, md) is positive.

where h_c(md) is a maximum value of h(β, md) at a specified measured depth.

where β_c(md) is the directional angle at a specified measured depth and h(β,md)=h_c(md).

FIGS. 15A-15C are conceptual diagrams of a string before and after loading into a wellbore, according to some embodiments. FIG. 15A is a conceptual diagram of a string 1500 having no loading (before loading into a wellbore). FIG. 15B is a conceptual diagram of a string 1520 having a straight loading into a wellbore. FIG. 15C is a conceptual diagram of a string 1540 having loading inside a wellbore.

Friction Factor and Deconvolution

The friction factor at the current depth may be obtained from the torque and drag calculation. In some implementations, it is expected that friction factor for the planned case should be lesser than the friction factor for the actual case. Improving the accuracy of the single friction coefficient may provide higher quality information for the string runnability operations. The single friction coefficient may be decomposed into one or more components (i.e., friction factors, where each of the decomposed friction factors may be separately estimated and calibrated against measured and collected sensor data).

Estimating and calibrating each friction factor separately from the other friction factors may improve the accuracy of the combined, (i.e., calculated, friction factor). In some aspects, each decomposed friction factor may be analyzed independent of the other decomposed friction factors to determine which one or more decomposed friction factors are driving a deviation from the calibration line. Adjustments may be made to the wellbore operations to bring these one or more identified decomposed friction factors closer to the measured friction of the wellbore operation.

Generally, the calibrated friction factor may be computed from a decomposed form of the friction data. For an interval of measured depth (for example, 40.0 feet) or another interval, the one or more contributing factors for the friction factor may be computed and combined to generate the calibrated friction factor. For example, the calibrated friction factor may be calculated using Equation 37:

$\begin{array}{cc}{\mathrm{FF}}_x=f_1+f_2+f_3+\dots f_n& \left(\mathrm{Eq}.37\right)\end{array}$

• • where FF_x are the decomposed friction factor functions.

In some aspects, the calibrated friction factor may be represented by specific types or groups of friction factors (for example, geomechanical, mechanical, fluid, geomechanical, etc.). For example, the calibrated friction factor using these types of factors may be calculated using Equation 38:

$\begin{array}{cc}{\mathrm{SR}}_i=\mathrm{geometrical}+\mathrm{mechanical}+\mathrm{fluid}+\mathrm{geomechanical}+\dots & \left(\mathrm{Eq}.38\right)\end{array}$

The data used as input for each of the included decomposed friction factors may be computed from offset wellbores, prior collected data, or from real-time or near real-time data received from sensors in or near the current wellbore. Geometrical friction factors may include zero or more of a wellbore curvature (such as a dogleg), a wellbore torsion, an inclination, an azimuth, or other geometrical friction factors.

Mechanical friction factors may include zero or more of a push force, a maximum bending, a maximum bending stress, a fatigue ratio, or other mechanical friction factors. Fluid friction factors may include zero or more of a viscous drag, a cuttings drag, or other fluid friction factors. Geomechanical friction factors may include zero or more of a wellbore instability, a rotational speed of downhole equipment, or other geomechanical friction factors.

In some implementations, the decomposed factors of the planned wellbore may be compared against the actual path of the wellbore in real-time. To illustrate, FIG. 16 is a block diagram of a flowchart of example operations for comparing decomposed factors of a planned wellbore against the actual wellbore path in real-time, according to some embodiments. In FIG. 16, a flowchart 1600 includes example operations that may be performed by hardware, firmware, software, or any combination thereof. For example, a processor positioned downhole and/or at the surface of the wellbore may perform at least some of these operations of the flowchart 1600. An example computer having such a processor is depicted in FIG. 18, which is further described below. Operations of the flowchart 1600 begin at block 1602.

At block 1602, data of factors related to condition of a wellbore is received. For example, the processor may receive the data. Operations of the flowchart 1600 continue at blocks 1604-1610 (which may be in parallel, partially in parallel, or serially).

At block 1604, geometrical factors are decomposed. For example, the processor may perform this operation. Operations of the flowchart 1600 continue at block 1612.

At block 1606, mechanical factors are decomposed. For example, the processor may perform this operation. Operations of the flowchart 1600 continue at block 1612.

At block 1608, fluid factors are decomposed. For example, the processor may perform this operation. Operations of the flowchart 1600 continue at block 1612.

At block 1610, geomechanics factors are decomposed. For example, the processor may perform this operation. Operations of the flowchart 1600 continue at block 1612.

At block 1612, real-time sensor data is compared to an estimated single friction factor. For example, the processor may perform this comparison.

Overall Stress Condition

In some embodiments, the quantity (bending stress magnification factor (BSMF)) may be defined as a ratio of the maximum of the absolute value of the curvature in the body of the string divided by the curvature of the wellbore axis. This factor may be applied as a multiplier on the bending stress calculations to more accurately calculate the bending stress in a string that has tool joints with outside diameters (OD) greater than the body of the string. This modified bending stress may then be used in the calculation of the von Mises stress of the string. BSMF may be useful in determining SRi because when a string with tool joint OD greater than the body OD is subjected to either a tensile or compressive axial load, the maximum curvature of the string wall exceeds that of the wellbore axis curvature. The string sections conform to the wellbore curvature primarily through contact at the tool joints.

In both tensile and compressive axial load cases, the average curvature between the joints of the string may not be changed. However, the local changes of curvature due to straightening effects of tension or the buckling effects of compression may be many times the average value. Therefore to accurately calculate the bending stress in the body of the string may include the determination of these local maximum curvatures, as defined by Equation 39:

$\begin{array}{cc}\mathrm{Fatigue}\mathrm{ratio}=\mathrm{bending}\mathrm{stress}\mathrm{corrected}\mathrm{by}\mathrm{bending}\mathrm{stress}\mathrm{magnification}\mathrm{factor}+\mathrm{Buckling}\mathrm{stress}/\mathrm{fatigue}\mathrm{limit}& \left(\mathrm{Eq}.39\right)\end{array}$

Van Mises Stress ratio is the ratio of the stress limit over the von Misses stress. If it is above one, it may be considered close to failure. The maximum permissible dog-leg severity may be calculated using Equation 40:

$\begin{array}{cc}c=\frac{432000{\sigma }_b}{\pi \mathrm{ED}}\frac{\tanh \mathrm{KL}}{\mathrm{KL}}& \left(\mathrm{Eq}.40\right)\end{array}$

• • where K may be calculated using Equation 41:

$\begin{array}{cc}K=\sqrt{\frac{T}{\mathrm{EI}}}& \left(\mathrm{Eq}.41\right)\end{array}$

• • where tensile stress (σ_t) in pounds per square inch (psi) may be calculated using Equation 42:

$\begin{array}{cc}{\sigma }_t=\frac{F_{\mathrm{dls}}}{A}\left(\mathrm{psi}\right)& \left(\mathrm{Eq}.42\right)\end{array}$

• • where A=cross sectional area of the body of the string in square inches,
  • where F_dls in pounds (lbs.) is the buoyed weight supported below the dog-leg,
  • where E=the Young's modulus (psi),
  • where D=string outer diameter (OD) in inches,
  • where L=half the distance between coupling in inches,
  • where I=moment of inertia with respect to its diameter and may be calculated using Equation 43:

$\begin{array}{cc}I=\frac{\pi }{64}\left(D^4-{\mathrm{ID}}^4\right){\mathrm{inches}}^4& \left(\mathrm{Eq}.43\right)\end{array}$

• • where σ_b=bending stress.

Overpull Limit

The calculation option “Maximum Overpull” may be used to determine an overpull limit. Overpull is the additional tensile force due to frictional drag while pulling the string out of the wellbore, “tripping out”. Overpull limit may be defined as the additional tensile force due to frictional drag required to generate a von Mises stress equal to the material yield stress multiplied by the stress limit factor.

The “stress limit factor” is input as a % of yield on the torque drag setup data dialog. The material yield stress may be determined from the grade of the specific string component. Starting at the bottom string section, the axial tensile force required to generate a von Mises stress equal to the stress limit multiplied by the % of Yield is induced. This procedure may then work its way up the string. The value of the axial force at the top of the string may be the value used as the final hook load. The maximum overpull may be defined as the hook load—the buoyed weight of the string.

The coupling of the geometrical twist and mechanical twist may be important for the string twist estimation. Also, it may be important to consider the magnitude of the twist for the stress calculations of the strings. As described, some embodiments may include the use of the top-down approach to couple the geometrical and mechanical parameters. Also, some embodiments may include the calculation of the pitch of the twist and the analysis of the results-which may be useful for future completion design.

Example Wellbore System

Example operations for monitoring wellbore string runnability for downhole operations may be performed at any of a number of different stages of a wellbore. For example, such operations may be performed during drilling, wireline, completion, production, etc. One example stage during which monitoring wellbore string runnability for downhole operations may be performed includes drilling, wherein the string is a drill string.

To illustrate, FIG. 17 is a conceptual diagram of an example wellbore system, according to some embodiments. In FIG. 17, a system 1700 includes a drill string 1726 disposed in a directional wellbore 1716. The drill string 1726 includes a directional drilling system 1728. A drilling platform 1702 supports a derrick 1704 having a traveling block 1706 for raising and lowering a drill string 1708. A kelly 1710 supports the drill string 1708 as the drill string 1708 is lowered through a rotary table 1712. In some embodiments, a top drive is used to rotate the drill string 1708 in place of the kelly 1710 and the rotary table 1712. A drill bit 1714 is positioned at the downhole end of the tool string 1726, and, in one or more embodiments, may be driven by a downhole motor (not shown) positioned in the tool string 1726 uphole of the rotary steering tool 1728 and/or rotation of the drill string 1708 from the surface. As the bit 1714 rotates, the bit 1714 creates the wellbore 1716 that passes through various formations 1718. A pump 1720 circulates drilling fluid through a feed pipe 1722 and downhole through the interior of drill string 1708, through orifices in drill bit 1714, back to the surface via the annulus 1736 around drill string 1708, and into a retention pit 1724. The drilling fluid transports cuttings from the wellbore 1716 into the pit 1724 and aids in maintaining the integrity of the wellbore 1716.

The tool string 1726 may include one or more logging-while-drilling (“LWD”)/measurement-while-drilling (“MWD”) tools 1732 that collect measurements including survey trajectory data, formation properties and various other drilling conditions as the bit 1714 extends the wellbore 1716 through the formations 1718. The MWD tool 1732 may include a device for measuring formation resistivity, a gamma ray device for measuring formation gamma ray intensity, devices for measuring the inclination and azimuth of the tool string 1726, pressure sensors for measuring drilling fluid pressure, temperature sensors for measuring borehole temperature, etc.

The tool string 1726 may also include a telemetry module 1734. The telemetry module 1734 receives data provided by the various sensors of the tool string 1726 (e.g., sensors of the MWD tool 1732), and transmits the data to a surface controller 1738. Similarly, data provided by the surface control unit 1738 is received by the telemetry module 1734 and transmitted to the tools (e.g., MWD tool 1732, rotary steering tool 1728, etc.) of the tool string 1726. In some embodiments, mud pulse telemetry, wired drill pipe, acoustic telemetry, or other telemetry technologies may be used to provide communication between the surface control unit 1738 and the telemetry module 1734.

The directional drilling system 1728 is configured to change the direction of the tool string 1726 and/or the drill bit 1714, such as based on information indicative of tool 1728 orientation and a desired direction of the tool string 1726. The directional drilling system 1728 includes a housing 1730 disposed about a steerable shaft 1740. In this embodiment, the steerable shaft 1740 transfers rotation through the directional drilling system 1728. A deflection or cam assembly surrounding the shaft 1740 is rotatable within the rotation resistant housing 1730 to orient the deflection or cam assembly such that the shaft 1740 can be eccentrically positioned in the borehole causing a change in trajectory. Most embodiments of intelligent directional drilling systems 1728 include or are coupled to directional sensors (e.g., a magnetometer, gyroscope, accelerometer, etc.) for determination of azimuth and inclination with respect to a reference direction (e.g., magnetic north) and reference depth. Steering can be automated within the toolstring or sent via telemetry from surface. In either manner, steering is based on measurements comprising the current measured depth, true vertical depth, inclination and azimuth. In one embodiment, the directional drilling system 1728 determines a suitable orientation of the deflection sleeve to steer the tool string 1726 in the desired direction.

Example Computer

FIG. 18 is a conceptual diagram of an example computer, according to some embodiments. A computer 1800 of FIG. 18 may perform at least some of the operations described herein. The computer 1800 includes a processor 1801 (possibly including multiple processors, multiple cores, multiple nodes, and/or implementing multi-threading, etc.). The computer 1800 includes memory 1807. The memory 1807 may be system memory or any one or more of the above already described possible realizations of machine-readable media. The computer 1800 also includes a bus 1803 and a network interface 1805. The computer 1800 can communicate via transmissions to and/or from remote devices via the network interface 1805 in accordance with a network protocol corresponding to the type of network interface, whether wired or wireless and depending upon the carrying medium. In addition, a communication or transmission can involve other layers of a communication protocol and or communication protocol suites (e.g., transmission control protocol, Internet Protocol, user datagram protocol, virtual private network protocols, etc.).

The computer 1800 also includes a data processor 1811 and a controller 1815 (which can perform the operations described herein). Any one of the previously described functionalities may be partially (or entirely) implemented in hardware and/or on the processor 1801. For example, the functionality may be implemented with an application specific integrated circuit, in logic implemented in the processor 1801, in a co-processor on a peripheral device or card, etc. Further, realizations may include fewer or additional components not illustrated in FIG. 18 (e.g., video cards, audio cards, additional network interfaces, peripheral devices, etc.). The processor 1801 and the network interface 1805 are coupled to the bus 1803. Although illustrated as being coupled to the bus 1803, the memory 1807 may be coupled to the processor 1801.

While the aspects of the disclosure are described with reference to various implementations and exploitations, it will be understood that these aspects are illustrative and that the scope of the claims is not limited to them. In general, techniques for seismic horizon mapping as described herein may be implemented with facilities consistent with any hardware system or hardware systems. Many variations, modifications, additions, and improvements are possible.

Plural instances may be provided for components, operations or structures described herein as a single instance. Finally, boundaries between various components, operations and data stores are somewhat arbitrary, and particular operations are illustrated in the context of specific illustrative configurations. Other allocations of functionality are envisioned and may fall within the scope of the disclosure. In general, structures and functionality presented as separate components in the example configurations may be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements may fall within the scope of the disclosure.

Embodiment #1: A method comprising: quantifying a condition of a wellbore into which a string is to be deployed, wherein quantifying the condition of the wellbore comprises, determining at least one geometrical parameter of the wellbore; and determining at least one mechanical parameter of the string that is caused by deploying the string downhole into the wellbore; and determining a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

Embodiment #2: The method of Embodiment #1, further comprising: deploying the string into the wellbore, in response to the string runnability index being equal to or less than a runnability threshold.

Embodiment #3: The method of Embodiment #2, in response to the string runnability index being greater than the runnability threshold, recursively performing the following operations until the string runnability index is equal to or less than the runnability threshold, performing a downhole operation to adjust the condition of the wellbore to lower the string runnability index; quantifying the condition of a wellbore; and determining the string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

Embodiment #4: The method of one or more of Embodiments #1-3, wherein quantifying the condition of the wellbore comprises quantifying the condition of the wellbore prior to deploying the string in the wellbore.

Embodiment #5: The method of one or more of Embodiments #1-4, wherein the string comprises at least one a casing, a tubing, a drill pipe, and a wireline.

Embodiment #6: The method of one or more of Embodiments #1-5, determining the at least one mechanical parameter of the string comprises determining at least one of a push force needed to position the string in the wellbore, a maximum bending of the string, a maximum bending stress of the string, and a fatigue ratio of the string.

Embodiment #7: The method of one or more of Embodiments #1-6, wherein determining the at least one geometrical parameter of the wellbore comprises determining at least one of a curvature of the path of the wellbore, and a torsion of the wellbore.

Embodiment #8: The method of one or more of Embodiments #1-7, further comprising: performing a downhole operation in the wellbore based on the string runnability index.

Embodiment #9: The method of Embodiment #8, wherein performing the downhole operation comprises adjusting drilling of the wellbore.

Embodiment #10: A non-transitory, computer-readable medium having instructions stored thereon that are executable by a processor, the instructions comprising: instructions to quantify a condition of a wellbore into which a string is to be deployed, wherein the instructions to quantify the condition of the wellbore comprises, instructions to determine at least one geometrical parameter of the wellbore; and instructions to determine at least one mechanical parameter of the string that is caused by deploying the string downhole into the wellbore; and instructions to determine a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

Embodiment #11: The non-transitory, computer-readable medium of Embodiment #10, wherein the instructions comprise: instructions to deploy the string into the wellbore, in response to the string runnability index being equal to or less than a runnability threshold.

Embodiment #12: The non-transitory, computer-readable medium of Embodiment #11, wherein the instructions comprise: instructions to recursively perform the following operations until the string runnability index is equal to or less than the runnability threshold, in response to the string runnability index being greater than the runnability threshold, instructions to perform a downhole operation to adjust the condition of the wellbore to lower the string runnability index; instructions to quantify the condition of a wellbore; and instructions to determine the string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

Embodiment #13: The non-transitory, computer-readable medium of one or more of Embodiments #10-12, wherein the string comprises at least one a casing, a tubing, a drill pipe, and a wireline.

Embodiment #14: The non-transitory, computer-readable medium of one or more of Embodiments #10-13, wherein the at least one mechanical parameter of the string comprises at least one of, a push force needed to position the string in the wellbore, a maximum bending of the string, a maximum bending stress of the string, and a fatigue ratio of the string.

Embodiment #15: The non-transitory, computer-readable medium of one or more of Embodiments #10-14, the at least one geometrical parameter of the wellbore comprises at least one of a curvature of the path of the wellbore, and a torsion of the wellbore.

Embodiment #16: A system comprising: a processor; and a computer-readable medium having instructions stored thereon that are executable by the processor to cause the processor to, quantify a condition of a wellbore into which a string is to be deployed, wherein the instructions executable by the processor to cause the processor to quantify the condition of the wellbore comprises instructions executable by the processor to cause the processor to, determine at least one geometrical parameter of the wellbore; and determine at least one mechanical parameter of the string that is caused by deploying the string downhole into the wellbore; and determine a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

Embodiment #17: The system of Embodiment #16, further comprising: the string to be deployed into the wellbore, wherein the instructions comprise instructions executable by the processor to cause the processor to, deploy the string into the wellbore, in response to the string runnability index being equal to or less than a runnability threshold; and recursively perform the following operations until the string runnability index is equal to or less than the runnability threshold, in response to the string runnability index being greater than the runnability threshold, perform a downhole operation to adjust the condition of the wellbore to lower the string runnability index; quantify the condition of a wellbore; and determine the string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

Embodiment #18: The system of Embodiment #17, wherein the string comprises at least one a casing, a tubing, a drill pipe, and a wireline.

Embodiment #19: The system of one or more of Embodiments #16-18, wherein the at least one mechanical parameter of the string comprises at least one of, a push force needed to position the string in the wellbore, a maximum bending of the string, a maximum bending stress of the string, and a fatigue ratio of the string.

Embodiment #20: The system of one or more of Embodiments #16-19, wherein the at least one geometrical parameter of the wellbore comprises at least one of, a curvature of the path of the wellbore, and a torsion of the wellbore.

Use of the phrase “at least one of” preceding a list with the conjunction “and” should not be treated as an exclusive list and should not be construed as a list of categories with one item from each category, unless specifically stated otherwise. A clause that recites “at least one of A, B, and C” may be infringed with only one of the listed items, multiple of the listed items, and one or more of the items in the list and another item not listed.

As used herein, the term “or” is inclusive unless otherwise explicitly noted. Thus, the phrase “at least one of A, B, or C” is satisfied by any element from the set {A, B, C} or any combination thereof, including multiples of any element.

Claims

1. A method comprising:

quantifying a condition of a wellbore into which a string is to be deployed, wherein quantifying the condition of the wellbore comprises, determining at least one geometrical parameter of the wellbore; and determining at least one mechanical parameter of the string that is caused by deploying the string downhole into the wellbore; and

determining a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

2. The method of claim 1, further comprising:

deploying the string into the wellbore, in response to the string runnability index being equal to or less than a runnability threshold.

3. The method of claim 2,

in response to the string runnability index being greater than the runnability threshold, recursively performing the following operations until the string runnability index is equal to or less than the runnability threshold, performing a downhole operation to adjust the condition of the wellbore to lower the string runnability index; quantifying the condition of the wellbore; and determining the string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

4. The method of claim 1, wherein quantifying the condition of the wellbore comprises quantifying the condition of the wellbore prior to deploying the string in the wellbore.

5. The method of claim 1, wherein the string comprises at least one a casing, a tubing, a drill pipe, and a wireline.

6. The method of claim 1, determining the at least one mechanical parameter of the string comprises determining at least one of

a push force needed to position the string in the wellbore,

a maximum bending of the string,

a maximum bending stress of the string, or

a fatigue ratio of the string.

7. The method of claim 1, wherein determining the at least one geometrical parameter of the wellbore comprises determining at least one of

a curvature of the path of the wellbore, and

a torsion of the wellbore.

8. The method of claim 1, further comprising:

performing a downhole operation in the wellbore based on the string runnability index.

9. The method of claim 8, wherein performing the downhole operation comprises adjusting drilling of the wellbore.

10. A non-transitory, computer-readable medium having instructions stored thereon that are executable by a processor, the instructions comprising:

instructions to quantify a condition of a wellbore into which a string is to be deployed, wherein the instructions to quantify the condition of the wellbore comprises, instructions to determine at least one geometrical parameter of the wellbore; and instructions to determine at least one mechanical parameter of the string that is caused by deploying the string downhole into the wellbore; and

instructions to determine a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

11. The non-transitory, computer-readable medium of claim 10, wherein the instructions comprise:

instructions to deploy the string into the wellbore, in response to the string runnability index being equal to or less than a runnability threshold.

12. The non-transitory, computer-readable medium of claim 11, wherein the instructions comprise:

instructions to recursively perform the following operations until the string runnability index is equal to or less than the runnability threshold, in response to the string runnability index being greater than the runnability threshold, instructions to perform a downhole operation to adjust the condition of the wellbore to lower the string runnability index; instructions to quantify the condition of the wellbore; and instructions to determine the string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

13. The non-transitory, computer-readable medium of claim 10, wherein the string comprises at least one a casing, a tubing, a drill pipe, and a wireline.

14. The non-transitory, computer-readable medium of claim 10, wherein the at least one mechanical parameter of the string comprises at least one of,

a push force needed to position the string in the wellbore,

a maximum bending of the string,

a maximum bending stress of the string, or

a fatigue ratio of the string.

15. The non-transitory, computer-readable medium of claim 10, the at least one geometrical parameter of the wellbore comprises at least one of

a curvature of the path of the wellbore, or

a torsion of the wellbore.

16. A system comprising:

a processor; and

a computer-readable medium having instructions stored thereon that are executable by the processor to cause the processor to, quantify a condition of a wellbore into which a string is to be deployed, wherein the instructions executable by the processor to cause the processor to quantify the condition of the wellbore comprises instructions executable by the processor to cause the processor to, determine at least one geometrical parameter of the wellbore; and determine at least one mechanical parameter of the string that is caused by deploying the string downhole into the wellbore; and determine a string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

17. The system of claim 16, further comprising:

the string to be deployed into the wellbore,

wherein the instructions comprise instructions executable by the processor to cause the processor to, deploy the string into the wellbore, in response to the string runnability index being equal to or less than a runnability threshold; and recursively perform the following operations until the string runnability index is equal to or less than the runnability threshold, in response to the string runnability index being greater than the runnability threshold, perform a downhole operation to adjust the condition of the wellbore to lower the string runnability index; quantify the condition of the wellbore; and determine the string runnability index for running the string into the wellbore based on the quantified condition of the wellbore.

18. The system of claim 17, wherein the string comprises at least one a casing, a tubing, a drill pipe, and a wireline.

19. The system of claim 16, wherein the at least one mechanical parameter of the string comprises at least one of,

a push force needed to position the string in the wellbore,

a maximum bending of the string,

a maximum bending stress of the string, or

a fatigue ratio of the string.

20. The system of claim 16, wherein the at least one geometrical parameter of the wellbore comprises at least one of,

a curvature of the path of the wellbore, or

a torsion of the wellbore.