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Cutting transport efficiency prediction using probabilistic CFD and DOE techniques
Accepted Manuscript Cutting transport efficiency prediction using probabilistic CFD and DOE techniques Meysam Naderi, Ehsan Khamehchi PII:
S0920-4105(17)31046-X
DOI:
10.1016/j.petrol.2017.12.083
Reference:
PETROL 4573
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 10 April 2017 Revised Date:
21 December 2017
Accepted Date: 28 December 2017
Please cite this article as: Naderi, M., Khamehchi, E., Cutting transport efficiency prediction using probabilistic CFD and DOE techniques, Journal of Petroleum Science and Engineering (2018), doi: 10.1016/j.petrol.2017.12.083. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Cutting transport efficiency prediction using probabilistic CFD and DOE techniques
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Meysam Naderi, Ehsan Khamehchi* Department of Petroleum Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Avenue, Tehran, Iran *Corresponding Author Email: [email protected]
Abstract
Efficient cutting transport plays an important role in drilling operation. This process is
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controlled by many factors such as well geometry, drilling fluid properties, geological features and rate of penetration. In order to minimize the operational cost of inefficient hole cleaning, it is crucial to thoroughly investigate the simultaneous effect of various
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factors on the process of cutting transport.
In this regard, computational fluid dynamic (CFD) and design of experiment (DOE) techniques were used to predict the cutting transport efficiency (CTE) as a function mud velocity (Vm), drilling rate of penetration (ROP), mud weight (MW), cutting weight (CW), mud viscosity (µm), pipe rotational speed (N), and cutting size (CS).
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The results of study based on probabilistic CFD calculations using DOE and Monte Carlo simulation (MCS) show that respectively factors of mud velocity, cutting weight, pipe rotational speed, mud weight, cutting diameter, mud viscosity, and drilling rate of penetration have the greatest impact on transportation of drilled cuttings from bottom
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of the well to the surface. In addition, result of MCS based on analysis of total variance reveals that 86.3% of cutting transport efficiency variation could be controlled by three
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factors of mud velocity, cutting weight and pipe rotational speed. Therefore, these factors should be carefully characterized during drilling and hole cleaning to maximize the cutting transport efficiency. Keywords: Cutting transport efficiency, Computational fluid dynamic, Design of experiment, Monte Carlo simulation
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1. Introduction A good drilling operation with maximum rate of penetration and minimum cost is a function of efficient cutting transport. Several factors influence the process of cutting motion toward the surface. Typical variables which determine the effectiveness of drilling mud in removing the cuttings from the wellbore are drilling fluid properties
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such as viscosity, yield point, fluid type, hole diameter and length, annular velocity, well inclination angle, size and shape of cutting, cutting weight, and drilling rate of penetration. The interaction between various factors makes the situation more complex.
problems and consequently unforeseen costs.
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Therefore, it is crucial to estimate the degree of hole cleaning to reduce drilling
Several authors have investigated the cutting transport problem. Udo Zeidler (1970)
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studied the effect of cutting dynamics on mud carrying capacity in a vertical well. The experimental study of Sifferman et al. (1974) using a full scale vertical annulus for different systems of drilling fluid showed that rotary speed, cutting generation rate, annular size and pipe eccentricity has minimal effect on cutting transport. Casing size and drilling fluid density showed a moderate effect. However, annular velocity and mud properties were the most cutting transport controlling factors. Hussain et al (1983)
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experimental study of cutting transport revealed that increased annular velocity and yield strength of drilling fluid are favorable conditions for efficient hole-cleaning. Syed and Jamal (1983) studied the cutting transport problem in vertical and inclined wellbores experimentally. The experimental study performed by Okrajni and Azar
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(1985) showed that transportation of cuttings is not influenced by yield point, and yield point to plastic viscosity ratio under turbulent regime. However, higher mud yield value
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shows a better transport performance for laminar flow in the range of low-angle wells. The study also showed that the effect of eccentricity is a function of inclination angle and flow regime. For high inclination angles between 55 and 90°, the effect of pipe eccentricity on hole cleaning is moderate under turbulent flow and significant for laminar flow. In general, they concluded that mud flow rate has a dominant effect on annular hole-cleaning. The experimental analysis of cutting transport phenomenon in an included wellbore by Ford et al. (1990) indicated that the velocity needed to initiates cuttings transport is sensitive to inclination angle. Pipe rotation significantly reduces the critical fluid transport velocity when circulating with medium or highly viscous fluids, and cutting removal is very effective under turbulent flow condition. Sifferman 2
ACCEPTED MANUSCRIPT and Becker (1992) performed an experimental study to evaluate the effect of several parameters on hole-cleaning in an inclined well. The parameters were mud velocity, mud density, mud rheology, mud type, cuttings size, rate of penetration, rotary speed, drill pipe eccentricity, diameter of drill pipe, and hole angle. The result of survey showed that mud velocity and mud weight have the greatest effect on hole-cleaning, and
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as the mud weight increases the cutting beds shows decreasing. In addition, the study revealed that pipe rotation effect on cutting buildup is greater for inclination angles near horizontal, small cuttings, and low ROP. Harel and Geir (1993) used two Invert Emulsion Mineral-Oil-Based and Water-Based Muds systems to experimentally
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investigate the limestone cutting transport behavior. For vertical or near vertical inclination angles, the study showed that cuttings transport rate increases as the yield point and plastic viscosity of both mud systems decreases but this effect is more severe
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in the inverted emulsion oil-base muds. For higher inclination angles, hole-cleaning for both mud types improves by simultaneous decreasing of yield point and plastic viscosity, and increasing flow rate. Belavadi and Chukwu (1994) investigated the relation between transportation of cuttings and the transport ratio and dimensionless quantities. Cho et al. (2002) used continuity and Navier Stokes equations to study the
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effect of annular velocity, pressure gradient and mud rheology on cuttings transport. Ramadan et al. (2002) introduced a mechanistic model to estimate the critical flow rate in inclined channel by analyzing the forces acting on spherical bed particles. Saeid et al. (2006) and Phuoc et al. (2007) experimental study showed that drag reduction and
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sand consolidation feature of nano-fluids improves drilling rate of penetration. Mingqin et al. (2007) developed a mechanistic model to estimate the critical velocity in order to
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predict which drilling fluid is effective in bed formation prevention and particles bed erosion. Abouzar et al. (2008) experimental study showed the positive effect of carbon black nano particles on the drilling mud performance for reducing mud filtrate and mud cake thickness. Piroozian et al. (2012) experimentally investigated the effect of the mud viscosity, fluid velocity and hole inclination on cuttings transport in horizontal and highly deviated wells. They considered three types of drilling fluid. The results indicated that cuttings transport efficiency increases by viscosity approximately 8 % at all angles provided the flow regime remained turbulent for constant flow velocity. However, further increase of viscosity reduces cutting transport performance by a total average of 12 % because of changing flow regime from turbulent into transient and laminar flow. 3
ACCEPTED MANUSCRIPT Li and Luft (2014) presented a critical review of the previous solids transport theoretical studies in both drilling and well interventions. In addition, they introduced a methodology for developing the empirical correlations and a mechanistic model. Li and Luft (2014) studied the cutting transport experimentally. They presented useful general guide to gather comprehensive laboratory flow loop test data required to validate the
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derived semi-empirical theoretical model to simulate the hole cleaning process. Ebrahimi and Khamehchi (2015) developed a robust model using artificial neural network for computing pressure drop in vertical multiphase flow that could be possibly used to optimize required surface pressure to have better mud carrying capacity. Song
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et al. (2017) experimentally investigated the effect of the flow rate, cutting diameter, rate of penetration, eccentricity, and wellbore diameter on cleaning performance in horizontal wells using a full-scale horizontal-cuttings-transport flow loop. In addition,
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they proposed a model for prediction of cuttings volumetric concentration and the cuttings-bed height based on dimensional analysis. The results of their study revealed that cutting transport efficiency in horizontal wells increases by increased flow rate, decreased ROP, lower eccentricity, and smaller ratio of drillpipe diameter to wellbore diameter.
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Review of previous studies shows that although many experimental and simulation works have been done regarding cutting transport process, the interaction effect of variables on cutting transport performance has never been investigated. The interaction effects play a crucial role in the cutting transport process. Because of complex nature of
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problem, it is very important to consider the variables simultaneously in order to find better hole cleaning strategy and improved drilling operation with minimum costs. In
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this regard, the paper aims to formulate cutting transport efficiency (CTE) as a function of mud velocity (Vm), drilling rate of penetration (ROP), mud weight (MW), cutting weight (CW), mud viscosity (µm), pipe rotational speed (N), and cutting size (CS) by using design of experiment (DOE) and computational fluid dynamic (CFD) calculations. Box-Behnken design (BBD) was used to run CFD to establish the mathematical relation between cutting transport efficiency and mentioned independent variables. CFD calculations to study the cutting transportation in the vertical annulus were done using ANSYS (FLUENT) commercial code, Reynolds-Averaged Navier-Stokes equations and discrete phase model (DPM). Next, the main and interaction effects of various factors on the transportation of cuttings will be analyzed using response surface methodology 4
ACCEPTED MANUSCRIPT (RSM). Finally, sensitivity and uncertainty analysis of cutting transport efficiency statistical model will be performed by applying Monte carlo simulation. The following section describes the CFD model used for calculating the cutting transport efficiency as a function of various factors. Section 3 presents the methodology used to derive cutting transport efficiency response function. Results of applying DOE, RSM and
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CFD will be presented and discussed in Section 4. Finally, Section 5 provides the core findings of this research.
2. Model description
In this survey, the annulus formed by the configurations of the wellbore and drill pipe is
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used to simulate virtual fluid flow system. The inner diameter of wellbore is 245 mm. The outer diameter of drill pipe is 140 mm. The total depth of the well is 1000 m.
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GAMBIT 2.4.6 software was used to model the computational mesh of the annulus. Discretisation of the annulus geometry using structured mesh results a total mesh layout of 250000 hexahedric cells. Grid sensitivity showed that this number of cells is adequate for current investigation.
In order to calculate the velocity components, first, it is required to integrate the Reynolds-averaged Navier-Stokes equations in each computational cell throughout the
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domain, then being discretized using finite volumes approach, and finally being linearized and solved numerically.
The PRESTO routine is used for the pressure discretisation scheme. Although, the CFD
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calculations based on PRESTO scheme is computationally costly, the results are more accurate than standard pressure discretisation. PRESTO discretisation method avoids interpolation errors and pressure gradient assumptions on boundaries. The SIMPLEC
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algorithm is used for the pressure-velocity coupling because of its ability to speed-up convergence by applying the increased under-relaxation factor. In order to consider the laminar and the turbulent regions by varying flow rate, the k −ε model of Lander and Spalding (1974) is selected to simulate the turbulent regimes. The Boussinesq hypothesis is used in the k −ε model. Although there are various numerical methods for simulation of turbulent flows by solving the Reynolds equations, the standard k −ε model is selected in this study because it is used in industrial flow simulations with excellent performance and widely validated as a two- equation eddy viscosity turbulence model.
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ACCEPTED MANUSCRIPT For discretisation of mass, momentum, turbulent kinetic energy and turbulent dissipation rate equations, QUICK method is applied because of its third order accuracy and better adaptation to structured meshes of hexahedric cells. All CFD calculations will be conducted using ANSYS (FLUENT) commercial code. In order to calculate the cutting transport efficiency, it is required to monitor the
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transportation of cuttings in the annulus from the well bottom to the surface. Cutting transport efficiency can be determined by the ratio between mass of drilled cuttings at the surface and the mass of generated cuttings at the bottom of wellbore under different operational conditions. This can be done using discrete phase model (DFM). Using DFM
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option in FLUENT, the user can inject particles with different injection rates, shapes, sizes, densities into the fluid flow system.
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3. Methodology
The present study investigates the effect of several important variables on cutting transportation inside annulus of vertical wells. There are many numbers of factors which control the transport efficiency in vertical wells. Typical factors include size, density and shape of cuttings, mud density, fluid viscosity and velocity, hole-pipe configuration, pipe eccentricity and pipe rotational speed. However, it is not affordable
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to include all variables in the model because the required number of CFD simulations increases very rapidly by the number of factors. In this regard, based on previous studies, experience and preliminary analysis of field data; seven major variables have
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been identified to be included in the CTE model. These factors are mud velocity, drilling rate of penetration, mud weight, cutting weight, mud viscosity, pipe rotational speed, and cutting size.
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In order to estimate the CTE, we used Box-Behnken design (1960) to perform CFD calculations. Box-Behnken design (BBD) is a type of response surface design that allows efficient estimation of the first- and second-order coefficients. Box-Behnken design often reduces the required number of simulation runs, and consequently it is less expensive to run than other response surface designs with the same number of factors. Based on Box-Behnken design, it is required to model and simulate 57 different CFD models for analyzing the effect of seven factors on cutting transport efficiency. Next, in order to establish the mathematical relation between independent factors and cutting transport efficiency, response surface methodology (RSM) was used. Response
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ACCEPTED MANUSCRIPT surface methodology is a collection of mathematical techniques to predict the relation between dependent and independent variables. More details about response surface methodology are given in Box and Wilson (1951). We used full quadratic form of multiple regression equation in order to predict CTE as a function of seven independent variables. The full quadratic form of a response surface is given by: ܨሺܺଵ , ܺଶ , ܺଷ … ܺே ሻ = ߙ + ߙ ܺ + ୀଵ
ே
ߙ ܺଶ ୀଵ
ேିଵ ே
+ ߙ ܺ ܺ ழ ୀଶ
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ே
(1)
Where F is the response function; ߙ is the intercept; αi, αii, αji are respectively the main, quadratic and interaction terms coefficients; Xi and Xj are independent factors and N is
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the number of independent factors. After collecting all necessary data, the regression coefficients can be estimated by applying least square method to minimize the error
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between observed and fitted data. It is worth to note that all collected data including mud weight, cutting weight, fluid velocity, mud viscosity, drilling rate of penetration, drill-string rotational speed and all related turbulency factors which have been used in this study are based on actual wells drilled in south of Iran.
Table 1 shows the range of factors, coded variables and transfer functions. In this table, X1, X2, X3, X4, X5, X6 and X7 are coded variables between -1 and +1 respectively for cutting
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size (CS), drilling rate of penetration (ROP), mud weight (MW), mud viscosity (µm), cutting weight (CW), mud velocity (Vm), and pipe rotational speed (N). Transfer functions are used for normalizing the range of factors between -1 and +1 with mean
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and variance of respectively 0 and 1. For example, the range of cutting size from 2 mm to 8 mm can be normalized between -1 and +1 using transfer function of
ௌିହ ଷ
.
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Table 2 shows the result of CFD calculations for estimation of CTE based on BBD for seven factors. By applying response surface methodology, the following response function was developed for CTE. CTE = 0.384+0.12 X1 + 0.017 X2–0.013 X3–0.098 X4 + 0.046 X5 + 0.0453 X6+ 0.0552 X7 + 0.07 X12+0.093 X22+0.081 X32–0.073 X52– 0.09 X62+0.07X72–0.125
(2)
X1X4 + 0.091 X1X7–0.087 X3X6–0.062 X4X7+ 0.067 X6X7 Where X1, X2, X3, X4, X5, X6 and X7 are coded variables between -1 and +1 for mentioned factors in Table 1. The coefficient of determination (R2) and adjusted coefficient of determination (R2adj) for CTE response function are 86.56 and 80.19% respectively. R2 is a measure of the proportion of the variance in the dependent variable that is 7
ACCEPTED MANUSCRIPT predictable from the fitted model. R2adj shows the goodness of fit for the regression adjusted for the number of terms. The low difference between R2adj and R2 indicates that the significant terms have been included in the model (Myers and Montgomery, 1995). The derived proxy has been validated by plotting predicted CTE using Eq. (2) versus actual values of CTE in Fig. 1. In addition, analysis of variance for derived proxy shows
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that all terms of Eq. (2) are significant at 5% of significance level for prediction at 95% confidence interval. Therefore, all performed tests on CTE response function reveal that Eq. (2) is statistically significant to study the transportation of drilled cuttings from well bottom to surface.
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The following section investigates the main and interaction effects of factors on the
4. Results and Discussion
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variation of cutting transport efficiency.
Investigation of Eq. (2) reveals that cutting transport efficiency is a function of main effects, interaction effects, and square power effects of factors. The constant in the first of equation implies that the cutting transport efficiency for base case model is equal to that constant. Main effects
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4.1.
Fig. 2 shows the main effects plot for cutting transport efficiency. The main effects plot shows the influence of individual factors while the other factors are kept constant at their middle values in coded units. The interaction between various factors can affect
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the main effect of factors on the response function. Therefore, the main effect of factors in Fig. 2 is only plotted for middle values of other factors. As can be seen, increasing cutting size and fluid viscosity respectively increases, and
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decreases cutting transport efficiency. Increasing drilling fluid viscosity is desirable to suspend cuttings inside the well and to avoid them from falling and settling at the wellbore bottom. However, high viscous drilling fluid increases the pumping pressures and consequently reduces the cutting carrying capacity. Increasing rate of penetration, first decreases cutting transport efficiency and then increases it. High rate of penetration limits the cutting transport efficiency due to increasing hydraulic requirement for effective wellbore cleaning. As can be clearly seen from Eq. (2), the main effect plot for mud weight could be changed because it has an interaction with fluid velocity. For example, for three 8
ACCEPTED MANUSCRIPT different values of fluid velocity, the main effect of mud weight varies differently. Eq. (2) indicates that for normalized fluid velocity of -1 (0.5 m/sec), as mud weight increases the cutting transport efficiency increases. In this case, the heavy muds give better cuttings transport than the middle and light weight muds. On the other hand, for normalized fluid velocity of +1 (2.1 m/sec), as mud weight increases the cutting
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transport efficiency decreases. In this case, the light muds give better cutting transport than the middle and heavy weight muds. However, for middle values of normalized fluid velocity of 0 (1.3 m/sec) which is shown in Fig. 2, as mud weight increases the cutting transport efficiency first decreases and then increases.
Increasing pipe rotation speed in the range of 10-20 rad/s (X7 between 0 and +1) shows
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significant increase in cutting transport efficiency. In the range of 0-10 rad/s (X7 between -1 and 0), the effect of pipe rotation speed shows insignificant changes.
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However, the effect of pipe rotation speed on cuttings transportation is a complex process and it depends on various factors like drilling fluid rheology, shape and size of cuttings, and flow rate. In sum, increasing pipe rotation reduces the mud viscosity which is normally a desirable property because it reduces pumping pressures inside drill pipe and increases cutting carrying capacity in the annulus showing effective hole cleaning. Cutting transport efficiency first increases and then decreases by increasing cutting
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weight. Increasing cutting weight, increases the particle slip velocity and consequently reduces the mud carrying capacity.
Increasing the drilling fluid velocity increases the annular velocity and consequently cuttings carrying capacity of fluid. However, frictional pressure drop increases by
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excessive drilling fluid velocity. In order to compensate the pressure drop, the pumping pressure should be increased which reduces the mud carrying capacity. Therefore, excessive flow rate is detrimental to the bottom hole cleaning which cause a reduction
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in the rate of penetration. 4.2.
Interaction effects
Fig. 3 shows the interaction effects plot for cutting transport efficiency. As can be seen from derived response function for CTE, five interaction terms of CS ×µm (X1× X4), CS ×N (X1× X7), MW × Vm (X3 × X6), µm × N (X4 × X7), and Vm× N (X6 × X7), are the most important pairs. Figs. 4 through 8 show the variation of cutting transport efficiency as a function of these interaction terms.
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ACCEPTED MANUSCRIPT 4.2.1. Interaction between cutting size and mud viscosity (CS × µm) Fig. 4 shows that increasing mud viscosity reduces cuttings removal from the well for almost all size of cuttings. This reduction of transport efficiency is due to increased pumping pressure and decreased cutting carrying capacity of the drilling fluid. However, for a small range of cutting sizes between 2 mm (X1= -1) and 2.75 mm (X1 = -
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0.75), hole cleaning improves by increasing mud viscosity. As can be seen, cuttings transport efficiency increases by decreasing mud viscosity as the cutting size increases. 4.2.2. Interaction between cutting size and pipe rotation speed (CS × N)
Fig. 5reveals that cutting transport efficiency improves by increasing pipe rotation speed for cutting sizes greater than 7.5 mm (X1 = 0.83). For values between 2 mm (X1 = -
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1) and 7.5 mm (X1 = 0.83), increasing pipe rotational speed first decreases cutting transport efficiency and then increases it. Figure also shows that cuttings removal
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increases by increasing pipe rotation speed as the cutting size increases. 4.2.3. Interaction between mud weight and fluid velocity (MW × Vm) Fig. 6 indicates that for all values of constant mud weight, increasing fluid velocity first increases cuttings removal efficiency and then decreases it. On the other hand, for all values of constant fluid velocity, increasing mud weight first decreases cuttings removal
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efficiency and then increases it. Therefore, as the mud weight increases, the fluid velocity should be optimally lowered in order to maximize cuttings transport efficiency. As can be seen from the figure, when the mud weight is low, it is required to keep the fluid velocity between 1.42 m/s (X6=0.15) and 2.06 m/s (X6=0.95) in order to maximize
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the cutting transport efficiency. However, for high values of mud weight, fluid velocity should be kept between 1.02 m/s (X6=-0.35) and 1.66 m/s (X6=0.45). In general, during
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drilling as depth gets deeper, mud weight should be increased in order to keep the wellbore stability and to overcome formation pore pressure. In this situation, in order to maximize the cutting transport efficiency, the fluid velocity should be optimally decreased from 2.1 (X6=+1) to 1.3 m/sec (X6=0). The exact optimum value of fluid velocity could be determined by using some optimization algorithms for various values of mud weight in order to maximize jet impact force or hydraulic horse power required for highest hole cleaning performance. In fact, the simultaneous increasing of mud weight and fluid velocity is not an optimum choice for efficient hole cleaning. Increasing fluid velocity above its optimum value results in additional frictional pressure drop and consequently the available energy at the bit for efficient hole cleaning reduces. 10
ACCEPTED MANUSCRIPT 4.2.4. Interaction between mud viscosity and pipe rotation speed (µm × N) Fig. 7 shows that cutting transport efficiency increases by increasing pipe rotational speed for mud viscosity between 10 cp (X4 = -1) and 14.5 cp (X4 = -0.55). For values greater than 14.5 cp, increasing pipe rotation first decreases and then increases cutting transport efficiency. On the other hand, increasing mud viscosity reduces efficiency of
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cutting transportation regardless of pipe rotational speed. As can be seen, this reduction is very sensitive for pipe rotational speed between 4.5 rad/s (X7 = -0.55) and 17 (X7 = 0.7) rad/s. As can be seen, maximum hole cleaning occurs at the low mud viscosity and high value of pipe rotation speed.
4.2.5. Interaction between fluid velocity and pipe rotation speed (Vm × N)
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Fig. 8 shows the contour plot of CTE versus fluid velocity and pipe rotation speed. As can be seen, cutting transport efficiency could be maximized by simultaneous increasing
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of fluid velocity and pipe rotation speed. On the other hand, by increasing pipe rotation speed above 7.5 rad/s (X7 = -0.25), cuttings removal gets better regardless of fluid velocity.
In sum, analysis of variance (Table 3) for CTE reveals that interaction terms of CS × µm (X1 × X4), CS × N (X1 × X7), MW × Vm (X3 × X6), µm × N (X4 × X7), and Vm × N (X6 × X7) respectively are the most significant terms in estimation of cutting transport efficiency.
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Therefore, they should be continuously optimized during drilling operation in order to have efficient hole cleaning. Cutting transport efficiency is a function of both controllable and uncontrollable variables. Cutting size, mud weight, mud viscosity and cutting weight are classified as uncontrollable variables because they are dependent on
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formation type, pore pressure and well depth. Factors of drilling rate of penetration, fluid velocity and pipe rotation speed are controllable factors. Optimizing controllable
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factors during drilling operation are practical and economical. Therefore, changing a controllable variable is preferred over uncontrollable factor. However, in order to maximize the cuttings removal efficiency at the given range of factors, it is required to determine all possible combinations of controllable and uncontrollable variables by applying an appropriate optimization method. 4.3.
Sensitivity and uncertainty analysis of CTE response function
The sensitivity analysis and uncertainty assessment of cutting transport efficiency was conducted using analysis of variance and performing Monte Carlo simulation. Monte Carlo simulation is applied to model the probability of different values of response function in a process that is under uncertainty and variability of the problem. Prior to 11
ACCEPTED MANUSCRIPT Monte Carlo simulation and generation of output distribution, it is required to assign appropriate probability distribution function for all factors included in the model. By using probability distribution functions, factors can have different probabilities of different outcomes occurring. Common probability distributions include normal, lognormal, uniform, triangular, etc. For the current study, statistical analysis of available
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data from real field revealed that truncated normal distribution is suitable one for all coded variables.
During a Monte Carlo simulation, random sampling from the input probability distribution functions is done. We used Latin Hypercube Sampling (LHS) to ensure
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sampling from the entire range of distribution functions. In addition, Latin hypercube sampling is more efficient than pure random sampling because it reduces iterations without changing the level of precision. Also LHS reflect more precisely the shape of a
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sampled distribution than pure random samples.
Fig. 9 shows the cumulative distribution of predicted CTE using Eq. (1) based on performing Monte Carlo simulation by considering Latin Hypercube Sampling (LHS) and generating 1000 random numbers from entire range of factors. It can be seen from Fig. 9 that the cutting transport efficiency could be accurately predicted at 95%
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confidence interval between 23 % and 68%.
Fig. 10 shows the results of sensitivity analysis in terms of contribution to total variance. As can be seen, respectively mud velocity (Vm), cutting weight (CW), pipe rotational speed (N), mud weight (MW), cutting size (CS), mud viscosity (µm), and
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drilling rate of penetration (ROP) have the greatest effect on final distribution of CTE. The sensitivity and uncertainty analysis of CTE in terms of contribution to total variance
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shows that cutting transport efficiency variation is dependent on three factors of mud velocity, cutting weight and pipe rotational speed by 86.3%. Therefore, these factors should be carefully characterized prior to drilling of a well for increasing cutting transport efficiency.
5. Conclusion In the present study, we examined the effect of various factors on cutting transport efficiency inside vertical well. The important factors that have been studied based on actual field data include mud velocity (Vm), drilling rate of penetration (ROP), mud weight (MW), cutting weight (CW), mud viscosity (µm), pipe rotational speed (N), and 12
ACCEPTED MANUSCRIPT cutting size (CS). Design of experiment (DOE) was used to perform the computational fluid dynamic (CFD) calculations in order to predict cuttings removal percentage from the well. After simulating all CFD models and extracting necessary information, response surface methodology (RSM) was used to develop a statistical mathematical model for prediction
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of CTE as a function of seven mentioned variables. In addition, sensitivity and uncertainty analysis of derived response function was done using Monte Carlo simulation (MCS). The main conclusions from this study are as follow:
1. Proposed statistical model based on combination of CFD calculations with DOE
process
by
considering
interaction
uncontrollable variables.
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and MCS provides detailed insight into the complex nature of cutting transport terms
between
controllable
and
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2. The sensitivity and uncertainty analysis of CTE response function in terms of contribution to total variance shows that factors of fluid velocity, cutting weight, pipe rotational speed, mud weight, cutting size, mud viscosity, and drilling rate of penetration respectively have the greatest effect on CTE variation. In addition, three factors of mud velocity, cutting weight and pipe rotational speed control
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CTE variation by 86.3 %. Therefore, these factors should be carefully characterized prior to drilling of a well to increase cleaning efficiency. 3. The statistical model of cutting transport efficiency reveals that five interaction terms of CS × µm (X1 × X4), CS × N (X1 × X7), MW × Vm (X3 × X6), µm × N (X4 × X7), •
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and Vm × N (X6 × X7) are the most important pairs. Interaction term of CS × µm shows that as the cutting size increases,
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cuttings transport efficiency could be increased by decreasing mud viscosity.
•
Interaction term of CS × N shows that as the cutting size increases, cuttings removal improves by increasing pipe rotation speed.
•
Interaction term of MW × Vm shows that as the mud weight increases, the fluid velocity should be optimally lowered in order to maximize cuttings transport efficiency. The simultaneous increasing of mud weight and fluid velocity is not an optimum choice for efficient hole cleaning. The optimum fluid velocity should be determined based on the value of mud weight for
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ACCEPTED MANUSCRIPT various drilling conditions in order to minimize the frictional pressure drop. •
Interaction term of µm × N shows that maximum hole cleaning occurs by simultaneous increase of pipe rotational speed and decrease of mud viscosity. Interaction term of Vm × N shows that cutting transport efficiency can be
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•
maximized by simultaneous increase of fluid velocity and pipe rotation speed.
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Mud viscosity Cutting size Cutting transport efficiency Cutting recovery factor Cutting weight Mud weight Pipe rotational speed Coefficient of determination Adjusted coefficient of determination Drilling rate of penetration Mud velocity Coded variable for cutting size Coded variable for drilling rate of penetration Coded variable for mud weight Coded variable for mud viscosity Coded variable for cutting weight Coded variable for mud velocity Coded variable for pipe rotational speed
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µm CS CTE CRF CW MW N R2 R2adj ROP Vm X1 X2 X3 X4 X5 X6 X7
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Nomenclature
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Bassal, A.A. 1995. A Study of the Effect of Drill Pipe Rotation on Cuttings Transport in Inclined Wellbores. MS thesis, U. of Tulsa, Tulsa, Oklahoma. Boussinesq, J. 1987. Essaisur la théorie des eauxcourantes, Mémoiresprésentés par divers savants à l'Académie des Sciences 23 (1): 1-680 Box, G. E. P. and Behnken, D. W. 1960. Some New Three Level Designs for the Study of Quantitative Variables, Technometrics, 2 (4): 455-475. Box, G.E.P., Wilson, K.B., 1951. On the experimental attainment of optimum conditions. J. R. Stat. Soc. Ser. B 13, 1-45. Cho, H., Shah, S.N. and Osisanya, S. O., 2002. A three-segment hydraulic model for cuttings transport in coiled tubing horizontal and deviated drilling. J. Can. Petroleum Technol., 41: 32-39. DOI: 10.2118/02-06-03. Ebrahimi A., and Khamehchi E., 2015. A robust model for computing pressure drop in vertical multiphase flow, Journal of natural gas science and engineering 26: 1306-1316 Ford J.T., Peden J.M., Oyeneyin M.B., Gao E., and Zarrough R., 1990. Experimental Investigation of Drilled Cuttings Transport in Inclined Boreholes, SPE 20421, SPE annual technical conference and exhibition, 23-26 September Harel and, Geir, 1993. Comparison of Cuttings Transport in Directional Drilling Using Low-Toxicity Invert Emulsion Mineral-Oil-Based and Water-Based Muds, SPE 25871-MS SPE Low Permeability Reservoirs Symposium, 26-28 April, Denver, Colorado Husssin, S.M., mrdJ.Azac, 1983. Experimental Study of Drilled Cutting Transport Using Common Drilling muds, SPEJ, pp. 11-20. Launder, B. and Spalding D., 1974. The numerical computation of turbulent flows, Comp. Methods in App. Mech and Eng., 3, 269-289. Li J., Luft B., 2014. Overview of Solids Transport Studies and Applications in Oil and Gas Industry - Experimental Work, SPE Russian Oil and Gas Exploration & Production Technical Conference and Exhibition, 14-16 October, Moscow, Russia, SPE-171285-MS. Li J., Luft B., 2014. Overview Solids Transport Study and Application in Oil-Gas IndustryTheoretical Work, International Petroleum Technology Conference, 10-12 December, Kuala Lumpur, Malaysia, IPTC-17832-MS. Mingqin, D., Stefan, M. and Claudia, Z., Nicholas, T. and Ramadan, A., 2007. Critical condition for effective sand-sized solids transport in horizontal and high angle wells, SPE paper 106707-MS. Mirzaeepeyman A., Bandar D.A., 2008. Using Nanoparticles to Decrease Differential Pipe Sticking and its feasibility in Iranian Oil Fields. Oil and Gas Business. Myers, R. H., and Montgomery, D. C., 1995. Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, New York, NY. Okrajni, S.S. and Azar, J.J., 1986. The Effects of Mud Rheology on Annular Hole Cleaning in Directional Wells, SPEDE 297-308; Trans., AIME, 285. Phuoc X, Tran R, Gupta LW, 2007. Nanofluids for Use as Ultra deep Drilling Fluids, R&D Facts National Energy Technology Laboratory. Piroozian A., Issham I., Zulkefli Y., Babakhani P., Ismail A. S. I., 2012. Impact of drilling fluid viscosity, velocity and hole inclination on cuttings transport in horizontal and highly deviated wells, J Petrol Explor Prod Technolvol (2):149–156 Ramadan, A., Skalle, P. and Johansen, S.T. 2002. A mechanistic model to determine the critical flow velocity required to initiate movement of spherical bed particles in inclined channels, Chem. Eng. Sci., vol (58): 2153-2163.
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Ramadan, A., Skalle, P. and Johansen, S.T. 2005. Application of a three layer modeling approach for solids in horizontal and inclined channels, Chem. Eng. Sci., vol (60): 25572570. Saeid M, Mariela AF, Rafiqul IM, 2006. Applications of Nanotechnology in Oil & Gas E & P. Journal of Petroleum Technology, vol (58). Sifferman T.R and Becker T.E., 1992. Hole Cleaning in Full Scale Inclined Wellbores, SPE Drilling Engineering, June. Sifferman, T.R. and Becker, T. E. 1992. Hole cleaning in full-scale inclined wellbores, SPE Paper 20422-PA. Sifferman, T.R. Myers, G.M. Haden, E.L. and Wahl, H.A., 1974. Drill cutting transport in Full-scale vertical annuli, J. Pet. Tech. Song X., Xu Z., Wang M., Li G., N. Shah S., Pang Z., 2017. Experimental Study on the Wellbore-Cleaning Efficiency of Microhole-Horizontal-Well Drilling, SPE Journal, SPE185965-PA. Syed, M.H. and Jamal, J.A., 1983. Experimental study of drilled cuttings transport using common drilling mud, SPE Paper 10674-PA. UdoZeidler, H. 1970. An experimental analysis of the transport of drilled particles, SPE Paper 3064-PA.
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ACCEPTED MANUSCRIPT 1 y = 0.9809x R² = 0.8477
0.9
0.7 0.6 0.5 0.4
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Predicted CTE
0.8
0.3 0.2 0.1 0 0.2
0.4 0.6 Actual CTE
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Fig. 1.Predicted CTE using Eq. (2) versus actual values of CTE
Main Effects Plot for CTE CS
ROP
MW
0.65
0.55
Mean
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Vm
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-1
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-1
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Fig.2 the main effects plot for cutting transport efficiency (the existence of interaction between factors can change the trend of main effect of factors on response for other levels than middle values)
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ACCEPTED MANUSCRIPT Interaction Effects Plot for CTE -1
0
1
-1
0
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-1
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-1
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ROP
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0.0 1.0
µm -1
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Vm
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Fig.3 the interaction effects plot for cutting transport efficiency
Contour Plot of CTE vs CS & µm
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0.0
2.75 mm
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µm
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1.0
Hold Values ROP 0 MW 0 CW 0 Vm 0 N 0
-0.5
-1.0 -1.0
CRF < 0.30 0.30 – 0.35 0.35 – 0.40 0.40 – 0.45 0.45 – 0.50 0.50 – 0.55 0.55 – 0.60 0.60 – 0.65 0.65 – 0.70 0.70 – 0.75 0.75 – 0.80 > 0.80
-0.5
0.0
0.5
1.0
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Fig. 4 the variation of cutting transport efficiency with cutting size and mud viscosity
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ACCEPTED MANUSCRIPT Contour Plot of CTE vs CS & N 1.0
CRF < 0.37 0.37 – 0.41 0.41 – 0.45 0.45 – 0.49 0.49 – 0.53 0.53 – 0.57 0.57 – 0.61 0.61 – 0.65 0.65 – 0.69 0.69 – 0.73 0.73 – 0.77 > 0.77
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N
0.5
7.5 mm
0.0
-0.5
0.0
0.5
Hold Values ROP 0 MW 0 µm 0 CW 0 Vm 0
1.0
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-1.0 -1.0
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-0.5
CS
Fig. 5 the variation of cutting transport efficiency with cutting size and pipe rotation speed
Contour Plot of CTE vs MW & Vm
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Vm
0.5
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1.0
Hold Values CS 0 ROP 0 µm 0 CW 0 N 0
-0.5
-1.0 -1.0
CRF < 0.235 0.235 – 0.260 0.260 – 0.285 0.285 – 0.310 0.310 – 0.335 0.335 – 0.360 0.360 – 0.385 0.385 – 0.410 0.410 – 0.435 0.435 – 0.460 0.460 – 0.485 > 0.485
-0.5
0.0
0.5
1.0
MW
Fig. 6 the variation of cutting transport efficiency as a function of mud weight and fluid velocity
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ACCEPTED MANUSCRIPT Contour Plot of CTE vs µm & N 1.0
CRF < 0.305477 0.305477 – 0.341090 0.341090 – 0.376703 0.376703 – 0.412316 0.412316 – 0.447929 0.447929 – 0.483542 0.483542 – 0.519155 0.519155 – 0.554768 0.554768 – 0.590381 0.590381 – 0.625994 0.625994 – 0.661607 > 0.661607
17 rad/s
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0.5
0.0
-0.5
Hold Values CS 0 ROP 0 MW 0 CW 0 Vm 0
4.5 rad/s
-0.5
0.0
0.5
1.0
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-1.0 -1.0
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N
14.5 cp
µm
Fig. 7 the variation of cutting transport efficiency as a function of mud viscosity and pipe rotation speed
1.0
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CRF < 0.24 0.24 – 0.27 0.27 – 0.30 0.30 – 0.33 0.33 – 0.36 0.36 – 0.39 0.39 – 0.42 0.42 – 0.45 0.45 – 0.48 0.48 – 0.51 0.51 – 0.54 > 0.54
0.0
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N
0.5
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Contour Plot of CTE vs Vm & N
7.5 rad/s
Hold Values CS 0 ROP 0 MW 0 µm 0 CW 0
-0.5
-1.0 -1.0
-0.5
0.0
0.5
1.0
Vm
Fig. 8 the variation of cutting transport efficiency with fluid velocity and pipe rotation speed
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0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.00
0.20
0.40
0.60
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Cumulative probability
0.9
0.80
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Cutting Transport Efficiency
1.00
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Fig. 9 the cumulative distribution of predicted CTE based on performing Monte Carlo simulation by considering Latin Hypercube Sampling (LHS)
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40 30 20
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10
90
Individual Effects
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Cumulative Effects
70 60 50 40
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Individual Percent
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100
30 20 10
0
Vm
Cumulative Percent
60
0 CW
N
MW
CS
µm
ROP
Fig. 10 the results of sensitivity analysis in terms of contribution to total variance for CTE response function
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ACCEPTED MANUSCRIPT Table 1 the range of factors, coded variables and transfer functions Coded Factor
Minimum Value
Mean Value
Maximum Value
CS (mm)
X1
2
5
8
ROP (Kg/s)
X2
0.1
0.3
0.5
MW (Kg/m3)
X3
1000
1250
1500
µm(cp)
X4
10
20
30
CW (Kg/m3)
X5
2200
2600
3000
Vm (m/s)
X6
0.5
1.3
2.1
N (rad/s)
X7
0
10
20
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Transfer Function ܵܥ− 5 3 ܴܱܲ − 0.3 0.2 ܹܯ− 1250 250 ߤ − 20 10 ܹܥ− 2600 400 ܸ − 1.3 0.8 ܰ − 10 10
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Factor
ACCEPTED MANUSCRIPT Table 2 the result of CFD calculation based on BBD for seven factors
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CW 1 0 -1 1 -1 0 0 0 0 -1 1 1 0 -1 -1 0 1 1 0 0 0 0 0 0 0 -1 0 -1 0 0 0 1 0 0 0 -1 1 1 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 -1 1 -1 0 -1
Vm 0 0 -1 0 0 -1 0 1 1 0 -1 1 0 1 0 -1 0 0 0 0 1 1 -1 -1 -1 0 1 0 0 -1 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 -1 0 -1 1 0 0 0 -1 -1 0 0 0
N 0 1 0 -1 0 -1 -1 -1 1 1 0 0 0 0 -1 0 0 -1 0 0 -1 0 1 1 0 0 0 0 0 -1 -1 0 0 0 1 0 1 0 -1 0 1 0 -1 1 1 0 0 0 0 0 1 0 0 0 -1 0 1
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CTE 0.36 0.47 0.12 0.52 0.36 0.35 0.48 0.45 0.85 0.46 0.03 0.39 0.43 0.38 0.43 0.37 0.72 0.44 1.00 0.37 0.37 0.41 0.56 0.35 0.35 0.37 0.37 0.46 0.38 0.47 0.39 0.38 0.94 0.41 0.77 0.50 0.63 0.57 0.44 0.39 0.34 0.41 0.55 0.72 0.49 0.61 0.46 0.54 0.37 0.47 0.41 0.35 0.00 0.00 0.46 0.37 0.40
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µm 0 1 -1 0 0 0 1 0 0 0 -1 1 0 1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 1 0 1 0 -1 0 -1 0 0 0 -1 0 0 -1 -1 -1 0 0 1 0 -1 1 1 1 1 1 0 -1 0
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MW -1 -1 0 0 1 0 -1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 -1 -1 -1 1 0 0 1 1 0 1 -1 -1 0 1 1 -1 0 0 -1 1 0 1 0 1 0 0 1 0 0 0 0 0 0
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ROP 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -1 -1 0 -1 1 -1 0 1 0 0 1 0 1 0 1 0 0 0 -1 -1 0 0 1 0 0 -1 0 0 0 0 -1 1 1 -1 0 -1 0 -1 0 0 1 1 -1
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CS -1 0 0 0 -1 -1 0 1 1 0 0 0 0 0 0 0 1 0 1 -1 -1 0 1 -1 0 -1 0 1 -1 1 0 -1 1 0 0 1 0 1 0 0 -1 0 0 0 0 0 1 0 0 1 0 -1 0 0 0 -1 0
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# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
ACCEPTED MANUSCRIPT Table 3 the result of Analysis of Variance for CTE response
Adj MS 0.091207 0.108517 0.344915 0.006689 0.003620 0.232270 0.049957 0.049184 0.072987 0.094162 0.048490 0.084807 0.063892 0.051968 0.079372 0.048920 0.063426 0.124249 0.066420 0.060445 0.030431 0.035586 0.006708
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F 13.60 16.18 51.42 1.00 0.54 34.63 7.45 7.33 10.88 14.04 7.23 12.64 9.53 7.75 11.83 7.29 9.46 18.52 9.90 9.01 4.54 5.31
P 0.000 0.000 0.000 0.324 0.467 0.000 0.010 0.010 0.002 0.000 0.011 0.001 0.004 0.008 0.001 0.010 0.000 0.000 0.003 0.005 0.040 0.027
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Adj SS 1.64173 0.75962 0.34492 0.00669 0.00362 0.23227 0.04996 0.04918 0.07299 0.56497 0.04849 0.08481 0.06389 0.05197 0.07937 0.04892 0.31713 0.12425 0.06642 0.06045 0.03043 0.03559 0.25489
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Seq SS 1.64173 0.75962 0.34492 0.00669 0.00362 0.23227 0.04996 0.04918 0.07299 0.56497 0.04649 0.12211 0.13286 0.05670 0.15790 0.04892 0.31713 0.12425 0.06642 0.06045 0.03043 0.03559 0.25489 1.89662
M AN U
DF 18 7 1 1 1 1 1 1 1 6 1 1 1 1 1 1 5 1 1 1 1 1 38 56
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Source Regression Linear CS ROP MW µm CW Vm N Square CS*CS ROP*ROP MW*MW CW*CW V*V N*N Interaction CS*µm CS*N MW*Vm µm *N Vm*N Residual Error Total
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Highlights
CFD and DOE techniques were used to predict the cutting transport efficiency.
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Box-Behnken Design was used to perform CFD calculations.
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Mud velocity (Vm), cutting weight (CW), pipe rotational speed (N), mud weight
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(MW), cutting size (CS), mud viscosity (µm), and drilling rate of penetration (ROP) have respectively the greatest effect on cuttings removal.
Three factors of mud velocity, cutting weight and pipe rotational speed control 86.3% of cuttings removal efficiency.
Statistical analysis shows that five interaction terms of CS × µm, CS × N, MW × Vm, µm × N, and Vm × N should be carefully characterized prior to drilling of a well to
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optimize cutting transport efficiency.
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S0920-4105(17)31046-X
DOI:
10.1016/j.petrol.2017.12.083
Reference:
PETROL 4573
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 10 April 2017 Revised Date:
21 December 2017
Accepted Date: 28 December 2017
Please cite this article as: Naderi, M., Khamehchi, E., Cutting transport efficiency prediction using probabilistic CFD and DOE techniques, Journal of Petroleum Science and Engineering (2018), doi: 10.1016/j.petrol.2017.12.083. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Cutting transport efficiency prediction using probabilistic CFD and DOE techniques
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Meysam Naderi, Ehsan Khamehchi* Department of Petroleum Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Avenue, Tehran, Iran *Corresponding Author Email: [email protected]
Abstract
Efficient cutting transport plays an important role in drilling operation. This process is
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controlled by many factors such as well geometry, drilling fluid properties, geological features and rate of penetration. In order to minimize the operational cost of inefficient hole cleaning, it is crucial to thoroughly investigate the simultaneous effect of various
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factors on the process of cutting transport.
In this regard, computational fluid dynamic (CFD) and design of experiment (DOE) techniques were used to predict the cutting transport efficiency (CTE) as a function mud velocity (Vm), drilling rate of penetration (ROP), mud weight (MW), cutting weight (CW), mud viscosity (µm), pipe rotational speed (N), and cutting size (CS).
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The results of study based on probabilistic CFD calculations using DOE and Monte Carlo simulation (MCS) show that respectively factors of mud velocity, cutting weight, pipe rotational speed, mud weight, cutting diameter, mud viscosity, and drilling rate of penetration have the greatest impact on transportation of drilled cuttings from bottom
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of the well to the surface. In addition, result of MCS based on analysis of total variance reveals that 86.3% of cutting transport efficiency variation could be controlled by three
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factors of mud velocity, cutting weight and pipe rotational speed. Therefore, these factors should be carefully characterized during drilling and hole cleaning to maximize the cutting transport efficiency. Keywords: Cutting transport efficiency, Computational fluid dynamic, Design of experiment, Monte Carlo simulation
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1. Introduction A good drilling operation with maximum rate of penetration and minimum cost is a function of efficient cutting transport. Several factors influence the process of cutting motion toward the surface. Typical variables which determine the effectiveness of drilling mud in removing the cuttings from the wellbore are drilling fluid properties
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such as viscosity, yield point, fluid type, hole diameter and length, annular velocity, well inclination angle, size and shape of cutting, cutting weight, and drilling rate of penetration. The interaction between various factors makes the situation more complex.
problems and consequently unforeseen costs.
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Therefore, it is crucial to estimate the degree of hole cleaning to reduce drilling
Several authors have investigated the cutting transport problem. Udo Zeidler (1970)
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studied the effect of cutting dynamics on mud carrying capacity in a vertical well. The experimental study of Sifferman et al. (1974) using a full scale vertical annulus for different systems of drilling fluid showed that rotary speed, cutting generation rate, annular size and pipe eccentricity has minimal effect on cutting transport. Casing size and drilling fluid density showed a moderate effect. However, annular velocity and mud properties were the most cutting transport controlling factors. Hussain et al (1983)
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experimental study of cutting transport revealed that increased annular velocity and yield strength of drilling fluid are favorable conditions for efficient hole-cleaning. Syed and Jamal (1983) studied the cutting transport problem in vertical and inclined wellbores experimentally. The experimental study performed by Okrajni and Azar
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(1985) showed that transportation of cuttings is not influenced by yield point, and yield point to plastic viscosity ratio under turbulent regime. However, higher mud yield value
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shows a better transport performance for laminar flow in the range of low-angle wells. The study also showed that the effect of eccentricity is a function of inclination angle and flow regime. For high inclination angles between 55 and 90°, the effect of pipe eccentricity on hole cleaning is moderate under turbulent flow and significant for laminar flow. In general, they concluded that mud flow rate has a dominant effect on annular hole-cleaning. The experimental analysis of cutting transport phenomenon in an included wellbore by Ford et al. (1990) indicated that the velocity needed to initiates cuttings transport is sensitive to inclination angle. Pipe rotation significantly reduces the critical fluid transport velocity when circulating with medium or highly viscous fluids, and cutting removal is very effective under turbulent flow condition. Sifferman 2
ACCEPTED MANUSCRIPT and Becker (1992) performed an experimental study to evaluate the effect of several parameters on hole-cleaning in an inclined well. The parameters were mud velocity, mud density, mud rheology, mud type, cuttings size, rate of penetration, rotary speed, drill pipe eccentricity, diameter of drill pipe, and hole angle. The result of survey showed that mud velocity and mud weight have the greatest effect on hole-cleaning, and
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as the mud weight increases the cutting beds shows decreasing. In addition, the study revealed that pipe rotation effect on cutting buildup is greater for inclination angles near horizontal, small cuttings, and low ROP. Harel and Geir (1993) used two Invert Emulsion Mineral-Oil-Based and Water-Based Muds systems to experimentally
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investigate the limestone cutting transport behavior. For vertical or near vertical inclination angles, the study showed that cuttings transport rate increases as the yield point and plastic viscosity of both mud systems decreases but this effect is more severe
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in the inverted emulsion oil-base muds. For higher inclination angles, hole-cleaning for both mud types improves by simultaneous decreasing of yield point and plastic viscosity, and increasing flow rate. Belavadi and Chukwu (1994) investigated the relation between transportation of cuttings and the transport ratio and dimensionless quantities. Cho et al. (2002) used continuity and Navier Stokes equations to study the
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effect of annular velocity, pressure gradient and mud rheology on cuttings transport. Ramadan et al. (2002) introduced a mechanistic model to estimate the critical flow rate in inclined channel by analyzing the forces acting on spherical bed particles. Saeid et al. (2006) and Phuoc et al. (2007) experimental study showed that drag reduction and
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sand consolidation feature of nano-fluids improves drilling rate of penetration. Mingqin et al. (2007) developed a mechanistic model to estimate the critical velocity in order to
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predict which drilling fluid is effective in bed formation prevention and particles bed erosion. Abouzar et al. (2008) experimental study showed the positive effect of carbon black nano particles on the drilling mud performance for reducing mud filtrate and mud cake thickness. Piroozian et al. (2012) experimentally investigated the effect of the mud viscosity, fluid velocity and hole inclination on cuttings transport in horizontal and highly deviated wells. They considered three types of drilling fluid. The results indicated that cuttings transport efficiency increases by viscosity approximately 8 % at all angles provided the flow regime remained turbulent for constant flow velocity. However, further increase of viscosity reduces cutting transport performance by a total average of 12 % because of changing flow regime from turbulent into transient and laminar flow. 3
ACCEPTED MANUSCRIPT Li and Luft (2014) presented a critical review of the previous solids transport theoretical studies in both drilling and well interventions. In addition, they introduced a methodology for developing the empirical correlations and a mechanistic model. Li and Luft (2014) studied the cutting transport experimentally. They presented useful general guide to gather comprehensive laboratory flow loop test data required to validate the
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derived semi-empirical theoretical model to simulate the hole cleaning process. Ebrahimi and Khamehchi (2015) developed a robust model using artificial neural network for computing pressure drop in vertical multiphase flow that could be possibly used to optimize required surface pressure to have better mud carrying capacity. Song
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et al. (2017) experimentally investigated the effect of the flow rate, cutting diameter, rate of penetration, eccentricity, and wellbore diameter on cleaning performance in horizontal wells using a full-scale horizontal-cuttings-transport flow loop. In addition,
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they proposed a model for prediction of cuttings volumetric concentration and the cuttings-bed height based on dimensional analysis. The results of their study revealed that cutting transport efficiency in horizontal wells increases by increased flow rate, decreased ROP, lower eccentricity, and smaller ratio of drillpipe diameter to wellbore diameter.
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Review of previous studies shows that although many experimental and simulation works have been done regarding cutting transport process, the interaction effect of variables on cutting transport performance has never been investigated. The interaction effects play a crucial role in the cutting transport process. Because of complex nature of
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problem, it is very important to consider the variables simultaneously in order to find better hole cleaning strategy and improved drilling operation with minimum costs. In
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this regard, the paper aims to formulate cutting transport efficiency (CTE) as a function of mud velocity (Vm), drilling rate of penetration (ROP), mud weight (MW), cutting weight (CW), mud viscosity (µm), pipe rotational speed (N), and cutting size (CS) by using design of experiment (DOE) and computational fluid dynamic (CFD) calculations. Box-Behnken design (BBD) was used to run CFD to establish the mathematical relation between cutting transport efficiency and mentioned independent variables. CFD calculations to study the cutting transportation in the vertical annulus were done using ANSYS (FLUENT) commercial code, Reynolds-Averaged Navier-Stokes equations and discrete phase model (DPM). Next, the main and interaction effects of various factors on the transportation of cuttings will be analyzed using response surface methodology 4
ACCEPTED MANUSCRIPT (RSM). Finally, sensitivity and uncertainty analysis of cutting transport efficiency statistical model will be performed by applying Monte carlo simulation. The following section describes the CFD model used for calculating the cutting transport efficiency as a function of various factors. Section 3 presents the methodology used to derive cutting transport efficiency response function. Results of applying DOE, RSM and
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CFD will be presented and discussed in Section 4. Finally, Section 5 provides the core findings of this research.
2. Model description
In this survey, the annulus formed by the configurations of the wellbore and drill pipe is
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used to simulate virtual fluid flow system. The inner diameter of wellbore is 245 mm. The outer diameter of drill pipe is 140 mm. The total depth of the well is 1000 m.
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GAMBIT 2.4.6 software was used to model the computational mesh of the annulus. Discretisation of the annulus geometry using structured mesh results a total mesh layout of 250000 hexahedric cells. Grid sensitivity showed that this number of cells is adequate for current investigation.
In order to calculate the velocity components, first, it is required to integrate the Reynolds-averaged Navier-Stokes equations in each computational cell throughout the
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domain, then being discretized using finite volumes approach, and finally being linearized and solved numerically.
The PRESTO routine is used for the pressure discretisation scheme. Although, the CFD
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calculations based on PRESTO scheme is computationally costly, the results are more accurate than standard pressure discretisation. PRESTO discretisation method avoids interpolation errors and pressure gradient assumptions on boundaries. The SIMPLEC
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algorithm is used for the pressure-velocity coupling because of its ability to speed-up convergence by applying the increased under-relaxation factor. In order to consider the laminar and the turbulent regions by varying flow rate, the k −ε model of Lander and Spalding (1974) is selected to simulate the turbulent regimes. The Boussinesq hypothesis is used in the k −ε model. Although there are various numerical methods for simulation of turbulent flows by solving the Reynolds equations, the standard k −ε model is selected in this study because it is used in industrial flow simulations with excellent performance and widely validated as a two- equation eddy viscosity turbulence model.
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ACCEPTED MANUSCRIPT For discretisation of mass, momentum, turbulent kinetic energy and turbulent dissipation rate equations, QUICK method is applied because of its third order accuracy and better adaptation to structured meshes of hexahedric cells. All CFD calculations will be conducted using ANSYS (FLUENT) commercial code. In order to calculate the cutting transport efficiency, it is required to monitor the
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transportation of cuttings in the annulus from the well bottom to the surface. Cutting transport efficiency can be determined by the ratio between mass of drilled cuttings at the surface and the mass of generated cuttings at the bottom of wellbore under different operational conditions. This can be done using discrete phase model (DFM). Using DFM
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option in FLUENT, the user can inject particles with different injection rates, shapes, sizes, densities into the fluid flow system.
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3. Methodology
The present study investigates the effect of several important variables on cutting transportation inside annulus of vertical wells. There are many numbers of factors which control the transport efficiency in vertical wells. Typical factors include size, density and shape of cuttings, mud density, fluid viscosity and velocity, hole-pipe configuration, pipe eccentricity and pipe rotational speed. However, it is not affordable
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to include all variables in the model because the required number of CFD simulations increases very rapidly by the number of factors. In this regard, based on previous studies, experience and preliminary analysis of field data; seven major variables have
EP
been identified to be included in the CTE model. These factors are mud velocity, drilling rate of penetration, mud weight, cutting weight, mud viscosity, pipe rotational speed, and cutting size.
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In order to estimate the CTE, we used Box-Behnken design (1960) to perform CFD calculations. Box-Behnken design (BBD) is a type of response surface design that allows efficient estimation of the first- and second-order coefficients. Box-Behnken design often reduces the required number of simulation runs, and consequently it is less expensive to run than other response surface designs with the same number of factors. Based on Box-Behnken design, it is required to model and simulate 57 different CFD models for analyzing the effect of seven factors on cutting transport efficiency. Next, in order to establish the mathematical relation between independent factors and cutting transport efficiency, response surface methodology (RSM) was used. Response
6
ACCEPTED MANUSCRIPT surface methodology is a collection of mathematical techniques to predict the relation between dependent and independent variables. More details about response surface methodology are given in Box and Wilson (1951). We used full quadratic form of multiple regression equation in order to predict CTE as a function of seven independent variables. The full quadratic form of a response surface is given by: ܨሺܺଵ , ܺଶ , ܺଷ … ܺே ሻ = ߙ + ߙ ܺ + ୀଵ
ே
ߙ ܺଶ ୀଵ
ேିଵ ே
+ ߙ ܺ ܺ ழ ୀଶ
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ே
(1)
Where F is the response function; ߙ is the intercept; αi, αii, αji are respectively the main, quadratic and interaction terms coefficients; Xi and Xj are independent factors and N is
SC
the number of independent factors. After collecting all necessary data, the regression coefficients can be estimated by applying least square method to minimize the error
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between observed and fitted data. It is worth to note that all collected data including mud weight, cutting weight, fluid velocity, mud viscosity, drilling rate of penetration, drill-string rotational speed and all related turbulency factors which have been used in this study are based on actual wells drilled in south of Iran.
Table 1 shows the range of factors, coded variables and transfer functions. In this table, X1, X2, X3, X4, X5, X6 and X7 are coded variables between -1 and +1 respectively for cutting
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size (CS), drilling rate of penetration (ROP), mud weight (MW), mud viscosity (µm), cutting weight (CW), mud velocity (Vm), and pipe rotational speed (N). Transfer functions are used for normalizing the range of factors between -1 and +1 with mean
EP
and variance of respectively 0 and 1. For example, the range of cutting size from 2 mm to 8 mm can be normalized between -1 and +1 using transfer function of
ௌିହ ଷ
.
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Table 2 shows the result of CFD calculations for estimation of CTE based on BBD for seven factors. By applying response surface methodology, the following response function was developed for CTE. CTE = 0.384+0.12 X1 + 0.017 X2–0.013 X3–0.098 X4 + 0.046 X5 + 0.0453 X6+ 0.0552 X7 + 0.07 X12+0.093 X22+0.081 X32–0.073 X52– 0.09 X62+0.07X72–0.125
(2)
X1X4 + 0.091 X1X7–0.087 X3X6–0.062 X4X7+ 0.067 X6X7 Where X1, X2, X3, X4, X5, X6 and X7 are coded variables between -1 and +1 for mentioned factors in Table 1. The coefficient of determination (R2) and adjusted coefficient of determination (R2adj) for CTE response function are 86.56 and 80.19% respectively. R2 is a measure of the proportion of the variance in the dependent variable that is 7
ACCEPTED MANUSCRIPT predictable from the fitted model. R2adj shows the goodness of fit for the regression adjusted for the number of terms. The low difference between R2adj and R2 indicates that the significant terms have been included in the model (Myers and Montgomery, 1995). The derived proxy has been validated by plotting predicted CTE using Eq. (2) versus actual values of CTE in Fig. 1. In addition, analysis of variance for derived proxy shows
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that all terms of Eq. (2) are significant at 5% of significance level for prediction at 95% confidence interval. Therefore, all performed tests on CTE response function reveal that Eq. (2) is statistically significant to study the transportation of drilled cuttings from well bottom to surface.
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The following section investigates the main and interaction effects of factors on the
4. Results and Discussion
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variation of cutting transport efficiency.
Investigation of Eq. (2) reveals that cutting transport efficiency is a function of main effects, interaction effects, and square power effects of factors. The constant in the first of equation implies that the cutting transport efficiency for base case model is equal to that constant. Main effects
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4.1.
Fig. 2 shows the main effects plot for cutting transport efficiency. The main effects plot shows the influence of individual factors while the other factors are kept constant at their middle values in coded units. The interaction between various factors can affect
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the main effect of factors on the response function. Therefore, the main effect of factors in Fig. 2 is only plotted for middle values of other factors. As can be seen, increasing cutting size and fluid viscosity respectively increases, and
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decreases cutting transport efficiency. Increasing drilling fluid viscosity is desirable to suspend cuttings inside the well and to avoid them from falling and settling at the wellbore bottom. However, high viscous drilling fluid increases the pumping pressures and consequently reduces the cutting carrying capacity. Increasing rate of penetration, first decreases cutting transport efficiency and then increases it. High rate of penetration limits the cutting transport efficiency due to increasing hydraulic requirement for effective wellbore cleaning. As can be clearly seen from Eq. (2), the main effect plot for mud weight could be changed because it has an interaction with fluid velocity. For example, for three 8
ACCEPTED MANUSCRIPT different values of fluid velocity, the main effect of mud weight varies differently. Eq. (2) indicates that for normalized fluid velocity of -1 (0.5 m/sec), as mud weight increases the cutting transport efficiency increases. In this case, the heavy muds give better cuttings transport than the middle and light weight muds. On the other hand, for normalized fluid velocity of +1 (2.1 m/sec), as mud weight increases the cutting
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transport efficiency decreases. In this case, the light muds give better cutting transport than the middle and heavy weight muds. However, for middle values of normalized fluid velocity of 0 (1.3 m/sec) which is shown in Fig. 2, as mud weight increases the cutting transport efficiency first decreases and then increases.
Increasing pipe rotation speed in the range of 10-20 rad/s (X7 between 0 and +1) shows
SC
significant increase in cutting transport efficiency. In the range of 0-10 rad/s (X7 between -1 and 0), the effect of pipe rotation speed shows insignificant changes.
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However, the effect of pipe rotation speed on cuttings transportation is a complex process and it depends on various factors like drilling fluid rheology, shape and size of cuttings, and flow rate. In sum, increasing pipe rotation reduces the mud viscosity which is normally a desirable property because it reduces pumping pressures inside drill pipe and increases cutting carrying capacity in the annulus showing effective hole cleaning. Cutting transport efficiency first increases and then decreases by increasing cutting
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weight. Increasing cutting weight, increases the particle slip velocity and consequently reduces the mud carrying capacity.
Increasing the drilling fluid velocity increases the annular velocity and consequently cuttings carrying capacity of fluid. However, frictional pressure drop increases by
EP
excessive drilling fluid velocity. In order to compensate the pressure drop, the pumping pressure should be increased which reduces the mud carrying capacity. Therefore, excessive flow rate is detrimental to the bottom hole cleaning which cause a reduction
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in the rate of penetration. 4.2.
Interaction effects
Fig. 3 shows the interaction effects plot for cutting transport efficiency. As can be seen from derived response function for CTE, five interaction terms of CS ×µm (X1× X4), CS ×N (X1× X7), MW × Vm (X3 × X6), µm × N (X4 × X7), and Vm× N (X6 × X7), are the most important pairs. Figs. 4 through 8 show the variation of cutting transport efficiency as a function of these interaction terms.
9
ACCEPTED MANUSCRIPT 4.2.1. Interaction between cutting size and mud viscosity (CS × µm) Fig. 4 shows that increasing mud viscosity reduces cuttings removal from the well for almost all size of cuttings. This reduction of transport efficiency is due to increased pumping pressure and decreased cutting carrying capacity of the drilling fluid. However, for a small range of cutting sizes between 2 mm (X1= -1) and 2.75 mm (X1 = -
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0.75), hole cleaning improves by increasing mud viscosity. As can be seen, cuttings transport efficiency increases by decreasing mud viscosity as the cutting size increases. 4.2.2. Interaction between cutting size and pipe rotation speed (CS × N)
Fig. 5reveals that cutting transport efficiency improves by increasing pipe rotation speed for cutting sizes greater than 7.5 mm (X1 = 0.83). For values between 2 mm (X1 = -
SC
1) and 7.5 mm (X1 = 0.83), increasing pipe rotational speed first decreases cutting transport efficiency and then increases it. Figure also shows that cuttings removal
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increases by increasing pipe rotation speed as the cutting size increases. 4.2.3. Interaction between mud weight and fluid velocity (MW × Vm) Fig. 6 indicates that for all values of constant mud weight, increasing fluid velocity first increases cuttings removal efficiency and then decreases it. On the other hand, for all values of constant fluid velocity, increasing mud weight first decreases cuttings removal
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efficiency and then increases it. Therefore, as the mud weight increases, the fluid velocity should be optimally lowered in order to maximize cuttings transport efficiency. As can be seen from the figure, when the mud weight is low, it is required to keep the fluid velocity between 1.42 m/s (X6=0.15) and 2.06 m/s (X6=0.95) in order to maximize
EP
the cutting transport efficiency. However, for high values of mud weight, fluid velocity should be kept between 1.02 m/s (X6=-0.35) and 1.66 m/s (X6=0.45). In general, during
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drilling as depth gets deeper, mud weight should be increased in order to keep the wellbore stability and to overcome formation pore pressure. In this situation, in order to maximize the cutting transport efficiency, the fluid velocity should be optimally decreased from 2.1 (X6=+1) to 1.3 m/sec (X6=0). The exact optimum value of fluid velocity could be determined by using some optimization algorithms for various values of mud weight in order to maximize jet impact force or hydraulic horse power required for highest hole cleaning performance. In fact, the simultaneous increasing of mud weight and fluid velocity is not an optimum choice for efficient hole cleaning. Increasing fluid velocity above its optimum value results in additional frictional pressure drop and consequently the available energy at the bit for efficient hole cleaning reduces. 10
ACCEPTED MANUSCRIPT 4.2.4. Interaction between mud viscosity and pipe rotation speed (µm × N) Fig. 7 shows that cutting transport efficiency increases by increasing pipe rotational speed for mud viscosity between 10 cp (X4 = -1) and 14.5 cp (X4 = -0.55). For values greater than 14.5 cp, increasing pipe rotation first decreases and then increases cutting transport efficiency. On the other hand, increasing mud viscosity reduces efficiency of
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cutting transportation regardless of pipe rotational speed. As can be seen, this reduction is very sensitive for pipe rotational speed between 4.5 rad/s (X7 = -0.55) and 17 (X7 = 0.7) rad/s. As can be seen, maximum hole cleaning occurs at the low mud viscosity and high value of pipe rotation speed.
4.2.5. Interaction between fluid velocity and pipe rotation speed (Vm × N)
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Fig. 8 shows the contour plot of CTE versus fluid velocity and pipe rotation speed. As can be seen, cutting transport efficiency could be maximized by simultaneous increasing
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of fluid velocity and pipe rotation speed. On the other hand, by increasing pipe rotation speed above 7.5 rad/s (X7 = -0.25), cuttings removal gets better regardless of fluid velocity.
In sum, analysis of variance (Table 3) for CTE reveals that interaction terms of CS × µm (X1 × X4), CS × N (X1 × X7), MW × Vm (X3 × X6), µm × N (X4 × X7), and Vm × N (X6 × X7) respectively are the most significant terms in estimation of cutting transport efficiency.
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Therefore, they should be continuously optimized during drilling operation in order to have efficient hole cleaning. Cutting transport efficiency is a function of both controllable and uncontrollable variables. Cutting size, mud weight, mud viscosity and cutting weight are classified as uncontrollable variables because they are dependent on
EP
formation type, pore pressure and well depth. Factors of drilling rate of penetration, fluid velocity and pipe rotation speed are controllable factors. Optimizing controllable
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factors during drilling operation are practical and economical. Therefore, changing a controllable variable is preferred over uncontrollable factor. However, in order to maximize the cuttings removal efficiency at the given range of factors, it is required to determine all possible combinations of controllable and uncontrollable variables by applying an appropriate optimization method. 4.3.
Sensitivity and uncertainty analysis of CTE response function
The sensitivity analysis and uncertainty assessment of cutting transport efficiency was conducted using analysis of variance and performing Monte Carlo simulation. Monte Carlo simulation is applied to model the probability of different values of response function in a process that is under uncertainty and variability of the problem. Prior to 11
ACCEPTED MANUSCRIPT Monte Carlo simulation and generation of output distribution, it is required to assign appropriate probability distribution function for all factors included in the model. By using probability distribution functions, factors can have different probabilities of different outcomes occurring. Common probability distributions include normal, lognormal, uniform, triangular, etc. For the current study, statistical analysis of available
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data from real field revealed that truncated normal distribution is suitable one for all coded variables.
During a Monte Carlo simulation, random sampling from the input probability distribution functions is done. We used Latin Hypercube Sampling (LHS) to ensure
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sampling from the entire range of distribution functions. In addition, Latin hypercube sampling is more efficient than pure random sampling because it reduces iterations without changing the level of precision. Also LHS reflect more precisely the shape of a
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sampled distribution than pure random samples.
Fig. 9 shows the cumulative distribution of predicted CTE using Eq. (1) based on performing Monte Carlo simulation by considering Latin Hypercube Sampling (LHS) and generating 1000 random numbers from entire range of factors. It can be seen from Fig. 9 that the cutting transport efficiency could be accurately predicted at 95%
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confidence interval between 23 % and 68%.
Fig. 10 shows the results of sensitivity analysis in terms of contribution to total variance. As can be seen, respectively mud velocity (Vm), cutting weight (CW), pipe rotational speed (N), mud weight (MW), cutting size (CS), mud viscosity (µm), and
EP
drilling rate of penetration (ROP) have the greatest effect on final distribution of CTE. The sensitivity and uncertainty analysis of CTE in terms of contribution to total variance
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shows that cutting transport efficiency variation is dependent on three factors of mud velocity, cutting weight and pipe rotational speed by 86.3%. Therefore, these factors should be carefully characterized prior to drilling of a well for increasing cutting transport efficiency.
5. Conclusion In the present study, we examined the effect of various factors on cutting transport efficiency inside vertical well. The important factors that have been studied based on actual field data include mud velocity (Vm), drilling rate of penetration (ROP), mud weight (MW), cutting weight (CW), mud viscosity (µm), pipe rotational speed (N), and 12
ACCEPTED MANUSCRIPT cutting size (CS). Design of experiment (DOE) was used to perform the computational fluid dynamic (CFD) calculations in order to predict cuttings removal percentage from the well. After simulating all CFD models and extracting necessary information, response surface methodology (RSM) was used to develop a statistical mathematical model for prediction
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of CTE as a function of seven mentioned variables. In addition, sensitivity and uncertainty analysis of derived response function was done using Monte Carlo simulation (MCS). The main conclusions from this study are as follow:
1. Proposed statistical model based on combination of CFD calculations with DOE
process
by
considering
interaction
uncontrollable variables.
SC
and MCS provides detailed insight into the complex nature of cutting transport terms
between
controllable
and
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2. The sensitivity and uncertainty analysis of CTE response function in terms of contribution to total variance shows that factors of fluid velocity, cutting weight, pipe rotational speed, mud weight, cutting size, mud viscosity, and drilling rate of penetration respectively have the greatest effect on CTE variation. In addition, three factors of mud velocity, cutting weight and pipe rotational speed control
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CTE variation by 86.3 %. Therefore, these factors should be carefully characterized prior to drilling of a well to increase cleaning efficiency. 3. The statistical model of cutting transport efficiency reveals that five interaction terms of CS × µm (X1 × X4), CS × N (X1 × X7), MW × Vm (X3 × X6), µm × N (X4 × X7), •
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and Vm × N (X6 × X7) are the most important pairs. Interaction term of CS × µm shows that as the cutting size increases,
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cuttings transport efficiency could be increased by decreasing mud viscosity.
•
Interaction term of CS × N shows that as the cutting size increases, cuttings removal improves by increasing pipe rotation speed.
•
Interaction term of MW × Vm shows that as the mud weight increases, the fluid velocity should be optimally lowered in order to maximize cuttings transport efficiency. The simultaneous increasing of mud weight and fluid velocity is not an optimum choice for efficient hole cleaning. The optimum fluid velocity should be determined based on the value of mud weight for
13
ACCEPTED MANUSCRIPT various drilling conditions in order to minimize the frictional pressure drop. •
Interaction term of µm × N shows that maximum hole cleaning occurs by simultaneous increase of pipe rotational speed and decrease of mud viscosity. Interaction term of Vm × N shows that cutting transport efficiency can be
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•
maximized by simultaneous increase of fluid velocity and pipe rotation speed.
EP
TE D
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Mud viscosity Cutting size Cutting transport efficiency Cutting recovery factor Cutting weight Mud weight Pipe rotational speed Coefficient of determination Adjusted coefficient of determination Drilling rate of penetration Mud velocity Coded variable for cutting size Coded variable for drilling rate of penetration Coded variable for mud weight Coded variable for mud viscosity Coded variable for cutting weight Coded variable for mud velocity Coded variable for pipe rotational speed
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µm CS CTE CRF CW MW N R2 R2adj ROP Vm X1 X2 X3 X4 X5 X6 X7
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Nomenclature
14
ACCEPTED MANUSCRIPT
References
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5
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Bassal, A.A. 1995. A Study of the Effect of Drill Pipe Rotation on Cuttings Transport in Inclined Wellbores. MS thesis, U. of Tulsa, Tulsa, Oklahoma. Boussinesq, J. 1987. Essaisur la théorie des eauxcourantes, Mémoiresprésentés par divers savants à l'Académie des Sciences 23 (1): 1-680 Box, G. E. P. and Behnken, D. W. 1960. Some New Three Level Designs for the Study of Quantitative Variables, Technometrics, 2 (4): 455-475. Box, G.E.P., Wilson, K.B., 1951. On the experimental attainment of optimum conditions. J. R. Stat. Soc. Ser. B 13, 1-45. Cho, H., Shah, S.N. and Osisanya, S. O., 2002. A three-segment hydraulic model for cuttings transport in coiled tubing horizontal and deviated drilling. J. Can. Petroleum Technol., 41: 32-39. DOI: 10.2118/02-06-03. Ebrahimi A., and Khamehchi E., 2015. A robust model for computing pressure drop in vertical multiphase flow, Journal of natural gas science and engineering 26: 1306-1316 Ford J.T., Peden J.M., Oyeneyin M.B., Gao E., and Zarrough R., 1990. Experimental Investigation of Drilled Cuttings Transport in Inclined Boreholes, SPE 20421, SPE annual technical conference and exhibition, 23-26 September Harel and, Geir, 1993. Comparison of Cuttings Transport in Directional Drilling Using Low-Toxicity Invert Emulsion Mineral-Oil-Based and Water-Based Muds, SPE 25871-MS SPE Low Permeability Reservoirs Symposium, 26-28 April, Denver, Colorado Husssin, S.M., mrdJ.Azac, 1983. Experimental Study of Drilled Cutting Transport Using Common Drilling muds, SPEJ, pp. 11-20. Launder, B. and Spalding D., 1974. The numerical computation of turbulent flows, Comp. Methods in App. Mech and Eng., 3, 269-289. Li J., Luft B., 2014. Overview of Solids Transport Studies and Applications in Oil and Gas Industry - Experimental Work, SPE Russian Oil and Gas Exploration & Production Technical Conference and Exhibition, 14-16 October, Moscow, Russia, SPE-171285-MS. Li J., Luft B., 2014. Overview Solids Transport Study and Application in Oil-Gas IndustryTheoretical Work, International Petroleum Technology Conference, 10-12 December, Kuala Lumpur, Malaysia, IPTC-17832-MS. Mingqin, D., Stefan, M. and Claudia, Z., Nicholas, T. and Ramadan, A., 2007. Critical condition for effective sand-sized solids transport in horizontal and high angle wells, SPE paper 106707-MS. Mirzaeepeyman A., Bandar D.A., 2008. Using Nanoparticles to Decrease Differential Pipe Sticking and its feasibility in Iranian Oil Fields. Oil and Gas Business. Myers, R. H., and Montgomery, D. C., 1995. Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, New York, NY. Okrajni, S.S. and Azar, J.J., 1986. The Effects of Mud Rheology on Annular Hole Cleaning in Directional Wells, SPEDE 297-308; Trans., AIME, 285. Phuoc X, Tran R, Gupta LW, 2007. Nanofluids for Use as Ultra deep Drilling Fluids, R&D Facts National Energy Technology Laboratory. Piroozian A., Issham I., Zulkefli Y., Babakhani P., Ismail A. S. I., 2012. Impact of drilling fluid viscosity, velocity and hole inclination on cuttings transport in horizontal and highly deviated wells, J Petrol Explor Prod Technolvol (2):149–156 Ramadan, A., Skalle, P. and Johansen, S.T. 2002. A mechanistic model to determine the critical flow velocity required to initiate movement of spherical bed particles in inclined channels, Chem. Eng. Sci., vol (58): 2153-2163.
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Ramadan, A., Skalle, P. and Johansen, S.T. 2005. Application of a three layer modeling approach for solids in horizontal and inclined channels, Chem. Eng. Sci., vol (60): 25572570. Saeid M, Mariela AF, Rafiqul IM, 2006. Applications of Nanotechnology in Oil & Gas E & P. Journal of Petroleum Technology, vol (58). Sifferman T.R and Becker T.E., 1992. Hole Cleaning in Full Scale Inclined Wellbores, SPE Drilling Engineering, June. Sifferman, T.R. and Becker, T. E. 1992. Hole cleaning in full-scale inclined wellbores, SPE Paper 20422-PA. Sifferman, T.R. Myers, G.M. Haden, E.L. and Wahl, H.A., 1974. Drill cutting transport in Full-scale vertical annuli, J. Pet. Tech. Song X., Xu Z., Wang M., Li G., N. Shah S., Pang Z., 2017. Experimental Study on the Wellbore-Cleaning Efficiency of Microhole-Horizontal-Well Drilling, SPE Journal, SPE185965-PA. Syed, M.H. and Jamal, J.A., 1983. Experimental study of drilled cuttings transport using common drilling mud, SPE Paper 10674-PA. UdoZeidler, H. 1970. An experimental analysis of the transport of drilled particles, SPE Paper 3064-PA.
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ACCEPTED MANUSCRIPT 1 y = 0.9809x R² = 0.8477
0.9
0.7 0.6 0.5 0.4
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Predicted CTE
0.8
0.3 0.2 0.1 0 0.2
0.4 0.6 Actual CTE
0.8
1
SC
0
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Fig. 1.Predicted CTE using Eq. (2) versus actual values of CTE
Main Effects Plot for CTE CS
ROP
MW
0.65
0.55
Mean
CW
Vm
N
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0.60
µm
0.50
EP
0.45
0.40
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0.35
0.30
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1
Fig.2 the main effects plot for cutting transport efficiency (the existence of interaction between factors can change the trend of main effect of factors on response for other levels than middle values)
17
ACCEPTED MANUSCRIPT Interaction Effects Plot for CTE -1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1 1.0
CS -1
0.5
CS
0 1
0.0 1.0 ROP -1 0.5
ROP
0 1
0.0 1.0
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MW -1
0.5
MW
0 1
0.0 1.0
µm -1
0.5
µm
0 1
0.0 1.0
CW
-1
0.5
CW
0
SC
1
0.0 1.0 Vm -1 0.5
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Vm
0 1
0.0
N
Fig.3 the interaction effects plot for cutting transport efficiency
Contour Plot of CTE vs CS & µm
EP
0.0
2.75 mm
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µm
0.5
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1.0
Hold Values ROP 0 MW 0 CW 0 Vm 0 N 0
-0.5
-1.0 -1.0
CRF < 0.30 0.30 – 0.35 0.35 – 0.40 0.40 – 0.45 0.45 – 0.50 0.50 – 0.55 0.55 – 0.60 0.60 – 0.65 0.65 – 0.70 0.70 – 0.75 0.75 – 0.80 > 0.80
-0.5
0.0
0.5
1.0
CS
Fig. 4 the variation of cutting transport efficiency with cutting size and mud viscosity
18
ACCEPTED MANUSCRIPT Contour Plot of CTE vs CS & N 1.0
CRF < 0.37 0.37 – 0.41 0.41 – 0.45 0.45 – 0.49 0.49 – 0.53 0.53 – 0.57 0.57 – 0.61 0.61 – 0.65 0.65 – 0.69 0.69 – 0.73 0.73 – 0.77 > 0.77
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N
0.5
7.5 mm
0.0
-0.5
0.0
0.5
Hold Values ROP 0 MW 0 µm 0 CW 0 Vm 0
1.0
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-1.0 -1.0
SC
-0.5
CS
Fig. 5 the variation of cutting transport efficiency with cutting size and pipe rotation speed
Contour Plot of CTE vs MW & Vm
EP
0.0
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Vm
0.5
TE D
1.0
Hold Values CS 0 ROP 0 µm 0 CW 0 N 0
-0.5
-1.0 -1.0
CRF < 0.235 0.235 – 0.260 0.260 – 0.285 0.285 – 0.310 0.310 – 0.335 0.335 – 0.360 0.360 – 0.385 0.385 – 0.410 0.410 – 0.435 0.435 – 0.460 0.460 – 0.485 > 0.485
-0.5
0.0
0.5
1.0
MW
Fig. 6 the variation of cutting transport efficiency as a function of mud weight and fluid velocity
19
ACCEPTED MANUSCRIPT Contour Plot of CTE vs µm & N 1.0
CRF < 0.305477 0.305477 – 0.341090 0.341090 – 0.376703 0.376703 – 0.412316 0.412316 – 0.447929 0.447929 – 0.483542 0.483542 – 0.519155 0.519155 – 0.554768 0.554768 – 0.590381 0.590381 – 0.625994 0.625994 – 0.661607 > 0.661607
17 rad/s
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0.5
0.0
-0.5
Hold Values CS 0 ROP 0 MW 0 CW 0 Vm 0
4.5 rad/s
-0.5
0.0
0.5
1.0
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-1.0 -1.0
SC
N
14.5 cp
µm
Fig. 7 the variation of cutting transport efficiency as a function of mud viscosity and pipe rotation speed
1.0
EP
CRF < 0.24 0.24 – 0.27 0.27 – 0.30 0.30 – 0.33 0.33 – 0.36 0.36 – 0.39 0.39 – 0.42 0.42 – 0.45 0.45 – 0.48 0.48 – 0.51 0.51 – 0.54 > 0.54
0.0
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N
0.5
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Contour Plot of CTE vs Vm & N
7.5 rad/s
Hold Values CS 0 ROP 0 MW 0 µm 0 CW 0
-0.5
-1.0 -1.0
-0.5
0.0
0.5
1.0
Vm
Fig. 8 the variation of cutting transport efficiency with fluid velocity and pipe rotation speed
20
ACCEPTED MANUSCRIPT 1
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.00
0.20
0.40
0.60
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Cumulative probability
0.9
0.80
SC
Cutting Transport Efficiency
1.00
M AN U
Fig. 9 the cumulative distribution of predicted CTE based on performing Monte Carlo simulation by considering Latin Hypercube Sampling (LHS)
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40 30 20
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10
90
Individual Effects
80
Cumulative Effects
70 60 50 40
EP
Individual Percent
50
100
30 20 10
0
Vm
Cumulative Percent
60
0 CW
N
MW
CS
µm
ROP
Fig. 10 the results of sensitivity analysis in terms of contribution to total variance for CTE response function
21
ACCEPTED MANUSCRIPT Table 1 the range of factors, coded variables and transfer functions Coded Factor
Minimum Value
Mean Value
Maximum Value
CS (mm)
X1
2
5
8
ROP (Kg/s)
X2
0.1
0.3
0.5
MW (Kg/m3)
X3
1000
1250
1500
µm(cp)
X4
10
20
30
CW (Kg/m3)
X5
2200
2600
3000
Vm (m/s)
X6
0.5
1.3
2.1
N (rad/s)
X7
0
10
20
SC
M AN U TE D EP AC C 22
Transfer Function ܵܥ− 5 3 ܴܱܲ − 0.3 0.2 ܹܯ− 1250 250 ߤ − 20 10 ܹܥ− 2600 400 ܸ − 1.3 0.8 ܰ − 10 10
RI PT
Factor
ACCEPTED MANUSCRIPT Table 2 the result of CFD calculation based on BBD for seven factors
AC C
CW 1 0 -1 1 -1 0 0 0 0 -1 1 1 0 -1 -1 0 1 1 0 0 0 0 0 0 0 -1 0 -1 0 0 0 1 0 0 0 -1 1 1 0 0 0 1 0 0 1 0 0 0 -1 0 0 0 -1 1 -1 0 -1
Vm 0 0 -1 0 0 -1 0 1 1 0 -1 1 0 1 0 -1 0 0 0 0 1 1 -1 -1 -1 0 1 0 0 -1 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 -1 0 -1 1 0 0 0 -1 -1 0 0 0
N 0 1 0 -1 0 -1 -1 -1 1 1 0 0 0 0 -1 0 0 -1 0 0 -1 0 1 1 0 0 0 0 0 -1 -1 0 0 0 1 0 1 0 -1 0 1 0 -1 1 1 0 0 0 0 0 1 0 0 0 -1 0 1
23
CTE 0.36 0.47 0.12 0.52 0.36 0.35 0.48 0.45 0.85 0.46 0.03 0.39 0.43 0.38 0.43 0.37 0.72 0.44 1.00 0.37 0.37 0.41 0.56 0.35 0.35 0.37 0.37 0.46 0.38 0.47 0.39 0.38 0.94 0.41 0.77 0.50 0.63 0.57 0.44 0.39 0.34 0.41 0.55 0.72 0.49 0.61 0.46 0.54 0.37 0.47 0.41 0.35 0.00 0.00 0.46 0.37 0.40
RI PT
µm 0 1 -1 0 0 0 1 0 0 0 -1 1 0 1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 1 0 1 0 -1 0 -1 0 0 0 -1 0 0 -1 -1 -1 0 0 1 0 -1 1 1 1 1 1 0 -1 0
SC
MW -1 -1 0 0 1 0 -1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 -1 -1 -1 1 0 0 1 1 0 1 -1 -1 0 1 1 -1 0 0 -1 1 0 1 0 1 0 0 1 0 0 0 0 0 0
M AN U
ROP 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -1 -1 0 -1 1 -1 0 1 0 0 1 0 1 0 1 0 0 0 -1 -1 0 0 1 0 0 -1 0 0 0 0 -1 1 1 -1 0 -1 0 -1 0 0 1 1 -1
TE D
CS -1 0 0 0 -1 -1 0 1 1 0 0 0 0 0 0 0 1 0 1 -1 -1 0 1 -1 0 -1 0 1 -1 1 0 -1 1 0 0 1 0 1 0 0 -1 0 0 0 0 0 1 0 0 1 0 -1 0 0 0 -1 0
EP
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
ACCEPTED MANUSCRIPT Table 3 the result of Analysis of Variance for CTE response
Adj MS 0.091207 0.108517 0.344915 0.006689 0.003620 0.232270 0.049957 0.049184 0.072987 0.094162 0.048490 0.084807 0.063892 0.051968 0.079372 0.048920 0.063426 0.124249 0.066420 0.060445 0.030431 0.035586 0.006708
EP AC C 24
F 13.60 16.18 51.42 1.00 0.54 34.63 7.45 7.33 10.88 14.04 7.23 12.64 9.53 7.75 11.83 7.29 9.46 18.52 9.90 9.01 4.54 5.31
P 0.000 0.000 0.000 0.324 0.467 0.000 0.010 0.010 0.002 0.000 0.011 0.001 0.004 0.008 0.001 0.010 0.000 0.000 0.003 0.005 0.040 0.027
RI PT
Adj SS 1.64173 0.75962 0.34492 0.00669 0.00362 0.23227 0.04996 0.04918 0.07299 0.56497 0.04849 0.08481 0.06389 0.05197 0.07937 0.04892 0.31713 0.12425 0.06642 0.06045 0.03043 0.03559 0.25489
SC
Seq SS 1.64173 0.75962 0.34492 0.00669 0.00362 0.23227 0.04996 0.04918 0.07299 0.56497 0.04649 0.12211 0.13286 0.05670 0.15790 0.04892 0.31713 0.12425 0.06642 0.06045 0.03043 0.03559 0.25489 1.89662
M AN U
DF 18 7 1 1 1 1 1 1 1 6 1 1 1 1 1 1 5 1 1 1 1 1 38 56
TE D
Source Regression Linear CS ROP MW µm CW Vm N Square CS*CS ROP*ROP MW*MW CW*CW V*V N*N Interaction CS*µm CS*N MW*Vm µm *N Vm*N Residual Error Total
ACCEPTED MANUSCRIPT
Highlights
CFD and DOE techniques were used to predict the cutting transport efficiency.
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Box-Behnken Design was used to perform CFD calculations.
•
Mud velocity (Vm), cutting weight (CW), pipe rotational speed (N), mud weight
RI PT
•
(MW), cutting size (CS), mud viscosity (µm), and drilling rate of penetration (ROP) have respectively the greatest effect on cuttings removal.
Three factors of mud velocity, cutting weight and pipe rotational speed control 86.3% of cuttings removal efficiency.
Statistical analysis shows that five interaction terms of CS × µm, CS × N, MW × Vm, µm × N, and Vm × N should be carefully characterized prior to drilling of a well to
EP
TE D
M AN U
optimize cutting transport efficiency.
AC C
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SC
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