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Updated criterion to select particle size distribution of lost circulation materials for an effective fracture sealing
Author’s Accepted Manuscript Updated Criterion to Select Particle Size Distribution of Lost Circulation Materials for an Effective Fracture Sealing Mortadha Alsaba, Mohammed F. Al Dushaishi, Runar Nygaard, Olav-Magnar Nes, Arild Saasen www.elsevier.com/locate/petrol
PII: DOI: Reference:
S0920-4105(16)30721-5 http://dx.doi.org/10.1016/j.petrol.2016.10.027 PETROL3687
To appear in: Journal of Petroleum Science and Engineering Received date: 4 January 2016 Revised date: 9 October 2016 Accepted date: 17 October 2016 Cite this article as: Mortadha Alsaba, Mohammed F. Al Dushaishi, Runar Nygaard, Olav-Magnar Nes and Arild Saasen, Updated Criterion to Select Particle Size Distribution of Lost Circulation Materials for an Effective Fracture S e a l i n g , Journal of Petroleum Science and Engineering, http://dx.doi.org/10.1016/j.petrol.2016.10.027 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 galley proof before it is published in its final citable 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.
Updated Criterion to Select Particle Size Distribution of Lost Circulation Materials for an Effective Fracture Sealing Mortadha Alsabaa*1, Mohammed F. Al Dushaishib, Runar Nygaardc1, Olav-Magnar Nesd, and Arild Saasend a
Australian College of Kuwait Missouri University of Science and Technology c Oklahoma State University d Aker BP, Formerly known as Det Norske Oljeselskap ASA b
* Corresponding author. [email protected]
Abstract This paper presents a new criterion to select particle size distribution (PSD) for an effective fracture sealing. The method was developed based on a comprehensive laboratory investigation that was conducted to determine the relationship between effectiveness of different lost circulation material (LCM) treatments in terms of the sealing efficiency and PSD. The results were compared with the current selection methods, which were developed to enhance the bridging capabilities for drill-in fluid, to investigate their applicability in designing effective treatments for fracture sealing. A statistical investigation was carried out to develop new criteria that suggest PSD based on the expected fracture width for an effective fracture sealing. The criteria suggest that both D50 and D90 should be equal or greater than 3/10 and 6/5 the fracture width, respectively. The suggested method showed a 90% match between the actual and predicted seal quality.
1
Formerly at Missouri University of Science and Technology
1
Keywords: Lost circulation, lost circulation material, particle size distribution, fluid losses, laboratory investigation
1. Introduction Lost circulation materials (LCM) are often used as a background treatment or spotted as a concentrated pill to stop or reduce fluid losses into the formation during drilling operations. The main objective when designing an effective treatment is to ensure that it is able to seal fractures effectively and stop losses at differential pressure. The differential pressure is caused by the elevated drilling fluid pressures compared to the pore fluid pressure in regular drilling operations or drilling fluid pressures exceeding the wellbore fracture pressure. To verify the designed treatments, laboratory evaluation prior to field application is required. Particle size distribution (PSD) is an essential parameter when designing these LCM treatments (Ghalambor et al. 2014; Savari et al, 2015). Different bridging theories have been introduced as guidelines to select PSD and enhance the bridging capabilities of drill-in fluids when drilling through reservoir sections (Abram’s, 1977; Smith et al. 1996; Hand 1998; Dick et al. 2000; Vickers et al. 2006; Lavrov 2016). The main goal of these guidelines is to minimize the formation damage caused by fluid invasion through the formation. Different laboratory tests were used to evaluate the effectiveness of bridging theories with respect to permeability reduction such as the dynamic mudding-off tests described by Nowak and Krueger (1951), mud impairment tests (Abram’s, 1977), return permeability tests (Dick et al. 2000), and static or dynamic filtration test (Vickers et al. 2006). All the previous methods were developed to select PSD for drill-in fluids based on the pore size distribution, which can be estimated from thin section analysis, scanning electron microscopy, mercury injection, or derived from permeability measurements (Dick et al. 2000; He and Stephens, 2011). However, the pore sizes dimensions are relatively small compared to fracture widths. Therefore, using the above theories might be somehow irrelevant for sealing
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fractures. A method to select PSD based on the expected fracture width rather than pore throat sizes, was proposed by Withfill (2008). This method suggests that the D50 value should be equal to the fracture width to ensure the formation of an effective seal or plug. In a recent investigation (Alsaba et al. 2014), graphite (G), nutshells (NS), sized calcium carbonate (SCC), and cellulosic fiber (CF) were used to formulate 40 different LCM blends. The blends were mixed with water-based mud (WBM) containing 7 wt./vol. % bentonite, which is equivalent to 24.5 ppb, and tested with a low-pressure apparatus to investigate their capability in sealing fractures. The tests were conducted at 6.9 bar (100 psi) using a set of different fracture width (1000 – 3000 microns), which were simulated using tapered discs. The blends that sealed at low pressure with low fluid loss values were tested at higher pressure to measure their seal integrity, which has been defined as the pressure at which the formed seal breaks and fluid losses resumes. In this study, dry sieve analysis technique was used to analyze the particle size distribution (PSD) of LCM treatments in order to understand how PSD could affect both the fracture sealing and the seal integrity for a known fracture width. The main objective of this investigation is to answer the following questions; what is the role of PSD in effective fracture sealing? Did effective blends follow a specific bridging theory? What is the best criterion to select PSD with respect to fracture width for an effective sealing? This paper introduces a new method to select PSD for LCM treatments for a known fracture width. The new method was developed based on a statistical analysis to correlate the measured PSD of LCM treatments with their sealing pressure, which was previously investigated.
3
2. Laboratory Evaluation 2.1 Fluid Used Unweighted water-based mud (WBM) containing 7 wt./vol. % bentonite was used to eliminate negative or positive effects, if any, of drilling fluid additives such as weighting materials and fluid loss reducers on LCM performance. In addition, a pre-mixed low-toxicity mineral oilbased mud (OBM) was used to investigate the effect base fluid on the performance of LCM. 2.2 Sealing Efficiency Evaluation Fig.1 shows a schematic diagram of the experimental setup that was used to evaluate the seal integrity of LCM treatments. A plastic accumulator (1) used to transfer the drilling fluids to the metal accumulator (2) prior to pressurizing the fluids containing the LCM treatments inside the testing cell (3) through the tapered discs (4) using IscoTM pump (DX100) (5) to provide the injection pressure, which was connected to a computer to record pressure and time. It’s worthwhile mentioning that the pump uses 1/8 inches’ stainless steel tubing with maximum pressure of 689.5 bar (10,000 psi).
4
(4) (1)
(2) (3)
(5)
Fig. 1. High pressure LCM testing apparatus
The test is run by pressurizing fluids containing LCMs, which were poured into the cell, at a constant flow rate of 25 ml/min until a rapid increase in the injection pressure is observed. This increase indicates the formation of a seal. Once the seal has formed, the drilling fluid, containing no LCMs, is injected continuously until the maximum sealing efficiency is reached. A significant drop in the pressure is observed as a result of breaking the seal. However, the test is repeated as cycles until no further seal can be formed. The seal integrity of the different LCM treatments was evaluated for a different set of fracture widths. 2.3 Particle Size Distribution Analysis Two methods are often used to run PSD analysis; sieve analysis and laser diffraction. However, since the provided D50 values (from manufacture) for some of the used LCMs in this study are 2000 microns and due to the limitation of the laser diffraction techniques in measuring particles larger than 2000 microns (Zang et al 2015), dry sieve analysis was used to analyze PSD.
5
Samples of LCM treatment were sieved through a series of stacked sieves. The cumulative weight percent retained for each sieve size was calculated from the measured weight retained in each sieve and then plotted versus the sieve sizes.
The main five
parameters, which were obtained from the resulting plot, are the D10, D25, D50, D75, and D90, measured in microns, for the different blends that sealed different fractures width. In addition, random blends that failed in creating a seal or resulted in a high fluid loss during the screening phase were analyzed to understand the reason behind their failure in forming a seal within the fracture.
3. Laboratory Results A summary of all the sealing efficiency results at the different test conditions and the corresponding PSD analysis for LCM treatments that were previously (Alsaba et al. 2014) investigated in addition to sealing pressures for LCM treatments that were tested at higher concentrations (105 ppb) as recommended by Det Norske Oljeselskap ASA for field applications using a pre-mixed oil-based mud (OBM) are tabulated as shown in Table 1. Table 1. Summary of sealing efficiency results at different fracture widths and PSD analysis # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
LCM Type G
Total LCM (kg/m3) 43 143 86
Total LCM (ppb) 15 50 30
G&SCC
Base Fluid
Fracture width (microns)
WBM
1000
WBM 228
80
G&SCC
300
105
OBM
SCC
143
50
WBM
43
15
NS
WBM 143
50
1000
Sealing Pressure (bar) 28.5 31.0 33.6
Sealing Pressure (psi) 414 449 487
1000 1500 1000 1000 1000 1500 1500 1500 1500 2000 3000 3000 1000 1500 1000 1500 2000 2000
40.3 15.4 108.2 8.1 102.7 14.1 0 11.3 117.8 115.1 7.6 0.0 40.6 11.2 67.8 120.9 23.9 30.4
584 224 1569 117 1489 205 0 164 1708 1669 110 0 589 162 984 1754 347 441
1000 1500
151.8 139.8
2202 2027
Particle Size Distribution (microns) D10
D25
D50
D75
D90
60 60 78
85 95 100
320 340 460
800 800 900
1300 1300 1300
80
120
480
900
1300
65 60 90 65 60 100 170 170 100 300
90 150 400 90 150 500 650 650 250 800
420 500 700 420 500 900 1300 1300 1000 1400
1100 700 1200 1100 700 1250 1900 1900 1800 1800
1400 900 1400 1400 900 1400 2600 2600 2400 2200
250
360
680
950
1200
180
400
1000
1600
2000
180
400
1000
1600
2400
6
24 25 26 27 28 29 30 31 32 33 34 35 36
57
20
G&NS
WBM 114
40
43
15
143
50
157
55
CF
G,SCC, & CF
WBM
WBM
2000 2000 1000 1500
154.2 52.1 163.5 55.5
2237 755 2372 805
1000 1500 2000 2000 1000
199.4 118.1 20.3 16.7 55.2
2892 1713 295 242 800
1000 1500 1000 1500
148.9 77.8 69.7 27.0
2160 1129 1011 391
65
180
500
1300
1900
80
180
580
1400
2000
90
140
220
700
1400
90
150
220
800
1400
55
100
450
850
1200
*NS=Nutshell, G= Graphite, SCC= Sized Calcium Carbonate, CF= Cellulosic Fiber
To qualitatively understand the overall trend of how PSD could affect the sealing pressure with respect to fracture width, all sealing pressure results in Table 1 for 1000, 1500, and 2000 microns fractures were plotted (black dots) regardless of the base fluid, concentration, or LCM type and sorted with the highest pressure to the right as shown in Fig. 2 to Fig. 4. The black dashed line is plotted as a reference line that represents the fracture width in microns. The quadratic regression fit lines for the five D-values as well as the sealing pressure were plotted in different colors, where D90 (red), D75 (orange), D50 (blue), D25 (green), and D10 (purple). The solid colored lines show the quadratic regression fit line of each parameter as the pressure increase to visualize the trend. Fig. 2 shows the sealing pressures (left y-axis) versus PSD (right y-axis) for 1000 microns fracture width. It is noticeable that higher sealing pressures are achieved with wider PSD; however no clear correlation that suggests the effect of a specific D-value could be observed.
7
80
1000
60 40
Particle Size
Sealing Pres
100
500
20 0
200 180 160
0
2500
Sealing Pressure (R_seq 98%) D10 (R_seq 14%) D25 (R_seq 17%) D50 (R_seq 9%) D75 (R_seq 43%) D90 (R_seq 52%)
2000
120
1500
100 80
1000
Particle Size (microns)
Sealing Pressure (bar)
140
60 40
500
20 0
0
Fig. 2. Sealing pressure as a function of the D-values for a fracture width of 1000 microns, where D90 (red), D75 (orange), D50 (blue), D25 (green), and D10 (purple)
Fig. 3 and Fig. 4 show the sealing pressure results2500versus PSD for 1500 microns and 200 180
2000 microns fracture widths, respectively. In general, the sealing pressure results tend to 160
2000
120
1500
Particle Size (microns)
Sealing Pressure (bar)
increase as the 140 particle size distribution gets coarser, i.e. wider PSD. In other words, blends with higher D-values resulted in higher sealing pressure. The D-values fit lines shows an 100 80
1000
upward increase with the sealing pressure. 60 40
500
20 0
200 180 160
0 Sealing Pressure (R_seq 94%) D10 (R_seq 59%) D25 (R_seq 24%) D50 (R_seq 35%) D75 (R_seq 46%) D90 (R_seq 64%)
2500
2000
120
1500
100 80
1000
Particle Size (microns)
Sealing Pressure (bar)
140
60 40
500
20 0
0
Fig. 3. Sealing pressure as a function of the D-values for a fracture width of 1500 microns
8
1500
100 80
1000
60 40
Particle Size (mic
Sealing Pressure
120
500
20 0
0 200
Sealing Pressure (R_seq 81%) D10 (R_seq 81%) D25 (R_seq 69%) D50 (R_seq 78%) D75 (R_seq 61%) D90 (R_seq 72%)
2500
2000
1500 100 1000
Particle Size (microns)
Sealing Pressure (bar)
150
50 500
0
0
Fig. 4. Sealing pressure as a function of the D-values for a fracture width of 2000 microns
Even though the observed PSD fit lines shows an increase with the sealing pressure, no clear conclusion could be made on the significance of each D-value contribution toward enhancing the sealing pressure from the results. From the qualitative analysis of the effect particle size distribution has on the sealing pressure, the improved performance of treatments containing nutshells could be attributed to the fact that the D90 values of these blends ranged between 1900 – 2400 microns (Table 1). In general, all LCM treatments having a D90 smaller than the fracture width failed to establish a seal within the fracture. This suggests that the D90 value should be selected such that it matches the fracture width to ensure an effective fracture sealing. When measuring PSD, the variation in particles shape in terms of sphericity needs to be taken into consideration to avoid inaccuracy in analyzing the PSD. The shape of the used LCMs was qualitatively inspected under an optical microscope (Fig. 5) and described using the sphericity and roundness chart by Powers (1953). Graphite (Fig. 5a), calcium carbonate (Fig. 5b), and nutshells (Fig. 5c) particles could be described as spherical with variation in the sphericity. However, cellulosic fiber (Fig. 5d) particles can be described as nonspherical
9
particles with some elongated and flat particles. Based on our observation when measuring the PSD of the different LCM treatments, it was found that blends containing cellulosic fibers tend to block the sieves with the elongated and flat particles, thus resulting in a false measurement of the sieve weight used to construct the PSD plots. Therefor, PSD analysis of those blends was found to be unrepresentative. For this reason it was decided to exclude the cellulosic fiber results (Tests 32-36) from the statistical analysis and limit it to granular materials only.
1 mm
(a) Graphite (60x)
1 mm
(b) Sized calcium carbonate (60x)
1 mm
1 mm
(c) Nut shells (60x)
(d) Cellulosic Fiber (30x)
Fig. 5. Optical microscopy images for (a) Graphite, (b) Calcium carbonate, (c) Nutshells, and (d) Cellulosic fiber
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4. Statistical Analysis and Model Development In normal overbalanced drilling operations (i.e. drilling fluid pressure higher than formation pressure), a minimum static overbalance pressure of 10.3 - 20.7 bar (150-300 psi) is required to prevent formation fluid influx (Jahn et al. 2008; Rehm et al. 2012; The Drilling Manual, 2015). Therefore, the formed seal within the fracture should withstand at least the minimum overbalance pressure without failing. In the statistical analysis, the sealing efficiency results of the different blends were grouped into two categories; weak and strong seal. The seals that failed to withstand an overbalance of 34.5 bar (500 psi) to (selected to account for the static and dynamic overbalance pressure) are considered weak seal and the ones that survived 34.5 bar (500 psi) or more are considered strong seal regardless of LCM type, concentration and fracture width. A statistical analysis was conducted to study the effect of fracture width, base fluid, total LCM concentration and the five D values on the performance of LCM in terms of the sealing pressure. The performed statistical techniques to characterize each parameter effect on sealing pressure include probability tests and multi-regression analysis. The probability test (F-test) was performed to test the influence of each parameter on sealing pressure. The F-test provides a P-value, where the P-value is a statistical probability that the predicted value (the F-value) is similar or very different from the measured value (Montgomery, 2001). Assuming a true null hypothesis (H0) that proposes no influence of a specific variable on the sealing pressure, with a confidence interval of 95% and type I error (α) of 0.05, a P-value less than 0.05 suggests the rejection of the null hypothesis (H0) and accepting an alternative hypothesis (H1). The alternative hypothesis suggests that the sealing pressure is influenced by a specific variable. The Effect Leverage plot (Sall, 1990) was used for the multi-regression analysis to show the actual and the predicated data of each test. Consequently, the Leverage plot shows the
11
impact of adding an effect (variable) to the overall predicated model. The Leverage plot is constructed by plotting a scatter plot of the X and Y residuals. The sealing pressure residuals are regressed on all predictors except for the variable of interest while the x-residuals (variable of interest) are regressed on all other predictors in the model. The mean of the sealing pressure, without the effect of the variable of interest, is plotted as well as a least square fit line and confidence interval for easier interpretation of the results significant at 5% level. The slope of the least squares fit line is a measure of how the tested variable affects the sealing pressure i.e. a non-zero slope implies that the tested variable will affect the sealing pressure (Sall, 1990). Fig. 6 Shows the Leverage plot for each parameter with the resulting P value (also summarized in Table 2). The blue dashed line represents the mean sealing pressure, the solid red line represents the fitted model, and the dashed red line represents the confidence interval (5% confident level). If the mean sealing pressure is inside the confidence interval envelope, the parameter does not have any significant effect on the sealing pressure. If the confidence interval crosses the mean pressure at a high angle, it has a significant contribution to sealing pressure.
Table 2. The P-Value showing the effect of base fluid, D-values, fracture width, LCM concentration on sealing pressure and model fit summary Parameter Unit P-Values Fracture Width (microns) 0.00001 D90 (microns) 0.08116 D50 (microns) 0.26377 D10 (microns) 0.44148 D75 (microns) 0.53233 Total LCM (ppb) 0.53522 D25 (microns) 0.85566 Base Fluid (WBM/OBM) 0.90849 Model Summary Fit R2 0.743
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( a
( b
( c
( d
( e
( g
(f )
( h
Fig. 6. Leverage plot of sealing pressure as a function of (a) Base Fluid (b) D10 (c) D25 (d) D50 (e) D75 (f) D90 (g) Fracture width, and (h) LCM concentration
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The overall model fit shown in Fig. 7 shows a good correlation with R2 of 74% and a Pvalue less than 0.05. The residual plot (not provided) showed the data being randomly distributed around x-axis, indicating that a linear model was appropriate for the collected data.
Figure 7. Leverage plot of the predicated sealing pressure
In order to develop a generalized model that predicts the sealing pressure for different fracture widths, statistical partition technique was used based on the obtained information from the previous model (Fig. 7). The statistical partition was performed using the four significant parameters; D90, D75, D50 and D10 as a function of fracture width and taking the total LCM as a weighted parameter. Sensitivity analysis was than performed by first taking the first three parameters (D90, D50 and D10) to predict sealing pressure and second by taking only the first two parameters (D90 and D50). The model using D90 and D50 to predict sealing pressure for a given fracture width gave a model fit similar (3% difference) to the model with the four parameters. Thus, the model using D90 and D50 was chosen, where the model have a better fit than the previous model (Fig. 7) with R2 of 74%. The statistical partition was then converted into a mathematical relationship that predicts a good sealing pressure, which was defined earlier as
14
any pressure >34.5 bar (500 psi), as a function of the selected PSD D-values. The obtained mathematical relationship suggests the following: -
D50 should be
-
the fracture width
D90 should be
the fracture width
5. Model Verification In order to validate the proposed selection criteria and compare it with the previous selection criteria discussed in the introduction, a comparison table was constructed. Table 3 lists the test number, the fracture width used, the measured seal integrity, and the predicted seal integrity.
Table 3. Comparison of measured and predicted PSD for effective fracture sealing Proposed Criterion
Abrams (1977)
D90 Rule (1996, 1998)
Vickers (2006)
Halliburton (2008)
Test #
FW (microns)
Measured
P
M
P
M
P
M
P
M
P
M
1
1000
W
S
N
W
Y
S
N
W
Y
W
Y
2
1000
W
S
N
S
N
S
N
W
Y
W
Y
3
1000
W
S
N
S
N
S
N
W
Y
W
Y
4
1000
S
S
Y
S
Y
S
Y
W
N
W
N
5
1500
W
W
Y
W
Y
W
Y
W
Y
W
Y
6
1000
S
S
Y
S
Y
S
Y
W
N
W
N
7
1000
W
W
Y
S
N
W
Y
W
Y
W
Y
8
1000
S
S
Y
S
Y
S
Y
W
N
W
N
9
1500
W
W
Y
W
Y
W
Y
W
Y
W
Y
10
1500
W
W
Y
S
N
W
Y
W
Y
W
Y
11
1500
W
W
Y
S
N
W
Y
W
Y
W
Y
12
1500
S
S
Y
S
Y
S
Y
W
N
W
N
13
2000
S
S
Y
S
Y
S
Y
W
N
W
N
14
3000
W
W
Y
S
N
W
Y
W
Y
W
Y
15
3000
W
W
Y
S
N
W
Y
W
Y
W
Y
16
1000
S
S
Y
S
Y
S
Y
W
N
W
N
17
1500
W
W
Y
S
N
W
Y
S
N
W
Y
18
1000
S
S
Y
S
Y
S
Y
W
N
S
Y
19
1500
S
S
Y
S
Y
S
Y
W
N
W
N
15
20
2000
W
W
Y
S
N
S
N
W
Y
W
Y
21
2000
W
W
Y
S
N
S
N
W
Y
W
Y
22
1000
S
S
Y
S
Y
S
Y
W
N
S
Y
23
1500
S
S
Y
S
Y
S
Y
W
N
W
N
24
2000
S
S
Y
S
Y
S
Y
W
N
W
N
25
2000
S
S
Y
S
Y
S
Y
W
N
W
N
26
1000
S
S
Y
S
Y
S
Y
W
N
W
N
27
1500
S
S
Y
S
Y
S
Y
W
N
W
N
28
1000
S
S
Y
S
Y
S
Y
W
N
W
N
29
1500
S
S
Y
S
Y
S
Y
W
N
W
N
30
2000
W
W
Y
W
Y
S
N
W
Y
W
Y
31
2000
W
W
Y
W
Y
S
N
W
Y
W
Y
Note:
Fracture width (FW)
Predicted (P)
Match (M)
Strong (S)
Weak (W)
Yes (Y)
No (N)
The measured seal integrity is based on the measured sealing pressure, i.e. if the measured sealing pressure is larger than 34.5 bar (500 psi), then the measured seal integrity is considered strong. If the measured sealing pressure is less than 34.5 bar, then the measured seal integrity is considered weak. In the comparison, it is assumed that following the selection criteria should result in a strong seal that could withstand pressures higher than 34.5 bar. The predicted seal integrity column is based on comparing the suggested D-Value by the selection criteria with the actual measured PSD. If the measured PSD is equal or larger than the suggested value by the selection criteria, the predicted seal integrity is considered strong. If the measured PSD is less than the suggested PSD, the predicted seal integrity is considered weak. The last step is to check if the measured seal integrity matches with the predicted one and calculate the overall match percentage. The overall match percentage of the 31 tests (excluding the cellulosic fiber blends) was calculated for the four models and the proposed criteria as shown in Table 4.
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Table 4. The percentage match of different PSD criteria with lab tests. Method Abram's Rule (Abrams, 1977) D90 Rule (Smith et al. 1996, Hands et al. 1998)
PSD Selection Criteria
Percentage Match with Lab Data
D50 ≥ 1/3 the formation average pore size
68 %
D90 = the formation pore size
77 %
Vickers’s Method (Vickers et al. 2006)
D90 = largest pore throat D75 < 2/3 the largest pore throat D50 ≥ 1/3 D25 = 1/7 the mean pore throat D10 > the smallest pore throat
45%
Halliburton Method (Whitfill, 2008)
D50 = fracture width
55 %
Proposed Method
D50 should be
the fracture width
D90 should be
the fracture width
90%
The verification showed a good match between the predicted seal integrity and the measured seal integrity with an overall match of 90% for the proposed selection criteria. Vickers method showed the lowest percentage match due to the number of D-values that needs to be satisfied. Halliburton’s method (Whitfill, 2008) also showed a low predictive match. Abrams and D90 rules had higher percentage match compared to Vickers and Halliburton’s methods. Since the validation was performed on the same dataset, additional testing would be beneficial to independently validate the proposed criteria. However, the results are in agreement with the qualitative analysis were a wide particle size distribution gave higher sealing pressure since smaller particles filled the voids between the larger particles in the formed plugs.
6. Conclusions -
An updated selection criterion for PSD selection for a known fracture width was developed stating that D50 and D90 should be equal or greater than 3/10 and 6/5 the fracture width, respectively.
-
The proposed criterion was verified with the lab results and it gave a 90% match between the actual and predicted performance.
17
-
Selecting PSD for LCM treatments based on the estimated fracture width is a crucial step to ensure effective fracture sealing.
-
Previous PSD optimization criteria are useful to enhance the bridging capabilities of drillin fluids; however, these criteria might not be applicable for fracture sealing.
-
From the results, D90 plays a significant role in initiating the seal by plugging the largest fracture width.
-
Blends containing nutshells were effective in sealing fractures at lower concentration while higher concentrations of graphite and calcium carbonate were required to enhance the sealing pressure. For example, low concentration of nutshells (15 ppb) were able to reach a sealing pressure of 67.8 bars for 1000 microns fracture as shown in Test # 18, while higher concentration of graphite and sized calcium carbonate (80 ppb) was only able to reach 40.3 bars to seal the same fracture width as shown in Test # 4.
-
The shape of LCM particles, in terms of sphericity and roundness, needs to be taken into consideration when analyzing PSD.
-
Based on the results, increasing the total concentration of LCM will improve the sealing efficiency of LCM treatments.
-
The statistical investigation agrees with the importance of D90 and D50 in forming an effective seal.
Acknowledgments The authors would like to acknowledge Det Norske Oljeselskap ASA (Now Aker BP) for the financial support under research agreement # 0037709; Dr. Galecki from Missouri University of Science and Technology for his help with the PSD analysis.
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References Abrams, A. 1977. Mud Design to Minimize Rock Impairment Due to Particle Invasion. Journal of Petroleum Technology 29 (5): 586-592. SPE-5713-PA. http://dx.doi.org/10.2118/5713-PA Alsaba, M., Nygaard, R., Saasen, A., and Nes, O. M. 2014. Lost Circulation Materials Capability of Sealing Wide Fractures. Presented at the SPE Deepwater Drilling and Completions Conference,
Galveston,
USA,
10–11
September.
SPE-170285-MS.
http://dx.doi.org/10.2118/170285-MS Dick, M. A., Heinz, T. J., Svoboda, C. F., and Aston, M. 2000. Optimizing the Selection of Bridging Particles for Reservoir Drilling Fluids. Presented at the SPE International Symposium on Formation Damage Control, Lafayette, Louisiana, 23-24 February. SPE58793-MS. http://dx.doi.org/10.2118/58793-MS Ghalambor, A., Salehi, S., Shahri, M. P., and Karimi, M. 2014. Integrated Workflow for Lost Circulation Prediction. Presented at the SPE International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, 26-28 February. SPE-168123-MS. http://dx.doi.org/10.2118/168123-MS Hands, N., Kowbel, K., Maikranz, S., and Nouris, R. 1998. Drill-in Fluid Reduces Formation Damage, Increases Production Rates. Oil & Gas Journal 96 (28): 65-69 He, W., and Stephens, M. P. 2011. Bridging Particle Size Distribution in Drilling Fluid and Formation Damage. Presented at the SPE European Formation Damage Conference, Noordwijk,
The
Netherlands,
7-10
June.
SPE-143497-MS.
http://dx.doi.org/10.2118/143497-MS Jahn, F., Cook, M., and Graham, M., 2008. Hydrocarbon Exploration & Production, 2nd Edition. Elsevier Science, Oxford, UK
19
Lavrov, Alexandre, 2016. Lost Circulation: Mechanisms and Solutions, 1st Edition. Elsevier Science, Oxford, UK. Montgomery, D. 2001. Design and Analysis of Experiments, 5th Edition. John Wiley & Sons, Inc., New York, NY. Nowak, T. J., and Krueger, R. F. 1951. The Effect of Mud Filtrates and Mud Particles upon the Permeabilities of Cores. API Drilling and Production Practice: 164-181. API-51-164. Powers M C (1953) A New Roundness Scale for Sedimentary Particles. J Sediment Petrol 23: 117-119 Rehm, B., Haghshenas, A., Paknejad A. S., Al-Yami, A., and Hughes, J., 2012. Underbalanced Drilling: Limits and Extremes. Gulf Publishing Company, Houston, TX Sall, J. 1990. Leverage Plots for General Linear Hypotheses. The American Statistician, Vol. 44 (4), pp. 308-315. Savari, S., Kulkarni, S. D., Whitfill, D. L., and Jamison, D. E. 2015. Engineering Design of Lost Circulation Materials (LCMs) is More than Adding a Word. Presented at the SPE/IADC Drilling Conference and Exhibition, London, UK, 17-19 March. SPE-173018-MS. http://dx.doi.org/10.2118/173018-MS Smith, P. S., Browne, S. V., Heinz, T. J., and Wise, W. V. 1996. Drilling Fluid Design to Prevent Formation Damage in High Permeability Quartz Arenite Sandstones. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, 6-9 October. SPE-36430MS. http://dx.doi.org/10.2118/36430-MS The Drilling Manual, Fifth Edition, 2015. CRC Press, Boca Raton, FL Vickers, S., Cowie, M., Jones, T., and Twynam, A. J. 2006. A New Methodology that Surpasses Current Bridging Theories to Efficiently Seal a Varied Pore Throat Distribution as Found in
20
Natural Reservoir Formations. Presented at the AADE Fluids Conference and Exhibition, Houston, Texas, USA, 11-12 April. AADE-006-DF-HO-16. Withfill, D. 2008. Lost Circulation Material Selection, Particle Size Distribution and Fracture Modeling with Fracture Simulation Software. Presented at the IADC/SPE Asia Pacific Drilling Technology Conference and Exhibition, Jakarta, Indonesia, 25-27 August. SPE115039-MS. http://dx.doi.org/10.2118/115039-MS Zhang, K., Chanpura, R. A., Mondal, S., Wu, C.-H., Sharma, M. M., Ayoub, J. A., and Parlar, M. 2015. Particle-Size-Distribution Measurement Techniques and Their Relevance or Irrelevance to Wire-Wrap-Standalone-Screen Selection for Gradual-Formation-Failure Conditions. SPE Drilling & Completion 30(2): 164-174. http://dx.doi.org/10.2118/168152-PA
Highlights
Different lost circulation materials at different concentration/formulations were evaluated. Fracture width ranging from 1000 – 3000 microns were tested Four common selection criteria were investigated and compared with the suggested criterion The presented criterion was based on both laboratory and statistical investigation The presented criteria suggest that both D50 and D90 should be equal or greater than 3/10 and 6/5 the fracture width, respectively. The suggested method showed a 90% match between the actual and predicted seal quality. This study shows that previous criteria might not be applicable for fracture sealing since they were developed for pore sizes ranges not fracture widths ranges.
21
PII: DOI: Reference:
S0920-4105(16)30721-5 http://dx.doi.org/10.1016/j.petrol.2016.10.027 PETROL3687
To appear in: Journal of Petroleum Science and Engineering Received date: 4 January 2016 Revised date: 9 October 2016 Accepted date: 17 October 2016 Cite this article as: Mortadha Alsaba, Mohammed F. Al Dushaishi, Runar Nygaard, Olav-Magnar Nes and Arild Saasen, Updated Criterion to Select Particle Size Distribution of Lost Circulation Materials for an Effective Fracture S e a l i n g , Journal of Petroleum Science and Engineering, http://dx.doi.org/10.1016/j.petrol.2016.10.027 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 galley proof before it is published in its final citable 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.
Updated Criterion to Select Particle Size Distribution of Lost Circulation Materials for an Effective Fracture Sealing Mortadha Alsabaa*1, Mohammed F. Al Dushaishib, Runar Nygaardc1, Olav-Magnar Nesd, and Arild Saasend a
Australian College of Kuwait Missouri University of Science and Technology c Oklahoma State University d Aker BP, Formerly known as Det Norske Oljeselskap ASA b
* Corresponding author. [email protected]
Abstract This paper presents a new criterion to select particle size distribution (PSD) for an effective fracture sealing. The method was developed based on a comprehensive laboratory investigation that was conducted to determine the relationship between effectiveness of different lost circulation material (LCM) treatments in terms of the sealing efficiency and PSD. The results were compared with the current selection methods, which were developed to enhance the bridging capabilities for drill-in fluid, to investigate their applicability in designing effective treatments for fracture sealing. A statistical investigation was carried out to develop new criteria that suggest PSD based on the expected fracture width for an effective fracture sealing. The criteria suggest that both D50 and D90 should be equal or greater than 3/10 and 6/5 the fracture width, respectively. The suggested method showed a 90% match between the actual and predicted seal quality.
1
Formerly at Missouri University of Science and Technology
1
Keywords: Lost circulation, lost circulation material, particle size distribution, fluid losses, laboratory investigation
1. Introduction Lost circulation materials (LCM) are often used as a background treatment or spotted as a concentrated pill to stop or reduce fluid losses into the formation during drilling operations. The main objective when designing an effective treatment is to ensure that it is able to seal fractures effectively and stop losses at differential pressure. The differential pressure is caused by the elevated drilling fluid pressures compared to the pore fluid pressure in regular drilling operations or drilling fluid pressures exceeding the wellbore fracture pressure. To verify the designed treatments, laboratory evaluation prior to field application is required. Particle size distribution (PSD) is an essential parameter when designing these LCM treatments (Ghalambor et al. 2014; Savari et al, 2015). Different bridging theories have been introduced as guidelines to select PSD and enhance the bridging capabilities of drill-in fluids when drilling through reservoir sections (Abram’s, 1977; Smith et al. 1996; Hand 1998; Dick et al. 2000; Vickers et al. 2006; Lavrov 2016). The main goal of these guidelines is to minimize the formation damage caused by fluid invasion through the formation. Different laboratory tests were used to evaluate the effectiveness of bridging theories with respect to permeability reduction such as the dynamic mudding-off tests described by Nowak and Krueger (1951), mud impairment tests (Abram’s, 1977), return permeability tests (Dick et al. 2000), and static or dynamic filtration test (Vickers et al. 2006). All the previous methods were developed to select PSD for drill-in fluids based on the pore size distribution, which can be estimated from thin section analysis, scanning electron microscopy, mercury injection, or derived from permeability measurements (Dick et al. 2000; He and Stephens, 2011). However, the pore sizes dimensions are relatively small compared to fracture widths. Therefore, using the above theories might be somehow irrelevant for sealing
2
fractures. A method to select PSD based on the expected fracture width rather than pore throat sizes, was proposed by Withfill (2008). This method suggests that the D50 value should be equal to the fracture width to ensure the formation of an effective seal or plug. In a recent investigation (Alsaba et al. 2014), graphite (G), nutshells (NS), sized calcium carbonate (SCC), and cellulosic fiber (CF) were used to formulate 40 different LCM blends. The blends were mixed with water-based mud (WBM) containing 7 wt./vol. % bentonite, which is equivalent to 24.5 ppb, and tested with a low-pressure apparatus to investigate their capability in sealing fractures. The tests were conducted at 6.9 bar (100 psi) using a set of different fracture width (1000 – 3000 microns), which were simulated using tapered discs. The blends that sealed at low pressure with low fluid loss values were tested at higher pressure to measure their seal integrity, which has been defined as the pressure at which the formed seal breaks and fluid losses resumes. In this study, dry sieve analysis technique was used to analyze the particle size distribution (PSD) of LCM treatments in order to understand how PSD could affect both the fracture sealing and the seal integrity for a known fracture width. The main objective of this investigation is to answer the following questions; what is the role of PSD in effective fracture sealing? Did effective blends follow a specific bridging theory? What is the best criterion to select PSD with respect to fracture width for an effective sealing? This paper introduces a new method to select PSD for LCM treatments for a known fracture width. The new method was developed based on a statistical analysis to correlate the measured PSD of LCM treatments with their sealing pressure, which was previously investigated.
3
2. Laboratory Evaluation 2.1 Fluid Used Unweighted water-based mud (WBM) containing 7 wt./vol. % bentonite was used to eliminate negative or positive effects, if any, of drilling fluid additives such as weighting materials and fluid loss reducers on LCM performance. In addition, a pre-mixed low-toxicity mineral oilbased mud (OBM) was used to investigate the effect base fluid on the performance of LCM. 2.2 Sealing Efficiency Evaluation Fig.1 shows a schematic diagram of the experimental setup that was used to evaluate the seal integrity of LCM treatments. A plastic accumulator (1) used to transfer the drilling fluids to the metal accumulator (2) prior to pressurizing the fluids containing the LCM treatments inside the testing cell (3) through the tapered discs (4) using IscoTM pump (DX100) (5) to provide the injection pressure, which was connected to a computer to record pressure and time. It’s worthwhile mentioning that the pump uses 1/8 inches’ stainless steel tubing with maximum pressure of 689.5 bar (10,000 psi).
4
(4) (1)
(2) (3)
(5)
Fig. 1. High pressure LCM testing apparatus
The test is run by pressurizing fluids containing LCMs, which were poured into the cell, at a constant flow rate of 25 ml/min until a rapid increase in the injection pressure is observed. This increase indicates the formation of a seal. Once the seal has formed, the drilling fluid, containing no LCMs, is injected continuously until the maximum sealing efficiency is reached. A significant drop in the pressure is observed as a result of breaking the seal. However, the test is repeated as cycles until no further seal can be formed. The seal integrity of the different LCM treatments was evaluated for a different set of fracture widths. 2.3 Particle Size Distribution Analysis Two methods are often used to run PSD analysis; sieve analysis and laser diffraction. However, since the provided D50 values (from manufacture) for some of the used LCMs in this study are 2000 microns and due to the limitation of the laser diffraction techniques in measuring particles larger than 2000 microns (Zang et al 2015), dry sieve analysis was used to analyze PSD.
5
Samples of LCM treatment were sieved through a series of stacked sieves. The cumulative weight percent retained for each sieve size was calculated from the measured weight retained in each sieve and then plotted versus the sieve sizes.
The main five
parameters, which were obtained from the resulting plot, are the D10, D25, D50, D75, and D90, measured in microns, for the different blends that sealed different fractures width. In addition, random blends that failed in creating a seal or resulted in a high fluid loss during the screening phase were analyzed to understand the reason behind their failure in forming a seal within the fracture.
3. Laboratory Results A summary of all the sealing efficiency results at the different test conditions and the corresponding PSD analysis for LCM treatments that were previously (Alsaba et al. 2014) investigated in addition to sealing pressures for LCM treatments that were tested at higher concentrations (105 ppb) as recommended by Det Norske Oljeselskap ASA for field applications using a pre-mixed oil-based mud (OBM) are tabulated as shown in Table 1. Table 1. Summary of sealing efficiency results at different fracture widths and PSD analysis # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
LCM Type G
Total LCM (kg/m3) 43 143 86
Total LCM (ppb) 15 50 30
G&SCC
Base Fluid
Fracture width (microns)
WBM
1000
WBM 228
80
G&SCC
300
105
OBM
SCC
143
50
WBM
43
15
NS
WBM 143
50
1000
Sealing Pressure (bar) 28.5 31.0 33.6
Sealing Pressure (psi) 414 449 487
1000 1500 1000 1000 1000 1500 1500 1500 1500 2000 3000 3000 1000 1500 1000 1500 2000 2000
40.3 15.4 108.2 8.1 102.7 14.1 0 11.3 117.8 115.1 7.6 0.0 40.6 11.2 67.8 120.9 23.9 30.4
584 224 1569 117 1489 205 0 164 1708 1669 110 0 589 162 984 1754 347 441
1000 1500
151.8 139.8
2202 2027
Particle Size Distribution (microns) D10
D25
D50
D75
D90
60 60 78
85 95 100
320 340 460
800 800 900
1300 1300 1300
80
120
480
900
1300
65 60 90 65 60 100 170 170 100 300
90 150 400 90 150 500 650 650 250 800
420 500 700 420 500 900 1300 1300 1000 1400
1100 700 1200 1100 700 1250 1900 1900 1800 1800
1400 900 1400 1400 900 1400 2600 2600 2400 2200
250
360
680
950
1200
180
400
1000
1600
2000
180
400
1000
1600
2400
6
24 25 26 27 28 29 30 31 32 33 34 35 36
57
20
G&NS
WBM 114
40
43
15
143
50
157
55
CF
G,SCC, & CF
WBM
WBM
2000 2000 1000 1500
154.2 52.1 163.5 55.5
2237 755 2372 805
1000 1500 2000 2000 1000
199.4 118.1 20.3 16.7 55.2
2892 1713 295 242 800
1000 1500 1000 1500
148.9 77.8 69.7 27.0
2160 1129 1011 391
65
180
500
1300
1900
80
180
580
1400
2000
90
140
220
700
1400
90
150
220
800
1400
55
100
450
850
1200
*NS=Nutshell, G= Graphite, SCC= Sized Calcium Carbonate, CF= Cellulosic Fiber
To qualitatively understand the overall trend of how PSD could affect the sealing pressure with respect to fracture width, all sealing pressure results in Table 1 for 1000, 1500, and 2000 microns fractures were plotted (black dots) regardless of the base fluid, concentration, or LCM type and sorted with the highest pressure to the right as shown in Fig. 2 to Fig. 4. The black dashed line is plotted as a reference line that represents the fracture width in microns. The quadratic regression fit lines for the five D-values as well as the sealing pressure were plotted in different colors, where D90 (red), D75 (orange), D50 (blue), D25 (green), and D10 (purple). The solid colored lines show the quadratic regression fit line of each parameter as the pressure increase to visualize the trend. Fig. 2 shows the sealing pressures (left y-axis) versus PSD (right y-axis) for 1000 microns fracture width. It is noticeable that higher sealing pressures are achieved with wider PSD; however no clear correlation that suggests the effect of a specific D-value could be observed.
7
80
1000
60 40
Particle Size
Sealing Pres
100
500
20 0
200 180 160
0
2500
Sealing Pressure (R_seq 98%) D10 (R_seq 14%) D25 (R_seq 17%) D50 (R_seq 9%) D75 (R_seq 43%) D90 (R_seq 52%)
2000
120
1500
100 80
1000
Particle Size (microns)
Sealing Pressure (bar)
140
60 40
500
20 0
0
Fig. 2. Sealing pressure as a function of the D-values for a fracture width of 1000 microns, where D90 (red), D75 (orange), D50 (blue), D25 (green), and D10 (purple)
Fig. 3 and Fig. 4 show the sealing pressure results2500versus PSD for 1500 microns and 200 180
2000 microns fracture widths, respectively. In general, the sealing pressure results tend to 160
2000
120
1500
Particle Size (microns)
Sealing Pressure (bar)
increase as the 140 particle size distribution gets coarser, i.e. wider PSD. In other words, blends with higher D-values resulted in higher sealing pressure. The D-values fit lines shows an 100 80
1000
upward increase with the sealing pressure. 60 40
500
20 0
200 180 160
0 Sealing Pressure (R_seq 94%) D10 (R_seq 59%) D25 (R_seq 24%) D50 (R_seq 35%) D75 (R_seq 46%) D90 (R_seq 64%)
2500
2000
120
1500
100 80
1000
Particle Size (microns)
Sealing Pressure (bar)
140
60 40
500
20 0
0
Fig. 3. Sealing pressure as a function of the D-values for a fracture width of 1500 microns
8
1500
100 80
1000
60 40
Particle Size (mic
Sealing Pressure
120
500
20 0
0 200
Sealing Pressure (R_seq 81%) D10 (R_seq 81%) D25 (R_seq 69%) D50 (R_seq 78%) D75 (R_seq 61%) D90 (R_seq 72%)
2500
2000
1500 100 1000
Particle Size (microns)
Sealing Pressure (bar)
150
50 500
0
0
Fig. 4. Sealing pressure as a function of the D-values for a fracture width of 2000 microns
Even though the observed PSD fit lines shows an increase with the sealing pressure, no clear conclusion could be made on the significance of each D-value contribution toward enhancing the sealing pressure from the results. From the qualitative analysis of the effect particle size distribution has on the sealing pressure, the improved performance of treatments containing nutshells could be attributed to the fact that the D90 values of these blends ranged between 1900 – 2400 microns (Table 1). In general, all LCM treatments having a D90 smaller than the fracture width failed to establish a seal within the fracture. This suggests that the D90 value should be selected such that it matches the fracture width to ensure an effective fracture sealing. When measuring PSD, the variation in particles shape in terms of sphericity needs to be taken into consideration to avoid inaccuracy in analyzing the PSD. The shape of the used LCMs was qualitatively inspected under an optical microscope (Fig. 5) and described using the sphericity and roundness chart by Powers (1953). Graphite (Fig. 5a), calcium carbonate (Fig. 5b), and nutshells (Fig. 5c) particles could be described as spherical with variation in the sphericity. However, cellulosic fiber (Fig. 5d) particles can be described as nonspherical
9
particles with some elongated and flat particles. Based on our observation when measuring the PSD of the different LCM treatments, it was found that blends containing cellulosic fibers tend to block the sieves with the elongated and flat particles, thus resulting in a false measurement of the sieve weight used to construct the PSD plots. Therefor, PSD analysis of those blends was found to be unrepresentative. For this reason it was decided to exclude the cellulosic fiber results (Tests 32-36) from the statistical analysis and limit it to granular materials only.
1 mm
(a) Graphite (60x)
1 mm
(b) Sized calcium carbonate (60x)
1 mm
1 mm
(c) Nut shells (60x)
(d) Cellulosic Fiber (30x)
Fig. 5. Optical microscopy images for (a) Graphite, (b) Calcium carbonate, (c) Nutshells, and (d) Cellulosic fiber
10
4. Statistical Analysis and Model Development In normal overbalanced drilling operations (i.e. drilling fluid pressure higher than formation pressure), a minimum static overbalance pressure of 10.3 - 20.7 bar (150-300 psi) is required to prevent formation fluid influx (Jahn et al. 2008; Rehm et al. 2012; The Drilling Manual, 2015). Therefore, the formed seal within the fracture should withstand at least the minimum overbalance pressure without failing. In the statistical analysis, the sealing efficiency results of the different blends were grouped into two categories; weak and strong seal. The seals that failed to withstand an overbalance of 34.5 bar (500 psi) to (selected to account for the static and dynamic overbalance pressure) are considered weak seal and the ones that survived 34.5 bar (500 psi) or more are considered strong seal regardless of LCM type, concentration and fracture width. A statistical analysis was conducted to study the effect of fracture width, base fluid, total LCM concentration and the five D values on the performance of LCM in terms of the sealing pressure. The performed statistical techniques to characterize each parameter effect on sealing pressure include probability tests and multi-regression analysis. The probability test (F-test) was performed to test the influence of each parameter on sealing pressure. The F-test provides a P-value, where the P-value is a statistical probability that the predicted value (the F-value) is similar or very different from the measured value (Montgomery, 2001). Assuming a true null hypothesis (H0) that proposes no influence of a specific variable on the sealing pressure, with a confidence interval of 95% and type I error (α) of 0.05, a P-value less than 0.05 suggests the rejection of the null hypothesis (H0) and accepting an alternative hypothesis (H1). The alternative hypothesis suggests that the sealing pressure is influenced by a specific variable. The Effect Leverage plot (Sall, 1990) was used for the multi-regression analysis to show the actual and the predicated data of each test. Consequently, the Leverage plot shows the
11
impact of adding an effect (variable) to the overall predicated model. The Leverage plot is constructed by plotting a scatter plot of the X and Y residuals. The sealing pressure residuals are regressed on all predictors except for the variable of interest while the x-residuals (variable of interest) are regressed on all other predictors in the model. The mean of the sealing pressure, without the effect of the variable of interest, is plotted as well as a least square fit line and confidence interval for easier interpretation of the results significant at 5% level. The slope of the least squares fit line is a measure of how the tested variable affects the sealing pressure i.e. a non-zero slope implies that the tested variable will affect the sealing pressure (Sall, 1990). Fig. 6 Shows the Leverage plot for each parameter with the resulting P value (also summarized in Table 2). The blue dashed line represents the mean sealing pressure, the solid red line represents the fitted model, and the dashed red line represents the confidence interval (5% confident level). If the mean sealing pressure is inside the confidence interval envelope, the parameter does not have any significant effect on the sealing pressure. If the confidence interval crosses the mean pressure at a high angle, it has a significant contribution to sealing pressure.
Table 2. The P-Value showing the effect of base fluid, D-values, fracture width, LCM concentration on sealing pressure and model fit summary Parameter Unit P-Values Fracture Width (microns) 0.00001 D90 (microns) 0.08116 D50 (microns) 0.26377 D10 (microns) 0.44148 D75 (microns) 0.53233 Total LCM (ppb) 0.53522 D25 (microns) 0.85566 Base Fluid (WBM/OBM) 0.90849 Model Summary Fit R2 0.743
12
( a
( b
( c
( d
( e
( g
(f )
( h
Fig. 6. Leverage plot of sealing pressure as a function of (a) Base Fluid (b) D10 (c) D25 (d) D50 (e) D75 (f) D90 (g) Fracture width, and (h) LCM concentration
13
The overall model fit shown in Fig. 7 shows a good correlation with R2 of 74% and a Pvalue less than 0.05. The residual plot (not provided) showed the data being randomly distributed around x-axis, indicating that a linear model was appropriate for the collected data.
Figure 7. Leverage plot of the predicated sealing pressure
In order to develop a generalized model that predicts the sealing pressure for different fracture widths, statistical partition technique was used based on the obtained information from the previous model (Fig. 7). The statistical partition was performed using the four significant parameters; D90, D75, D50 and D10 as a function of fracture width and taking the total LCM as a weighted parameter. Sensitivity analysis was than performed by first taking the first three parameters (D90, D50 and D10) to predict sealing pressure and second by taking only the first two parameters (D90 and D50). The model using D90 and D50 to predict sealing pressure for a given fracture width gave a model fit similar (3% difference) to the model with the four parameters. Thus, the model using D90 and D50 was chosen, where the model have a better fit than the previous model (Fig. 7) with R2 of 74%. The statistical partition was then converted into a mathematical relationship that predicts a good sealing pressure, which was defined earlier as
14
any pressure >34.5 bar (500 psi), as a function of the selected PSD D-values. The obtained mathematical relationship suggests the following: -
D50 should be
-
the fracture width
D90 should be
the fracture width
5. Model Verification In order to validate the proposed selection criteria and compare it with the previous selection criteria discussed in the introduction, a comparison table was constructed. Table 3 lists the test number, the fracture width used, the measured seal integrity, and the predicted seal integrity.
Table 3. Comparison of measured and predicted PSD for effective fracture sealing Proposed Criterion
Abrams (1977)
D90 Rule (1996, 1998)
Vickers (2006)
Halliburton (2008)
Test #
FW (microns)
Measured
P
M
P
M
P
M
P
M
P
M
1
1000
W
S
N
W
Y
S
N
W
Y
W
Y
2
1000
W
S
N
S
N
S
N
W
Y
W
Y
3
1000
W
S
N
S
N
S
N
W
Y
W
Y
4
1000
S
S
Y
S
Y
S
Y
W
N
W
N
5
1500
W
W
Y
W
Y
W
Y
W
Y
W
Y
6
1000
S
S
Y
S
Y
S
Y
W
N
W
N
7
1000
W
W
Y
S
N
W
Y
W
Y
W
Y
8
1000
S
S
Y
S
Y
S
Y
W
N
W
N
9
1500
W
W
Y
W
Y
W
Y
W
Y
W
Y
10
1500
W
W
Y
S
N
W
Y
W
Y
W
Y
11
1500
W
W
Y
S
N
W
Y
W
Y
W
Y
12
1500
S
S
Y
S
Y
S
Y
W
N
W
N
13
2000
S
S
Y
S
Y
S
Y
W
N
W
N
14
3000
W
W
Y
S
N
W
Y
W
Y
W
Y
15
3000
W
W
Y
S
N
W
Y
W
Y
W
Y
16
1000
S
S
Y
S
Y
S
Y
W
N
W
N
17
1500
W
W
Y
S
N
W
Y
S
N
W
Y
18
1000
S
S
Y
S
Y
S
Y
W
N
S
Y
19
1500
S
S
Y
S
Y
S
Y
W
N
W
N
15
20
2000
W
W
Y
S
N
S
N
W
Y
W
Y
21
2000
W
W
Y
S
N
S
N
W
Y
W
Y
22
1000
S
S
Y
S
Y
S
Y
W
N
S
Y
23
1500
S
S
Y
S
Y
S
Y
W
N
W
N
24
2000
S
S
Y
S
Y
S
Y
W
N
W
N
25
2000
S
S
Y
S
Y
S
Y
W
N
W
N
26
1000
S
S
Y
S
Y
S
Y
W
N
W
N
27
1500
S
S
Y
S
Y
S
Y
W
N
W
N
28
1000
S
S
Y
S
Y
S
Y
W
N
W
N
29
1500
S
S
Y
S
Y
S
Y
W
N
W
N
30
2000
W
W
Y
W
Y
S
N
W
Y
W
Y
31
2000
W
W
Y
W
Y
S
N
W
Y
W
Y
Note:
Fracture width (FW)
Predicted (P)
Match (M)
Strong (S)
Weak (W)
Yes (Y)
No (N)
The measured seal integrity is based on the measured sealing pressure, i.e. if the measured sealing pressure is larger than 34.5 bar (500 psi), then the measured seal integrity is considered strong. If the measured sealing pressure is less than 34.5 bar, then the measured seal integrity is considered weak. In the comparison, it is assumed that following the selection criteria should result in a strong seal that could withstand pressures higher than 34.5 bar. The predicted seal integrity column is based on comparing the suggested D-Value by the selection criteria with the actual measured PSD. If the measured PSD is equal or larger than the suggested value by the selection criteria, the predicted seal integrity is considered strong. If the measured PSD is less than the suggested PSD, the predicted seal integrity is considered weak. The last step is to check if the measured seal integrity matches with the predicted one and calculate the overall match percentage. The overall match percentage of the 31 tests (excluding the cellulosic fiber blends) was calculated for the four models and the proposed criteria as shown in Table 4.
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Table 4. The percentage match of different PSD criteria with lab tests. Method Abram's Rule (Abrams, 1977) D90 Rule (Smith et al. 1996, Hands et al. 1998)
PSD Selection Criteria
Percentage Match with Lab Data
D50 ≥ 1/3 the formation average pore size
68 %
D90 = the formation pore size
77 %
Vickers’s Method (Vickers et al. 2006)
D90 = largest pore throat D75 < 2/3 the largest pore throat D50 ≥ 1/3 D25 = 1/7 the mean pore throat D10 > the smallest pore throat
45%
Halliburton Method (Whitfill, 2008)
D50 = fracture width
55 %
Proposed Method
D50 should be
the fracture width
D90 should be
the fracture width
90%
The verification showed a good match between the predicted seal integrity and the measured seal integrity with an overall match of 90% for the proposed selection criteria. Vickers method showed the lowest percentage match due to the number of D-values that needs to be satisfied. Halliburton’s method (Whitfill, 2008) also showed a low predictive match. Abrams and D90 rules had higher percentage match compared to Vickers and Halliburton’s methods. Since the validation was performed on the same dataset, additional testing would be beneficial to independently validate the proposed criteria. However, the results are in agreement with the qualitative analysis were a wide particle size distribution gave higher sealing pressure since smaller particles filled the voids between the larger particles in the formed plugs.
6. Conclusions -
An updated selection criterion for PSD selection for a known fracture width was developed stating that D50 and D90 should be equal or greater than 3/10 and 6/5 the fracture width, respectively.
-
The proposed criterion was verified with the lab results and it gave a 90% match between the actual and predicted performance.
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-
Selecting PSD for LCM treatments based on the estimated fracture width is a crucial step to ensure effective fracture sealing.
-
Previous PSD optimization criteria are useful to enhance the bridging capabilities of drillin fluids; however, these criteria might not be applicable for fracture sealing.
-
From the results, D90 plays a significant role in initiating the seal by plugging the largest fracture width.
-
Blends containing nutshells were effective in sealing fractures at lower concentration while higher concentrations of graphite and calcium carbonate were required to enhance the sealing pressure. For example, low concentration of nutshells (15 ppb) were able to reach a sealing pressure of 67.8 bars for 1000 microns fracture as shown in Test # 18, while higher concentration of graphite and sized calcium carbonate (80 ppb) was only able to reach 40.3 bars to seal the same fracture width as shown in Test # 4.
-
The shape of LCM particles, in terms of sphericity and roundness, needs to be taken into consideration when analyzing PSD.
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Based on the results, increasing the total concentration of LCM will improve the sealing efficiency of LCM treatments.
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The statistical investigation agrees with the importance of D90 and D50 in forming an effective seal.
Acknowledgments The authors would like to acknowledge Det Norske Oljeselskap ASA (Now Aker BP) for the financial support under research agreement # 0037709; Dr. Galecki from Missouri University of Science and Technology for his help with the PSD analysis.
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Highlights
Different lost circulation materials at different concentration/formulations were evaluated. Fracture width ranging from 1000 – 3000 microns were tested Four common selection criteria were investigated and compared with the suggested criterion The presented criterion was based on both laboratory and statistical investigation The presented criteria suggest that both D50 and D90 should be equal or greater than 3/10 and 6/5 the fracture width, respectively. The suggested method showed a 90% match between the actual and predicted seal quality. This study shows that previous criteria might not be applicable for fracture sealing since they were developed for pore sizes ranges not fracture widths ranges.
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