# Thermal and rheological properties improvement of drilling fluids using functionalized carbon nanotubes

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## Abstract

The application of functionalized/unfunctionalized (multi-walled) carbon nanotubes (CNT) was investigated in the context of formulating nano-based drilling fluids from water/oil-based fluid templates. CNT functionalization was attempted by applying hydrophilic functional groups onto the surface of the nanotubes via acid treatment. Experimental data were collected for thermal conductivity, viscosity/yield point, and filtrate amount in all samples. The time evolution of thermal conductivity was studied, as well as the effects of temperature and CNTs volume fraction on the parameter. Scanning electron microscopy (SEM) was used to monitor CNTs dispersion quality. The thermal conductivity results unveil considerable enhancements, by as much as 23.2 % (1 % vol. functionalized CNT) in CNT-water-based case at ambient temperature, with extended improvement of 31.8 % at an elevated temperature of 50 °C. Corresponding results for the CNT-oil-based case exhibit an improvement in thermal conductivity by 40.3 % (unfunctionalized) and 43.1 % (functionalized) and 1 % volume fraction of CNT. The rheological results follow an analogous improvement trend. For the CNT-oil-based case, the filtration tests conducted at 138 °C and 500 (psi) show a 16.67 % reduction in filtrate amount (1 % vol. CNT). The time evolution of thermal conductivity was found to nearly equalize (at an amount of 9.7 %) after 100 h of sample preparation in both functionalized and unfunctionalized CNT-oil-based cases.

## Keywords

Thermal conductivity Annular viscosity API filtration Scanning electron microscopy (SEM)## Introduction

The success of a drilling operation depends heavily on the fate of the drilling fluid being used, to fulfill certain functional tasks. Presently, the industry is faced with a range of material-based challenges in designing high performance fluids to overcome the technical/environmental-related issues pertaining to petroleum drilling. Nonetheless, the available experience indicates that it is often impossible to address specific functional requirements (needed to challenge drilling environments) by merely using conventional macro-sized mud additives. Nano-sized entities, on the other hand, have shown to hold conspicuous characteristics to fill this gap.

In general, proximity to atomic scales may induce different governing laws for material behavior than the corresponding macro/micro-sized scales. An example of which is the drastically different behavior of carbon nanotubes (CNT) and fullerenes from those of corresponding (mother) graphite (Smalley and Yakobsonb 1998; Zhou et al. 2005). To some extent, such altered behavior is accounted by the extreme surface area to volume ratio of nano-materials (more than a million-time increase compared to the same mass in millimeters size). Such enormous ratio along with the predominant role of surface. Van der Waals, molecular/atomic forces in nano-scaled environments form the basis for a game-changing scenario for nano-materials enabling nanos to act effectively in fluid systems, in essentially tiny concentrations (<1 %).

For a drilling fluid to function in an effective manner, it must have the correct heat transfer and fluid flow characteristics. Furthermore, it must be environmentally benign. During the deep-hole and geothermal drilling operations, the temperature and pressure may reach excessively high values, in such a way that the heat transfer demands on the drilling fluid may seem impossible to meet. It is, therefore, industrially advantageous to explore ways to enhance the thermal properties of the drilling fluid.

The concept of preparing stable emulsions of nano-sized entities (i.e. nano-particles, CNT) in a base fluid (nanofluid) has evolved over the past decade. The experiments have unveiled improvements in the rheological (Aladag et al. 2012; Chen et al. 2011; Jyothirmayee Aravind et al. 2011; Lei et al. 2008; Murshed et al. 2008; Hobbie and Fry 2007; Vakili-nezhaad and Dorany 2009; Phuoc et al. 2011; Liu et al. 2005) as well as in the thermal (Ding et al. 2006; Hwang et al. 2006; Kalinina et al. 2011; Özerinç et al. 2010; Venkata Sastry et al. 2008; Xie and Chen 2009; Kleinstreuer and Feng 2011; Choi et al. 2001; Karthikeyan et al. 2008; Xie et al. 2002) properties of the nanofluid system, compared to its base fluid.

Recently, Amanullah et al. (2011) attempted formulating nano-based drilling fluids from three industrially available nano-particles. Their results indicated improved rheological stability/gelling property as well as favorably ultra-thin mud cake quality. They projected the possibility of spurt loss elimination (and subsequent formation damage reduction) by applying customized nano-based drilling fluids. Moreover, they estimated dramatic decrease in differential pipe sticking, based on their ultra-think mud cake results, enabling nano-based fluid to be applied to highly permeable formations. More recently, Nwaoji (2012) studied the application of Iron (III) hydroxide and calcium carbonate nano-particles in drilling fluid blends for wellbore strengthening by conducting hydraulic fracture tests on Roubidoux sandstone and concrete cores. Their results revealed an increase in core fracture breakdown pressure by as much as 70.31 and 36.39 % in water/oil-based cases, respectively.

The promising potential of nanos, to be used in drilling operations in specific, is conceivably due to a number of facts. First, their huge surface area provides them with increased interaction site/potential with the reactive shale to sort of resolving borehole problems. Second, the less kinetic energy impact of nano-particles brings about negligible abrasive effect, which alleviates down-hole equipment damage. Last, but not least, is their effectiveness in relatively low concentrations (<1 %), which will be advantageous in an environmental/industrial perspective.

The positive reported outcomes of the above-mentioned literature on effectiveness of CNTs in nanofluids served as our motivation to investigate the applicability of using CNTs in improving the thermal and rheological properties of drilling fluids. To our knowledge, there are no available data on the CNTs performance in water/oil-based drilling fluids, which may further signify the present analysis.

## Sample preparation and research methodology

^{2}/gr), as received. For MIX-2, the technical specifications of the base fluid used in formulation are listed in Table 1.

Technical specifications of the base fluid in MIX-2

Item | |
---|---|

Mud weight (pcf) | 75 |

Oil/water ratio | 73/27 |

Fluid lost (cc) | 3 |

Alkalinity | 4.5 |

Chloride (ppm) | 345,000 |

Solid (%) | 16 |

Yield point (lb/100 ft | 10 |

Viscosity (cp) | 49 |

Thermal conductivity (W/m.K) | 0.275 |

Diesel oil (bbl) | 0.73 |

Calcium chloride water (bbl) | 0.27 |

Primary emulsifier (gal) | 1 |

Fluid lost controller (lb) | 14 |

Limestone (lb) | 13 |

Secondary emulsifier (gal) | 0.5 |

Drill gel (lb) | 1 |

- 1.
Preparing 350 cm

^{3}of the water-based mud with a concentration equivalent of 17 pounds of bentonite in a Barrel (17 lb/bbl). - 2.
Agitating the fluid mixture for at least 15 min.

- 3.Preparing four different kinds of CNT-formulated mud samples by adding various amounts of unfunctionalized (MIX-1-1)/ball-milled (MIX-1-2)/functionalized (MIX-1-3)/functionalized + ball-milled (MIX-1-4) CNTs (Fig. 2).
- 4.
Agitating each nanofluid mixture sample with a high-speed mixer at 6,000 rpm for 5 min.

The present methodology involves analysis of CNT presence influence, by considering the effects of CNTs volume fraction/system temperature/time on thermal conductivity of MIX/1/MIX-2. Moreover, nano-contained samples were tested against any alteration in rheological behavior (viscosity, yield point), compared to the base fluid. API filtration tests were additionally implemented on MIX-1/MIX-2 to evaluate filtrate quantity, a parameter of typical interest in drilling operations.

## Results and discussions

The experimental results presented in this section will mainly focus on the effects of CNT presence on important (drilling) fluid characteristics; namely, the thermal conductivity and shear stress. The results will initially be presented on CNTs influence on thermal conductivity, in which the change in volume fraction of CNTs on the parameter will be discussed. Later, the analysis is extended to study the time evolution of thermal conductivity, as well as the impact of system temperature on altering this parameter in nano-contained samples. The results on rheological measurements will next be presented. This will be ensued by our API filtration results, conducted under high temperature high pressure (HTHP) regime.

### Effect of CNT on thermal conductivity

#### Effect of CNTs volume fraction on thermal conductivity

For CNT + DW system, aggregation and precipitation to the bottom takes place, if the nanotubes are functionalized. CNTs cannot be dispersed into polar liquids such as DW. Because of bentonite existence and gel-strengthening properties of the base fluid, CNT precipitation occurs slowly and the nanofluid in this case will be more stable.

*K*(W m

^{−1}K

^{−1}), was measured via THW technique. In a nutshell, the THW technique relies on determining the thermal conductivity, from calculating the slope of linear portion of temperature rise (\(\varDelta T\)) vs. the natural logarithm of the time evolution (ln(

*t*)). Assuming the temperature at any time (

*t*) and distance (

*r*) from a hot-wire probe as \(T (r ,t )\), the following relationship exists (Kleinstreuer and Feng 2011):

^{−1}) is the heat flux, \(\alpha\) (m

^{2}s

^{−1}) is the thermal diffusivity, \(r\) is the radial distance (m), and \(\gamma = 0. 5 7 7 2\) is the Euler`s constant. Assuming the higher order terms in Eq. (1) to be negligible, the thermal conductivity can be approximated by (Kleinstreuer and Feng 2011):

Given temperature measurements over two different time intervals, the thermal conductivity is obtainable from Eq. (2). Having determined *K*, the increase is evaluated against the corresponding (mother) base fluid values, the results of which are given in Fig. 4. The experimental uncertainty concomitant with the data is approximated at ~2 %, which is based on the accuracy of the THW method employed. Nevertheless, the uncertainty was not reflected in the graphs, so as to preserve visual clarity.

In MIX-1 cases, the thermal conductivity shows an increasing trend with an increase in volume fraction of CNTs. The maximum thermal conductivity increase belonged to functionalized + ball-milled case (MIX-1-4), with an increase of 23.2 % (1 % CNT).

In the case of functionalized CNT, thermal conductivity increase has been more significant than simple and ball-milled CNTs. This phenomenon is due to introducing hydrophilic functional group onto the surface of nanotubes to disperse more efficiently in the water-based mud. This figure also shows that thermal conductivity enhancement for typical water-based mud is linear to some extent for volume fractions lower than 0.4 % and ball-milling is not crucial for increasing thermal conductivity for these samples. The comparison of the experimental data suggests that thermal conductivity of the base fluid, volume fraction of CNTs and dispersion, play a dominant role in the thermal conductivity enhancement in a water-based mud.

Due to strong van der Waals attractive forces, nearly all the CNTs are in the form of agglomerates with much larger dimensions than the primary particles, as shown in Fig. 3a. The degree of agglomeration changes for ball-milled MWCNTs, but still not dispersed effectively, Fig. 3b. By introducing hydrophilic functional group onto the surface of CNTs, it dispersed more effectively in the water-based mud and it seems that CNTs conduct heat more efficiently by passing through bentonite layers as it is shown in Fig. 3c, d.

In MIX-2 cases, both unfunctionalized and functionalized MWCNT systems seem to put a similar impact on thermal conductivity alteration in the region (with CNT vol. fraction <0.4 %). In the MIX-2-2 system, however, more increase is incurred to the thermal conductivity, as the CNT volume fraction is increased. This may be credited towards the better dispersion quality of functionalized CNTs in oil-based systems (with 27 % water presence). Improvements as much as 40.3 and 43.05 % in thermal conductivity have been measured (1 % CNT vol. fraction) for MIX-2-1/MIX-2-2 systems, respectively.

#### Effect of time on thermal conductivity of CNT-contained samples

*K*shows a lower slope, after a threshold time (\({\text{log(}}t )> 2. 1\)), which can be due to the gel-strengthening properties of the water-based mud.

In MIX-2 cases, the *K*-reduction-percentage profile follows an analogous trend (as to MIX-1 situation) in the sense that *K*-reduction percentage recorded in the MIX-2-1 (unfunctionalized) system surpassed the MIX-2-2 (functionalized) system, typically in the first 10 h of sample preparation. Following this threshold time, the declining slope diminishes in both MIX-2 cases, and reaches comparably similar values of 9.79 and 9.73 %, for MIX-2-1/MIX-2-2 samples, respectively.

#### Effect of temperature on thermal conductivity of CNT-contained samples

### Effect of CNT on rheology

^{−2}sec

^{−1}), \(\gamma\) is the shear stress (dyne cm

^{−2}), and \(\tau\) is the shear rate (sec

^{−1}). Then, shear stress/rate can be obtained from the viscometer readings using the following equations:

^{−1}), \(\zeta_{ 2}\) is the shear stress constant for effective bob surface (cm

^{−3}), \(\theta\) is the Fann viscometer dial reading (degree), \(\zeta_{ 3}\) is the shear rate constant (sec

^{−1}rpm

^{−1}), and \(N\) is the rate of revolution of outer cylinder (rpm). The measurements were conducted over rotation speeds of 300 and 600 rpm. These two speeds of rotation are typically available in all viscometer instruments, and are considered as industry benchmarks. Subsequently, the plastic viscosity/yield point of fluid sample can be computed using the 300/600 rpm measurement values (Fann viscometer manual):

^{2}). Also, \(\theta_{600}\) and \(\theta_{300}\) represent the viscometer dial readings at 600 and 300 rpm rotation speeds, respectively (1°Fann ~1.065 lb/100 ft

^{2}). Alternatively, the effective viscosity (in cP) can be computed by the following equation in Fann Viscometer readings/speed:

Shear stress data for the classic water-based (WBM)/oil-base (OBM) muds, and MIX-1/MIX-2 samples at different rotation speeds

Fluid | Bentonite content (lb/bbl) | Rotation speed (rpm) | Shear stress (lb/100 ft |
---|---|---|---|

WBM | 16 | 300 | 4.84 |

WBM | 16 | 600 | 6.57 |

WBM | 18 | 300 | 7.82 |

WBM | 18 | 600 | 10.55 |

WBM | 22 | 300 | 9.81 |

WBM | 22 | 600 | 13.03 |

WBM | 24 | 300 | 12.84 |

WBM | 24 | 600 | 14.40 |

MIX-1-3 | 16 | 300 | 5.21 |

MIX-1-3 | 16 | 600 | 7.44 |

MIX-1-3 | 18 | 300 | 8.31 |

MIX-1-3 | 18 | 600 | 11.66 |

MIX-1-3 | 22 | 300 | 10.67 |

MIX-1-3 | 22 | 600 | 13.28 |

MIX-1-3 | 24 | 300 | 14.15 |

MIX-1-3 | 24 | 600 | 16.26 |

OBM | 17 | 300 | 38.50 |

OBM | 17 | 600 | 65.45 |

MIX-2-2 | 17 | 300 | 43.63 |

MIX-2-2 | 17 | 600 | 71.92 |

Yield point data for MIX-1/MIX-2

Fluid | Bentonite content (lb/bbl) | Yield point (lb/100 ft2) |
---|---|---|

WBM | 16 | 2.9 |

WBM | 18 | 4.9 |

WBM | 22 | 6.9 |

WBM | 24 | 10.8 |

MIX-1-3 | 16 | 3.2 |

MIX-1-3 | 18 | 4.9 |

MIX-1-3 | 22 | 7.6 |

MIX-1-3 | 24 | 11.6 |

OBM | 17 | 10 |

MIX-2-2 | 17 | 20 |

In spite of the fact that mixtures of water and bentonite generally exhibit a pseudo-plastic rheological behavior, we chose the Bingham model for the purpose. Our reason for the Bingham model choice was twofold. First, the direct-indicating rotational rheometer apparatus used is specifically designed to apply the Bingham plastic fluid model. Second, the Bingham model is widely used in drilling fluids industry to describe flow characteristics of many types of muds. The YP value, in this model, typically represents the ability of a mud to lift cuttings out of the annulus. Practically, YP should be high enough to carry cuttings out of the hole, but not large as to an extent to create excessive pump pressure. Moreover, a high YP implies non-Newtonian behavior of a fluid. Reversely, the PV in the model should be as low as possible to contribute to fast drilling. The rheological results indicate that adding functionalized CNTs to water-based mud increases the shear stress, and that the increase becomes larger at higher rotational speeds. This phenomenon could be explained in terms of improved CNT dispersion at high shear rates (i.e. 600 rpm). In MIX-1 case, the yield points have pointed to a larger value, compared to their classic mud counterparts. Consequently, greater pressure-lost values should be expected (by adding functionalized CNTs); especially in the portions of wellbore in which the flow regime is laminar. Also, as explained earlier, the larger YP values in CNT-contained samples convey the better cutting-removal characteristics of nanofluids for drilling operations. The CNT impact on rheological behavior follows a similar trend in MIX-2. The YP shows a substantial increase by 100 % in MIX-2-2, compared to the corresponding mother-fluid value. The plastic viscosity also gets a favorably decreased value, for instance, from a value of 28 (cP) in classic oil-based mud to a value of 24 (cP) in MIX-2-2 (~14 % reduction). Such decreased PV value should be interpreted in favor of better suitability of CNT-contained fluids for fast drilling operations.

### Filtrate properties of CNT-contained samples

^{2}. Below the support was a drain tube for discharging the filtrate into the graduated cylinder. The result of the experiments on MIX-1 case is shown in Fig. 7. The classic water-based mud (WBM) system was prepared by adding 24 g of bentonite to 350 cm

^{3}of DW to form 24 lb/bbl of drilling fluid. The amount of filtrate for WBM system after 30 min (which is in accordance with the API filtration test) was 28.4 cm

^{3}, while this parameter becomes 26.3 cm

^{3}after adding 1 vol. % functionalized CNTs to the sample. This means that the amount of filtrate decreases by 7.4 % after using CNTs. Moreover, the amount of spurt lost (at the beginning of the test) had decreased from a value of 0.57 cm

^{3}to a value of 0.44 cm

^{3}, which emphasizes the fact the mud cake created by CNT-contained samples is fairly more uniform than base mud.

For MIX-2 case, the filtration test was conducted under HTHP conditions, owing to high viscosity of the oil-based mud considered (~49 cP). Hence, the results should further relate to actual wellbore conditions. The experimental temperature and pressure were set to 138 °C and 500 psi, respectively. The results unveil a 16.6 % reduction in filtrate amount from a typical value of 3.6 cm^{3} (OBM) to a value of 3 cm^{3} (MIX-2-2). This reduction in filtrate quantity should cause added convenience during a typical drilling operation.

## Conclusions

CNT presence brought about favorable changes in nearly every corner of the drilling fluid characteristics studied. The thermal conductivity was increased in both MIX-1/MIX-2 cases, with maximum attained percentage increases of 31.8 and 40.3 %, respectively. The functionalizing + ball-milling process yielded the best results in terms of thermal conductivity enhancement of nanofluid. The evolution of time decreased the thermal conductivity of MIX-1/MIX-2, which was more conspicuous in water-based system. The time effect became nearly identical in MIX-2 cases, after a threshold time, with comparably similar values of 9.79 % (MIX-2-1) and 9.73 % (MIX-2-2) in thermal conductivity declining slope. The rise in temperature increased the thermal conductivity of CNT-contained samples. Yet, the increasing rate was diminished after a threshold temperature of 35 °C (MIX-1) and 40 °C (MIX-2). Rheological results point to increased values of shear stress/yield and lower plastic viscosity for MIX-1/MIX-2, compared to the corresponding base fluids. The filtrate quantity also showed decrease in MIX-1/MIX-2 samples, which was further found to sustain through HTHP conditions.

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