Characterization of Plg

The chemical composition of Plg includes silica, alumina and hematite as the main constituents. It also has a low concentration of calcium oxide (Silva et al., Reference Silva, Gois, Ramme, Castro Dantas, Barillas and Santanna2021). The mineralogical composition and thermogravimetric analyses of Plg can be seen in the work of Silva et al. (Reference Silva, Gois, Ramme, Castro Dantas, Barillas and Santanna2021). The morphology and surface charge of Plg from the São Pedro mines were given by Baltar et al. (Reference Baltar, Luz, Baltar, Oliveira and Bezerra2009), where the samples show a large number of particles of acicular habit and isoelectric points at pH 3.3. Plg also has a specific area of ~113 m² g^–1 (Araújo et al., Reference Araújo, Santana, Cavalcante, Nunes, Bertolino and Brito2020).

Preparation of drilling fluid

Drilling fluids viscosified with Plg (Plg fluid) and polymers (XG and CMC) contaminated with Ca(OH)₂ and brine were formulated. Plg was used at a concentration of 17.5 g 350 mL^–1 to prepare the water-based drilling fluid, as defined by Baltar et al. (Reference Baltar, Luz, Baltar, Oliveira and Bezerra2009) and Santanna et al. (Reference Santanna, Silva, Silva and Castro Dantas2020). In the water-based drilling fluid with polymers, XG and CMC were used at concentrations of 1.5 and 2.0 g 350 mL^–1, respectively. These polymer concentrations are used often in the oil industry (Soares et al., Reference Soares, Scheid, Marques and Calçada2020; Borges et al., Reference Borges, Oechsler, Oliveira, Andrade, Calçada, Scheid and Calado2021). The fluids were contaminated with 0.5 g 350 mL^–1 Ca(OH)₂ and with 10% brine (71 g L^–1 NaCl and 40 g L^–1 KCl solution). Low concentrations of contaminants were used, as there is limited literature addressing the action of contaminants, especially in fluids with Plg. The compositions of the fluids studied are shown in Tables 1 and 2.

Table 1. Composition of the salted water-based drilling fluid with Plg (Plg fluid).

Table 2. Composition of the salted water-based drilling fluid with polymers (polymeric fluid).

A Hamilton Beach stirrer (Fann, TX, USA) was used to prepare all fluids (API Specification 13A, 2010). After adding each component, as listed in Tables 1 and 2, the fluid was stirred at 17,000 rpm for 10 min. Then, each fluid was aged in a Fann Roller oven (model 704ES) for 16 h at 180°C. After ageing, the properties of each fluid were measured, and, prior to each characterization, the fluid was stirred again at 17,000 rpm for 10 min.

Characterization of the drilling fluid

Following API Recommended Practice 13B-1 (2009), the drilling fluid samples were prepared and their parameters measured following previously established specifications and standard procedures (API Specification 13A, 2010). Apparent viscosity (μ_a), plastic viscosity (μ_p), yield point (YP) and gel strength (GS) were measured with a rotational Ofite viscosimeter (model 800) and calculated according to Equations 1–4, following API Recommended Practice 13B-1 (2009):

(1)$$\rm \mu _a( {cP} ) = {\it L}_{600}/2$$

(2)$$ \rm \mu _p( {cP} ) = {\it L}_{600}- {\it L}_{300}$$

where L ₆₀₀ = dial reading at 600 rpm of the rotational viscometer and L ₃₀₀ = dial reading at 300 rpm of the rotational viscometer.

(3)$$ \rm YP( {lbf \,100\, ft^{- 2}} ) = {\it L}_{300}- \mu _p$$

(4)$$\rm GS( {lbf \,100 \,ft^{- 2}} ) = {\it G}_{\,final}- {\it G}_{initial}$$

where lbf is pounds of force, G _initial is the initial GS after 10 s of suspension not under shear, obtained from the initial dial reading of the rotating viscometer at 3 rpm after 10 s of suspension and G _final is the final GS after 10 min of suspension not under shear, obtained from the final dial reading of the rotating viscometer at 3 rpm after 10 min of suspension. GS refers to the strength of shear thixotropy or shear thinning of the drilling fluid at a low shear rate.

The pH of each sample was determined initially by means of a commonly used digital pH meter. The densities of all fluids were determined on a Halliburton Service pressurized densimetric balance. An Ofite API press filter was used to measure fluid FV. A pressure of 100 psi was applied and the test period began at the time of pressure application. At the end of 30 min, the volume of filtrate collected was measured. All experiments were performed at room temperature (~25°C).

Alkalinity and salinity tests were performed using titration. The P _f and P _m values were determined using 0.02 N sulfuric acid (H₂SO₄; purchased from Dinâmica) as a titrant. P _f represents the number of millilitres of 0.02 N acid required per millilitre of filtrate. P _m is the number of millilitres of 0.02 N acid required per millilitre of drilling fluid. Fluid salinity was obtained using 0.282 N silver nitrate (AgNO₃; purchased from Vetec) as a titrant. The NaCl concentration of the filtrate (mg L^–1) was calculated according to Equation 5:

(5)$$ \rm NaCl\, ( {mg\,L}^{-1} ) = 1.65 \times 10,\hskip -2.5pt000 \times {\it V}_{sn}$$

where V _sn is the volume of 0.282 N silver nitrate solution (mL).

Cutting transport ratio

The correlations of Moore (Reference Moore1974), Chien (Reference Chien1994) and Walker & Mayes (Reference Walker and Mayes1975) have also been used for characterizing particle slip velocity (Jafarifar et al., Reference Jafarifar, Dehkordi, Abbasi, Schaffie and Ranjbar2020). In the correlations of Moore (Reference Moore1974) and Chien (Reference Chien1994), particles are considered as spheres. The particle's Reynolds number (N _Re) is calculated as a function of apparent viscosity, as described mathematically in Equation 6:

(6)$$N_{\rm Re} = \displaystyle \rm {{928\;\times \;\rho _f\;\times \;{\it v}_{sl}\;\times \;{\it d}_s} \over {\mu _a}}$$

where ρ_f = density of drilling fluid (lb gal^–1), v _sl = cutting slip velocity (ft s^–1), d _s = cutting diameter (in) and μ_a = apparent viscosity (cP).

In Moore's correlation (Bourgoyne Jr et al., Reference Bourgoyne, Millheim, Chenever and Young1991) the apparent viscosity is calculated considering that the fluid presents power-law behaviour, as per Equation 7:

(7)$${\rm \mu }_{\rm a} = \displaystyle{K \over {144}}\left({\displaystyle{{d_2-d_1} \over {v_{\rm a}}}} \right)^{1-n}\left({\displaystyle{{2 + 1/n} \over {0.0208}}} \right)^n$$

where v _a = annular fluid velocity (ft s^–1), d ₂ = outside diameter of the inner pipe (in) and d ₁ = inside diameter of the outer pipe (in). The values of K (consistency index, mPa s^–n) and n (flow-behaviour index) are obtained from Equations 8 and 9:

(8)$$n = 3.32{\rm log}\left({\displaystyle{{L_{600}} \over {L_{300}}}} \right)$$

(9)$$K = \displaystyle{{510L_{300}} \over {{511}^n}}$$

For N _Re > 300, the flow around the particle is fully turbulent and the particle slip velocity can be described by Equation 10 (Bourgoyne Jr et al., Reference Bourgoyne, Millheim, Chenever and Young1991):

(10)$$v_{{\rm sl}} = 1.54\sqrt {d_{\rm s}\displaystyle{{( {{\rm \rho }_{\rm s}{\rm \;}-{\rm \;}{\rm \rho }_{\rm f}} ) } \over {{\rm \rho }_{\rm f}}}} $$

where ρ_s = density of cutting (lb gal^–1).

For N _Re ≤ 3, the flow is considered to be laminar and the particle slip velocity can be described by Equation 11:

(11)$$v_{{\rm sl}} = 82.87\displaystyle{{d_{\rm s}^2 } \over {{\rm \mu }_{\rm a}}}( {{\rm \rho }_{\rm s}-{\rm \rho }_{\rm f}} ) $$

For transitional flow (3 < N _Re < 300), the particle slip velocity can be obtained using Equation 12:

(12)$$v_{{\rm sl}} = \displaystyle{{2.9d_{\rm s}{( {{\rm \rho }_{\rm s}{\rm \;}-{\rm \;}{\rm \rho }_{\rm f}} ) }^{0.667}} \over {{\rm \rho }_{\rm f}^{0.333} {\rm \mu }_{\rm a}^{0.333} }}$$

Bourgoyne Jr et al. (Reference Bourgoyne, Millheim, Chenever and Young1991) recommended computing apparent viscosity using Equation 13 for polymer-based drilling fluids using Chien's (Reference Chien1994) correlation:

(13)$${\rm \mu }_{\rm a} = {\rm \mu }_{\rm p} + 5\displaystyle{{{\rm \tau }_{\rm s}d_{\rm s}} \over {v_{\rm a}}}$$

where μ_p = plastic viscosity (cP) and τ_s = shear stress (lbf 100 ft^–2).

According to Bourgoyne Jr et al. (Reference Bourgoyne, Millheim, Chenever and Young1991), Chien's (Reference Chien1994) correlation is similar to Moore's (Reference Moore1974) in that it obtains the apparent viscosity of non-Newtonian fluids for use in N _Re. For clay suspensions, it is recommended to use plastic viscosity (μ_p) as the apparent viscosity (Bourgoyne Jr et al., Reference Bourgoyne, Millheim, Chenever and Young1991). Under these conditions, the apparent viscosity is obtained using Equation 14 (Bourgoyne Jr et al., Reference Bourgoyne, Millheim, Chenever and Young1991):

(14)$$\rm \mu _a = \mu _p = {\it L}_{600}- {\it L}_{300}$$

The slip velocity for Chien's (Reference Chien1994) correlation to N _Re < 100 (transitional flow) is given by Equation 15 (Bourgoyne Jr et al., Reference Bourgoyne, Millheim, Chenever and Young1991):

(15)$$v_{{\rm sl}} = 0.0075\left({\displaystyle{{{\rm \mu }_{\rm a}} \over {{\rm \rho }_{\rm f}d_{\rm s}}}} \right)\left[{\sqrt {\displaystyle{{36800d_s} \over {{\left({\displaystyle{{{\rm \mu }_{\rm a}} \over {{\rm \rho }_{\rm f}d_{\rm s}}}} \right)}^2}}\left({\displaystyle{{{\rm \rho }_{\rm s}{\rm \;}-{\rm \;}{\rm \rho }_{\rm f}} \over {{\rm \rho }_{\rm f}}}} \right) + 1} -1} \right]$$

In the correlation of Walker & Mayes (Reference Walker and Mayes1975), according to Bourgoyne Jr et al. (Reference Bourgoyne, Millheim, Chenever and Young1991), the particle is considered a circular disc in flat fall (i.e. falling flat side down, which represents the condition of the greatest terminal settling velocity). For the calculation of apparent viscosity one needs to obtain the shear stress (τ_s) and shear rate (γ_s) according to Equations 16 and 17:

(16)$${\rm \tau }_{\rm s} = 7.9\sqrt {h( {\rm \rho }_{\rm s}-{\rm \rho }_{\rm f}} = 1.067{\rm \theta }$$

(17)$$\rm \gamma _s = 1.703 \it N$$

where h = thickness of the disk (in), θ = dial reading, γ_s = shear rate (s^–1) and N = rotor speed (rpm).

Thus, calculating the apparent viscosity is done according to Equation 18:

(18)$$\rm \mu _a = 479( { {\rm \tau}_{\rm s}/ {\rm \gamma}_{\rm s}} ) $$

For N _Re > 100, the flow is turbulent and the particle slip velocity is given by Equation 19 (Bourgoyne Jr et al., Reference Bourgoyne, Millheim, Chenever and Young1991):

(19)$$v_{{\rm sl}} = 2.19\sqrt {h\displaystyle{{( {{\rm \rho }_{\rm s}{\rm \;}-{\rm \;}{\rm \rho }_{\rm f}} ) } \over {{\rm \rho }_{\rm f}}}} $$

For N _Re < 100, transitional flow is given by Equation 20 (Bourgoyne Jr et al., Reference Bourgoyne, Millheim, Chenever and Young1991):

(20)$$v_{{\rm sl}} = 0.0203{\rm \tau }_{\rm s}\sqrt {\displaystyle{{( {d_{\rm s}{\rm \gamma }_{\rm s}} ) } \over {\sqrt {{\rm \rho }_{\rm f}} }}} $$

Equation 21 shows the transport velocity (Bourgoyne Jr et al., Reference Bourgoyne, Millheim, Chenever and Young1991). The rock cutting advances towards the surface when there is a difference between the annular fluid and particle slip velocities:

(21)$$v_{\rm T} = v_{\rm a} - v_{\rm sl}$$

where v _T = transport velocity (ft s^–1).

According to Bourgoyne Jr et al. (Reference Bourgoyne, Millheim, Chenever and Young1991), the cutting transport ratio (F _T) is an excellent measure of the carrying capacity of a drilling fluid, and it is determined by dividing the transport velocity by the annular velocity as per Equation 22:

(22)$$F_{\rm T} = {\rm \;}\displaystyle{{v_{\rm T}} \over {v_{\rm a}}} = 1-\left({\displaystyle{{v_{{\rm sl}}} \over {v_{\rm a}}}} \right)$$