SECTION A7 THERMOPHYSICAL PROPERTIES

Transcription

1 FORMATE TECHNICAL MANUAL CHEMICAL AND PHYSICAL PROPERTIES SECTION A7 THERMOPHYSICAL PROPERTIES A7.1 Introduction...2 A7.2 Practical importance...2 A7.3 Coefficient of thermal conductivity...2 A7.3.1 Medium temperature range...2 A7.3.2 Lower temperature range (<10 C / 50 F)...3 A7.3.3 Higher temperature range (>70 C / 160 F)...3 A7.3.4 Pressure dependence...3 A7.4 Specific heat capacity... 4 A7.4.1 Medium temperature range...4 A7.4.2 Lower temperature range (<10 C / 50 F)...4 A7.4.3 Higher temperature range (>70 C / 160 F)...5 References... 5 The Formate Technical Manual is continually updated. To check if a newer version of this section exists please visit cabotcorp.com/formatemanual NOTICE AND DISCLAIMER. The data and conclusions contained herein are based on work believed to be reliable; however, CABOT cannot and does not guarantee that similar results and/or conclusions will be obtained by others. This information is provided as a convenience and for informational purposes only. No guarantee or warranty as to this information, or any product to which it relates, is given or implied. CABOT DISCLAIMS ALL WARRANTIES EXPRESS OR IMPLIED, INCLUDING MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE AS TO (i) SUCH INFORMATION, (ii) ANY PRODUCT OR (iii) INTELLECTUAL PROPERTY INFRINGEMENT. In no event is CABOT responsible for, and CABOT does not accept and hereby disclaims liability for, any damages whatsoever in connection with the use of or reliance on this information or any product to which it relates Cabot Corporation, MA, USA. All rights reserved. CABOT is a registered trademark of Cabot Corporation.

2 FORMATE TECHNICAL MANUAL A7.1 Introduction Heat can be transferred by three means: conduction, convection, and radiation. Conduction and convection are important properties in well operations. Conduction is the movement of heat through a substance by the collision of molecules. Conductive heat transfer occurs when two objects at different temperatures are in contact with each other. Heat flows from the warmer to the cooler object until they are both at the same temperature. Convective heat transfer is usually the most efficient heat transfer method in liquids and gasses. Convection occurs when warmer bodies of a liquid or gas rise to cooler areas in the liquid or gas. As this happens, cooler liquid or gas takes the place of the warmer bodies, which have risen higher. This cycle results in a continuous circulation pattern and heat is transferred to cooler areas. There are several dimensionless numbers used in calculations of heat transfer in fluids: The Nusselt number (Nu) is a function of the pipe diameter, the convective heat coefficient, and the fluid s thermal conductivity. This number relates to the heat transfer properties of a specific fluid in a specific system. The Prandtl number (Pr) is the number used to describe a fluid s heat transfer properties and is a function of the fluid s heat capacity, viscosity, and thermal conductivity. The Reynolds number (Re) is a function of a fluid s density, viscosity, flowing velocity, and pipe diameter. This number assists in defining a flow regime for a specific fluid in a specific system. The following correlation applies: Nu = C Re (1) where m n Pr hd Nu = is the Nusselt number, k (2) ρd υ Re = µ is the Reynolds number, (3) Pr = Cp µ is the Prandtl number, and k (4) where: h = convective heat transfer coefficient D = internal pipe diameter k = coefficient of thermal conductivity C p = heat capacity ρ = fluid density μ = fluid viscosity ν = fluid velocity C, m, n = correlation parameters When comparing the properties of two fluids, higher heat transfer coefficients indicate a greater ability to move heat. A7.2 Practical importance For drilling fluid applications, high thermal conductivity and high specific heat capacity are favorable as they contribute to lower bottom-hole circulating temperatures. Low bottom-hole circulating temperatures provide the following benefits: Prevents exposure of logging / MWD tools to high temperatures Protects polymers from thermal degradation Allows quicker temperature equalization when the well is left static, resulting in much faster well stabilization. This means that flow checks can be completed in a shorter period Water-based fluids, such as formate brines, have a relatively high thermal conductivity and specific heat capacity. Therefore they are better than oil-based muds at maintaining a low bottom-hole circulating temperature. Field experience with formate-based drilling fluids has shown that they provide lower bottom-hole circulating temperatures than OBMs and, when the well is left static, the temperature equalizes much quicker. A7.3 Coefficient of thermal conductivity Thermal conductivity is defined as the quantity of heat, Q, transmitted through a thickness, L, in a direction normal to a surface of area A, due to a temperature difference ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient. k= ( Q L ) ( A ΔT) (5) Where: k = coefficient of thermal conductivity (Wm -1 K -1 ) Q = heat flow rate (W) L = distance (m) A = area (m 2 ) ΔT = temperature gradient (K) A7.3.1 Medium temperature range Thermal conductivity coefficients have been measured on 12 formate brines / blends by the Thermophysical Research Laboratory (Gembarovic and Taylor, 2003). These were single-salt sodium formate brines in the lower density range, blends of concentrated sodium and potassium formate brines in the middle density PAGE 2 SECTION A7

3 SECTION A: CHEMICAL AND PHYSICAL PROPERTIES range, and blends of concentrated cesium and potassium formate brines in the higher density range. Exact compositions of the brines are shown in Table 1. Figure 1 shows thermal conductivity coefficients as a function of fluid density at the three test temperatures. Table 2 lists thermal conductivity at 10 C / 50 F as a function of fluid density with linear temperature corrections. This data is guaranteed within an experimental error of +/- 7%. A7.3.2 Lower temperature range (<10 C / 50 F) Some data is available in the literature for water (CRC Handbook) and diluted single-salt potassium formate brine used in the coolant industry (Addcon, 2007; Addcon, 2014; Eastman, 2016). These are plotted in Figure 2 along with the TPRL data for the same density brines. The spread in these data makes it difficult to determine if the linear relationship is valid in the lower temperature range. A7.3.3 Higher temperature range (>70 C / 160 F) No reliable data have been found for the conductivity of formate brines in the higher temperature range. The only data that have been found are for water (JacobCHR) and zinc chloride brine (Abdulagatov and Magomedov, 1998). The available data for these fluids systems are shown in Figure 3. Both fluids show a maximum thermal conductivity at about 140 C / 284 F. Previous thermal conductivity data for other aqueous salt solutions have shown that the thermal conductivity temperature curves at constant concentration are parallel to those of pure water (Abdulagatov and Magomedov, 1998). It is likely that this would also be the case for formate brines. A7.3.4 Pressure dependence No pressure dependence data is available in the literature for the thermal conductivity of formate brines. A study of zinc chloride (up to 25 wt%) (Abdulagatov and Magomedov, 1998) at pressures up to 100 MPa / 14,500 psi has shown that the thermal conductivity increases linearly with pressure at all isotherms for each concentration, typically in the range of W/m/k/MPa. Based on this, one could assume that thermal conductivity also increases with pressure in formate brines. Table 1 Compositions for 12 formate brines used for testing of thermophysical properties at the Thermophysical Properties Research Laboratory (TPRL). Brine Freshwater Sodium formate [1.33 g/cm 3 / lb/gal] Potassium formate [1.57 g/cm 3 / lb/gal] Cesium formate [2.20 g/cm 3 / lb/gal] [g/cm 3 ] [lb/gal] [ml] [g] [ml] [g] [ml] [g] [ml] [g] Water Na formate Na formate Na formate Na/K formate K/Na formate K/Cs formate K/Cs formate K/Cs formate Cs/K formate Cs/K formate Cs/K formate Cs/K formate SECTION A7 PAGE 3

4 FORMATE TECHNICAL MANUAL Table 2 Coefficient of thermal conductivity as a function of formate brine density. The temperature correlations are valid in the temperature range C / F. The data is based on measurements of single-salt sodium formate in the lower density range, blends of concentrated sodium and potassium formate in the medium density range, and blends of concentrated potassium and cesium formate in the higher density range. Density [g/cm 3 ] K at 10 C [W/(m K)] Temperature correction increase per 10 C Valid in the range C Density [lb/gal] K at 50 F [BTU/ (hr ft F)] Temperature correction increase per 10 F Valid in the range F A7.4 Specific heat capacity Heat capacity is a physical quantity that characterizes the ability of a body to store heat. It is defined as the amount of heat required at the given conditions and state of the body (foremost temperature) to raise its temperature by one degree. The specific heat capacity (Cp) of a substance is defined as heat capacity per unit mass, which is the amount of energy required to raise the temperature of one kilogram of the substance by one Kelvin. Water has the highest heat capacity of all common substances. A7.4.1 Medium temperature range Specific heat capacity as a function of formate brine density is shown in Table 3 and Figure 4. The data are based on measurements carried out by Thermophysical Research Laboratory (TPRL) on brines covering the whole formate density range (Abdulagatov and Magomedov, 1998). These were single-salt sodium formate brines in the lower density range, blends of concentrated sodium and potassium formate brines in the middle density range, and blends of concentrated cesium and potassium formate in the higher density range. Exact compositions of the brines are shown in Table 1. The data, which were measured with a Perkin-Elmer DSC-2 instrument, is guaranteed to be valid within an experimental error of +/- 7% in the temperature range C / F. Within this temperature range, the temperature dependence has been found to be insignificant compared to the dependence on the brine composition. A7.4.2 Lower temperature range (<10 C / 50 F) Some specific heat capacity data is available in the literature for diluted single-salt potassium formate brines used in the coolant industry (Addcon, 2007; Addcon, 2014; Eastman, 2016). These data are shown in Figure 5 together with the data measured by TPRL. Both these data sets, which indicate a slight decrease in heat capacity with decreasing temperature, seem to show some more temperature dependence, also in the medium temperature range. This is not consistent with the measurements conducted by TPRL or with PAGE 4 SECTION A7

5 SECTION A: CHEMICAL AND PHYSICAL PROPERTIES Table 3 Heat capacity as a function of brine density for formate brines. The data is based on heat capacity data measured on diluted single-salt sodium formate in the lowest density range, blends of concentrated sodium and potassium formate brines in the medium density range, and blends of concentrated potassium and cesium formate brines in the highest density range. Temperature dependence is insignificant in the temperature range where the measurements are performed, i.e C / F. Density [g/cm 3 ] Cp [J/(g K)] Density [lb/gal] Cp [BTU/(lb F)] reference data on water. The reliability of these data sets is therefore uncertain. The data do, however, indicate that diluted potassium formate brine has a lower heat capacity than diluted sodium formate brine of the same density. A7.4.3 Higher temperature range (>70 C / 160 F) There is no specific heat capacity data on formates available in the higher temperature range. Reference data available for water up to 100 C / 212 F (Gembarovic and Taylor, 2003) is plotted in Figure 5 together with the heat capacity data from TPRL. From this, one could expect that at least for low-density formate brines the temperature dependence, also in the higher temperature range, is negligible compared with the dependence on the brine composition / density. References Abdulagatov, I.M. and Magomedov, U.B Thermal Conductivity of Aqueous ZnCl 2 Solutions at High Temperatures and High Pressures, Ind. Eng. Chem. Res., 37, Addcon HYCOOL 50 Product Specification. Addcon HYCOOL 20 Product Specification. CRC Press Handbook of Chemistry and Physics, 60th edition. Eastman Freezium -60 C Material Data Sheet. Gembarovic, J. and Taylor, R.E.: Thermophysical Properties of Twelve Water Solutions, report # 2965, Thermophysical Research Laboratory Inc., April JacobCHR: Water reference (from jjj.jacobchr.com accessed in September 2013). SECTION A7 PAGE 5

6 Thermal conductivity k [BTU/(hr ft F)] Thermal conductivity k [W/(m K)] FORMATE TECHNICAL MANUAL 0.70 Thermal conductivity vs. density 0.65 NaFo 0.60 NaKFo C 22 C 66 C 0.45 KCsFo Density [g/cm 3 ] 1.2 Thermal conductivity vs. density 1.1 NaFo NaKFo 72 F 50 F 151 F 0.8 KCsFo Density [lb/gal] Figure 1 Coefficient of thermal conductivity (metric and field units) as a function of formate density. The data are based on single-salt sodium formate in the lower density range, blends of concentrated sodium and potassium formate in the medium density range, and blends of concentrated cesium and potassium formate in the higher density range. PAGE 6 SECTION A7

7 SECTION A: CHEMICAL AND PHYSICAL PROPERTIES 0.70 Thermal conductivity temperature dependence (low temperatures, low-density brines) Water CRC Handbook Thermal conductivity k [W/(m K)] Temperature [ C] Water 1.00g/cm 3 NaFo 1.10 g/cm 3 NaFo 1.20 g/cm 3 NaFo 1.30 g/cm 3 Na/KFo 1.40 g/cm 3 K/NaFo 1.50 g/cm 3 KFo 1.19 g/cm 3 (HYCOOL 20) KFo 1.35 g/cm 3 (HYCOOL 50) KFo 1.34 g/cm 3 (Freezium) Thermal conductivity temperature dependence (low temperatures, low-density brines) 1.20 Thermal conductivity k [BTU/(hr ft F)] Temperature [ F] Water CRC Handbook Water 8.3 lb/gal NaFo 9.2 lb/gal NaFo 10.0 lb/gal NaFo 10.8 lb/gal Na/KFo 11.7 lb/gal K/NaFo 12.5 lb/gal KFo 10.0 lb/gal (HYCOOL 20) KFo 11.3 lb/gal (HYCOOL 50) KFo 11.1 lb/gal (Freezium) Figure 2 Comparison of thermal conductivity data for low-density formate brines ( g/cm 3 / lb/gal) over the low to medium temperature range. SECTION A7 PAGE 7

8 FORMATE TECHNICAL MANUAL M E T R IC Thermal conductivity temperature dependence (high temperatures) Thermal conductivity k [W/(m K)] Water CRC Handbook Water reference Water 1.00 g/cm 3 NaFo 1.10 g/cm 3 NaFo 1.20 g/cm 3 NaFo 1.30 g/cm 3 Na/KFo 1.40 g/cm 3 K/NaFo 1.50 g/cm 3 K/CsFo 1.60 g/cm 3 K/CsFo 1.70 g/cm 3 K/CsFo 1.80 g/cm 3 Cs/KFo 1.90 g/cm 3 Cs/KFo 2.00 g/cm 3 Cs/KFo 2.10 g/cm 3 Cs/KFo 2.20 g/cm 3 ZnCl 2 15 wt% ZnCl 2 25 wt% Temperature [ C] Thermal conductivity temperature dependence (high temperatures) Thermal conductivity k [BTU/(hr ft F)] Thermal 0.6 Conductivity, k [BTU/hr/ft/F] Temperature [ F] Water CRC Handbook Water reference Water 8.3 lb/gal NaFo 9.2 lb/gal NaFo 10.0 lb/gal NaFo 10.8 lb/gal Na/KFo 11.7 lb/gal K/NaFo 12.5 lb/gal K/CsFo 13.4 lb/gal K/CsFo 14.2 lb/gal K/CsFo 15.0 lb/gal Cs/KFo 15.9 lb/gal Cs/KFo 16.7 lb/gal Cs/KFo 17.5 lb/gal Cs/KFo 18.3 lb/gal ZnCl 2 15 wt% ZnCl 2 25 wt% Figure 3 Thermal conductivity for various water and brine systems as a function of temperature in the high temperature range. Data for water and zinc chloride are taken from the literature. PAGE 8 SECTION A7

9 SECTION A: CHEMICAL AND PHYSICAL PROPERTIES Cp vs. density C Specific heat capacity Cp [J/(g K)] NaFo NaKFo KCsFo Density [g/cm 3 ] 1.1 Cp vs. density F 1.0 Specific heat capacity Cp [BTU/(lb F)] NaFo NaKFo KCsFo Density [lb/gal] Figure 4 Heat capacity as a function of density for typical formate brines. The brines are diluted single-salt sodium formate in the lowest density range (red curve), blends of saturated sodium formate and saturated potassium formate in the middle density range (purple curve), and blends of saturated potassium and saturated cesium formate in the higher density range (black curve), and it is valid for these exact brines and blends only. The temperature dependence is insignificant within the temperature range where the measurements are performed, i.e C / F. SECTION A7 PAGE 9

10 FORMATE TECHNICAL MANUAL Specific heat capacity Cp [J/(g K)] Specific heat capacity vs. temperature Temperature [ C] Water CRC Handbook Water 1.00 g/cm 3 NaFo 1.10 g/cm 3 NaFo 1.20 g/cm 3 NaFo 1.30 g/cm 3 Na/KFo 1.40 g/cm 3 K/NaFo 1.50 g/cm 3 K/CsFo 1.60 g/cm 3 K/CsFo 1.70 g/cm 3 K/CsFo 1.80 g/cm 3 Cs/KFo 1.90 g/cm 3 Cs/KFo 2.00 g/cm 3 Cs/KFo 2.10 g/cm 3 Cs/KFo 2.20 g/cm 3 KFo1.19 g/cm 3 (HYCOOL 20) KFo1.35 g/cm 3 (HYCOOL 50) KFo1.34 g/cm 3 (Freezium) Specific heat capacity vs. temperature Specific heat capacity Cp [BTU/(lb F)] Temperature [ F] Water CRC Handbook Water8.3 lb/gal NaFo 9.2 lb/gal NaFo 10.0 lb/gal NaFo 10.8 lb/gal Na/KFo1 1.7 lb/gal K/NaFo12.5 lb/gal K/CsFo13.4 lb/gal K/CsFo14.2 lb/gal K/CsFo15.0 lb/gal Cs/KFo15.9 lb/gal Cs/KFo16.7 lb/gal Cs/KFo17.5 lb/gal Cs/KFo 18.3 lb/gal KFo lb/gal (HYCOOL 20) KFo lb/gal (HYCOOL 50) KFo lb/gal (Freezium) Figure 5 Comparison of specific heat capacity data from CRC Handbook (water reference), TPRL, and other heat capacity data available on formate brines as a function of temperature. PAGE 10 SECTION A7