Wellbore and Formation Temperatures During Drilling , Cementing of Casing and Shut-in

The knowledge of downhole and surrounding the wellbore formations temperature is an essential factor during drilling operations, shut p-in and cementing of casing periods. The downhole temperatures while drilling affects the viscosity of the drilling mud and, subsequently, the frictional pressure losses; the performance of drilling bits in hot wells; the density of drilling fluids a.o. In deep and hot wells, the densities of water/oil muds and brines can be significantly different from those measured at surface conditions. For this reason determining the density of drilling mud under downhole conditions is needed for calculating the actual hydrostatic pressure in a well. It is very important to estimate the effect of pressure and temperature on the density of the formation fluid. This will permit a more accurate prediction of differential pressure at the bottom-hole and will help to reduce the fluid losses resulting from miscalculated pressure differentials. In areas with high geothermal gradients, the thermal expansion of drilling muds can lead to unintentional underbalance, and a kick may occur. The effect of the borehole temperature recovery process (disturbed by drilling operations) affects the technology of the casing cementing operations. The design of cement slurries becomes more critical when a casing liner is used because the performance requirements should be simultaneously satisfied at the top and at the bottom of the liner. For these reasons it is logical to assume that the bottomhole shut-in temperature should be considered as parameter in the cement slurry design. Assessment of the temperature development during hydration is necessary to determine how fast the cement will reach an acceptable compressive strength before the casing can be released. Temperature surveys following the cementing operation are used for locating the top of the cement column behind casing. Field experience shows that in some cases the temperature anomalies caused by the heat of cement hydration can be very substantial. Thus, it is very important to predict the temperature increase during the cement setting. This will enable to determine the optimal time lapse between cementing and temperature survey. During the shut-in period in the wellbore are conducted transient downhole and bottomhole temperature surveys and geophysical logging. In interpretation of geophysical data is used the temperature dependence of mechanical and electrical properties of formations. In the paper we present methods of determination of the drilling mud circulation temperatures, borehole temperatures during cementing of casing and temperature in surrounding wellbore formations during drilling and shut-in periods. We also present several techniques of calculation of the static formation temperatures. 1 DRILLING PERIOD The wellbore temperature during drilling is a complex function of wellbore geometry, wellbore depth, penetration rate, flow rate, duration of the shut-in intervals, pump and rotary inputs, fluid and formation properties (Eppelbaum et al., 2014). Two approaches are used in the studies of heat interactions of the circulating fluid with formation. In the first case heat interactions of circulating fluid and formation are treated under the condition of constant-bore face temperature or heat flux (e.g. Edwardson et al., 1962; Ramey, 1962; Lachenbruch and Brewer, 1959; Shen and Beck, 1986; Kutasov, 1999). In the second approach the thermal interaction of the circulating fluid with formation is approximated by the Newton relationship on the bore-face (Raymond, 1969; Holmes and Swift, 1970; Keller et al., 1973; Sump and Williams, 1973; Wooley, 1980; Thompson and Burgess, 1985; Hasan and Kabir, 1994; Fomin et al., 2003; Espinosa-Paredes et al., 2009, a.o.). However, the discontinuity of the mud circulation process during drilling poses a serious problem in using the Newton relationship for determining the heat flow from the mud in the drill pipe to the wall of the drill pipe as well as the heat flow through the formation-annulus interface (qf). According to the Newton relationship ) ( fa m fa f T T q   , (1) where αfa is the film heat transfer coefficient from mud in the annulus to the formation, Tm is the average mud temperature (in annulus section), and Tfa is the temperature at the formation-annulus interface. For a developed turbulent flow the Dittus-Boelter formula is usually used to estimate the value of the film heat transfer coefficient and for applications in which the temperature influence on fluid properties is significant, Sieder-Tate correlation is recommended (Bejan, 1993). On theoretical grounds the Newton equation is applicable only to steady-state conditions. This means that in our case both temperatures (Tfa, Tm) cannot be time dependent functions. In practice, however, the Newton relationship is successfully used in many areas when the temperature of the fluids and the temperatures at the fluid-solid wall interfaces are slowly changing with time. Therefore, it is necessary to find out under which conditions Eq. (1) can be used to predict the wellbore temperatures during drilling. Some results of field investigations in the USA and Russia have shown that using conventional values of the film heat transfer coefficients in predicting wellbore temperatures during drilling are very questionable (Deykin et al., 1973; Sump and Williams, 1973). Predictions using Raymond’s (1969) method for 7 wells, for example, differed from the measured values by 12 percent on the average (Figure 1) and in one case missed the measured temperature by 65F (36C) (Sump and Williams, 1973). Kutasov and Eppelbaum 2 Figure 1: Comparison of measured and predicted mud temperatures from Well 1 (Sump and Williams, 1973) As correctly mentioned by Fomin et al. (2003) the first approach can be used in the case of highly intensive heat transfer between the circulating fluid and surrounding rocks, which takes place for fully developed turbulent flow in the well. However, in all our studies we used the term effective temperature (at a given depth) of the drilling fluid (Kutasov, 1999; Kutasov and Eppelbaum, 2005). This unknown parameter is introduced only to evaluate the amount of heat obtained (or lost) during the entire drilling period. In their classical work Lachenbruch and Brewer (1959) have shown that the wellbore shut-in temperature mainly depends on the amount of thermal energy transferred to (or from) formations during drilling. 2 Radial Temperature Distribution The results of field and analytical investigations have shown that in many cases the temperature of the circulating fluid (mud) at a given depth Tm(z) can be assumed constant during drilling or production (Lachenbruch and Brewer, 1959; Ramey, 1962; Edwardson et al., 1962; Jaeger, 1961; Kutasov et al., 1966; Raymond, 1969). However for super deep wells (5000-7000 m) the temperature of the circulating fluid is a function of the vertical depth (z) and time (t). Thus the estimation of heat losses from the wellbore is an important factor which shows to what degree the drilling process disturbs the temperature field of formations surrounding the wellbore. It is known that, if the temperature distribution T(r, z, t) or the heat flow rate q(r = rw, z, t) (rw is the well radius) are known for a case of a well with a constant bore-face temperature, then the functions T(r, z ,t) and q(r = rw, z, t) for a case of time dependent bore-face temperature can be determined through the use of the Duhamel’s integral. To determine the temperature distribution T(r, t) in formations near a wellbore with a constant bore-face temperature it is necessary to obtain a solution of the diffusivity equation for the following boundary and initial conditions: