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Estimating heat flow from an unsteady temperature log of submarine borehole BDP-98 (Lake Baikal)
Russian Geology and Geophysics 50 (2009) 131–135 www.elsevier.com/locate/rgg
Estimating heat flow from an unsteady temperature log of submarine borehole BDP-98 (Lake Baikal) A.D. Duchkov a,*, I.M. Kutasov b, L.S. Sokolova a a
Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch of the RAS, 3 prosp. Akad. Koptyuga, Novosibirsk, 630090, Russia b Pajarito Enterprises, 640 Alta Vista, Suite 124, Santa Fe, New Mexico 87505, USA Received 18 February 2008; received in revised form 23 May 2008; accepted 16 June 2008
Abstract We have applied the method of one temperature log suggested by Kutasov in 1987 to process an unsteady temperature log of the 674 m deep submarine borehole BDP-98-2 (Akademichesky Ridge, Lake Baikal) and found it suitable to reconstruct the primary steady thermal gradient not disturbed by drilling. The steady gradient we derived using a special formalism, with reference to drilling conditions and measured thermal properties of sediments, was 63 mK/m, more than two times the unsteady gradient at different depths. Heat flow calculated with this 2 gradient and a mean thermal conductivity of 1.1 W/(m⋅K) was 70 mW/m , which is consistent with earlier geothermal data from the same area. Thus, the one-log procedure is a useful tool to predict the original undisturbed thermal gradients and estimate approximate heat flows if a single unsteady temperature log is available. © 2009, IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. Keywords: Unsteady temperature log; one-log procedure; borehole BDP-98-2; Lake Baikal
Introduction The available heat flow (q) determinations in Lake Baikal are derived mainly from measurements of temperature (T), geothermal gradient (g), and thermal conductivity (λ) in the uppermost 1 to 5 m of sediments. Marine heat flow data are normally of best quality if measurements are at water depths below 300–400 m, but shallow determinations in seas are also reliable enough, as it was proved by temperature logging in submarine and onshore boreholes. However, shallow heat flow data from Baikal may be worse because of the lake’s complex bottom topography, active near-bottom water circulation, and hydrothermal venting. Deep drilling experiments as part of the Baikal Drilling project (Kuz’min et al., 2001) have offered a unique opportunity to measure the temperatures and thermal conductivities of lake sediments to far greater depths than before and thus to check the previous results. The first two BDP boreholes were drilled during the 1993 experiment in the lake central part (Buguldeika Saddle) to depths of about 100 m, where temperature was logged and
* Corresponding author. E-mail address: [email protected] (A.D. Duchkov)
thermal conductivity of sediments was measured to 90 m below the bottom (Duchkov and Kazantsev, 1996; Duchkov et al., 2001). The heat flow derived from those measurements, more than ten times deeper than before, almost coincided with the shallow estimates. Two following boreholes were drilled in 1996, to total subbottom depths of 100 and 300 m, near the top of the submerged Akademichesky Ridge (Fig. 1). One hole was logged with a streamer to a depth of 100 m, and the log data, together with thermal conductivity measurements, were used to determine heat flows (The BDP Group, 1998; Duchkov et al., 2001), which were likewise similar to the known values from shallowest sediments at the Akademichesky Ridge site. Further experiments of 1997–1999 (Fig. 1) yielded several holes more, of which one (BDP-98) penetrated deeper than 600 m (Kuz’min et al., 2001). Temperature logging in those boreholes was soon after the cessation of drilling and fluid circulation, but precise geothermal measurements suitable for heat flow determination were impossible for different reasons. The logs showed unsteady temperature patterns disturbed mostly by flushing. Unsteady logs are known to be unfit for processing, and the possibility to use them for predicting the steady-state geothermal parameters was a challenge (Carslaw
1068-7971/$ - see front matter D 2009, IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.rgg.2008.06.020
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knowledge of all these factors, plus the time elapsed after the cessation of drilling (shut-in time). If the circulating drilling fluid is assumed to have a constant temperature, the dimensionless temperature TsD at the borehole wall, at a certain depth and at any time after drilling, is (Kutasov, 1987, 1999) ∗
TsD = 1 −
Ei[−β(1 + tD /tsD)] Ei(−β)
.
(1)
Or, with real temperatures: TsD =
Fig. 1. Bathymetry of Lake Baikal and locations of BDP-96 and BDP-98 sites. Solid line is segment of CMP profile 92-15, after (BDP Group, 2000).
Ts − T Tc − T
.
(2)
1 In (1) and (2) Ei(x) is the exponential integral, β = ∗ , 4tD kts tsD = 2 , T is the undisturbed formation temperature before rω drilling, Tc is the fluid circulation temperature, Ts is the logged temperature at time ts after the cessation of drilling (or shut-in temperature, where ts is shut-in time), tc is the time of fluid circulation, rω is the hole radius, tD is the dimensionless circulation time, k is the formation thermal diffusivity, and tsD is the dimensionless shut-in time. ∗
and Jaeger, 1959; Cheremenskii, 1972; Kutasov, 1976, 1987, 1999; Putikov, 1970). The required temperature recovery (shut-in time) in boreholes drilled through impermeable sediments should be ten to twenty times as long as the duration of drilling, but such a long shut-in is rarely feasible in practice. Thus, it is important to learn how to infer undisturbed thermal gradients from unsteady temperature logs. We report one such method which we applied to process an unsteady log of the deepest (670 m) BDP-98 borehole and described very briefly in (BDP Group, 2000).
Processing unsteady logs The common earlier practice (Kutasov, 1976) was to use at least two logs recorded at different times elapsed after drilling to reconstruct the original formation temperatures and thermal gradients disturbed by the drilling process (method of two temperature logs). Later one of us (Kutasov, 1987, 1999) developed a procedure to estimate steady gradients from a single log (method of one temperature log). This is of special interest in our case because only one unsteady log is available from the BDP-98 site. The theory of the method is briefly as follows. Drilling may disturb the formation temperature patterns in different ways depending on drilling technology, hole radius, duration of fluid circulation (flushing), formation-fluid temperature difference, and formation thermal diffusivity. High-quality prediction of the primary steady thermal gradients requires
The value of tD is found from two equations below, ktc depending on tD = 2 : rω 1 ∗ n tD = tD 1 + , where F = [ln (1 + tD)] , n = 2/3, A = 1 + AF 7/8, at tD ≤ 10. ln tD − exp(−0.236√ tD ) , at tD > 10 (our case). lntD − 1 Equation (1) was derived assuming constant temperature of drilling fluid, but this temperature is rarely exactly constant in reality and, moreover, sometimes remains unknown. Therefore, is it usually assumed to be constant but unknown, and equation (2) thus includes two unknowns (T and Tc), which rules out T estimation. Kutasov (1987, 1999) showed that one can solve (2) only with respect to a steady gradient introduced through the steady temperature T. This makes the one-log method advantageous because the gradient is a differential parameter and, hence, recovers faster than the temperature. Furthermore, when estimating the gradient, one avoids errors associated with constraining steady formation temperatures. There are several straightforward transformations necessary to proceed to the sought steady gradient from (1) and (2). In a steady temperature field, the thermal gradient (G) between two points at depths h1 and h2 is ∗
tD = tD
G = (T2 – T1)/(h2 – h1),
(3)
where T1 and T2 are undisturbed formation temperatures at h1 and h2 (h2 > h1). We can rewrite (3) as T = T1 + G⋅(h − h1), h2 ≥ h > h1.
(4)
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Combining (1) and (4) gives, for the depth h1, TsD =
Ts − T Tc − T
=
Ts − T1 − G⋅(h − h1) Tc − T1 − G⋅(h − h1)
or Ts = G⋅h⋅(1 − TsD) + B,
(5)
where B = T1 − G⋅h1⋅(1 − TsD) + TsD⋅(Tc − T1). Ts in the left-hand side of (5) is the temperature corresponding to the unsteady log. The right-hand side includes three unknowns: the sought steady gradient G, the steady temperature T1 at h1, and the circulation temperature Tc; the dimensionless temperature TsD is found by (1). For specific drilling and formation parameter, TsD is a function of circulation and shut-in times, TsD = f(tD, tsD), and thus changes with depth, but it can be assumed constant within small depth intervals. When G is found at depths from h1 to h2, first (1) is applied to find TsD at the mean depth point hav = (h2 + h1)/2, for which, in turn, one has to know the circulation time tc, at the respective depth, tc ≈ tt − tav, where tt is the total drilling time, and tav is the time required to reach the depth hav. The time tav is commonly taken from the log book but, if the latter is unavailable, one may use the approximation equation hav tc = tt 1 − , H where H is the total hole depth. Then G is found within the h2–h1 range using linear equations (5), assuming constant G, TsD, and Tc. Theoretically, it is enough to obtain gradients for a single depth range, but processing a set of Ts and h values with a linear regression code improves the processing quality. The respective algorithm was implemented as a Fortran code.
Borehole BDP-98 During the 1998 experiment, three boreholes were drilled at the Akademichesky Ridge site (BDP Group, 2000). The deepest borehole penetrated 674 m of sediments under 333 m of water. Drilling continued from February 1 to March 23 (44 days), using a raiser fixed at a subbottom depth of 180 m. The hole diameter was 300 mm above 190 m and 213 mm below; the borehole was flushed with a 25–27 °C fluid of 1050–1060 kg/m3 circulating in a close system collar–face– collar. The BDP-98-2 section, cored to a depth of 600 m with a few gaps, consists of fine pelitic-silty biogenic and terrigenous mud, with a denser and more silty part of the section below 200 m.
Fig. 2. Unsteady log of BDP-98 recorded during tool lowering (left) and measured unsteady gradient (right). Gradients calculated from data sampled at every 1 m.
Temperature logging was performed by geophysicists from the Nedra Enterprise with standard well resistivity thermometers at a mean rate of 600 m/h. The logging followed almost immediately after drilling (shut-in time never exceeded 36 hours). Temperatures were measured along the entire section, in water and in sediments, as the tool went up and down. The log data are courtesy of L. Pevzner. See Fig. 2 for the unsteady log recorded during tool lowering and the respective gradient plot (Gms). The water-sediment interface is prominent in both the log and the Gms plot. The temperature in sediments increases rapidly from 4.3 to 7 °C and then it increases more slowly. The measured gradient is 20–30 mK/m on average over most of the section (500 m) but reaches as high as 100 mK/m below 500 m. The temperature at the bore face is 31–32 °C. The log has generally a concave geometry, mostly controlled by depth-dependent variations in the disturbing effects, especially fluid circulation. Much greater T and G in the lower section appear to be due to a greater speed of drilling which was already without coring, and the formation temperature near the bore face was thus less disturbed by the drilling process. Other causes, such as depth-dependent thermal conductivity decrease or proximity to hydrothermal vents, are unlikely: on the contrary, the measured thermal conductivity grows higher
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Fig. 3. Thermal conductivity-diffusivity plots for soft bottom sediments (Wright and Louden, 1989). Curves 1 and 4 were plotted according to k = [λ /(ρw⋅Cw)]× {[1 + (1 − W)⋅ρw /W⋅ρs]/[1 + (1 − W)⋅Cs /(W⋅Cw)]}, λ = (a⋅W + b)−1, where W is water content, a and b are empirical coefficients, ρw and Cw are water density and specific heat, respectively, and ρs and Cs are density and specific heat of dry sediment, respectively, which were assumed to be λ = (682W + 175)−1, ρw = 1030 kg/m3, Cw = 3930 J/(kg⋅K), ρs = 2500 kg/m3, and Cs = 770 J/(kg⋅K) (Bullard and Day, 1961) in curve 1 and λ = (709W + 91)−1 and ρs = 2500 kg/m3, with the same ρw, Cw, and Cs (Lachenbruch and Marshall, 1966) in curve 4. Curves 2 and 3 were plotted according to k = λ /[106 (5.79 − 3.67λ + 1.016λ2)] (Hyndman et al., 1979) and k = (3.66λ − 0.7)⋅10−7 (Von Herzen and Maxwell, 1959), respectively.
with depth (see below), and hydrothermal venting is unknown in the area. The equations in the one-log procedure include thermal diffusivity of sediments. It was never measured in the BDP-98 core but its approximate value can be inferred from thermal conductivity, which was measured many times (BDP Group, 2000; Dorofeeva and Shapova, 2003) using a needle-probe and a thermal conductivity comparator (by V.A. Golubev and R.P. Dorofeeva, respectively, both from the Institute of the Earth’s Crust, Irkutsk). Both independent measurements showed almost stable conductivities averaging about 1.0 W/(m⋅K) above 350 m and then increasing linearly to 1.2 W/(m⋅K) to hold at that level in the remainder of the section. The mean thermal conductivity over the whole section was 1.1 W/(m⋅K). We obtained preliminary estimates of thermal diffusivity from relationships between λ and k (Fig. 9 in Wright and Louden, 1989). According to these relationships based on measured λ, k, and water content (W) of bottom sediments and theoretical data (Fig. 3), with the above conductivity λ, thermal diffusivity of the BDP-98 core was estimated to range from 3⋅10−7 to 4.3⋅10−7 m2/s, with the mean 3.5⋅10−7 m2/s. Thus found diffusivity normally bears an error increasing with λ (Fig. 3), being 1% at λ = 0.7 W/(m⋅K), 8% at λ = 1.0 W/(m⋅K), and 20% at λ = 1.4 W/(m⋅K) (Wright and Louden, 1989). In our case of λ = 1.1 W/(m⋅K), the error was about 10%.
Fig. 4. Steady gradients for BDP-98-2, smoothed (dotted line) and not smoothed (solid line), reconstructed using one-log procedure for 30 m intervals of log in Fig. 2. Inset shows histograms of reconstructed gradients at depth from 40 to 500 m. N is number of values.
One-log reconstruction of steady gradients We applied the one-log procedure to calculate steady formation thermal gradients for 30-m intervals of the BDP-98 log, assuming a constant drilling speed. The results (Fig. 4) were analyzed without the upper (10–30 m) and lower (below 500 m) segments of the G plot where T and Gms showed a rapid irregular increase. As we wrote, the uppermost segment was disturbed by bottom effects and the lowermost one by drilling technology changes (no coring, faster drilling). The G plot was smoothed to make the analysis easier, which was appropriate and even necessary in our case. Smoothing eliminated the measurement errors caused by nonuniform logging rate (a rate change was evident, for instance, from a sudden temperature jump of 2 °C at a depth of about 590 m). The mean smoothed gradient (dotted line in Fig. 4) was 56 mK/m between 30 and 200 m and 63 mK/m between 200 and 500 m. The gradient was slightly lower in the upper layer, possibly, because the borehole was cemented to a depth of 189 m when the riser was mounted. That effect was hard to estimate exactly but it was expected to show up as a gradient decrease. We additionally plotted a histogram of
A.D. Duchkov et al. / Russian Geology and Geophysics 50 (2009) 131–135
gradients in the 30-m intervals (inset in Fig. 4) in order to improve the mean G estimates, and finally obtained a corrected gradient of G = 63 mK/m between 30 and 500 m, or two or three times the measured gradient (at least to 500 m). The corresponding formation temperature at the borehole face must be 42 °C, which is 10 °C above the log data. The heat flow at the BDP-98 site determined using the gradient G = 63 mK/m and the mean thermal conductivity of λ = 1.1 W/(m⋅K) was 70 mW/m2. It is pertinent to check our thermal gradient and heat flow estimates against the available data from the Akademichesky Ridge and the neighbor BDP-96 site. Shallow geothermal measurements near the Akademichesky Ridge gave generally high heat flows and gradients from 60 to 100 mW/m2 and 67–110 mK/m, respectively (Golubev, 1982). The gradient in upper 100 m of sediments derived from an unsteady temperature log of the deeper borehole at the BDP-96 site (BDP-96-1, 300 m) measured right after drilling (The BDP Group, 1998) was about 42 mK/m. The gradient for the other borehole (BDP-96-2) was found using a special processing technique (Duchkov et al., 2001) from 200 hours of data from a three-thermistor streamer (The BDP Group, 1998). It was as high as 86 mK/m, or twice the unsteady gradient in BDP-96-1. Heat flow determined from these gradients and λ = 0.9 W/(m⋅K) mean thermal conductivity of sediments at the site, as measured by V. Golubev (The BDP Group, 1998), was 77 mW/m2. Thus, with the one-log reconstructed steady thermal gradient for BDP-98, we arrived at a heat flow generally consistent with the earlier geothermal data from the Akademichesky Ridge.
Conclusions We have applied the one-log procedure suggested earlier by one of us (Kutasov, 1987, 1999) to predict the steady formation thermal gradient at the site of submarine borehole BDP-98 (Akademichesky Ridge, Lake Baikal). The measured (unsteady) gradient was 20–30 mK/m, and the steady gradient was reconstructed from an unsteady temperature log recorded during tool lowering, taking into account the parameters of the drilling and recovery processes (hole size, temperature of circulating fluid, circulation time, shut-in time, etc.) and the thermal properties of the drilled formation. Thus determined mean undisturbed gradient at depths between 30 and 470 m was 63 mK/m, i.e., drilling may cause a two- or three-fold decrease of thermal gradients. Heat flow estimated from this steady gradient and a mean thermal conductivity of 1.1 W/(m⋅K) was about 70 mW/m2, which is generally consistent with earlier geothermal data from the same area. Thus, the one-log method has proved to be workable in reconstructing undisturbed formation thermal gradients and subsequent heat flow determination to get an approximate but realistic idea of the geothermal setting in an area. If interpreted
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with the reported method, unsteady logs, which are commonly culled out, may be used together with logs recorded after complete temperature recovery. The drilling and logging data from BDP-98 are courtesy of M.I. Kuz’min and people from the Nedra Enterprise. The study was carried out as part of Interdisciplinary Integration Project 87 of the Siberian Branch of the Russian Academy of Sciences.
References Baikal Drilling Project Group, 2000. Late Cenozoic paleoclimate record in bottom sediments of Lake Baikal (600 m of deep drilling data). Geologiya i Geofizika (Russian Geology and Geophysics) 41 (1), 3–32 (1–29). Bullard, E.C., Day, A., 1961. The flow of heat through the floor of the Atlantic Ocean. Geophys. J. Roy. Astron. Soc. 4, 284. Carslaw, H.S., Jaeger, J.C., 1959. Conduction of Heat in Solids. Oxford University Press, Oxford—New York. Cheremenskii, G.A., 1972. Geothermics [in Russian]. Nedra, Leningrad. Dorofeeva, R.P., Shapova, M.V., 2003. Geothermal studies of underwater boreholes in Lake Baikal, in: Kashiwaya, K. (Ed.), Long Continental Records from Lake Baikal. Tokyo, Springer-Verlag, pp. 43–60. Duchkov, A.D., Kazantsev, S.A., 1996. Temperature measurements in first underwater boreholes in Lake Baikal. Geologiya i Geofizika (Russian Geology and Geophysics) 37 (6), 95–103 (94–101). Duchkov, A.D., Lee, T.-S, Morozov, S.G., 2001. Thermal properties of bottom sediments of Lake Baikal from modeling of thermal recovery in underwater boreholes. Geologiya i Geofizika (Russian Geology and Geophysics) 42 (1–2), 298–307 (288–296). Golubev, V.A., 1982. Geothermics of Lake Baikal [in Russian], Nauka, Novosibirsk. Hyndman, R.D., Davis, E.E., Wright, J.A., 1979. The measurement of marine geothermal heat flow by a multipenetration probe with digital acoustic telemetry and in situ thermal conductivity. Mar. Geophys. Res. 4, 181–205. Kutasov, I.M., 1976. Thermal Logging in Permafrost [in Russian]. Nedra, Moscow. Kutasov, I.M., 1987. Dimensionless temperature, cumulative heat flow and heat flow rate for a well with a constant bore-face temperature. Geothermics 16 (5/6), 467–472. Kutasov, I.M., 1999. Applied Geothermics for Petroleum Engineers. Elsevier, Amsterdam, Tokyo. Kuz’min, M.I., Karabanov, E.B., Kawai, T., Williams, D., Bychinskii, V.A., Kerber, E.V., Kravchinskii, V.A., Bezrukova, E.V., Prokopenko, A.A., Geletii, V.F., Kalmychkov, G.V., Goreglyad, A.V., Antipin, B.C., Khomutova, M.Yu., Soshina, N.M., Ivanov, E.V., Khursevich, G.K., Tkachenko, L.L., Solotchina, E.P., Ioshida, N., Gvozdkov, A.N., 2001. Deep drilling on Lake Baikal: Main results. Geologiya i Geofizika (Russian Geology and Geophysics), 42 (1–2), 8–34 (3–28). Lachenbruch, A.H., Marshall, B.V., 1966. Heat flow through the Arctic Ocean floor: the Canada Basin–Alpha Rise boundary III. Geophys. Res. 71 (4), 1223–1248. Putikov, O.F., 1970. Theory of Geothermal Logging [in Russian]. Author’s Abstract. Candidate Thesis. Leningrad Mining Institute, Leningrad. The Baikal Drilling Project Group, 1998. A continuous record of climate changes for the last five million years from the bottom sediments of Lake Baikal. Geologiya i Geofizika (Russian Geology and Geophysics) 39 (2), 139–156 (135–152). Von Herzen, R.P., Maxwell, A.E., 1959. The measurement of thermal conductivity of deep-sea sediments by a needle probe method. J. Geophys. Res. 64 (10), 1557–1563. Wright, J.A., Louden, K.E. (Eds.), 1989. Handbook of Seafloor Heat Flow. CRC Press, Inc., Boca Raton.
Editorial responsibility: M.I. Epov
Estimating heat flow from an unsteady temperature log of submarine borehole BDP-98 (Lake Baikal) A.D. Duchkov a,*, I.M. Kutasov b, L.S. Sokolova a a
Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch of the RAS, 3 prosp. Akad. Koptyuga, Novosibirsk, 630090, Russia b Pajarito Enterprises, 640 Alta Vista, Suite 124, Santa Fe, New Mexico 87505, USA Received 18 February 2008; received in revised form 23 May 2008; accepted 16 June 2008
Abstract We have applied the method of one temperature log suggested by Kutasov in 1987 to process an unsteady temperature log of the 674 m deep submarine borehole BDP-98-2 (Akademichesky Ridge, Lake Baikal) and found it suitable to reconstruct the primary steady thermal gradient not disturbed by drilling. The steady gradient we derived using a special formalism, with reference to drilling conditions and measured thermal properties of sediments, was 63 mK/m, more than two times the unsteady gradient at different depths. Heat flow calculated with this 2 gradient and a mean thermal conductivity of 1.1 W/(m⋅K) was 70 mW/m , which is consistent with earlier geothermal data from the same area. Thus, the one-log procedure is a useful tool to predict the original undisturbed thermal gradients and estimate approximate heat flows if a single unsteady temperature log is available. © 2009, IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. Keywords: Unsteady temperature log; one-log procedure; borehole BDP-98-2; Lake Baikal
Introduction The available heat flow (q) determinations in Lake Baikal are derived mainly from measurements of temperature (T), geothermal gradient (g), and thermal conductivity (λ) in the uppermost 1 to 5 m of sediments. Marine heat flow data are normally of best quality if measurements are at water depths below 300–400 m, but shallow determinations in seas are also reliable enough, as it was proved by temperature logging in submarine and onshore boreholes. However, shallow heat flow data from Baikal may be worse because of the lake’s complex bottom topography, active near-bottom water circulation, and hydrothermal venting. Deep drilling experiments as part of the Baikal Drilling project (Kuz’min et al., 2001) have offered a unique opportunity to measure the temperatures and thermal conductivities of lake sediments to far greater depths than before and thus to check the previous results. The first two BDP boreholes were drilled during the 1993 experiment in the lake central part (Buguldeika Saddle) to depths of about 100 m, where temperature was logged and
* Corresponding author. E-mail address: [email protected] (A.D. Duchkov)
thermal conductivity of sediments was measured to 90 m below the bottom (Duchkov and Kazantsev, 1996; Duchkov et al., 2001). The heat flow derived from those measurements, more than ten times deeper than before, almost coincided with the shallow estimates. Two following boreholes were drilled in 1996, to total subbottom depths of 100 and 300 m, near the top of the submerged Akademichesky Ridge (Fig. 1). One hole was logged with a streamer to a depth of 100 m, and the log data, together with thermal conductivity measurements, were used to determine heat flows (The BDP Group, 1998; Duchkov et al., 2001), which were likewise similar to the known values from shallowest sediments at the Akademichesky Ridge site. Further experiments of 1997–1999 (Fig. 1) yielded several holes more, of which one (BDP-98) penetrated deeper than 600 m (Kuz’min et al., 2001). Temperature logging in those boreholes was soon after the cessation of drilling and fluid circulation, but precise geothermal measurements suitable for heat flow determination were impossible for different reasons. The logs showed unsteady temperature patterns disturbed mostly by flushing. Unsteady logs are known to be unfit for processing, and the possibility to use them for predicting the steady-state geothermal parameters was a challenge (Carslaw
1068-7971/$ - see front matter D 2009, IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.rgg.2008.06.020
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knowledge of all these factors, plus the time elapsed after the cessation of drilling (shut-in time). If the circulating drilling fluid is assumed to have a constant temperature, the dimensionless temperature TsD at the borehole wall, at a certain depth and at any time after drilling, is (Kutasov, 1987, 1999) ∗
TsD = 1 −
Ei[−β(1 + tD /tsD)] Ei(−β)
.
(1)
Or, with real temperatures: TsD =
Fig. 1. Bathymetry of Lake Baikal and locations of BDP-96 and BDP-98 sites. Solid line is segment of CMP profile 92-15, after (BDP Group, 2000).
Ts − T Tc − T
.
(2)
1 In (1) and (2) Ei(x) is the exponential integral, β = ∗ , 4tD kts tsD = 2 , T is the undisturbed formation temperature before rω drilling, Tc is the fluid circulation temperature, Ts is the logged temperature at time ts after the cessation of drilling (or shut-in temperature, where ts is shut-in time), tc is the time of fluid circulation, rω is the hole radius, tD is the dimensionless circulation time, k is the formation thermal diffusivity, and tsD is the dimensionless shut-in time. ∗
and Jaeger, 1959; Cheremenskii, 1972; Kutasov, 1976, 1987, 1999; Putikov, 1970). The required temperature recovery (shut-in time) in boreholes drilled through impermeable sediments should be ten to twenty times as long as the duration of drilling, but such a long shut-in is rarely feasible in practice. Thus, it is important to learn how to infer undisturbed thermal gradients from unsteady temperature logs. We report one such method which we applied to process an unsteady log of the deepest (670 m) BDP-98 borehole and described very briefly in (BDP Group, 2000).
Processing unsteady logs The common earlier practice (Kutasov, 1976) was to use at least two logs recorded at different times elapsed after drilling to reconstruct the original formation temperatures and thermal gradients disturbed by the drilling process (method of two temperature logs). Later one of us (Kutasov, 1987, 1999) developed a procedure to estimate steady gradients from a single log (method of one temperature log). This is of special interest in our case because only one unsteady log is available from the BDP-98 site. The theory of the method is briefly as follows. Drilling may disturb the formation temperature patterns in different ways depending on drilling technology, hole radius, duration of fluid circulation (flushing), formation-fluid temperature difference, and formation thermal diffusivity. High-quality prediction of the primary steady thermal gradients requires
The value of tD is found from two equations below, ktc depending on tD = 2 : rω 1 ∗ n tD = tD 1 + , where F = [ln (1 + tD)] , n = 2/3, A = 1 + AF 7/8, at tD ≤ 10. ln tD − exp(−0.236√ tD ) , at tD > 10 (our case). lntD − 1 Equation (1) was derived assuming constant temperature of drilling fluid, but this temperature is rarely exactly constant in reality and, moreover, sometimes remains unknown. Therefore, is it usually assumed to be constant but unknown, and equation (2) thus includes two unknowns (T and Tc), which rules out T estimation. Kutasov (1987, 1999) showed that one can solve (2) only with respect to a steady gradient introduced through the steady temperature T. This makes the one-log method advantageous because the gradient is a differential parameter and, hence, recovers faster than the temperature. Furthermore, when estimating the gradient, one avoids errors associated with constraining steady formation temperatures. There are several straightforward transformations necessary to proceed to the sought steady gradient from (1) and (2). In a steady temperature field, the thermal gradient (G) between two points at depths h1 and h2 is ∗
tD = tD
G = (T2 – T1)/(h2 – h1),
(3)
where T1 and T2 are undisturbed formation temperatures at h1 and h2 (h2 > h1). We can rewrite (3) as T = T1 + G⋅(h − h1), h2 ≥ h > h1.
(4)
A.D. Duchkov et al. / Russian Geology and Geophysics 50 (2009) 131–135
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Combining (1) and (4) gives, for the depth h1, TsD =
Ts − T Tc − T
=
Ts − T1 − G⋅(h − h1) Tc − T1 − G⋅(h − h1)
or Ts = G⋅h⋅(1 − TsD) + B,
(5)
where B = T1 − G⋅h1⋅(1 − TsD) + TsD⋅(Tc − T1). Ts in the left-hand side of (5) is the temperature corresponding to the unsteady log. The right-hand side includes three unknowns: the sought steady gradient G, the steady temperature T1 at h1, and the circulation temperature Tc; the dimensionless temperature TsD is found by (1). For specific drilling and formation parameter, TsD is a function of circulation and shut-in times, TsD = f(tD, tsD), and thus changes with depth, but it can be assumed constant within small depth intervals. When G is found at depths from h1 to h2, first (1) is applied to find TsD at the mean depth point hav = (h2 + h1)/2, for which, in turn, one has to know the circulation time tc, at the respective depth, tc ≈ tt − tav, where tt is the total drilling time, and tav is the time required to reach the depth hav. The time tav is commonly taken from the log book but, if the latter is unavailable, one may use the approximation equation hav tc = tt 1 − , H where H is the total hole depth. Then G is found within the h2–h1 range using linear equations (5), assuming constant G, TsD, and Tc. Theoretically, it is enough to obtain gradients for a single depth range, but processing a set of Ts and h values with a linear regression code improves the processing quality. The respective algorithm was implemented as a Fortran code.
Borehole BDP-98 During the 1998 experiment, three boreholes were drilled at the Akademichesky Ridge site (BDP Group, 2000). The deepest borehole penetrated 674 m of sediments under 333 m of water. Drilling continued from February 1 to March 23 (44 days), using a raiser fixed at a subbottom depth of 180 m. The hole diameter was 300 mm above 190 m and 213 mm below; the borehole was flushed with a 25–27 °C fluid of 1050–1060 kg/m3 circulating in a close system collar–face– collar. The BDP-98-2 section, cored to a depth of 600 m with a few gaps, consists of fine pelitic-silty biogenic and terrigenous mud, with a denser and more silty part of the section below 200 m.
Fig. 2. Unsteady log of BDP-98 recorded during tool lowering (left) and measured unsteady gradient (right). Gradients calculated from data sampled at every 1 m.
Temperature logging was performed by geophysicists from the Nedra Enterprise with standard well resistivity thermometers at a mean rate of 600 m/h. The logging followed almost immediately after drilling (shut-in time never exceeded 36 hours). Temperatures were measured along the entire section, in water and in sediments, as the tool went up and down. The log data are courtesy of L. Pevzner. See Fig. 2 for the unsteady log recorded during tool lowering and the respective gradient plot (Gms). The water-sediment interface is prominent in both the log and the Gms plot. The temperature in sediments increases rapidly from 4.3 to 7 °C and then it increases more slowly. The measured gradient is 20–30 mK/m on average over most of the section (500 m) but reaches as high as 100 mK/m below 500 m. The temperature at the bore face is 31–32 °C. The log has generally a concave geometry, mostly controlled by depth-dependent variations in the disturbing effects, especially fluid circulation. Much greater T and G in the lower section appear to be due to a greater speed of drilling which was already without coring, and the formation temperature near the bore face was thus less disturbed by the drilling process. Other causes, such as depth-dependent thermal conductivity decrease or proximity to hydrothermal vents, are unlikely: on the contrary, the measured thermal conductivity grows higher
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Fig. 3. Thermal conductivity-diffusivity plots for soft bottom sediments (Wright and Louden, 1989). Curves 1 and 4 were plotted according to k = [λ /(ρw⋅Cw)]× {[1 + (1 − W)⋅ρw /W⋅ρs]/[1 + (1 − W)⋅Cs /(W⋅Cw)]}, λ = (a⋅W + b)−1, where W is water content, a and b are empirical coefficients, ρw and Cw are water density and specific heat, respectively, and ρs and Cs are density and specific heat of dry sediment, respectively, which were assumed to be λ = (682W + 175)−1, ρw = 1030 kg/m3, Cw = 3930 J/(kg⋅K), ρs = 2500 kg/m3, and Cs = 770 J/(kg⋅K) (Bullard and Day, 1961) in curve 1 and λ = (709W + 91)−1 and ρs = 2500 kg/m3, with the same ρw, Cw, and Cs (Lachenbruch and Marshall, 1966) in curve 4. Curves 2 and 3 were plotted according to k = λ /[106 (5.79 − 3.67λ + 1.016λ2)] (Hyndman et al., 1979) and k = (3.66λ − 0.7)⋅10−7 (Von Herzen and Maxwell, 1959), respectively.
with depth (see below), and hydrothermal venting is unknown in the area. The equations in the one-log procedure include thermal diffusivity of sediments. It was never measured in the BDP-98 core but its approximate value can be inferred from thermal conductivity, which was measured many times (BDP Group, 2000; Dorofeeva and Shapova, 2003) using a needle-probe and a thermal conductivity comparator (by V.A. Golubev and R.P. Dorofeeva, respectively, both from the Institute of the Earth’s Crust, Irkutsk). Both independent measurements showed almost stable conductivities averaging about 1.0 W/(m⋅K) above 350 m and then increasing linearly to 1.2 W/(m⋅K) to hold at that level in the remainder of the section. The mean thermal conductivity over the whole section was 1.1 W/(m⋅K). We obtained preliminary estimates of thermal diffusivity from relationships between λ and k (Fig. 9 in Wright and Louden, 1989). According to these relationships based on measured λ, k, and water content (W) of bottom sediments and theoretical data (Fig. 3), with the above conductivity λ, thermal diffusivity of the BDP-98 core was estimated to range from 3⋅10−7 to 4.3⋅10−7 m2/s, with the mean 3.5⋅10−7 m2/s. Thus found diffusivity normally bears an error increasing with λ (Fig. 3), being 1% at λ = 0.7 W/(m⋅K), 8% at λ = 1.0 W/(m⋅K), and 20% at λ = 1.4 W/(m⋅K) (Wright and Louden, 1989). In our case of λ = 1.1 W/(m⋅K), the error was about 10%.
Fig. 4. Steady gradients for BDP-98-2, smoothed (dotted line) and not smoothed (solid line), reconstructed using one-log procedure for 30 m intervals of log in Fig. 2. Inset shows histograms of reconstructed gradients at depth from 40 to 500 m. N is number of values.
One-log reconstruction of steady gradients We applied the one-log procedure to calculate steady formation thermal gradients for 30-m intervals of the BDP-98 log, assuming a constant drilling speed. The results (Fig. 4) were analyzed without the upper (10–30 m) and lower (below 500 m) segments of the G plot where T and Gms showed a rapid irregular increase. As we wrote, the uppermost segment was disturbed by bottom effects and the lowermost one by drilling technology changes (no coring, faster drilling). The G plot was smoothed to make the analysis easier, which was appropriate and even necessary in our case. Smoothing eliminated the measurement errors caused by nonuniform logging rate (a rate change was evident, for instance, from a sudden temperature jump of 2 °C at a depth of about 590 m). The mean smoothed gradient (dotted line in Fig. 4) was 56 mK/m between 30 and 200 m and 63 mK/m between 200 and 500 m. The gradient was slightly lower in the upper layer, possibly, because the borehole was cemented to a depth of 189 m when the riser was mounted. That effect was hard to estimate exactly but it was expected to show up as a gradient decrease. We additionally plotted a histogram of
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gradients in the 30-m intervals (inset in Fig. 4) in order to improve the mean G estimates, and finally obtained a corrected gradient of G = 63 mK/m between 30 and 500 m, or two or three times the measured gradient (at least to 500 m). The corresponding formation temperature at the borehole face must be 42 °C, which is 10 °C above the log data. The heat flow at the BDP-98 site determined using the gradient G = 63 mK/m and the mean thermal conductivity of λ = 1.1 W/(m⋅K) was 70 mW/m2. It is pertinent to check our thermal gradient and heat flow estimates against the available data from the Akademichesky Ridge and the neighbor BDP-96 site. Shallow geothermal measurements near the Akademichesky Ridge gave generally high heat flows and gradients from 60 to 100 mW/m2 and 67–110 mK/m, respectively (Golubev, 1982). The gradient in upper 100 m of sediments derived from an unsteady temperature log of the deeper borehole at the BDP-96 site (BDP-96-1, 300 m) measured right after drilling (The BDP Group, 1998) was about 42 mK/m. The gradient for the other borehole (BDP-96-2) was found using a special processing technique (Duchkov et al., 2001) from 200 hours of data from a three-thermistor streamer (The BDP Group, 1998). It was as high as 86 mK/m, or twice the unsteady gradient in BDP-96-1. Heat flow determined from these gradients and λ = 0.9 W/(m⋅K) mean thermal conductivity of sediments at the site, as measured by V. Golubev (The BDP Group, 1998), was 77 mW/m2. Thus, with the one-log reconstructed steady thermal gradient for BDP-98, we arrived at a heat flow generally consistent with the earlier geothermal data from the Akademichesky Ridge.
Conclusions We have applied the one-log procedure suggested earlier by one of us (Kutasov, 1987, 1999) to predict the steady formation thermal gradient at the site of submarine borehole BDP-98 (Akademichesky Ridge, Lake Baikal). The measured (unsteady) gradient was 20–30 mK/m, and the steady gradient was reconstructed from an unsteady temperature log recorded during tool lowering, taking into account the parameters of the drilling and recovery processes (hole size, temperature of circulating fluid, circulation time, shut-in time, etc.) and the thermal properties of the drilled formation. Thus determined mean undisturbed gradient at depths between 30 and 470 m was 63 mK/m, i.e., drilling may cause a two- or three-fold decrease of thermal gradients. Heat flow estimated from this steady gradient and a mean thermal conductivity of 1.1 W/(m⋅K) was about 70 mW/m2, which is generally consistent with earlier geothermal data from the same area. Thus, the one-log method has proved to be workable in reconstructing undisturbed formation thermal gradients and subsequent heat flow determination to get an approximate but realistic idea of the geothermal setting in an area. If interpreted
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with the reported method, unsteady logs, which are commonly culled out, may be used together with logs recorded after complete temperature recovery. The drilling and logging data from BDP-98 are courtesy of M.I. Kuz’min and people from the Nedra Enterprise. The study was carried out as part of Interdisciplinary Integration Project 87 of the Siberian Branch of the Russian Academy of Sciences.
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Editorial responsibility: M.I. Epov