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GEOPHYSICS, VOL. 73, NO. 6 �NOVEMBER-DECEMBER 2008�; P. E187–E196, 8 FIGS., 4 TABLES.10.1190/1.2976629

epth-time correction of petroleum bottom-holeemperatures in the Po Plain, Italy

. Pasquale1, P. Chiozzi1, G. Gola1, and M. Verdoya1

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ABSTRACT

We have analyzed a wide set of time-temperature datafrom petroleum wells in two areas of the Po Plain, Italy, andpropose empirical temperature corrections for mud circula-tion. Formation thermal parameters and the temperature de-pendence of thermal conductivity are taken into account.Analyses show that formation equilibrium temperaturescomputed with the Horner method compare well with thoseobtained by the Cooper and Jones method, which gives, onaverage, temperatures lower by only 2 °C for shut-in timesless than 10 hours. The corrected temperatures comparedwith temperatures measured during drillstem tests show thatthe proposed corrections are relatively accurate. The two datasets give coherent results, and the inferred average geother-mal gradient is 21.5 mK/m in the Apenninic buried arc areaand 25.2 mK/m in the South Piedmont Basin–Pedealpinehomocline area. The Horner slope data as a function of depthare then fitted with a second-order polynomial, and depth-time-correction equations are calibrated for the two areas. Fi-nally, we propose an empirical function for the estimate of themud-circulation time, which is often unavailable.

INTRODUCTION

A temperature measured at the hole bottom of oil and gas wellsuring geophysical logging reflects thermal conditions of the mud,ot those of the undisturbed rock. Apart from the immediate surfacetrata, the mud is cooler than the formations being drilled, so it tendso cool the rocks near the bottom of the hole and warm those near theop �Wyllie, 1963; Beardsmore and Cull, 2001�. The difference be-ween the mud and the rock-equilibrium temperature depends on

any factors, e.g., the depth of the formation relative to the total

Manuscript received by the Editor 15 February 2008; revised manuscript r1Università di Genova, Dipartimento per lo Studio del Territorio e della s

hiozzi�rp@tiscali.it; gianluca.gola@dipteris.unige.it; verdoya@dipteris.un2008 Society of Exploration Geophysicists.All rights reserved.

E187

epth of the hole, the time taken to drill the hole, the natural thermalradient, the porosity of the formation, the well radius, thermal con-uctivities and volumetric heat capacities of the mud and formation,nd the time that elapses between the end of mud circulation and theeginning of logging.

Many methods and algorithms have been proposed to obtain theormation equilibrium temperature from bottom-hole temperatureBHT� values, measured soon after circulation has stopped �duringhermal relaxation�. Some concentrate on the bottom of the boreholehere the temperature value is measured; others simulate the evolu-

ion of the temperature of the complete mud column �see Beck andalling, 1988; Cao et al., 1988; Hermanrud and Shen, 1989�. Most

echniques treat temperature as a transient function, i.e., they involverogressive measurements of temperature with time after circulationas stopped. The most recent trend involves the application of math-matical inversion techniques �generally based on finite-elementodels�, which work backward from the observed data to infer val-

es of the input parameters �Deming, 1989; McPherson and Chap-an, 1991�.In this paper, we review the simple method of Horner �1951�,

hich requires two or more measurements of BHT carried out at theame depth but at different shut-in times, and the more sophisticatedechnique of Cooper and Jones �1959�, in which several physical pa-ameters of the mud and formation must be known. The two methodsre applied to data from a number of deep petroleum wells located inhe Po Plain of northern Italy. The objective is to elaborate a workingormula usable for computing the undisturbed formation tempera-ure in this oil field.

Figure 1 shows an outline of the Po Plain, a complex foredeepith thrusts active in its substratum. Two areas in particular haveeen widely explored and thus present abundant temperature data:he South Piedmont Basin–Pedealpine homocline �PPH� and theAp-nninic buried arc �ABA�. In these areas, mainly terrigenous sedi-ents of great thickness, which denote accentuated subsidence and

mportant detrital contribution, have been deposited on a thick car-onatic layer during two main sedimentary cycles in Tertiary and

8 May 2008; published online 14 November 2008.rse, Settore di Geofisica, Genova, Italy. E-mail: pasquale@dipteris.unige.it;

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E188 Pasquale et al.

uaternary times. The first cycle occurred in the Oligo-Miocene andnded with marls and Messinian evaporites. The second cycle start-d with Messinian lagoon sediments and finished with marine de-osits in the Pleistocene. Such a lithostratigraphic evolution haseen produced by a chain-foredeep system migrating northeastwardrom the end of the Miocene until early Pleistocene times througheveral tectonic episodes that caused shortening and overthrustingPieri and Groppi, 1981; Pasquale and Verdoya, 1990; Pasquale etl., 1993�.

The location of the petroleum wells used in our thermal analysis islso shown in Figure 1. The available data consist of �1� circulationimes before shut-in, �2� multiples of couples of BHT-te �elapsedime since the end of the mud circulation�, �3� density and specificeat of the drilling mud and borehole radius at a fixed depth, and �4�emperatures from drillstem tests �DSTs�.

CORRECTION METHODS

Hermanrud et al. �1990� have conducted a study on the inherentccuracy of 22 different correction methods. They conclude that theethod of Horner �1951� has an inherent bias that reduces its accura-

y, but the method of Cooper and Jones �1959� is more accurate.The most commonly used method for computing equilibrium

emperature after drilling is the Horner method. It was originally de-ised to correct pressure buildup data from drill-stem tests, but it wasdapted for temperature correction by Lachenbruch and Brewer1959�. The thermal effect of drilling is approximated by a constantinear heat source, modeled through the following equation:

�rcr�T

� t� kr

� 2T

� 2r�

kr

r

�T

� r, �1�

here T, t, and r are borehole temperature, time, and radial distance,espectively. The parameters �r, cr, and kr are the density, specificeat, and thermal conductivity of the formation. The solution ofquation 1 is

BHT�t� � TH �H

4�krln�1 �

tc

te� , �2�

igure 1. Physiographic boundaries of the Po Plain and locations ofhe South Piedmont Basin–Pedealpine homocline �PPH� and the AABA� areas. Wells providing BHTs and DST temperatures are indpen circles, respectively.

here TH is the equilibrium temperature, H is the heat supplied pernit length and unit time, tc is the time before circulation ceased, and

e is the shut-in time, i.e., the time elapsed between the end of mudirculation and the BHT measurement. Equation 2 represents atraight line when BHTs are plotted against ln�1 � tc/te�, whose ex-rapolation to te→� should yield TH. The slope of the line is a func-ion of kr and H.

The Cooper and Jones method models the physical conditionithin the drill hole. It assumes a long hole of small diameter haseen drilled quickly and filled with a fluid cooler than the formation.he temperature of the mud approaches that of the formation as heatows radially inward from the walls of the borehole. These process-s are modeled with the following equation:

BHT�t� � Tf � �TCJ � Tf��1 � F��,� �� , �3�

here TCJ is the equilibrium temperature and Tf is the temperature ofhe drilling mud. The function F��,� � can be expressed as �Bullard,947�

F��,� � �4�

�2�0

�

exp��� u2�u�u

du , �4�

ith

�u � �uJ0�u� � �J1�u��2 � �uY0�u� � �Y1�u��2. �5�

ere, Jn and Yn are Bessel functions of order n of the first and secondind, respectively. The parameter � is twice the ratio of the heat ca-acity of the formation �r cr �density multiplied by specific heat� tohe heat capacity of the mud � f cf:

� � 2�r cr

� f cf. �6�

he value � is given by

� �krte

�r crrb2 , �7�

where rb is radius of the borehole. As in the Hor-ner method, equilibrium temperatures are com-puted plotting BHT�t� versus �1 � F��,� ��. Theresult is a straight line with slope �TCJ-Tf� and in-tercept Tf.

DATA PROCESSING

Data sources

Several hundred wells were drilled in the PoPlain as a result of extensive petroleum explora-tion. BHTs suitable for our analysis are located inthe data file of the Italian Economic DevelopmentMinistry. For the application of the correctionmethods, from a set of about 40 wells having two

gas wells atic buried arcby filled and

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Correction of bottom-hole temperatures E189

r more temperature measurements at a single depth, we selected 18ells with BHTs recorded at te larger than 3.5 hours �Figure 1�; the

ime span between measurements varied from 1 to 21 hours. On thehole, 71 couples of BHT-te data were available. The mud-circula-

ion time tc was lower or equal to 4.5 hours, with the exception ofhree couples of data �Corte Vittoria well, tc � 8 hours�. The data tohich the Horner method can be applied consist of 19 sets of two,

even sets of three, and three sets of four BHTs. Table 1 reports thealues of BHT, tc, and te for the 29 sets of data.

Besides the foregoing data, the Cooper and Jones method requireshysical parameters of the mud and rock at the temperature-mea-urement depth and the radius of the well. Table 2 shows the valuesf density and specific heat of the circulating mud and formation andhe hole radius rh. The mud density and rh are included in well-com-letion reports, from which they can be extracted, as well as litholo-y information. The mud specific heat obviously varies, dependingn mud type and operating conditions; however, as a result of theack of information, it is difficult to have proper estimates, so mudpecific heat was calculated from the weighted mean of specificeats of water and saturated, compacted bentonite clay. For clay vol-metric heat capacity and specific heat, we took constant values of.2 106 J/�m3K� and 1590 J/�kgK�, respectively, as suggested byadsen �1998�.

hermal-conductivity estimation

The bulk thermal conductivity ks under in situ conditions was esti-ated using the geometric mean function:

ks � km�1���kw

� , �8�

here kw and km are the thermal conductivity of the water and rockatrix, respectively, and � is the porosity that decays exponentiallyith depth of burial z according to

� � �o exp�� �z� , �9�

ith �0 the porosity at the surface �z � 0� and � the compaction fac-or.

Pasquale et al. �2008a, 2008b� attempt to remedy the deficiency ofhermal-conductivity data of sedimentary rocks in the Po Plain withseries of laboratory measurements on several core samples, recov-red from petroleum-exploration wells and representative of theain sedimentary rocks. They develop a model for calculating km asfunction of mineral composition based on the fabric theory and ex-erimental thermal-conductivity data. The conductivity of clay min-rals present in most Po Plain formations is poorly defined, so theypply an inverse approach, in which mineral conductivities are cal-ulated one by one, on the condition that the sample bulk thermalonductivity, the porosity, and the amount of each mineral phase arenown. Table 3 lists the matrix thermal conductivity and volumetric

eat capacity at room conditions obtained for the major sedimentaryocks, along with estimates of �0 and �, taken from the literatureMagarà, 1986; Deming and Chapman, 1988a; Wang et al., 2001�.

To take into account the temperature dependence of thermal con-uctivity, we assume that km is proportional to the reciprocal of thebsolute temperature �Deming and Chapman, 1988b�:

km�T� � kmr� 293

T � 273� , �10�

here kmr is the matrix thermal conductivity at room conditions and�in °C� is the temperature, estimated assuming a thermal gradient

f 25 mK/m. For the kw�T� function, a least-squares fit to the data byreith �1973� yields

kw�T� � 0.56 � 1.7710�3T � 6.1810�6T2. �11�

he volumetric heat capacity of the bulk rock was calculated as theeighted average of the values of the matrix and the pore-fluid fill-

ng. It does not depend significantly on the temperature because thepecific heat varies little in the temperature range of 23°–153°C ob-erved in the wells.

Table 2 shows the values of formation thermal conductivity kr cal-ulated at BHT depth. The lithologic data, deduced either from drilluttings or geophysical logs, were extracted from the same file as theemperature data. The values of kr result from the geometric mean ofonductivities of the main lithotypes of the formation. In the Morettaell, a bulk thermal conductivity of 2.6 W/�mK� and volumetriceat capacity of 2500 kJ/�m3K� was assumed for gneiss.

RESULTS AND DISCUSSION

The undisturbed formation temperatures obtained with the twoorrection methods are shown in Table 1; BHT�t� versus �1 � F�,� �� for the whole data set is plotted in Figure 2. The Horner meth-d gives lower equilibrium temperatures, on average, by 1.03°C,nd the maximum difference is 6.7°C. The difference between theemperature predicted with Horner and those calculated with Coopernd Jones as a function of � and te is shown in Figure 3. For � 2,he scatter of temperature data becomes negligible. This agrees withrevious work �e.g., Shen and Beck, 1986�, suggesting that onehould avoid the Horner method when the radius is too large or,quivalently, te is too small. By processing BHT data from an indus-rial well in the North Sea with an inverse modeling that includes thenite dimension of the borehole and the thermal properties of therilling mud and the formation, Nielsen et al. �1990� argues that theorner method seems to underestimate formation temperatures, on

verage, by 5%, and for short shut-in times, up to about 10%. Figureb shows that for te 10 hours, TH must be corrected on average bybout 2°C to have equilibrium temperatures comparable to those ob-ained with the Cooper and Jones method.

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E190 Pasquale et al.

able 1. Undisturbed formation temperatures predicted with the Horner (1951) TH and Cooper and Jones (1959) TCJ methodsrom BHT data (see Figure 1). Values of time elapsed between cessation of mud circulation and measurement of temperature te,irculation time before shut-in tc, and Horner slope Hs, also are shown.

ell Latitude N Longitude EAlt.�m�

Depth�m�

BHT�°C�

te

�hr�tc

�hr�TH

�°C�Hs

�°C�TCJ

�°C�

ascina Riviero 45°39.63� 09°54.37� 248 2383 61.0 14.5 2.0 66.1 �39.4 66.3

2383 63.0 24.5 2.0

3756 97.0 12.3 2.0 98.7 �11.5 98.7

3756 97.5 18.6 2.0

3756 98.0 27.5 2.0

3756 98.0 33.0 2.0

ascina S. Pietro 45°26.50� 09°32.67� 95 1750 50.0 8.2 1.5 55.4 �31.9 59.9

1750 54.5 15.5 0.5

1750 54.5 20.0 0.5

astano 45°32.42� 08°45.81� 175 5289 149.0 20.5 4.5 152.7 �18.5 153.2

5289 150.0 29.0 4.5

ranciacorta 45°36.11� 09°59.53� 244 1962 57.0 11.5 2.0 66.5 �55.3 67.6

1962 59.0 12.5 2.0

1962 61.0 18.0 2.0

1962 62.0 25.0 2.0

3328 86.0 7.5 2.5 93.2 �26.1 93.5

3328 88.0 13.0 2.5

3328 90.0 22.0 2.5

3328 92.0 36.5 2.5

alossa 45°30.37� 09°34.39� 122 1149 38.0 3.8 1.0 43.0 �21.7 44.5

1149 40.0 6.7 1.0

onte Acuto 45°04.50� 09°24.93� 71 1324 52.0 13.0 4.5 54.9 �9.7 55.6

1324 53.0 21.0 4.5

2677 79.0 13.0 4.0 82.0 �11.1 82.4

2677 80.0 20.5 4.0

oretta 44°45.13� 07°33.17� 260 2016 52.0 7.5 3.0 54.7 �8.4 54.8

2016 52.7 12.5 3.0

2016 53.7 20.0 3.0

3096 77.0 7.0 2.5 93.9 �55.2 97.1

3096 83.0 11.5 2.5

ovi Ligure 44°45.83� 08°48.92� 188 1700 43.0 3.5 1.5 54.3 �31.8 61.0

1700 46.0 5.0 1.5

ommariva 44°47.03� 07°47.10� 300 1595 50.5 5.3 3.3 54.0 �7.0 54.5

1595 52.2 9.2 3.3

1595 52.5 13.1 3.3

2900 80.5 9.3 2.3 88.4 �35.7 90.2

2900 83.3 15.0 2.3

3801 101.6 11.5 2.5 113.3 �61.1 115.4

3801 102.7 13.3 2.5

3801 104.4 15.3 2.5

orrente Riglio 45°00.13� 09°48.88� 58 1542 41.0 7.0 4.3 42.5 �3.2 43.2

1542 41.5 11.3 4.3

3816 87.0 13.0 4.0 94.6 �28.3 95.0

3816 89.0 18.3 4.0

edeschi 44°25.43 11°51.41 14 2139 68.0 7.5 1.5 74.7 �36.7 77.2

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Correction of bottom-hole temperatures E191

Corrected TH values for the two areas of the Po Plain as a functionf depth are presented in Figure 4. The least-squares regressionields an average geothermal gradient of 25.2 mK/m for PPH �Fig-re 4a� and 21.5 mK/m for ABA �Figure 4b�, for a mean annual sur-ace temperature of 12.5° and 13.0°C, respectively.

Table 4 shows the large number of temperatures measured duringSTs available in the two areas of the Po Plain. This kind of tempera-

ure is measured in the fluid recovered in the drill pipe through tem-orary relief of back pressure imposed on the formation. The fluid isonsidered to come a distance away from the thermally disturbedone around the borehole; consequently, its temperature is verylose to the formation equilibrium temperature �Beardsmore andull, 2001�. Thus, DST temperatures can be taken to test the validityf BHTs. The available DST temperatures, produced versus depth inigure 5, show average thermal gradients that match well those ob-

ained from the BHTs corrected with the Horner method. At PPHFigure 5a�, the straight-line fitting data has a slope of 25.0 mK/m.he data matching forABA �Figure 5b� give a slope of 21.5 mK/m.Given that the applied Horner method, after a correction of 2°C

or te 10 hours, is precise enough, as suggested by Deming andhapman �1988a�, a BHT depth-time correction can be based on the

able 1. (continued).

ell Latitude N Longitude EAlt.�m�

osco Rosso 44°55.12� 10°28.41� 25

ascina Nuova 44°54.73� 11°33.40� 8

orte Mezzo 44°45.47� 12°01.54� 0

orte Vittoria 44°54.08� 11°59.26� 0

oro 44°52.26� 12°18.97� 0

ussi 44°21.16� 12°02.52� 10

alle Isola 44°42.79� 12°11.72� 0

orrelation between the Horner slope and depth. The function cho-en should be constrained to yield a slope of zero at zero depth be-ause the temperature of the drilling mud at the bottom of extremelyhallow holes should be approximately the same as the temperaturef the ground surface. The slope of the Horner line must then in-rease with depth as the cooler drilling mud encounters progressive-y hotter temperatures at the bottom of the deeper holes. Figure 6hows the Horner slope data of Table 1 as a function of depth for �a�PH and �b� ABA. For the best fit of data, we used a quadratic func-

ion:

Hs � az � bz2, �12�

here depth z is in kilometers and the coefficients are equal to �18.9nd �16.3 for PPH and 2.7 and 2.1 for ABA. Attempts to decreasehe scatter by assuming, for example, that slopes determined fromhree and four data points are better than that those determined fromwo yield marginal improvements.

Using these results and equation 2, for te 10 hours, the tempera-ure correction �T � TH � BHT�t� as a function of depth z, shut-inime te, and circulation time of the drilling mud tc is

BHT�°C�

te

�hr�tc

�hr�TH

�°C�Hs

�°C�TCJ

�°C�

70.0 11.0 1.5

68.0 13.0 3.0 74.8 �32.8 75.2

70.0 19.0 3.0

59.0 10.0 3.0 65.6 �25.0 65.4

61.0 15.0 3.0

88.0 16.0 2.0 90.3 �18.8 90.3

89.0 26.0 2.0

89.0 32.0 2.0

48.0 9.0 1.3 52.2 �31.2 53.1

49.0 12.0 1.3

70.0 8.3 1.0 71.8 �16.7 72.2

70.0 12.0 1.0

71.0 16.0 1.0

68.0 20.4 3.5 75.6 �47.9 76.3

70.0 28.3 3.5

124.0 18.5 8.0 136.1 �34.4 135.9

127.0 28.5 8.0

130.0 38.0 8.0

20.0 7.0 1.0 23.1 �23.5 24.2

21.0 10.5 1.0

35.0 6.5 2.0 37.1 �8.0 37.7

36.0 13.0 2.0

76.0 10.3 3.0 81.2 �20.5 81.9

78.0 17.5 3.0

84.0 10.0 4.0 91.9 �23.5 89.7

86.0 14.0 4.0

Depth�m�

2139

3400

3400

1718

1718

3200

3200

3200

1610

1610

2485

2485

2485

2299

2299

5804

5804

5804

270

270

1200

1200

3770

3770

4170

4170

Tw�s

W

P

C

C

C

F

M

M

M

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T

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E192 Pasquale et al.

able 2. Geometric and physical parameters used in the Cooper and Jones (1959) method at a fixed depth and lithology for theells in Table 1. In the last column, the rock type is shown. Cl � clay, SH � shale, SS � sandstone, QS � quartz-sandstone, SLsiltstone, LS � limestone, DO � dolomite, MA � marl, GN � gneiss. Density of the formation is �r, drilling mud is �f,

pecific heat of the formation is cr, mud is cf, thermal conductivity of the formation is kr. and borehole radius is rb.

ellz

�m�rb

�m�kr

�W/�mK���r

�kg/m3�cr

�J/�kgK��� f

�kg/m3�cf

�J/�kgK��0 Rock code

PH area

ascina Riviero 2383 0.100 2.1 2590 1180 1260 3650 MA

3756 0.100 3.5 2695 1210 1250 3665 DO

ascina S. Pietro 1750 0.130 2.4 2540 1055 1250 3665 SS

astano 5289 0.130 1.5 2710 880 2020 2875 SH, 90%; SS, 10%

ranciacorta 1962 0.130 2.2 2425 1395 1160 3830 LS

3328 0.100 2.2 2520 1210 1170 3810 LS

alossa 1149 0.100 1.9 2430 1390 1120 3910 SH, 75%�; SS, 25%

onte Acuto 1324 0.165 2.0 2480 1390 1550 3265 MA

2677 0.130 2.1 2595 1130 2010 2880 MA, 80%; SL, 20%

oretta 2016 0.130 4.2 2430 1280 1200 3755 QS

3096 0.130 2.6 2630 950 1300 3585 GN

ovi Ligure 1700 0.130 2.1 2510 1295 1320 3555 MA, 80%; SS, 20%

ommariva 1595 0.165 4.1 2390 1360 1220 3720 QS

2900 0.130 1.9 2655 955 1260 3650 SH, 75%; SS, 25%

3801 0.130 2.5 2540 1050 1260 3650 SS

orrente Riglio 1542 0.165 1.8 2535 1230 1250 3670 SH

3816 0.100 1.9 2665 890 2150 2795 SH �50%�; SL �50%�

BA area

edeschi 2139 0.100 1.1 2685 1110 1320 3555 CL

osco Rosso 3400 0.130 3.3 2525 1090 1340 3525 QS �60%�; SL �40%�

ascina Nuova 1718 0.130 1.8 2565 1170 1720 3100 SH

3200 0.100 2.3 2515 1225 1120 3910 LS

orte Mezzo 1610 0.130 2.8 2415 1375 1230 3700 QS �60%�; SH �40%�

2485 0.130 2.5 2470 1205 1300 3585 SS

orte Vittoria 2299 0.165 3.2 2470 1245 1300 3585 QS, 70%; SH �30%

5804 0.130 2.3 2600 930 1200 3755 SS

oro 270 0.165 3.4 2205 1735 1140 3865 QS

ussi 1200 0.130 1.9 2455 1370 1220 3720 SH, 90%; QS �10%�

alle Isola 3770 0.130 2.5 2540 1055 1530 3285 SS

4170 0.130 1.3 2735 920 1900 2955 SH, 60%; CL �40%�

f

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ididaBsct

md1ord

fPlo5t

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FBSaNuova; 6, Corte Mezzo; 7, Cascina S. Pietro; 8, Moretta.

Correction of bottom-hole temperatures E193

�TPPH � �18.9z � 2.7z2�ln�1 �tc

te� �13�

or PPH and

�TABA � �16.3z � 2.1z2�ln�1 �tc

te� �14�

or ABA. For te 10 hours, a further temperature correction of 2°Cust be added, as deduced by comparing the two methods �Figure�.

Deming �1989� stresses that the main practical difficulty in apply-ng equations 13 and 14 could lie in the fact that information on theuration of mud circulation is almost always unavailable. Variousnvestigators have circumvented this difficulty by assuming stan-ard circulation times, varying from 4 to 6 hours �e.g., Chapman etl., 1984; Reiter and Jessop, 1985; Deming and Chapman, 1988b;rigaud et al., 1992�. Even if Luheshi �1983� shows that tc is not a

ensitive parameter, Scott �1982� argues that, though a standard cir-ulation time of 4 or 5 hours is probably a reasonable choice, situa-ions in which tc is as large as 30 hours may be common.

In the study areas, the data set of the Italian Economic Develop-ent Ministry includes 156 values of tc from 21 wells. Within a

epth ranging between 270 and 6675 m, tc varies from 0.3 and0.5 hours, with an average value of 3.0. Figure 7 shows the increasef circulation time versus depth. This increase does not depend onock type, and the best-fitting relation between tc �in hours� andepth z �in kilometers� is polynomial:

tc � 1.7 � 0.05z � 0.10z2. �15�

Figure 8 shows the depth-time correction of temperature for dif-erent shut-in times ranging between 5 and 50 hours obtained forPH and ABA. If one considers the average minimum te of the ana-

yzed BHTs �about 10 hours�, the maximum temperature correctionf 10.1°C is observed at a depth of 4.6 km at PPH and 10.7°C at.1 km at ABA. Such a correction decreases with increasing shut-inime, and it is about 1°C for te � 100 hours at both areas.

able 3. Matrix thermal conductivity kmr, matrix volumetriceat capacity �mrcmr at room conditions, porosity at surfaceo and compaction factor � of major sedimentary rocks.

ithologykmr

�W/�mK���mrcmr

�kJ/�m3K�� �o

��1/m�

lay 1.3 2565 0.5 0.0010

hale 2.2 2380 0.5 0.0010

iltstone 3.1 2200 0.3 0.0008

andstone 3.5 2200 0.3 0.0004

uartz-sandstone 6.5 2200 0.3 0.0004

imestone 3.3 2275 0.3 0.0003

olomite 5.5 2585 0.2 0.0002

arl 2.8 2420 0.3 0.0005

igure 2. Cooper and Jones �1959� plot for the wells with number ofHT�t� larger than two �see Table 1�. 1, Corte Vittoria; 2a and b,ommariva �3801 and 1595 m, respectively�; 3, Cascina Riviero; 4and b, Franciacorta �3328 and 1962 m, respectively�; 5, Cascina

Figure 3. Differences between predicted tempera-tures with Horner TH and Cooper and Jones TCJ as afunction of �a� the dimensionless parameter � and�b� te.

T

W

P

P

C

S

C

C

B

D

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R

O

L

P

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S

M

O

M

L

M

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F�

E194 Pasquale et al.

able 4. DST temperatures from selected wells of the Po Plain, Italy (Figure 1).

ellLatitude

NLongitude

EAlt.�m�

Prof.�m�

Temp.�°C� Well

LatitudeN

LongitudeE

Alt.�m�

Prof.�m�

Temp.�°C�

PH area ABA area

onte Tidone 45°03.17� 09°32.52� 67 1328 42 Santerno 44°19.28� 11°39.84� 80 1605 50

remona 45°09.95� 09°49.44� 42 1070 43 Cotignola 44°22.25� 11°55.36� 19 1040 31

oresina 45°16.23� 09°47.11� 57 1450 47 Imola 44°23.05� 11°44.89� 30 1385 39

aviaga 45°16.28� 09°34.20� 72 1890 62 Budrio 44°29.36� 11°41.46� 15 2543 60

ornegliano 45°17.25� 09°28.24� 80 1435 53 Alfonsine 44°31.00� 12°00.00� 10 1785 45

ordolano 45°17.50� 09°58.36� 65 1903 61 Spilamberto 44°31.90� 11°03.80� 67 1463 44

esana 45°18.50� 08°18.86� 142 2432 74 Selva 44°35.70� 11°35.40� 15 1360 41

ipalta 45°19.03� 09°40.02� 70 1565 54 Minerbio 44°37.00� 11°30.00� 16 1765 49

omanengo 45°22.92� 09°48.16� 85 1763 57 Traversetolo 44°39.85� 10°20.50� 177 1138 40

rzinuovi 45°23.36� 09°56.40� 81 1877 61 Porto Verrara 44°41.46� 11°51.88� 2 842 34

eno 45°23.65� 10°12.11� 72 1385 47 S. Pietro Casale 44°42.58� 11°25.09� 16 890 38

andino 45°24.85� 09°27.92� 85 1930 63 Vigatto 44°42.84� 10°18.14� 130 820 32

oncino 45°25.03� 09°49.91� 86 1824 60 Gallare 44°45.00� 12°03.40� 1 1855 63

ergnano 45°25.63� 09°41.89� 94 1367 48 Correggio 44°47.30� 10°44.60� 30 1243 40

ontirone 45°26.37� 10°13.16� 94 819 30 Sabbioncello 44°48.31� 11°53.56� 4 1150 43

rzivecchi 45°27.18� 09°56.99� 98 973 37 Tresigallo 44°49.43� 11°55.77� 2 1392 48

aclodio 45°28.00� 10°08.19� 110 903 33 Busseto 44°58.27� 10°01.76� 42 1555 48

ambrate 45°02.46� 09°15.12� 114 1326 48 Cortemaggiore 44°59.73� 09°59.28� 50 1575 47

alossa 45°30.37� 09°33.52� 115 5745 156 Palazzetto 44°41.76� 10°19.19� 146 2910 73

rugherio 45°32.78� 09°17.09� 152 1107 41 Casteggio 45°01.04� 09°06.72� 88 1523 48

usano 45°33.32� 09°08.79� 156 965 38

gnadello 45°26.82� 09°30.72� 96 1456 48

alossa 45°29.15� 09°33.67� 106 6430 168

igure 4. BHTs corrected with the Horner method versus depth fora� PPH and �b�ABAareas.

etemtut

mppastBimw

lt1JweBa

rltwt

DapUse

Fa

Fa

Fd

Ft

Correction of bottom-hole temperatures E195

CONCLUSIONS

Although ample BHT data are available for sedimentary basinsxplored for hydrocarbons, their usefulness for estimating the terres-rial heat flow is minimal unless raw thermal data are treated for mudffects. Mud circulation during the drilling process disturbs the ther-al regime of a well; as a consequence, BHT is generally lower than

he equilibrium formation temperature. We have deduced equilibri-m temperature from a series of BHT measurements of two areas ofhe Po Plain and propose empirical depth-time corrections for BHTs.

The two correction methods we applied require at least two orore BHT measurements at a given depth but at different times. The

roblem with the Horner method is that it assumes implicitly nohysical property contrast between circulating mud and formationnd that the borehole is infinitesimally thin, i.e., it acts as a lineource. This has been criticized by many authors. The accuracy ofhe predicted temperatures depends on the reliability and accuracy ofHT, te, and tc, and the error increases with the decrease of the shut-

n time. On the other hand, the Cooper and Jones method providesore reliable results but requires physical parameters that are not al-ays available.As expected, because BHTs are measured in a period that is often

imited to a few hours, the Horner method underestimates the undis-urbed formation temperature when shut-in time is less than0 hours, whereas it provides results consistent with the Cooper andones method for longer times. However, the magnitude of this biasas found to be average 2°C at the two areas of the Po Plain. The av-

rage geothermal gradients of PPH andABAinferred from correctedHTs are identical to those obtained with the DST temperatures, i.e.,bout 21.5 mK/m for theABAand 25.2 mK/m for the PPH.

The obtained depth-time-correction equations, based on the cor-elation between the Horner slope and depth, correct for mud circu-ation for each area when only one couple of BHT-te is available. Ifhe value of the time before circulation stopped is not included on theell-log header, we propose an empirical equation obtained from

ime data as a function of depth applicable for all of the Po Plain.

ACKNOWLEDGMENTS

The authors are particularly indebted to the Italian Economicevelopment Ministry for providing thermal data measured in oil

nd gas wells �http://unmig.sviluppoeconomico.gov.it/unmig/stat/ozzi/pozzidisponibili.htm�. This work was supported partly by theniversity of Genoa and the Scientific Research Ministry. A discus-

ion with A. Frixa of the Eni E&P Division, Milan, also is acknowl-dged.

a) b)

igure 8. Temperature correction versus depth for different shut-inimes for �a� PPH and �b�ABAareas.

igure 5. DST temperature �see Table 4� versus depth for �a� PPHnd �b�ABAareas.

igure 6. Horner slope as function of depth for �a� PPH and �b�ABAreas.

igure 7. Plot of the circulation time before shut-in tc as a function ofepth.

B

B

B

B

C

C

C

D

D

—

H

H

H

K

L

L

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E196 Pasquale et al.

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