CC BY
27
УДК 550.832.9
DOI: 10.33764/2618-981Х-2019-2-3-38-46
ВЛИЯНИЕ ТЕПЛООБМЕНА НА ЯМР КАРОТАЖ ВО ВРЕМЯ БУРЕНИЯ
Олег Алексеевич Шушаков
БейкерХьюз, Новосибирский технологический центр, 630090, Россия, г. Новосибирск, ул. Кутателадзе, 4а; Институт химической кинетики и горения СО РАН, 630090, Россия, г. Новосибирск, ул. Институтская, 3; Новосибирский национальный исследовательский государственный университет, 630090, Россия, г. Новосибирск, ул. Пирогова, 1, кандидат физико-матемитических наук, доцент, старший научный сотрудник, e-mail: Oleg.Shushakov@bakerhughes.com
Олег Борисович Бочаров
БейкерХьюз, Новосибирский технологический центр, 630090, Россия, г. Новосибирск, ул. Кутателадзе, 4а, кандидат физико-матемитических наук, доцент, заместитель директора, e-mail: Oleg.Bocharov@bakerhughes. com
Раду Коман
Бейкер Хьюз, a GE Company, Целле технологический центр, 29221, Германия, Целле, 1, Бей-кер Хьюз Штрассе, Ph. D., ведущий инженер, e-mail: Radu.Coman@bakerhughes.com
Холгер Терн
Бейкер Хьюз, a GE Company, Целле технологический центр, 29221, Германия, Целле, 1, Бейкер Хьюз Штрассе, геофизик, e-mail: Holger.Thern@bakerhughes.com
Исследовалось влияние температуры на ядерный магнитно-резонансный (ЯМР) каротаж во время бурения. Изучались как влияние теплопередачи, так и влияние проницаемости в зоне проникновения бурового раствора Аналитические решения и численные расчеты были проверены на примере полевых данных ЯМР-каротажа во время бурения.
Ключевые слова: ЯМР каротаж во время бурения, влияние теплопередачи, влияние проницаемости.
HEAT EXCHANGE IMPACT ON NMR LOGGING WHILE DRILLING
Oleg A. Shushakov
Baker Hughes, Novosibirsk Technology Center, 4a, Kutateladze St., Novosibirsk, 630090, Russia; Institute of Chemical Kinetics and Combustion SB RAS, 3, Institutskaya St., Novosibirsk, 630090, Russia; Novosibirsk National Research State University, 1, Pirogova St., Novosibirsk, 630073, Russia, Ph.D., Senior Researcher, e-mail: Oleg.Shushakov@bakerhughes.com
Oleg B. Bocharov
Baker Hughes, Novosibirsk Technology Center, 4a, Kutateladze St., Novosibirsk, 630090, Russia, Ph. D., Associate Professor, Deputy Director, e-mail: Oleg.Bocharov@bakerhughes.com
Radu Coman
Baker Hughes, a GE Company, Celle Technology Center, 1, Baker-Hughes St., Celle, 29221, Germany, Ph. D., Engineering Manager, e-mail: Radu.Coman@bakerhughes.com
Holger Them
Baker Hughes, a GE Company, Celle Technology Center, 1, Baker-Hughes St., Celle, 29221, Germany, Geophysicist, e-mail: Holger.Thern@bakerhughes.com
The effect of temperature on nuclear magnetic resonance (NMR) logging while drilling (LWD) has been studied. Heat conduction and permeability effects in the near wellbore invasion zone have been taken into account. Analytical solutions and numerical calculations have been exemplified and verified with the use of NMR LWD field data.
Key words: NMR logging while drilling, heat transfer effect, permeability effect.
Temperature affects nuclear magnetic resonance (NMR) measurements acquired by well logging. Both nuclear spin magnetization and NMR signal are inversely proportional to the absolute temperature (Curie-Langevin law). In a magnetic field Bo, a macroscopic magnetization M0 (r) of a unit volume in thermal equilibrium state is described by:
where n (r) is the number of magnetic nuclei per unit volume, r is the position vector, iis the gyromagnetic ratio for protons, S=1/2 is the nuclear spin, h and k are Planck and Boltzmann constants, respectively, and T is the absolute temperature of the formation [1].
In both wireline NMR logging and NMR logging while drilling (LWD) the measured mud temperature on signed level is used as a proxy temperature of the NMR sensitive volume situated several centimeters deep into the formation from the borehole surface. In NMR LWD (in contrast to wireline NMR logging) the temperature of the mud and the near-wellbore formation can be significantly different from the temperature of the native formation. This can occur if during drilling operations the circulating mud temperature is not in equilibrium with the surrounding formation temperature. The temperaturedifference will bias the NMR-derived porosities, but a correction of this effect is not yet a standard procedurein MMR LWD [2].
For NMR LWD temperature correction, we have to estimate the temperature in the NMR sensitive volume and compare it to the temperature of the mud, which under certain circumstances may be cooler or warmer as the formation. Since the sensitive volume is situated only several centimeters into the formation from the borehole wall [3], the near well-bore temperature behavior needs to be investigated as a function of mud temperature, formation properties, and time.
A heat conduction equation in cylindrical coordinate frame is
Introduction
Mo(r) = n (r)i2h2 S (S +1) • Bo,
(1)
Theory
dT ^ (d2T 1 dT 1
f -i2
where DT is the rock thermal conductivity. For dimensionless parameters tt= Dt t/a and p=r/a (where a is the borehole radius), the solution of the heat conduction equation with initial and boundary conditions (T(rT,1)=T1(tt), T(0,p) = T0(p)) for tt>0 and p>1 is
T = j e~TT"2 k0(j>, u ) •<
jTo(P) •Ko(P,u)PdP
Ko(p,u) =
Jo(uP) • Yo(u) ~ Yo(uP) •Jo(u) i' 02 (u ) + Yo2(u )
1 j
e'T" f (Tt) • dTi
K
V'o2(u ) + Yo2(u )
udu
(3)
where Jo and Yoare Bessel and Neumann functions [4].
For constant initial and boundary conditions ( 1=const, To = const ) the analytical solution is more simple:
T - To T - To
1H— j exp(-TTu2)
2. Jo(up)Yo(u) -Yo(up)Jo(u) du
Jo2(u) + Yo2(u)
u
(4)
And a small-times expansion is
T - To T - To
*-!=•efc VP
f \ P-1
2\JTT
(5)
Fig. 1 compares the solutions (4) and (5) for parameter values typical for NMR LWD conditions: rT=o.3, 1, 3 (for DT =o.oicm2/s, t=36oos, and a=io.8 cm TT=o.3). This shows that the small-times expansion (5) can be used for NMR LWD temperature correction at times of NMR measurement since drilled in the order of 1 hour.
The heat conduction equation considering mud invasion is
T1
-= div (DT ■ gradT - v • T),where vis the rate of mud filtration through the near-
ô t v 1 7
wellbore formation. In a cylindrical coordinate frame for constant radial flux • er (v0 = const is the filtration flow rate at r=a, er is the unit vector along ra-
v„ • a
v =
dius r). In dimensionless form with fi=voa/2DT we have ôT = ô 1 + 1 2P ôT . For
ÔTT ôp P ôp
constant initial and boundary conditions ( 1=const, To = const) the solution for p >1 and tt>0 is
T - To = 1 + 2p 1 - To
fi
K
j exp(-TTu 2)
2) Jp(uP) • Yfi(u) -Yp(uP) • Jfi(u) du
Jfi(u) + Yfi(u)
(6)
u
x>
4o
where Jp and Yp are Bessel and Neumann functions.The convection parameter p has to be obtained from solving the filtration problem.
r/a
Fig. 1. A comparison of the exact solution (4) and its approximation (5) for rj=0.3, 1, 3
The conduction equation for the pore pressure P in a cylindrical coordinate frame for dimensionless tp= Dp t/a (where DP=k/(nsç) is the piezo-conductivity coefficient, k is permeability, n is viscosity, q> is the porosity of the movable fluid in the
ÔP
pores, and s is the formation compressibility) is
drP
d2P 1 SP
—- +---. For initial and
dp p dp
boundary conditions ( Pfe,p)=P=const, P(0,p)=P0 = const) the solution for p >1 and tp>0 is similar to [4] with Treplaced by P. The mud-filtration rate, thus, is
Vo = —
a dp
I dr
k Pi~Po! r
r a UJ 0
2 ^2 ^ exp(-TPu2 ) • du
Jo2(u) + 7o2(u )
(7)
And the convection parameter ß takes the form
ß=-
k P - P0
r 2Dt
■.2 œ
2
exp(-TPu ) • du Jo2(u) + Yo2(u) '
(8)
Fig. 2 compares the mud-filtration rate (7) for different rock permeabilities k =1, 10, 100md.
Fig. 3 compares the behavior of the convection parameter pderived by (8) for different permeabilities k=1, 10, 100 md, illustrating its sensitivity to rock permeability. Only in a high permeability rockthe parameter p varies significantly versus
time.For LWD measurementsthis corresponds to the time since drilled with mud circulating through the borehole.
Time since drilled (h)
Fig. 2. Comparison of the mud-filtration rate for different permeabilities
k =1, 10, 100 md
Time since drilled (h)
Fig. 3. Comparison of the convection parameter ¡3 for different permeability k=1, 10, 100 md
Fig. 4 compares the solution (6) for temperature versus distance from the borehole axis with the parameters values: rj=0.3,k=0 (¡=0), k=1 (¡=0.25), k=10 (¡=2), k=100 (¡=17). The black dashed line represents the location of the NMR sensitive volume in the formation.
0.8
0.6
0.4
0.2
Permeability (DTt/a2 = 0.3): k = 100 md k = 10 md k = 1 md
Sensitive volume
r/a
Fig. 4. Comparison of the temperature versus distance from the borehole axis for different permeabilities k = 1, 10, 100 md
0
Fig. 5 compares the solution (6) for temperature versus time since drilled with the parameters: tt=0.3, k =0 (fi =0), k =1 (fi =0.25), k =10 (fi =2), k =100 (fi =17). Fig. 4 and 5 show that for low permeability the near-wellbore temperature, which may be strongly affected by the mud temperature, starts to equilibrate with the formation temperature. This reduces the temperature effect on the NMR measurement and the resulting porosity bias. For high permeability, the mud is also invading into the formation. This counteracts the temperature equilibration process, resulting in a larger temperature difference and a larger porosity bias. Therefore, the required NMR signal correction will be larger in formations with high permeability.
i -
0.8
¡2T 0.6
fc 0.4
0.2
0 -
0 2 4 6 8 10
Time sincedrilled(h)
Fig. 5. Comparison of the temperature versus time since drilled for different permeabilities k=1, 10, 100 md at the location of the NMR sensitivevolume (compare Fig. 4)
Application
Fig. 6 exemplifies the effect of temperature on a short NMR LWD echo train acquired in a shale zone with low permeability. Fig. 6 a) shows the measured temperature in the borehole, the formation temperature estimated using an expected geo-thermal gradient, and the temperature of NMR LWD sensitive volume calculated by our model at different borehole vertical depths. The data have been obtained with a rate of penetration (ROP) of 20 m/h, and a bit-sensor offset (the distance between bit and the NMR LWD sensor) of 20 m, which leads to a time since drilled of 1 hour.
The parameters used for the temperature modeling are: the borehole diameter is 8.5
2 2
in, the sensitive-volume diameter is 13.2 in, the thermal diffusivity DT is 10 cm /s,
2 2 1 the viscosity n is 10 poise, the compressibility s is 5-10" Pa , <^=20%, the pressure
difference Pi-Po is 20 atm, and the geothermal gradient is 3K/100m.
----Formation geothermal gradient estimated
- Temperature of sensitive volume calculated
© Borehole temperature measured
a)
1223 1227 1231 Vertical depth (m)
Clay-bound water NMR signal
—®- borehole-temperature calibrated
----formation-temperature calibrated
b)
4 8 12
NMR decay time (ms)
25
328
20
15
324
10
320
5
0
1219
Fig. 6. a) Temperature of borehole, formation, and sensitive volume vs vertical depth, b) temperature effect on NMR LWD signal at vertical depth 1215m to1239m
The resulting effect of temperature on the NMR LWD echo amplitude shown in Fig. 6 b) is 2%. It is caused by the 6 K difference between the temperature measured by the tool and the temperature calculated for the formation at the sensitive volume. The resulting change in porosity (e.g., 0.5 pu for a formation with 25 pu) is below the accuracy of the measurement of ±1 pu and, therefore, can be neglected. If the initial temperature difference is larger or time since drilled is decreased (e.g., by higher ROP), the temperature effect will become significantly larger and the NMR porosity bias and its correction will become relevant.
Fig. 7 presents data from the same borehole as Fig. 6 but for a longer depth interval including permeable layers between 1600 and 1700 m. For the permeable lay-
ers the temperature of the NMR LWD sensitive volume is equal to the temperature measured in the borehole. The average temperature difference is 8 K, resulting in an average temperature difference between the tool and the sensitive volume of 5 K. Only in the high permeability layers between 1600 and 1700 m (Fig. 7), the calculated temperature in the sensitive volume is up to 8 K different from the tool. For a 25 pu formation this causes a bias of 0.6 pu, which is below the accuracy of the NMR measurement. The effect will become more relevant for larger temperature difference, but a correction with this method can also be applied in this situation.
Fig. 7. Temperature of borehole, formation, and sensitive volume, andpermeability measured by NMR LWD versus the borehole vertical depthwith permeable layers between 1550 and 1750 m. Note the effect of the permeable layers on the calculated temperature at the NMR sensitive volume
Summary
This publication presents an analytical approach for the estimation of the NMR LWD temperature effect. The model applies when the temperature measured in the logging tool (i.e., in the borehole) is different from the actual formation temperature. In addition, to the heat transport through the formation, it includes the treatment of convective heat transfer for permeable layers invaded by mud filtrate. The theoretical results show that the heat transfer with convection is sensory adaptive to permeable layers. Due to the mud invasion in permeable zones, the temperature of NMR LWD sensitive volume is close to the measured temperature in the borehole, i.e., the mud temperature. Based on the results, a temperature effect
correction for NMR LWD data can be implemented and conducted during standard NMR LWD data processing.
REFERENCES
1. Abragam, A. Principles of Nuclear Magnetism. - Oxford, Clarendon Press, 1961. - 599 p.
2. Field test of NMR LWD device / M.G. Prammer, G.D. Goodman, S.K. Menger, M. Morys, S. Zannoni, J.H. Dubley // Proceeding of the SPWLA 41st Annual Logging Symposium (Dallas, USA, 4-7 June, 2000) - Dallas, USA, 2000. - Paper SPWLA-2000-EEE - 9 p.
3. Coman R., Tietjen H. Temperature correction in NMR logging while drilling // Proceeding of the SPE Oil and Gas India Conference and Exhibition (Mumbai, India, 4-6 April, 2017). - Mum-bai, India, 2017. - Paper SPE-185334-MS. - 19 p.
4. Carslaw H.S., Jaeger J.C. Conduction of heat in solids. - Oxford, Clarendon Press, 1959. -386 pp.
© О. А. Шушаков, О. Б. Бочаров, Раду Коман, Холгер Терн, 2019
