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Estimation of Saturation Exponent from NuclearMagnetic Resonance (NMR) Logs in LowPermeability Reservoirs
Liang Xiao Zhi-qiang Mao Gao-ren Li Yan Jin
Received: 26 November 2011 / Revised: 3 May 2012 / Published online: 3 June 2012
Abstract The resistivity experimental measurements of 36 core samples, whichwere drilled from low permeability reservoirs of southwest China, illustrate that the
saturation exponents are not agminate, but vary from 1.627 to 3.48; this leads to a
challenge for water saturation estimation in low permeability formations. Based on the
analysis of resistivity experiments, laboratory nuclear magnetic resonance (NMR)
measurements for all 36 core samples, and mercury injection measurements for 20 of
them, it was observed that the saturation exponent is proportional to the proportion of
small pore components and inversely proportional to the logarithmic mean of NMR T2spectrum (T2lm). For rocks with high proportion of small pore components and lowT2lm, there will be high saturation exponents, and vice versa. The proportion of smallpore components is characterized by three different kinds of irreducible water satu-
rations, which are estimated by defining 30, 40 and 50 ms as T2 cutoffs separately. Byintegrating these three different kinds of irreducible water saturations and using T2lm, atechnique of calculating the saturation exponent from NMR logs is proposed and the
corresponding model is established. The credibility of this technique is confirmed by
L. Xiao (&)Key Laboratory of Geo-detection, China University of Geosciences, Beijing, Ministry of Education,
No. 29, Xueyuan Road, Haidian, Beijing 100083, Peoples Republic of China
e-mail: [email protected]
College of Geophysics and Information Engineering, China University of Petroleum,
Beijing, Peoples Republic of China
Research Institute of Exploration and Development, Changqing Oilfield Company,
PetroChina, Shaanxi, Peoples Republic of China
Southwest Oil and Gas Field Branch Company, PetroChina,
Sichuan, Peoples Republic of China
Appl Magn Reson (2013) 44:333347
comparing the predicted saturation exponents with the results from the core analysis.
For more than 85 % of core samples, the absolute errors between the predicted satu-
ration exponents from NMR logs and the experimental results are lower than 0.25.
Once this technique is extended to field application, the accuracy of water saturation
estimation in low permeability reservoirs will be improved significantly.
Water saturation (thus related to hydrocarbon saturation) is an indispensable input
parameter in formation evaluation, and it also plays a very important role in
reservoir development program formulation. Generally, water saturation is calcu-
lated using Archies equations after the necessary parameters have been obtained
. Archies equations can be expressed as Eqs. (1) and (2):
F R0Rw a
Ir RtRo b
where R0 is the rock resistivity at full water saturation, Rt the true formationresistivity, Rw the formation water resistivity, the units of which are X m, F theformation factor, Ir the resistivity index, / the porosity in fraction, a and b thelithology factors, m the cementation exponent, Sw the water saturation in fraction,and n is the saturation exponent.
Combining with Eqs. (1) and (2), a derivative expression can be written as follows:
a b Rw/m Rt
From Eq. (3), it can be observed that the values of a, b, m, n, Rw, / and Rt mustbe obtained first for the water saturation calculation, / and Rt can be acquired fromconventional logs , and Rw can be checked from the formation water salinityusing Schlumbergers log interpretation charts .
2 Determination of the Values of a, b, m and n
To calculate water saturation from conventional logs using Archies equation, the
determinations of the values of a, b, m and n are crucial. Generally, thedeterminations of a, b, m and n rely on the resistivity experimental measurements ofthe target core samples. To obtain the necessary resistivity experimental data, the
needed procedures should be applied as follows: (1) every waterless core sample is
saturated using the used saline water, and the rock resistivity R0 at full watersaturation is measured; in this study, the salinity of the used saline water is
13.00 mg/l. (2) The oil is used as the displacing medium, and the centrifugal method
is used to vary the water saturation (Sw) of core samples, and the corresponding rock
334 L. Xiao et al.
resistivity Rt of every core sample under different water saturations are measured.(3) R0, Rt and Sw are collected as a data set to obtained the value a, b, m and n.
For conventional reservoirs, after the representative core samples were drilled
from the intended intervals for the resistivity experiment, the fixed values of a, b,m and n can separately be obtained from the cross plots of the porosity with theformation factor, and the water saturation with the resistivity index using the power
function. However, for low permeability sands, not rigorous power function exists
between the porosity and the formation factor, the water saturation and the resistivity
index due to the complicated pore structure and the strong heterogeneity . Wang
and Sharma  and Mao et al. [8, 9] had proposed that the tendency of porosity and
formation factor would be changed when the porosities of core samples are lower
than 9.0 %, and they had demonstrated that this change is caused by the poor pore
structure of low permeability plug samples. Mao et al.  had developed a novel
method to obtain the accurate values of a and m from the porosity using binaryregression. This method has been confirmed to be effective and is used widely . In
the low permeability formations mentioned in this study, a and m can be determinedusing Maos method precisely. Thus, the technique of determining a and m from theporosity that has been proposed by Mao et al.  is not introduced in this paper.
It is really a challenge to determine the saturation exponent in low permeability
reservoirs, as the cross plot of the water saturation with the resistivity index is
divergent and a fixed saturation exponent is difficult to acquire. Figure 1 shows the
cross plot of the water saturation with the resistivity index of 36 core samples,
which were drilled from low permeability reservoirs of southwest China. It can be
observed that the relationship between the water saturation and the resistivity index
for all core samples is not consistent. The saturation exponent for single core sample
varies from 1.627 to 3.48. In this case, water saturation calculated using the
regressed fixed saturation exponent from all 36 core samples would be inaccurate.
y = 1.0415x-2.0797
R2 = 0.9054
Water saturation, fraction
Fig. 1 Relationship of water saturation and resistivity index for 36 core samples in low permeabilitysands of southwest China
Estimation of Saturation Exponent from NMR Logs 335
The best method is to estimate the water saturation using various saturation
exponents along with the target intervals.
3 Influencing Factors of Saturation Exponent in Low Permeability Sandstones
To acquire accurate saturation exponents for water saturation estimation at low
permeability, it is necessary to understand the influencing factors and the variation
of the saturation exponent. Based on the qualitative analysis of the core thin section
and mercury injection capillary pressure experimental data, Mao et al.  had point
out that the saturation exponents were related to rock pore structure. However, the
quantitative relationship between them was not established, and an applicable
technique was not proposed. Nuclear magnetic resonance (NMR) logs have a unique
advantage in indicating reservoir pore structure. From the measured NMR T2distribution, the information of pore size and distribution can be obtained .
Rocks with macropore and good pore structure will display long transversal
relaxation time, and wide T2 distribution due to the contribution of surfacerelaxation. On the contrary, short transversal relaxation time and narrow NMR T2distribution mean poor pore structure for rocks (Fig. 2). Mercury injection capillary
pressure curves can be used to obtain the pore throat radius distribution, which is
useful in evaluating the pore throat size and the connectivity [15, 16].
To quantitatively display the relationship between the saturation exponents with the
pore structure, all 36 core samples, shown in Fig. 1, have been chosen for rock
resistivity and laboratory NMR experimental measurements; 20 of them were studied
in mercury injection experiments. The experimental parameters of NMR measure-
ments are designed as follows: polarization time (TW): 6.0 s; inter-echo spacing (TE):
0.2 ms; the number of echoes per echo train (NE): 4096; scanning number: 128.
To illustrate the factors that heavily affect the saturation exponent, the resistivity
and laboratory NMR experimental results for 36 core samples and mercury injec