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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

    Springer-Verlag 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]

    Z. Mao

    College of Geophysics and Information Engineering, China University of Petroleum,

    Beijing, Peoples Republic of China

    G. Li

    Research Institute of Exploration and Development, Changqing Oilfield Company,

    PetroChina, Shaanxi, Peoples Republic of China

    Y. Jin

    Southwest Oil and Gas Field Branch Company, PetroChina,

    Sichuan, Peoples Republic of China


    Appl Magn Reson (2013) 44:333347

    DOI 10.1007/s00723-012-0366-1


    Magnetic Resonance

  • 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.

    1 Introduction

    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

    [1]. 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:

    Sw ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

    a b Rw/m Rt



    : 3

    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 [24], and Rw can be checked from the formation water salinityusing Schlumbergers log interpretation charts [5].

    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 [6]. Wang

    and Sharma [7] 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. [8] 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 [6]. 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. [8] 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



    0.1 1

    Water saturation, fraction



    ity e




    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. [8] 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 [1014].

    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