Predicting the cation exchange capacity of reservoir rocks from complex dielectric permittivity measurements

Abstract

Dimensional analysis was performed to understand the physics of ionic dispersion in reservoir rocks and to identify the factors influencing the cation exchange capacity (CEC) of these rocks. Dimensional analysis revealed the existence of a general relation independent of the unit system between two dimensionless groups denoted as the cationic dispersion number [Formula: see text] and the conductivity number [Formula: see text]. The former group [Formula: see text] stands for the ratio of the CEC to the electrical double-layer dispersion. The latter group [Formula: see text] represents the ratio of the low-frequency ionic conductivity to the high-frequency electronic polarization. Complex dielectric permittivity measurements on 121 water-saturated sandstone and carbonate rock samples were used to validate the dimensionless groups. In retrospect, dimensional analysis was useful in identifying variables influencing the CEC of hydrocarbon rocks. In particular, these variables consist of rock porosity [Formula: see text], specific surface area, and five other parameters of the Cole-Cole function, which describes the frequency dependence of the complex permittivity of rock samples in the range 10–1300 MHz. The Cole-Cole function parameters are [Formula: see text], which is a characteristic relaxation time; [Formula: see text] is the so-called spread parameter; [Formula: see text] is the real DC conductivity of water-saturated rocks; and [Formula: see text] and [Formula: see text], which are the real numbers representing the static and the high-frequency dielectric permittivities of the water-saturated rock, respectively. A general regression neural network (GRNN) model was developed to predict the CEC of shaly sandstones and carbonate rocks as a function of the variables identified by the dimensional analysis as essential in predicting the CEC. The CEC prediction capability of the GRNN model has been tested with a blind data set, and it has been compared with the CEC prediction capability using a nonlinear regression model developed in this study and using a linear regression model available in the literature. The GRNN model outperformed both of these empirical models. With the GRNN model, it is possible to obtain reliable quantitative estimates of the CEC of shaly sandstone and carbonate rocks using nondestructive frequency-dependent dielectric permittivity measurements that are rapid, economic, and accurate. In return, accurate and fast estimates of the CEC are useful in many petroleum engineering applications. They can be used to identify clay types and can also be used to quantify the volume of hydrocarbon in shaly sands using well-log resistivity data. The results of this study represent a major advantage for formation evaluation, wellbore stability analysis, and designing stimulation jobs.

A pragmatic approach for optimizing gas lift operations

“…For carefully defined variables contributing to the functional relation (Eq. (17)), a unique plot of χ 1 versus χ 2 is likely to lead to a general relation, between the groups, that might be applied for similar systems (Garrouch 2018;Garrouch and Al-Sultan 2019). This particular inference can only be confirmed with gas lift production data.…”

“…Garrouch (2018) applied dimensional analysis for characterizing the electrical double-layer polarization and the high-frequency electronic polarization, in porous and permeable reservoir rocks. An analytical model for estimating the cation exchange capacity of rocks from fast, reliable, and noninvasive complex impedance measurements has emanated, as a consequence (Garrouch 2018).…”

“…GRNN is an attractive nonlinear prediction method because of its fast learning capability and sturdiness in the presence of noise. Al-Omair and Garrouch (2015), Al-Dousari et al (2016), and Garrouch (2018) give applications of GRNN for building predictive models of petrophysical properties for small datasets. GRNN establishes empirically the functional form between a dependent variable Y, and an independent variable X, based on the data using nonparametric estimators (Specht 1991).…”

Inversion of Vertical Electrical Sounding Data by Using General Regression Neural Network

“…Ji ve diğerleri [40] yakın zamanda GRNN yöntemini yatay-düşey spektral orana (HVSR) dayalı bir zemin sınıflandırmasında kullanmıştır. Garrouch [41] karmaşık dielektrik geçirgenlik ölçümlerinden rezervuar kayalarının katyon değişim kapasitesinin tahmin edilmesinde GRNN yöntemini kullanmıştır. Wiszniowski [42] GRNN yöntemini yer hareketi modellerinin tahmini için uygulamıştır.…”

The frequency exponent of artificial sandstone's complex resistivity spectrum

“…The resistivity of the formation exhibits complex characteristics and change with frequency, which is called the complex resistivity spectrum and contains a lot of useful information (Snyder et al ., 1977; Poley et al ., 1978). A large amount of petrophysical experiment research on the complex resistivity of rocks was carried out in the past few decades (Vinegar and Waxman, 1984; Knight and Nur, 1987; Revil and Florsch, 2010; Revil et al ., 2012; Norbisrath et al ., 2017; Garrouch, 2018; Norbisrath et al ., 2018;Jia et al ., 2019, 2020), and the complex resistivity spectrum has gradually shown broad application prospects in the exploration of petroleum and mineral resources.…”