The use of nuclear magnetic resonance (NMR) has been widely used in many fields of scientific research to study the composition and structure of matter, as well as its state. Intensive use of the NMR is associated with the production of down hole equipment for pulsed nuclear magnetic logging in the 90s of the last century, in order to study the porosity and permeability properties of rocks penetrated by a well [1-3]. Over this period, a large number of scientific papers have been published focusing on reservoir properties, rock structure, type and rheological properties of fluids containing hydrocarbons, and the characterization of reservoir fluids [4 -7]. It is known that the determination of the rheological properties of oil and other fluids at an early stage in the study of oil and gas reservoirs is extremely important, since they determine the productivity of the formation. Based on the characteristic decay times of the longitudinal (T1) and transversal (T2) components of the macroscopic magnetization vector, the NMR method allows the evaluation of the oil viscosity, including measurements at well sites [8-11]. Recently, the issue of effective development of fields with hard-to-recover reserves of high-viscosity oil remains relevant [12-14], therefore, NMR studies are being carried out intensively in this direction as well.

Along with the rheological properties, it is important to know the composition of the fluid when studying oil and condensate samples. The composition of oil can affect its viscosity, as has been demonstrated in experiments examining the effects of asphaltene compounds on the viscosity of oil samples [15,16]. Considering how oil can be assessed by its group composition, K Mirotchnik [17,18] proposed an experimental method for assessing the ratio of aromatic, saturated, resinous and asphaltene compounds by using NMR-relaxometry.

Since NMR experiments usually take a few seconds to a few minutes, this method can be used both in the laboratory and during well drilling or operation to rapidly evaluate rheological properties and compositions of oil and condensate samples. Laboratory NMR study of fluids is required to study relaxation characteristics, the results of which are necessary for the interpretation of NMR data. Research in the present work focuses on the development of laboratory NMR relaxometry for evaluating the rheological properties and group composition of oil and condensate.

Over 90 fluid samples were analyzed using NMR, including oil samples with viscosities ranging from 1.5 to 120 mPa.s (at 20 ° C) and oil condensates with fractions boiling off at temperatures lower than and higher than 200 °C. An analysis of the research results was carried out by comparing them with the rheological characteristics and the group composition obtained by standard geochemical methods. The NMR measurements were conducted with an MCT-05 relaxometer at a temperature of 22 °C with a magnetic field induction of 55 mT and an operating frequency of 2.2 MHz. The permanent magnets in the relaxometer are made of an alloy of samarium and cobalt that can operate between -60 °C and +350 °C. In the experiment, the pulse sequence used was Carr-Purcell-Meiboom-Gill (CPMG), with the registration of the spin-echo signals. Experience has been gained in the use of an NMR relaxometer for studying the composition of core samples [19,20], as well as fluids [21-23].

For oil samples of different viscosity, continuous and discrete spectra T2 were determined, as shown in Figure 1. The continuous spectrum shows that the higher the viscosity of the fluid, the lower the T2 associated with an increase in the proportion of resinous-asphaltene compounds in the sample (Figure 1a). These compounds are large aggregates-clusters with a complex supramolecular structure [24-26].The presence of such structures hinders the free movement of molecules in a fluid and, thus, leads to an acceleration of relaxation processes and a decrease in T2, respectively.

Figure 1: Continuous (a) and discrete (b) T2 spectrum for oil samples of different viscosities. (The line cipher corresponds to the sample number. The viscosity of sample 1 is 1.6 mPa.s, sample 2 is 9 mPa.s, and sample 3 is 110 mPa.s).

The discrete spectrum was obtained by minimizing the number of components in the continuous T2 spectrum (Figure 1b).This processing result makes it possible to isolate the main groups of components and obtain their relative ratio, which can be used for preliminary or express assessments of the group composition of the fluid.

It is widely believed that the average logarithmic value of , which is calculated as follows, characterizes the T₂ spectrum:

Where T_2i is the relaxation time for the i^th component, αi is the fraction of the i^th component in the T₂ spectrum.

NMR relaxometry was used to examine the possibilities of group analysis and the assessment of rheological properties for oil and condensate samples collected from a number of hydrocarbon fields. The NMR characteristics of oil and condensate samples have been compared with their rheological properties (Table 1), as well as their group composition (Table 2), measured by standard laboratory methods. In the tables, oil is classified according to Russian oil general specifications.

According to Table 1,  and dynamic viscosity coefficient exhibit a good correlation. Based on the research results, the following equation was obtained that relates the viscosity coefficient to :

 -------- (2)

Where η is the coefficient of dynamic viscosity (mPa.s), T is the temperature at which the measurements are carried out (° K), is the average T₂ (ms), constant α = 2.31. The formula was derived with a coefficient of determination of (R² = 0.95).

Table 1: Laboratory NMR measurements and standard measurements of rheological properties of hydrocarbons.

In light of this, a formula (Equation 2) has been derived for determining the dynamic viscosity coefficient of oil samples collected from a number of hydrocarbon fields based on the data collected by NMR relaxometry. As far as the possibility of determining the group composition is concerned, there is a clear correlation between NMR measurements and results obtained via standard methods (see Table 2).

Table 2: Results of laboratory NMR measurements and standard measurements of hydrocarbon group composition.

Condensate and extra light oil concentration data are not available because the MCT-05 NMR relaxometer requires a time between echo pulses equivalent to the time T2 characteristic of resins and asphaltenes in order to record a signal. During this time, the nuclei of hydrogen atoms in these compounds have time to relax and do not make a noticeable contribution to the NMR signal. The relative error in determining the composition of groups for light and medium oil samples does not exceed 10%.This makes it possible to use the NMR relaxometry method for rapid assessment of the rheological properties of fluids. A decline in correlation is observed in samples of heavy and bituminous oil, explained by the high proportion of resinous-asphaltene compounds, which requires further investigation to improve results. The data in tables 1 and 2 confirm the fact that the increase in viscosity is associated with the presence of resinous-asphaltene constituents. An increase in oil viscosity leads to a shift in the T2 spectrum towards the "dead" time of the device, and hence a decrease in the accuracy of the results, since the most rapidly relaxing components cannot be recorded with the required accuracy.

This research showed that the NMR-relaxometry laboratory approach has high accuracy of measurements and high information content of data obtained when using it to study oil and condensate samples.

NMR Study of Model Samples

To substantiate the performed experiments and the obtained estimates, NMR measurements of model samples were carried out, including mixtures of benzene and petroleum ether (PE) at different ratios. The study was carried out with the aim of assessing the influence of the group composition (the ratio of aromatic / saturated compounds) on the determined NMR characteristics, including depending on the temperature. It is not a coincidence that benzene and petroleum ether were chosen, since petroleum ether is a mixture of light saturated alkanes - pentane and hexane - and benzene belongs to the aromatic series. As part of the model experiment, 11 samples were prepared: 100% benzene, 100% petroleum ether, and 9 samples of benzene / petroleum ether mixtures with proportions ranging from 10% to 90%. After processing the data obtained, the dependence of the average  of the mixture on the temperature and concentration of petroleum ether, illustrated in Figure 2, was established. As concentrations of petroleum ether and temperature rise, the average  of the mixture increases due to an increase in molecular mobility.

Figure 2: Dependence of the average  of benzene-petroleum ether mixture on the temperature and concentration of petroleum ether.

In light of the results obtained, a detailed analysis of the dependences of the average  of Benzene-Petroleum Ether mixtures in a 1: 1 ratio on temperature and concentration of Petroleum Ether at 20 °C was conducted. Accordingly, the dependence of the average  on the temperature, given a 1: 1 rate of benzene to petroleum ether, shows a linear relationship, for the temperature range of 5 ° C to 40 ° C with 7 ° C steps. This confirms the earlier established dependence (Equation 2).

Figure 3: Dependences of the average  of a mixture of benzene petroleum ether in a 1: 1 ratio on temperature (a) and concentration of petroleum ether at 20 ° C (b).

According to Figure. 3b, the dependence of the average  on the concentration of petroleum ether at a temperature of 20 ° C indicates that it obeys hyperbolic law:

Where C_i is the concentration of the i-th compound, k_i is a coefficient equal to 1 if the compound acts as a solvent, otherwise -1; T_2i is the characteristic T₂ of the i^th compound, P is the total number of compounds that make up the given model sample. This equation is consistent with the classical theory of NMR relaxation: the relaxation rate linearly depends on the concentration.

According to Figure 3, saturated and aromatic compounds have different times, and the average  of the mixture is inversely proportional to their concentrations. Below are the results of a numerical model to confirm the possibility of determining the oil and condensate group composition based on the analysis of discrete NMR spectra this model is based on the fact that protons belonging to different kinds of compounds (saturated and aromatic compounds, resins, and asphaltenes) can be divided into several groups.

Each group of protons has its own characteristic T₂. In this case, the total signal is a superposition of signals from protons of different groups. In this work, 4 models are considered - protons of one group with T₂ = 1000 ms, two groups T₂ = {1000, 100} ms, three groups T₂ = {1000, 100, 10} ms and four groups T₂ = {1000, 100, 10, 1} ms. In the context of these models, the mathematical modeling of synthetic NMR data was performed by making use of the following function:

Where f_i is the simulated signal of the magnetization decay at time t_j, a_i is the fraction of protons in the i^th group (a_i in each of the cases are selected in a 1: 1 ratio), N = {1, 2, 3, 4} is the total number of proton groups, ε (t_j) is the noise distributed according to the normal law with a variance of 0.05.

The solution to the inverse problem associated with determining the content of different types of compounds is based on solving the system of linear algebraic equations (SLAE) Ba = f, where the SLAE matrix takes the form:

The least-squares method is used to solve the SLAE by minimizing the residual function. Along with this method for solving the inverse problem, a solution based on the inverse Laplace transform [27-30] is also used. In the case of noisy synthetic data, numerical inversion can be utilized to estimate the accuracy of recovering the coefficients a_i, which represent the quantitative content of the i^th group of protons. The results of numerical experiments are presented in Figure. 4, which shows the continuous and discrete spectra of T₂ for the simulated decays of the magnetization signal.

Figure 4: Continuous (a) and discrete (b) T2 spectra for noisy synthetic NMR data.

The laboratory and numerical experiments performed have shown that the NMR relaxometry method can be widely used for rapid assessments of the rheological and compositional properties of oil and condensate samples. As a means of improving the results of studying samples of heavy and bituminous oil, as well as bitumoids extracted from oily core, which contain large amounts of resinous-asphaltene compounds, it is necessary to enhance the processing method for NMR data. As well, it is necessary to improve the method of using laboratory equipment to increase resolution, by providing a more uniform magnetic field and a greater magnetic induction magnitude.

Thus, laboratory NMR experiments have demonstrated a strong correlation between the transverse relaxation time of oil and its rheological properties, in accordance with which a relationship equation has been developed between the average  and the coefficient dynamic viscosity. It was calculated that the coefficient of determination (R² = 0.95) was derived from the equation.

On the basis of NMR-relaxometry data, it is demonstrated that the group composition of oil and condensate samples can be determined, which is supplemented by experimental results carried out on model samples and supported by numerical simulations. In oils and condensates, for example, it has been shown that saturated and aromatic compounds have different relaxation times and that the average  is inversely proportional to the concentration of each compound.

Furthermore, further research is needed in order to improve the accuracy of NMR results through the improvement and development of both the data processing technique based on modern mathematical apparatus, as well as the experimental base, thereby increasing the magnitude and uniformity of the magnetic field.

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