Predicting oil saturation of tight conglomerate reservoirs via well logs based on reconstructing nuclear magnetic resonance T2 spectrum under completely watered conditions


 Due to complex lithology, strong heterogeneity, low porosity and permeability; resistivity logging faces great challenges in oil saturation prediction of tight conglomerate reservoirs. First, 10 typical core samples were selected to measure and analyse the porosity, permeability, nuclear magnetic resonance (NMR) T2 spectrum and mercury injection capillary pressure (MICP) curve. Second, an empirical method was proposed for reconstructing the NMR T2 spectrum under completely watered conditions using MICP curve based on the ‘three-piece’ power function. The parameters of different models were calibrated via experimental data analysis, respectively. The 180 core experimental data from an MICP curve were used as the input database. Porosity and permeability were regarded as the MICP data selection criteria to apply this model in formation evaluation. The comparison results show good application effects. Finally, to reflect oil saturation, the ratio of T2 geometric means of NMR T2 spectra under oil-bearing and completely watered conditions was proposed. Then, the quantitative relation between oil saturation and the proposed ratio was established via experimental data from the sealed cores, which established a quantitative prediction on oil saturation of tight conglomerate reservoirs. This showed a good application effect. The average relative error and the root mean square error (RMSE) of the predicted oil saturation and sealed coring measurement were around 10 and 3%, respectively. As the proposed method is only influenced by the wettability of reservoir and viscosity of oil, it is not only appropriate for the studied area, but also for other water-wet reservoirs containing light oil. It is important for identifying oil layers, calculating oil saturation and improving log interpretation accuracy in tight conglomerate reservoirs.


Introduction
Reservoir fluid property identification and oil saturation calculation are important contents of formation evaluation via log data. According to resistivity logging and NMR logging, scholars have carried out in-depth studies and have formed a series of achievements.
Previous researches mainly include the qualitative method (fluid property identification) and the quantitative method (oil saturation calculation). The qualitative method is quick and visual. The two most common types are the cross plot method and overlapping method (Zhang et al. 2008). The former develops a cross plot with log data or calculated parameters, then identifies the fluid property according to the distribution characteristics of data points on the cross plot. For example; for resistivity, use a porosity cross plot and for oil saturation, use a porosity cross plot. The latter adopts the log curve or the calculated parameter curve drawn by uniform dimensions and proportions. Then, it overlaps these curves and carries out reservoir fluid property identification according to curve amplitude; for example, double-porosity and three-porosity curve overlapping methods (Zhang et al. 2008). Along with the introduction of NMR logging, the differential spectrum method and shift spectrum method are frequently used in the identification of reservoir fluid properties (Deng 2010;Wang et al. 2016;Sun et al. 2017). With the increasing wide application of Artificial Intelligence in the oil and gas industry, researchers apply the model of an artificial neural network, support vector machine and Bayes decision function for identification of oil and water layers.
Nowadays, most petrophysicists have built quantitative evaluation models for oil saturation prediction besides the qualitative method. The quantitative method can be dated back to the Archie formula proposed in 1942, which is mainly applicable to pure sandstone or sandstone reservoirs with little shale (Archie 1942). On such a basis, Waxman and Smits improved and proposed a kind of resistivity model for shaly sandstones according to additional conductivity of clay (Waxman & Smits 1968). In 1984, Clavier et al. proposed a dual-water model by distinguishing bound water from free water (Clavier et al. 1984). Most quantitative evaluation methods at present are established based on these three methods (Bruce et al. 2004;Herrick & Kennedy 2009;Li et al. 2012;Song et al. 2014;Zhang et al. 2016). Combining mathematical statistics, machine learning and other theories, scholars also developed the following methods: multiparameter identification method, artificial neural network method and multivariate statistics method (Yang et al. 2007;Chen et al. 2010;Dong 2016;Li 2016). The advantage of these methods appears in the more convenient correlation of oil saturation and log data without the necessity for calculating step by step in strict accordance with a theoretical formula.
For the moment, the methods of identifying the oil layer and calculating oil saturation in conventional reservoirs are relatively perfect. However, due to complex lithology, low matrix porosity and strong heterogeneity of tight conglomerate reservoirs, resistivity log response is affected seriously by rock matrix and pore structure, while the effect of fluid property is weak (Chatterjee et al. 2016). It is difficult to identify the reservoir fluid property and predict the oil saturation of tight conglomerate reservoirs (Chen et al. 2010;Zhang et al. 2015). Recently, NMR logs are being applied more and more commonly to fluid analysis and evaluation. Feng et al. (2017a) investigated the relation of oil saturation and NMR log response. Fang et al. (2019) analysed a T 2 spectrum for pore-scale situation evaluation and, in turn, velocity prediction. This paper carries out a study on oil saturation prediction in tight conglomerate reservoirs via NMR logs. First, according to experimental data analysis, an empirical method is proposed to reconstruct the NMR T 2 spectrum under completely watered conditions using the mercury injection capillary pressure (MICP) curve based on the 'three-piece' power function. Here, T 2 means the transverse relaxation time. Second, the T 2 geometric means of T 2 spectra under oil-bearing and completely watered conditions are extracted and the quantitative relation between oil saturation and their ratio is established to predict oil saturation of tight conglomerate reservoirs. Finally, the established method and the model are verified and applied in log data processing and interpretation with good application effect.

Geological background
Junggar Basin is situated in the Xinjiang Uygur Autonomous Region (figure 1a) in Northwest China. It shows a near triangular shape on the topographic map and is 700 km long (E-W) and 370 km wide (S-N). The Basin is high in the east and low in the west with multiple formations of the Carboniferous-Quaternary period deposited, which refers to the Neopaleozoic-Mesozoic and Cenozoic multicycle superimposed basin. The basin evolution experienced three stages: foreland basin, depression basin and regenerated foreland basin. The basin is rich in petroleum, and the studied area refers to the Mahu Foreland Sag in the northwestern margin of Junggar Basin (figure 1b). As shown in figure 1c, the Wuxia fault belt lies in the north of the studied area, Kebai fault belt in the northwest, Zhongguai swell in the southwest, Dabasong swell in the south, Xiayan swell in the east and Luliang swell in the northeast. The structure of the studied area shows a southeast-inclining gentle monocline, with lowamplitude platform, anticline or nose structure developed locally. The target studied area is the Triassic Baikouquan and Permian Urho Formation, where the fan delta mainly develops. The reservoir lithology mainly refers to a conglomerate of varying sizes: generally between 0.5-2 cm and up to about 10 cm at most. Porosity and permeability change greatly. Pore type in the reservoir is classified into interparticle dissolution pore, interparticle dissolution pore, residual interparticle pore and interfacial pore, which refer to the main storage space for oil and gas accumulation.

Experiments
In order to set a better petrophysical model, systematic petrophysical experiments were carried out. First, 10 typical core plunger samples were selected from the target interval of five prospecting and evaluation wells with the lithology of the conglomerate. Second, experiments of helium porosity and air permeability were conducted, and the results showed a large variation range with the mean value of 9.68% and 0.55 × 10 −3 m 2 , respectively. Then, the cores were saturated with formation water and the NMR T 2 spectra under completely watered conditions were measured via a tester manufactured by Oxford Instruments (figure 2). The echo interval and waiting time of the NMR T 2 spectrum measurements were 0.1 ms and 6 s, respectively. The result shows a great difference in the NMR T 2 spectrum of different cores. The T 2 transverse relaxation time is mainly distributed between 0.1 and 1000 ms, while long and short relaxation time peak are, respectively, 10-100 and 1-10 ms. The MICP curves were then measured, as given in figure 3. The results show a great difference, with the threshold pressure varying Mercury saturation (%) Capillary pressure (MPa) from 0.16 to 1.28 MPa. It can be learnt from the comparison that the reservoir physical properties reflected by porosity, permeability, T 2 spectrum and MICP curve are basically consistent.

A method of reconstructing the NMR T 2 spectrum under completely watered conditions using the MICP curve based on the 'three-piece' power function
In the 1990s, petrophysicists began trying to continuously predict capillary pressure curve via NMR logs, so as to realize the pore structure of formation continuously and quantitatively. According to the principle of NMR logging, only an NMR T 2 spectrum under completely watered conditions can completely reflect reservoir pore structure (Ge et al. 2015(Ge et al. , 2018Feng et al. 2016Feng et al. , 2017b, therefore, the MICP curve can be used to reconstruct the spectrum under such conditions. The data in figure 2 accumulated from small to large according to NMR T 2 transverse relaxation time, to construct an accumulation curve close to the MICP curve, which mainly reflects rock pore structure. Next, the water saturation is fixed. Under the premise of not changing the curve  shape, the pressure value of the MICP curve and the T 2 value of the NMR T 2 spectrum accumulation curve are unified to fixed water saturation via interpolation. It is discovered that the T 2 value and the reciprocal of mercury injection pressure present the 'three-piece' feature on the log-log coordinate (figure 4). In combination with the lithologic characteristics of conglomerate, a long relaxation time section exhibits the properties between large gravel, sand and cement in conglomerate reservoirs. A medium relaxation time section exhibits the properties between medium-small gravel and fine silt, while a short relaxation time part exhibits the properties between fine silt and cement (figure 5).
Based on the model proposed by He et al. and the above piecewise characteristics (He et al. 2005), a method of reconstructing an NMR T 2 spectrum under completely watered conditions using the MICP curve based on a 'threepiece' power function is proposed. It is known from the NMR logging principle that the NMR T 2 time can be calculated as follows without the influence of diffusion relaxation (Deng 2010): where T 2 refers to the transverse relaxation time, in ms; T 2B refers to the bulk relaxation time of fluid, in ms; 2 refers to the surface relaxation strength of rock, in m ms −1 ; S refers to the pore surface area of rock, in cm 2 and V refers to the pore bulk of rock, in cm 3 . The specific surface of rock pore is related to the pore structure. When a spherical or columnar simplified pore structure is applied, the specific surface is in linear relation to the pore diameter. Due to the extremely complex pore structure in tight conglomerate reservoirs, the specific surface is in non-linear relation to the pore diameter. Moreover, T 2B >> T 2 . So equation (1) can be simplified into: where r c refers to the pore radius, in m and f(r c ) refers to the non-linear function when r c is an independent variable. The relation between pore throat radius and capillary pressure is written as follows: where refers to contact angle of the fluid in the wetting phase and the rock surface,°, refers to the surface tension of two fluids, dyn cm −1 and P c refers to the capillary pressure, dyn cm −2 . From these equations, the relation between T 2 and P c can be inferred as follows: where g(1/P c ) refers to the non-linear function when 1/P c is an independent variable. As shown in figure 4, through experimental analysis, it is considered that g(1/P c ) is the power function and the coefficients of the three in large, medium and small pores are different, so equation (4) can be expressed as: where m i and n i refer to the model coefficients with different pore types.

Predicting oil saturation quantitatively based on the ratio of the NMR T 2 geometric means of the T 2 distributions under oil-bearing and completely watered conditions
In the studied area, the conglomerate reservoir shows the water-wet property via a geological background and core sample observation. According to NMR logging principle, the NMR T 2 spectrum under completely watered condition refers to the surface relaxation characteristics of water, reflecting the pore structure of reservoir. When the conglomerate reservoir is saturated with oil, the short relaxation time part of the NMR T 2 spectrum measured refers to the surface relaxation characteristics of water. It reflects the pore structure of bound water part, while the long relaxation time part refers to the bulk relaxation characteristics of oil. Hence, two crude oil (light oil) samples were collected for NMR measurements. Their viscosity are 5.13 mPa.s and 6.64 mPa.s at 80°C. The measured bulk relaxation of oil samples are presented in figure 6. The peaks of the distributions are about 500 ms. They have big differences compared with the surface relaxation of water in figure 2.
To sum up, it can be concluded that the measured NMR T 2 spectrum shows an obvious difference when the reservoir is full of water and saturated with oil. They basically coincide in the short relaxation time part and show obvious differences in long relaxation time part. Thus, it shows that the differences of the NMR T 2 spectra of conglomerate reservoir under completely watered conditions and oil-saturated conditions can be used to identify the fluid property.
The above theoretical analysis can be used to identify oil and water layers of the conglomerate reservoirs, but cannot determine their oil saturation. Therefore, it is necessary to build a model for predicting oil saturation in a quantitative way. The difference between the two NMR T 2 spectra can be reflected in a quantitative way by extracting the ratio of geometric means of the NMR T 2 spectra under oil-bearing and completely watered conditions. As it is shown in figure 3, the maximum of the mercury injection saturation can be almost 80%, indicating that the reconstructing T 2 spectra are incomplete and only have the right part compared with the measured ones ( figure 11). Therefore, the reconstructing T 2 spectra and the corresponding part of the NMR T 2 spectra under completely watered conditions are used to calculate the T 2lm_o and T 2lm_w , which is defined as follows: where T 2lm_o refers to the T 2 geometric mean of NMR T 2 spectrum under oil-bearing conditions in ms; T 2lm_w refers to the T 2 geometric mean of NMR T 2 spectrum under completely watered conditions in ms and refers to the ratio of T 2 geometric means under different conditions. It can be seen from this theoretical analysis that when oil saturation is larger, the T 2 geometric mean of NMR T 2 spectrum under oil-bearing condition increases, which means that the ratio of T 2 geometric means grows. Hence, the ratio of T 2 geometric means should have a positive correlation relation to the oil saturation of the reservoir. Then the relation is established based on the measured oil saturation and T 2 geometric mean of sealed cores, as shown in equation (7): where, S o refers to the oil saturation in % and t( ) refers to the function with as an independent variable, either a linear or non-linear function.
After the parameter in the function t( ) in equation (7) is obtained by regression, the new empirical model is built for predicting oil saturation based on the ratio of NMR T 2 geometric means.

Model parameter calibration
In the studied area, the experimental data on T 2 spectra and MICP curves of the 10 cores are used for modelling. First, the amplitude in NMR T 2 spectrum experiment data is reversely accumulated based on the sequence from high to low of T 2 value. Then, under the premise of not changing the curve shape, the pressure value of the MICP curve and the T 2 value of the NMR T 2 spectrum accumulation curve are unified to fixed water saturation via interpolation, which is used to build the cross plot of NMR T 2 transverse relaxation time and mercury injection pressure under fixed water saturation, as shown in figure 7. Based on the multivariate statistics regression model; the m and n parameters of large, medium and small pore models can be acquired with high correlation coefficients. The classification standards of the large, medium and small pores are higher than 0.184, 0.011-0.184 and lower than 0.011 m, respectively. And the correlation between T 2 relaxation time and mercury injection pressure is also established.
The MICP curve data serving as the input in the model are from the experiment rather than continuous log data. Hence, the experimental data on the MICP curve of 180 cores in the studied area are collected to ensure better application of the model in actual formation evaluation, as shown in figure 8. Therein, the variation ranges of porosity, permeability, composite physical property index (the square root of the ratio between permeability and porosity) and medium radius are 3.3-17.4%, 0.029 × 10 −3 -127 × 10 −3 m 2 , 0.083-4.613 and 0.0013-0.610 m, respectively. Their distributions are presented in figures 9 and 10. By using the porosity, permeability and composite physical property index as the selection criteria, the corresponding MICP curve is substituted into equation (5) and Table 1 to acquire the porosity component under the corresponding T 2 transverse relaxation time. Then it is converted into a curve to obtain the reconstructed NMR T 2 spectrum under completely watered conditions.

Verification of the NMR T 2 spectrum prediction model
The experimental data of the MICP curve of another two conglomerate cores are substituted into equation (5) and Table 1 for comparative analysis between the predicted and the experimental results. As shown in figure 11, figure 11a presents the experimental data of the MICP curve of the two cores (V1 and V2). The blue delta and red circle in figure 11b and figure 11c, respectively, refer to the predicted NMR T 2 spectra and the corresponding experimental results. It can be seen from figure 11 that the NMR T 2 spectra reconstructed show a good consistency with the corresponding experimental results, except that T 2 time bears a large error at around 10 ms, the remaining part of the two shares a high coincidence degree. It indicates that the method of reconstructing the NMR T 2 spectrum under completely watered conditions using the MICP curve based on the 'three-piece' power function is reliable.

Building the oil saturation prediction model
To ensure a good application of the oil saturation prediction model proposed in an actual formation evaluation, sealed coring experimental data are selected as the basis to build and calibrate the model and parameters in equation (7). Based on the sealed coring experimental data of three wells, equation (5) and the model built in Table 1 are used to reconstruct the NMR T 2 spectrum under completely watered conditions. Further, the T 2 geometric means of the reconstructed NMR T 2 spectrum and the corresponding NMR log data are extracted. The used log data are acquired from MRIL-P logging, whose echo interval and waiting time are 0.9 ms and 13 s, respectively. Finally, the oil saturation measured through sealed coring and the ratio of the T 2 geometric means is used to draw the scatter plot, as shown in figure 12. It is discovered from the analysis of figure 12 that the two bear good relevance. The model of predicting the oil saturation by using the ratio of T 2 geometric means through statistical regression is given in equation (8). The correlation coefficient of linear fitting is 0.82, indicating high reliability of the model.

Verification of the oil saturation prediction model
The sealed coring interval of the well that is not used in modelling is selected to test the oil saturation prediction model. First, the method is used to reconstruct NMR T 2 spectrum under completely watered conditions. Then the T 2 geometric means in the reconstructed NMR T 2 spectrum and corresponding NMR log data are extracted. This is substituted into equations (6) and (8) to calculate the oil saturation of the sealed cores. The comparison between the predicted oil saturation and the oil saturation measured by the sealed coring experiment is presented in figure 13. It can be seen from the figure that the x-and y-axes, respectively, refer to the oil saturation measured by the experiment and the one predicted. The data points are distributed near the diagonal with the mean relative error and root mean square error (RMSE) around 10 and 3%, respectively, indicating high reliability of the oil saturation prediction model.

Application of the models
In the process of log data processing and interpretation, the porosity and permeability of the reservoir are calculated first. According to them, the corresponding capillary pressure curves are selected from the experimental database of Figure 14. A field study of tight conglomerate reservoirs of Well A in the studied area.
the MICP curve (figure 8). The MICP curves are converted into the NMR T 2 spectrum under completely watered conditions by applying equation (5) and the models in Table 1. Then, the NMR log data and the reconstructed NMR T 2 spectrum are compared. If the two bear little difference or are identical, it indicates that the corresponding formation is filled with water. A great difference in large porosity part of the two would reflect that the corresponding formation is either the oil layer or the oil-water layer. In this way, it is possible to identify whether there are oil and gas shown in tight conglomerate reservoirs. Finally, the T 2 geometric means of the corresponding NMR log data and the reconstructed NMR T 2 spectrum are extracted, which are then substituted into equation (8) to calculate the oil saturation.
For verifying whether the model built is suitable for popularization and application, the actual log data are processed and interpreted. Figure 14 presents the resulting plot of the log data processing and interpretation results of Well A in the studied area. The first three lines refer to the conventional log curves, and the fifth to the tenth lines refer to the porosity, permeability, MICP curve, NMR T 2 spectrum, and oil saturation, respectively. The red and green NMR T 2 spectra in the line eight are the measured and predicted T 2 spectra, respectively. The black curves and red dots in the tenth line are the predicted and the measured oil saturation, respectively. It can be directly seen from the plot that there is an obvious difference in the long relaxation time part of the predicted NMR T 2 spectra under completely watered 9 conditions and the NMR log data, indicating that the reservoir of that interval is an oil layer. Also, the oil saturation calculated by the ratio of T 2 geometric means coincides well with the result of sealed coring experiments with a slight error.
Based on the verification of core and formation evaluation effects, it is clear that the NMR T 2 spectrum prediction method and oil saturation prediction method are highly reliable and they can be applied well in tight conglomerate reservoirs. As the proposed method is only influenced by the wettability of reservoir and viscosity of oil, it is not only appropriate for the studied area, but also other water-wet reservoirs containing light oil. Hence, they can be propagable too.

Conclusions
Through the comparative analysis of the experimental data of T 2 distribution and MICP curve of tight conglomerate cores, a method is proposed of reconstructing the NMR T 2 spectrum under completely watered conditions using the MICP curve based on the 'three-piece' power function. The jointly measured experimental data are used for parameter calibration. The 180 measured MICP curves are used as the input database. The porosity and permeability are regarded as the MICP data selection criteria to apply this model in formation evaluation. Then, the reconstructed NMR T 2 spectrum and NMR log result are compared to identify oil layers. On such a basis, the T 2 geometric means of NMR T 2 spectra under oil-bearing and completely watered conditions are extracted. The quantitative relation is established between the ratio of the two and the oil saturation measured by a sealed coring experiment for the quantitative prediction of oil saturation of tight conglomerate reservoirs. The model is verified by the core experimental data to prove high reliability and favourable application effects. As the proposed method is only influenced by the wettability of reservoir and viscosity of oil, it is not only appropriate for the studied area, but also other water-wet reservoirs containing light oil. It is important to identify oil layers, to calculate oil saturation and to improve log interpretation accuracy in tight conglomerate reservoirs.