Elastic-Electrical Rock-Physics Template for the Characterization of Tight-Oil Reservoir Rocks

Tight-oil reservoirs have low porosity and permeability, with microcracks, high clay content, and a complex structure resulting in strong heterogeneities and poor connectivity. Thus, it is a challenge to characterize this type of reservoir with a single geophysical methodology. We propose a dual-porosity-clay parallel network to establish an electrical model and the Hashin-Shtrikman and di ﬀ erential e ﬀ ective medium equations to model the elastic properties. Using these two models, we compute the rock properties as a function of saturation, clay content, and total and microcrack porosities. Moreover, a 3D elastic-electrical template, based on resistivity, acoustic impedance, and Poisson ’ s ratio, is built. Well-log data is used to calibrate the template. We collect rock samples and log data (from two wells) from the Songliao Basin (China) and analyze their microstructures by scanning electron microscopy. Then, we study the e ﬀ ects of porosity and clay content on the elastic and electrical properties and obtain a good agreement between the predictions, log interpretation, and actual production reports.

Many studies have been performed on the pore structure and mineral composition of tight-oil rocks [25][26][27][28][29]. In particular, Sun et al. [6] established a pore-network model by using 3D digital cores to simulate the influences of the size, length, and inclination of microcracks. Yan et al. [4] studied physical properties, such as porosity, permeability, pore structure, and wettability, on samples with different saturations, based on nuclear magnetic resonance and imbibition methods. Tan et al. [29] analyzed the tight-oil rock characteristics by utilizing scanning electron microscopic (SEM) and ultrasonic experiments on core samples to construct a brittleness model. By using a single-scattering model and the spectral-ratio method, Ma and Ba [28] estimated the coda and intrinsic attenuation of tight-oil siltstones and analyzed the effects of saturation, pore structure, and mineral content on wave attenuation. In geophysical exploration, the evaluations of tight-oil reservoirs are mainly based on acoustic/elastic data. However, the use of a single technique cannot be enough to characterize these reservoirs [30], and seismic-electromagnetic methods are increasingly applied [31][32][33][34][35][36][37].
Several experimental and theoretical studies have been performed to analyze the relationship between the elastic and electrical properties of porous rocks [31,[38][39][40].
[50] to add pores, microcracks, and clay minerals into the solid mixture. Finally, the Gassmann equation [51] yields the elastic modulus of the saturated rock. These models allow us to analyze how the elastic and electrical properties are affected by water saturation, total and microcrack porosities, and clay content. By combining the two models, a 3D elasticelectrical template is built, and data from core samples and logging curves from two wells of the Songliao Basin are used. The results are then compared with the log interpretation and actual production reports.

Reservoir Characteristics
The reservoirs are located within the Qingshankou Formation in the G area of Songliao Basin, China, which has developed high-quality source rocks with a broad-range distribution and good continuity [52]. The target formation shows high oil saturation, light-oil characteristics, low ratio of movable water, and a thickness of 70-110 m. The porepressure range is 22-32 MPa, and the temperature is around 80°C [27]. The porosity range is 4%-15%, with an average of 8.5%, and the permeability ranges from 0.01 mD to 0.5 mD. The lithology of the reservoirs is dominated by tight siltstones with high clay content.

Lithosphere
The SEM results of core samples are shown in Figure 1. The reservoir storage space mainly includes intergranular and dissolved pores, with clay minerals, mostly illite. The nonconductive minerals (excluding clay) are quartz, feldspar, and small amounts of dolomite and calcite.
We have collected 12 tight-oil rock specimens and performed ultrasonic experiments at in situ conditions (80°C, confining pressure of 50 MPa, and pore pressure of 25 MPa). The samples are collected at a depth of 2200 m (cylinders of 25 mm in diameter and 50-56 mm in length), whose physical properties are given in Table 1. The acoustic wave velocities of oil (kerosene)-saturated and water-saturated states are measured at a frequency of 1 MHz [25,28]. The results are given in Figure 2, showing the velocities as a function of porosity at full water/oil saturation, where the color bar represents clay content. The velocities decrease with increasing clay content and porosity. The P-wave velocities of the oil-and water-saturated samples are similar when the porosity is small. However, they tend to differ as porosity increases. The S-wave velocity is similar in the two cases.
The reservoir resistivity, porosity, and natural gamma values of Well A are obtained from log data. Clay content is determined from the gamma-ray log (see Appendix A). Figure 3 shows the resistivity as a function of clay content and porosity. The rocks have a high clay content, which ranges between 5% and 30%, and the porosity from 5% to 15%. The resistivity decreases with increasing clay content and porosity.

Rock-Physics Models
3.1. Elastic Model. Figure 4 shows the flowchart of the elasticelectrical model. First, we obtain the properties of the mineral mixture with the HS equation (see Appendix B). The stiff pores and soft microcracks are assumed to be spherical and oblate, with aspect ratios of 1 and 0.002, respectively. Then, the DEM theory (Appendix B) is used to add pores and microcracks into the mineral mixture and obtain the properties of the rock frame. Moreover, by using the DEM equation,  3 Lithosphere clay minerals are added to the frame (with an aspect ratio of 0.1).
The fluid properties are reservoir pressure/temperature conditions which are obtained with the equations of Batzle and Wang [53], and an approximate method (see Appendix B) is used to estimate the effective bulk modulus of the fluid mixture [54,55]. Finally, the Gassmann equation yields the properties of the wet rock.

Electrical Model.
Archie [56] assumed a rock without clay and other conductive minerals, so that the rock conductivity only depends on the formation water in the pore space. The Archie equation for sandstone containing only intergranular pores is where F is the formation factor; ϕ is the porosity; m is the porosity exponent; R 0 is the rock resistivity; R w is the resistivity of brine (water); I is the resistivity index, a function of brine saturation, S w ; a and b are lithology coefficients; and n is the saturation exponent. The complex pore structure of reservoir rocks restricts the application of the Archie equation and affects the estimation of the hydrocarbon saturation. Aguilera and Aguilera [48] proposed a dual-porosity model, where the porecontaining matrix is paralleled with the microcracks, to obtain the electrical resistivity (see Appendix C). However, this model does not consider the clay content, which significantly decreases the resistivity (2-6 ohm-m, see [40,45]). We then add the effects of clay and develop a dual-porosity-clay (DPCL) parallel network model, as is shown in Figure 4. The total resistivity R t is where R 0 is the resistivity of the frame (with intergranular pores); ϕ c is the microcrack porosity; R c is the resistivity of the microcracks, which equals R w when the water saturation is 1 ( [48]); V sh is the clay content; and R sh is the resistivity of the clay minerals. It is according to the Archie equation, where ϕ 0 is the matrix porosity,  Figure 4: Flowchart of the elastic-electrical model. 4 Lithosphere which are given in Appendix C. The rock parameters are: a = b = 1, m 0 = m = n = 2, the resistivity of clay is 5 ohm-m, and the resistivity of brine is 0.41 ohm-m (according to [58]). Figure 5 shows the resistivity estimated with the three models as a function of water saturation at two total porosities (3% and 15%), microcrack porosities (1% and 0.01%), and clay contents (10% and 0.1%). The resistivity decreases when these quantities increase, with that of the DPCL model significantly smaller, compared to the other two models, when the microcrack porosity and clay content are high ( Figure 5(a)). In Figure 5(b), as the microcrack porosity and clay content decrease, the difference among the results of the three models becomes smaller, approaching zero when porosity and water saturation increase. All the three models reduce to the classical Archie equation when the microcrack porosity and clay content are set to 0. It can be seen that the resistivity predicted by the DPCL model is strongly affected by the two properties at low water saturation. The model can be applied at high oil saturation. Then, the DPCL model is used to analyze the effects of porosity, microcrack porosity, clay content, and water saturation on the electrical properties of tight-oil rocks. Let us consider full water saturation and a clay content of 5%. By adjusting the content of pores and microcracks, the effects of the total and microcrack porosities can be analyzed. Figure 6(a) shows that the resistivity decreases when the two porosities increase. Next, the total and microcrack porosities are set to 10% and 0.05%, respectively, to analyze the influence of clay content and water saturation (Figure 6(b)). The resistivity decreases if these quantities increase, as expected.

Elastic
Response. In this case, the properties are as follows. The bulk and shear moduli and density of the frame are 43 GPa, 42 GPa, and 2.65 g/cm 3 , and those of the clay minerals are 10.5 GPa, 3.5 GPa, and 2.55 g/cm 3 , respectively. The water bulk modulus is 2.24 GPa, the water density is 1.0016 g/cm 3 , the oil bulk modulus is 1.27 GPa, and the oil density is 0.79 g/cm 3 .

Lithosphere
We consider full water saturation and clay content of 5% to analyze the effects of the total and microcrack porosities on the elastic wave velocities, as shown in Figures 7(a) and  7(b). Similarly, the relation between microcrack porosity, aspect ratio, and density ( [59,60]) is considered to analyze the effects of microcrack density on the elastic responses (see Figures 7(c) and 7(d)). Then, the total and crack porosities are assumed to be 10% and 0.1%, respectively, and the influence of clay content and water saturation is shown in  6 Lithosphere porosities and clay content increase and are slightly affected by saturation, with the S-wave velocity almost independent of the type of fluid.

Electrical Model and Well-Log Data.
We compare the log data of Well A with the model results. Two cases are considered, namely, high resistivity (full oil saturation): a microcrack porosity of 0.01% and a clay resistivity of 6 ohm-m, and low resistivity (full water saturation): a microcrack porosity of 1% and a clay resistivity of 2 ohm-m. We adjust the porosity and clay content and keep the other parameters constant. Figure 8 shows the resistivity for the two cases (upper and lower surfaces), compared to the log data. As can be seen, resistivity decreases with increasing porosity and clay content, and the data (scatters) are all within the intermediate range between the two cases. Then, we assume an oil saturation of 70%, a clay resistivity of 2 ohm-m, and a microcrack porosity accounting for 5% of total porosity, to match the data, as shown in Figure 9, where the agreement is good. Another set of data (Well B) is selected to verify the DPCL model with the same parameters ( Figure 10) and to compare it with the other two electrical models (see Figure 11). The results show that the DPCL model is also consistent with the data of Well B, while the resistivity predicted by the other models is significantly higher. where the microcrack porosities are 0.01% and 0.8% (the range of the data). Figure 12 shows the P-and S-wave velocities as a function of porosity and clay content. The velocities decrease with increasing porosity and clay content, which is consistent with the data.

Elastic
Then, the velocity, porosity, and clay content of Well A are considered. Since the frequencies of the well-log data and ultrasonic are different, there is a difference in velocity (dispersion). Therefore, the model is calibrated with the ultrasonic data and then extrapolated according to the welllog data. According to the reservoir characteristics, we assume 70% oil saturation and microcrack porosities of 0.04% and 1%. The comparison with the log data is shown in Figure 13, where we can see that, similarly to the ultrasonic data, the log (scatters) and model velocities decrease with porosity and clay content.

Elastic-Electrical Template
5.1. Set-Up and Calibration. Next, a 3D elastic-electrical rock-physics template based on resistivity, P-wave impedance, and Poisson's ratio is built. This requires adjusting the total and microcrack porosities and clay content (see the parameters in Table 2). Figure 14 shows the template and log data of Well A. The color bar indicates the porosity (a) and clay content (b), and the black, red, and blue lines are isolines of constant total porosity, microcrack porosity, and clay content, respectively, where the corresponding ranges are given in Table 2. As can be seen, the porosity and clay content of the template are in agreement with the data (scatters). Thus, a quantitative prediction of the reservoir properties can be achieved by overlapping the data on the template.

Results
. We superimpose the elastic and electrical attributes on the 3D template and use a grid searching method to estimate the reservoir properties at Wells A and B. These are assigned to the data by minimizing the sum of squares of the differences between the well-log data and the results provided by the template for the three attributes. Figures 15  and 16 show the results and log interpretation results, where total porosity ranges from 3% to 15%, microcrack porosity from 0.2% to 1.2%, and clay content from 5% to 30%. The porosity and clay content curves of the two wells are basically consistent with the predicted curves.
In the actual reports, the producing depth intervals of Wells A and B are mainly at 2105-2200 m and 2250-2300 m

Conclusions
We have built an elastic/electrical rock-physics template based on electrical resistivity, acoustic impedance, and Poisson's ratio to estimate the properties of tight-oil reservoirs, basically total porosity, microcrack porosity, and clay content. A set of rock samples has been collected and analyzed with scanning electron microscopy and ultrasonic experi-ments. The gamma-ray value has been used to calculate the clay content, and the resistivity has been obtained as a function of porosity and clay content with a novel dual-porosity model. The results show that high clay content is closely related to high electrical conductivity (or low resistivity), as expected. On the other hand, the Hashin-Shtrikman and differential effective medium equations have been used to establish an elastic model and obtain the P-and S-wave    10 Lithosphere velocities. Then, the effects of water saturation, total porosity, microcrack porosity, and clay content on wave velocity and resistivity are analyzed, and the results are compared with ultrasonic and well-log data. The presence of pores and microcracks improves the fluid flow properties, while clay content works in the opposite direction. The template is calibrated with well-log data, and the predictions are compared to log interpretation results and oil production reports of two wells, showing a good agreement. It is shown that the template can effectively be applied to tight-oil reservoirs for the inversion of relevant properties to hydrocarbon exploration.