Permeability Data Treatment from Analogous Outcrop for use in Three-Dimensional Reservoir Model

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Introduction
Modeling the petrophysics properties of oil reservoirs is one of the key stages for a successful production decision tree since those models allow better selection of the position of new wells, getting more efficient strategies to enhance the production rates, and to plain the best logistics of all production equipment installation.Direct data, like sidewall samples and well-core samples, have high costs and low accuracy due to the lithological and structural variability usually found in natural geological conditions.So, a practice frequently used by the industry to improve the efficiency of reservoir simulation predictions is the study of analogous outcrops.This type of study makes it possible to acquire a significant amount of information from specific geological aspects equivalent to those found in subsurface reservoirs, directly and with lower costs.This approach favors the establishment of the three-dimensional sedimentary facies distribution and their relationships in the depositional system, and the tectonic structures framework on subseismic scales (Howell, Martinius & Good 2014).
The use of analogous outcrops also helps to understand the relationship between rocks and their porosity and permeability properties.However, these parameters may suffer significant value variations when the rocks are submitted to subsurface confining pressures, or when the outcrops are under unconfined pressure conditions.When rocks are buried, the porosity and permeability values tend to decrease due to the material compaction, whereas when the rocks are at the surface, or near it, these properties are closer to the original values.Concerning this question, it becomes essential to evaluate how measurements obtained in outcrops can be used in a geological reservoir model.
In this study, we present a proposal for a method to turn compatible the permeability values obtained in an outcrop to the permeability values at a confined pressure equivalent to Maastrichtian reservoir found in the Southeastern Brazilian marginal basin, estimated at 2,000 psi.

Geological Setting
The outcrop investigated in this study is in the Volta Redonda Basin (Figure 1), which is the smallest of the Cenozoic basins in the Central Segment of the Continental Rift of Southeastern Brazil (Negrão et al. 2015;Negrão et al. 2020;Riccomini, Sant'anna & Ferrari 2004;Sanson 2006).
According to Negrão et al. (2020), the main stratigraphic unit of the Volta Redonda Basin is the Resende Formation (Eocene), which is composed of lenticular to tabular intervals of poorly consolidated stratified feldspathic sandstones, interbedded with fine conglomerates and greenish mudstones.These deposits are related to the sedimentation in braided rivers and alluvial fans during the rift formation.Alkaline ultrabasic volcanic rocks (Casa de Pedra Basanite) are also associated with the rift phase.Oligocene braided fluvial deposits form the Pinheiral Formation, in an erosive contact over the Resende Formation e Casa de Pedra Basanite.Above the Paleogene units, there are Quaternary colluvial and alluvial deposits.
The Volta Redonda Basin evolved in the context of the Continental Rift of Southeastern Brazil (RCSB -Riccomini 1989; Riccomini et al. 2004), in which five tectonics events are identified: Paleogene NW-SE extension (E1) -rift phase; Miocene E-W sinistral strike-slip event (ST); Pleistocene E-W dextral strike-slip event (DT); Holocene NW-SE extension (E2); and the modern E-W compression (C).
The studied outcrop is approximately 18 m high and 54 m long, and it is subdivided into two slopes (lower and upper) separated by a berm (Figure 2).The outcrop is predominantly composed of deposits of the Resende Formation.At the upper part of the outcrop, there is a small and quite weathered exposure of Pinheiral Formation deposits.Two normal faults ("F1" and "F2") with ENE-WSW orientation and opposite dips split the outcrop into three main sectors (north, central, and south -Maciel, Mello & Silva 2017).Other secondary faults also occur through the outcrop and deformation band zones are concentrated at the south sector.The main faults and the deformation  band zones are associated with the strike-slip events and were reactivated during the E2 event; and the secondary faults present in the central sector are related to the E2 event (Fiuza, Mello & Ribeiro 2020;Maciel, Mello & Silva 2017).

Materials and Methods
The main dataset analyzed in the present study comprises more than 5,000 in-situ permeability measurements collected by Galvão (2018) and Andrade (2020) on the studied outcrop using a TinyPerm3 mini-permeameter.These data include permeability measurements in three orthogonal directions (two horizontal and one vertical).Horizontal readings were obtained parallel and perpendicular to the main faults (F1 and F2).Data acquisition was guided by a regular 2x2 m grid along the outcrop, which also served as the basis for the representation of the sedimentary layers and tectonic structures (deformation bands and faults) in a geological section at a scale of 1:50 (Mello et al. 2021; Figure 3).Galvão (2018) and Andrade (2020) collected more than 10 permeability readings in each orthogonal direction by each cell grid to guarantee the best accuracy of the mean value calculated for each direction.
Another dataset here analyzed corresponds to porosity and permeability measurements obtained in the laboratory.These measurements were carried out by Galvão (2018), Vogel (2018), and Mello et al. (2021) from plugs extracted from the rock blocks collected at the outcrop.
The in-situ permeability values from previous studies (Galvão 2018; Andrade 2020) needed to be statistically processed to adjust the results from the unconfined pressure conditions to the confined pressure found in reservoir conditions.
The first stage of the statistical processing (Figure 4) was the calculation of the geometric mean for each permeability direction (i.e., vertical, parallel, and perpendicular) on each cell grid (Table 1).The geometric mean was adopted because it is the calculation modality most used in the petroleum industry, applied in cases where permeability changes smoothly (Liao 2018).The next step was to transform the geometric mean values to pressure conditions equivalent to 2,000 psi.For this, regression curves were made using the permeability data acquired in the laboratory by Galvão (2018) and Mello et al. (2021) for a set of samples submitted to different confinement pressures (500; 1,000; 1,500; 2,000 psi; Table 2) to achieve an estimated permeability at 0 psi.Following, a new regression curve was built using the estimated permeability values at 0 psi in relation to the permeability values at 2,000 psi, for each sample.The resulting equation was applied to the geometric mean values at 0 psi permeability dataset to obtain the geometric mean values at 2,000 psi.

Results
The geometric mean values of the in-situ permeability data collected by Andrade (2020) for different lithologies allow to classify them into reservoir facies, considering their order of magnitude variability (Table 3).This way, claystone and siltstone can be grouped as non-reservoir, fine sandstone and muddy sandstone as poor reservoir, and medium to coarse sandstone, conglomerate and intraformational breccia as good reservoir.The geometric mean values of the insitu measurements done for each cell grid are presented in Figure 5.The geometric mean for each reservoir facies versus the dispersion of the in-situ permeability values is shown in Figure 6.
The regression curves obtained to estimate the in-situ permeability at 0 psi using the permeability values of the samples analyzed in the laboratory at different confining pressures (500, 1,000, 1,500 and 2,000 psi -Figure 7) show coefficient of determination values greater than 0.92, indicating that the models have an excellent fit, as presented in Table 4.The values estimated at 0 psi with the regression curve for each sample showed results with the same order of magnitude as the geometric mean of the in situ permeability measurements obtained by Andrade (2020) in each corresponding cell grid.
The regression function obtained from the correlation between the measured permeability values at a confinement pressure of 2,000 psi and the estimated permeability values at 0 psi for all samples (Equation 1) presented a coefficient of determination (R 2 ) equal to 0,7985 (Figure 8).Although this coefficient of determination is lower than the ones obtained in the previous methodological step, it still presents good reliability to be applied for the conversion of the in-situ permeability dataset to the confined permeability at 2,000 psi.     Figure 7 Example of the regression curve used to estimate the in-situ permeability at 0 psi using the permeability data analyzed in the laboratory at different confining pressures.These graphs were done for the 11 samples listed in Table 2.    4.
Considering this reliability, Equation 1 was applied to convert the geometric mean permeability values at 0 psi (Figure 5) to geometric mean permeability values at 2,000 psi, as presented in Figure 9. Analyzing the dataset obtained it is possible to observe that the permeability values have a 25-39% loss when adjusted from 0 to 2,000 psi, reducing the order of the magnitude as expected (Figure 10, Table 5).The lowest reduction in permeability values was observed in the non-reservoir lithologies but with higher variability (25-33%).The poor and good reservoir facies showed a major reduction in permeability values with minor variability (34-39%).It is observed that there is a subtle change in the distribution of the pattern of the permeability values, which can be attributed to the change in the threshold values of each class in the histogram.

Conclusion
The goal of this study was to develop a method to make the permeability values collected in an outcrop compatible with confining pressure conditions equivalent to real reservoirs in the subsurface.
The results obtained produced a reliable equation for converting permeability values from the surface condition (@0 psi) to a usual confining pressure condition for important Maastrichtian reservoirs of the Brazilian Southeastern Margin (@2,000 psi).In addition, the application of this method to the database obtained for the Resende Formation outcrop studied in the Volta Redonda basin (RJ), with 5,000 in-situ permeability measurements, demonstrated how significant the reduction of permeability values can be in poorly consolidated sandstone reservoirs when they are under subsurface conditions.Furthermore, the permeability variation is enhanced by textural aspects and deformational structures (faults and deformation bands) present in the outcrop.This variation affects the fluid flow through a real reservoir, on which the previous knowledge is an important subsidy for planning production strategies.
The method proposed in this study can be applied in the oil industry and produce a new adjusted database.The results obtained show that it is possible to use the outcrop data in the same conditions of the analogous reservoir, and then apply the measurements in the geological model to fill the lack of information, reducing the uncertainty on these models and allowing better production management.
Based on the results achieved, a model analogous to poorly consolidated and tectonically deformed sandstone reservoirs will be built using the outcrop stratigraphical and structural characterization.This model will be filled with permeability data converted to depth conditions to carry out 3D flow simulations.

Figure 1
Figure 1 Map of the Cenozoic sedimentary units of the Volta Redonda Basin over the relief shading model, emphasizing the strong control of the distribution of Paleogene deposits by NE-SW structures and, subordinately, NW-SE structures.The yellow star indicates the location of the studied outcrop.Modified from Negrão et al. (2015).

Figure 2
Figure 2 General aspects of the studied outcrop, showing the main lithologic contacts and the major tectonic structures: A. Deformation bands in the south sector; B. Ferruginized plane of Fault F1; C. Clay smear on Fault F2.

Figure 5
Figure 5 Geometric mean values of the permeability raw data collected by Andrade (2020) for each cell grid, according to Figure 3.

Figure 6
Figure 6 Frequency histogram for each permeability direction at 0 psi, grouped by reservoir facies.The red dot represents the geometric mean for each reservoir facies.

Figure 8
Figure 8 Estimated permeability at 0 psi versus measured permeability at 2,000 psi based on the samples presented in Table4.

Figure 9
Figure 9 Geometric mean values of the permeability raw data collected by Andrade (2020) for each cell grid, according to Figure 3, converted to confinement pressure at 2,000 psi.

Figure 10
Figure 10Frequency histogram for each permeability direction converted to confinement pressure at 2,000 psi, grouped by reservoir facies.The red dot represents the geometric mean for each reservoir facies.

Table 3
Geometric mean values of the permeabilities at 0 psi separated by lithology.

Table 4
Estimated permeability values at 0 psi after applying the respective regression function for each sample analyzed.

Table 5
Geometric mean values of the permeabilities at 0 and 2,000 psi separated by lithology.