# A new approach to reduce uncertainty in reservoir characterization using saturation height modeling, Mesaverde tight gas sandstones, western US basins

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## Abstract

Tight gas sandstone (TGS) reservoirs are one of the most integral parts of the unconventional reservoirs pyramid. Uncertainty in petrophysical properties of a TGS reservoir will cause great challenges in reservoir characterization and also 3D properties modeling. The main goal of this study is to implement a new workflow based on saturation height modeling (SHM) to reduce this uncertainty in a TGS reservoir by acquiring a global in situ water saturation function and also calculating more accurate permeability values. Capillary pressure curves and well logs from ten different wells in four different giant basins of western US TGS reservoirs are the input data in this study. After grouping the capillary pressure curves based on the corresponding cores sorting, size, and texture, and also applying some initial corrections, five different SHM methods have been applied to each group. Using regression methods, the function of each model has been rewritten based on the cores’ petrophysical properties. By entering the porosity and permeability logs of each well in the rewritten functions and by implementing the height above free water level (HAFWL), a water saturation profile has been calculated for each well. Using standard error of estimate analysis between the calculated water saturation profile and the log-based water saturation profile as the base one, the most reliable SHM method has been recognized. Using water saturation and porosity logs and also HAFWL value in each well, accurate permeability values have been calculated based on the saturation height function of the best model. Finally, the regression method between the calculated permeability and the accurate cores permeability values approves the reliability of the results.

## Keywords

SHM MICP Permeability In situ water saturation## List of symbols

- \((P_{\mathrm{c}})_{\mathrm{stress}\text{-}{\mathrm{corr}}}\)
Stress-corrected capillary pressure (psi)

- \((P_{\mathrm{c}})_{\mathrm{lab}}\)
Laboratory capillary pressure (psi)

- \(\phi _{\mathrm{res}}\)
Core porosity at reservoir conditions, fraction

- \(\phi _{\mathrm{lab}}\)
Core porosity at laboratory conditions, fraction

- \(\sigma\)
Interfacial tension (dyne/cm)

- \(\theta\)
Contact angle \((^{\circ })\)

- \(S_{\mathrm{w}}\)
Water saturation, fraction

- \(S_{\mathrm{wirr}}\)
Irreducible water saturation, fraction

- K
Permeability (mD)

## Introduction

Although the conventional hydrocarbon reservoirs are playing the most important role in meeting the energy demand of the today’s world, this role will be degraded in a few next decades because of dramatic development of unconventional reservoirs. Unconventional reservoirs include: coal bed methane (CBM), oil shale, tight gas sandstone (TGS), organic-rich shale, and also hydrates. TGS reservoirs are one of the most integral parts of the unconventional reservoirs pyramid. According to the United States government gas policy in the 1970s, a tight gas reservoir is one with gas flow permeability less than 0.1 mD. This definition is only based on a governmental tax decision. “The best definition of tight gas reservoir is a reservoir that cannot be produced at economic flow rates nor recover economic volumes of natural gas unless the well is stimulated by a large hydraulic fracture treatment or produced by use of a horizontal wellbore or multilateral wellbores” (Holditch 2006).

Permeability and in situ water saturation values are essential data for reservoir characterization and also 3D properties modeling. Using saturation height modeling (SHM), it is possible to calculate permeability more precisely and predict in situ water saturation based on petrophysical properties. In this study, different saturation height models have been applied on Mesaverde TGS reservoirs which are one of the most important parts of unconventional gas reservoirs in western US basins. The input data include some parts of core analysis and well logs from ten different wells in four different basins including: Washakie, Uinta, Piceance, and Upper Greater Green River (Byrnes et al. 2008). The main goal of this study is to implement a new workflow based on SHM to reduce the uncertainty in reservoir characterization of such a vast area with four giant basins by acquiring a global in situ water saturation function and also computing the permeability values in a more accurate way. Uncertainty reduction in 3D properties modeling could be another advantage of this workflow.

## Method and theory

### Capillary pressure data classification

There are three main methods for measuring the capillary pressure curve of a core: Porous Plate, Centrifugal, and Mercury Injection Capillary Pressure (MICP) method. In comparison to the other methods, the MICP method is more common in petroleum industry because of its rapidness and low measurement costs (Dandekar 2013). Capillary pressure curves in this study are based on air-mercury MICP measurements in which the air is the wetting phase and the mercury is the nonwetting phase, respectively (Byrnes et al. 2008). According to the laboratory analysis, the corresponding cores of the MICP data in this study could be classified into four groups based on their size, sorting, and texture:

Group 1: Moderately shaly sandstones with 10–40% clay and silt (12 cores)

Group 2: Very fine sandstones (6 cores)

Group 3: Fine sandstones (11 cores)

Group 4: Medium sandstones (17 cores)

Grouping the MICP curves using this classification could increase the SHM accuracy.

### Capillary pressure data correction

It is obvious that only a corrected input data can lead us to the desirable goals from SHM. Therefore, four corrections have been applied to the MICP curves subsequently.

#### Out of trend data elimination

#### Closure correction

#### Stress correction

#### Conversion to reservoir fluid conditions

### Applying different saturation height models

“A saturation height model is an equation that represents the water saturation profile in a reservoir interval as a function of the fluid/rock properties and the distance above the Free Water Level (FWL) and is constructed from capillary pressure data” (Valentini et al. 2017). There are many Saturation Height Models with specific fitting parameters which are in use in petroleum industry. To predict the in situ water saturation in an un-cored depth of a reservoir, it is crucial to generalize these models. This generalization is possible using regression methods between fitting parameters of a model and cores’ petrophysical properties (like porosity, permeability, and also square root of permeability/porosity). In this study, we applied five important Saturation Height Models on each of the groups.

#### Brooks–Corey (Brooks and Corey 1964)

*N*:

*K*, and also \(\sqrt{\frac{K}{\phi }}\)) have been investigated using regression methods. The \(S_{\mathrm{wirr}}\) has been set to zero as a numerical artifact. Finally, and in part (c), rewriting Eq. 3 based on regression results, it is possible to calculate the capillary pressure curves using the petrophysical properties (red color curves).

#### Leverett-J (Leverett et al. 1941)

*a*and

*b*are the fitting parameters of the model. Figure 6 represents the capillary pressure curves of the group 3 (in gray color) and also their approximation after applying the Leverett-J model.

#### Skelt–Harrison (Skelt et al. 1995)

*A*,

*B*,

*C*, and

*D*are the parameters of the model, and

*h*is HAFWL in meter.

#### Lambda (Wiltgen et al. 2003)

*A*,

*B*, and \(\lambda\) are the parameters of the model, and

*h*is HAFWL in meter.

#### Thomeer (Thomeer et al. 1960)

By plotting each of the constants of a specific SHM equation versus porosity, permeability, and square root of permeability/porosity and also using regression methods, it is possible to rewrite the equation as a function of the mentioned petrophysical properties.

### Acquiring a global in situ water saturation function

*g*is the gravitational constant.

Water saturation SEE values of medium sandstone intervals of a well in the Washakie basin (based on the group 4 models)

Model | SEE |
---|---|

Brooks–Corey | 0.196 |

Lambda | 0.213 |

Skelt–Harrison | 0.208 |

Leverett-J | 0.349 |

Thomeer | 0.205 |

### Calculating accurate permeability values using SHM

## Conclusions

Uncertain petrophysical properties can cause fundamental problems in unconventional reservoir characterization and also 3D properties modeling. Reducing this uncertainty by implementing a new workflow based on saturation height modeling is the main goal of this study. Capillary pressure curves and well logs from ten different wells in four different giant basins of western US tight gas sandstone reservoirs are the input data in this study. The capillary pressure curves have been classified based on cores sorting, size, and texture. After correcting the curves in four subsequent steps, five different saturation height models have been applied on each class: Brooks–Corey, Lambda, Skelt–Harrison, Leverett-J, and Thomeer. Using regression methods, the function of each model has been rewritten based on the cores petrophysical properties. A water saturation profile has been calculated for each well by entering its porosity and permeability logs in the rewritten functions and also using HAFWL values. After employing the SEE analysis to compare the log-based with the calculated water saturation profiles, the Brooks–Corey has been recognized as the most accurate model. Finally, precise permeability values have been calculated for each well by entering its porosity and water saturation logs and also HAFWL values in the Brooks–Corey saturation height function of each group. The accuracy of the results has been approved by high coefficient of determination \((R^{2})\) between the calculated and the cores’ permeability values.

## Notes

### Acknowledgements

The authors would like to thank Universiti Teknologi Malaysia (UTM) for its financial supports.

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## Copyright information

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