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Unconventional hydrocarbon reserves substantially surpass those of conventional resources and therefore are extremely economically attractive. However, exploration and production of uncon-ventional reserves is challenging. This paper demonstrates that one can observe significant induced polarization effects in shale reservoir rocks, which can be used in exploration for unconventional reserves. The generalized effective-medium theory of induced polarization (GEMTIP) was used to model the complex resistivity of shale rocks. We demonstrate that GEMTIP modeling provides an evaluation of mineral composition and volume fractions in rock samples. We have conducted spectral induced polarization (IP) measurements using different types of shale rocks to test the feasibility of the IP method and GEMTIP modeling for studying unconventional hydrocarbon (HC) reservoir rocks.

The development of innovative methods for discovering and monitoring of unconventional reserves represents an important task of geophysics. This paper investigates the possibility of using the IP effect in studying the unconventional reservoir rocks, e.g., oil- and gas-shale and tight sands. We demonstrate that, one can observe significant induced polarization (IP) effects in shale reservoir rocks, which can be used in exploration for unconventional reserves.

The IP method is used in different geological applications: mineral exploration [

Shale rocks with a percentage of total organic carbon (TOC) above 3% are usually considered as organic-rich shales. These shales may be deposited over a wide range of depositional environments ranging from terrestrial to marine. They may have a wide geographic distribution, and they occur in sediments of all ages, from modern to Precambrian. The geochemical variations within black shales may reflect depositional conditions, including water-column conditions and those within the sediment, sediment provenance, variations in the source of organic matter, diagenetic alteration including hydrothermal alteration, and even weathering processes [

This study is based on application of the generalized effective medium theory of induced polarization (GEMTIP) to the analysis of the complex resistivity (CR) of oil- and gas-shale rocks. GEMTIP modeling provides a basis for remote petrophysical analysis of shale rocks, which we compare with actual structural analysis of shale rocks using a Quantitative Evaluation of Minerals by Scanning Electron Microscopy (QEMSCan) and core analysis. Based on this analysis we have found that, GEMTIP modeling provides a useful evaluation of the mineral composition and volume fractions in the shale rock samples.

Over the last 40 years several resistivity relaxation models have been developed, which provided quantitative characterization of the electric charging phenomena, including the empirical Cole-Cole model [

One of the most widely used models is the Cole-Cole resistivity relaxation model introduced in the pioneering work of Pelton et al. [

where

We should note that, the Cole-Cole model uses empirical parameters, while the GEMTIP model uses the effective medium theory to describe the complex resistivity of heterogeneous rocks. At the same time, it was shown by Zhdanov [

In the framework of the GEMTIP model, we represent a complex heterogeneous rock formation as a composite model formed by a homogeneous host medium of a volume V with a complex conductivity tensor ^{th} grain type having complex tensor conductivity^{th} type have a volume fraction f_{l} in the medium and a particular shape and orientation. Following [

where ^{th} type. The last formula provides a general solution of the effective conductivity problem for an arbitrary multiphase composite polarized medium. This formula allows us to find the effective conductivity for inclusions with arbitrary shape and electrical properties. That is why the new composite geoelectrical model of the IP effect may be used to construct the effective conductivity for realistic rock formations typical for mineralization zones and/or HC reservoirs.

For this study, we have developed the three-phase ellipsoidal GEMTIP model for a medium with randomly oriented ellipsoidal inclusions. The expression for GEMTIP model in this case takes the following form:

where

The _{l}. If all the grains are oriented in one specific direction, the effective conductivity of this medium will become anisotropic. Thus, the effective conductivity may be a tensor in spite of the fact that the background medium and all the grains are electrically isotropic.

The terms “two-phase” and “three-phase” model are related to structural model, which is characterized by one type of inclusions in the host medium or two types of inclusions, respectively. In the first case, for example, we may have pyrite in the host rock, while in the second case we may have the pyrite grains and pores in the host reservoir rock. The classic Cole-Cole model corresponds to a two-phase system with the host rock and one type of grains (e.g. pyrite). Equation (3) describes a three-phase model, which represents the host rock and two types of inclusions—grains of pyrite and pores filled with HC. Note that,a three-phase Cole-Cole model [

GEMTIP model, Equation (3), can be formed by more than three phases as well. The exact choice of thenumber of phases depends on the structure and composition of the rock sample. Each phase should produce the IP effect, observable in the resistivity relaxation curve. It was demonstrated [

We introduce a vector, m, of the unknown model parameters:

where A_{IP} is a forward modeling operator described by the corresponding analytical equations of GEMTIP model, Equation (3).

We can solve the inverse problem described by Equation (4) by using the regularized conjugate gradient method as follows [

where _{IP} at iteration n, which can be found analytically by calculating the first variation of A_{IP}, and

The viability of the GEMTIP conductivity model was tested with multifrequency EM measurements acquired for shale-oil, laminated shale gas, and shale gas samples. Shale-oil, laminated shale gas, and shale gas samples (#8, #33, and #45) were provided by TerraTek. The shale samples and their thin sections are shown in

The shale samples were examined using Quantitative Evaluation of Minerals by Scanning Electron Microscopy (QEMSCan) for structural analysis and phase evaluation [

We have conducted complex resistivity measurements for each sample at 27 frequencies over a range from 0.005 Hz to 1000 Hz using the TechnoImaging’s experimental lab. The details of CR measurement system were reported [

Figures 2-4 present the results of QEMSCan analysis for shale samples. Note that, according to the QEMSCan results, sample #8 contains 6.64% of the disseminated pyrite, sample #33 has 1.47% of the pyrite, and sample #45contains 3.53% of the pyrite, respectively.

Figures 5-7 show imaginary parts of the complex resistivity spectra measured for samples # 8, # 33, and # 45, respectively. We have inverted the observed complex resistivity data for the parameters of the GEMTIP models using two-phase and three-phase models. Both two- and three-phase models produce good misfits, which were 5% for two-phase and 3.2% for three-phase models, respectively, for sample #8; 5% and 3.5% for sample #33; and 7% and 6.2% for sample #45, respectively.

Figures 8-10 show the maps of the misfit functional for three-phase models for samples #8, #33, and #45, respectively, plotted as a function of the relaxation parameter (C) and the time constant (τ). The shaded isolines in this plot signify the direction of decreasing misfit. The paths of the conjugate gradient inversions are shown by the red lines. The final models are represented by red triangles. One can see that, for all three rock samples, the inversion converges rapidly to the specific parameters of the GEMTIP models. The corresponding GEMTIP parameters, produced by the inversion, are shown in the tables provided below.

_{gas} = 6.34%) determined by the core analysis.

_{gas} = 8.11%) determined by the core analysis.

_{gas} = 1%) determined by the core analysis.

It is important to note that, the three-phase inversion makes it possible to estimate separately the volume fraction of one phase in the GEMTIP model representing the polarization caused by disseminated pyrite, and that of another phase representing induced polarization caused by the presence of HC in the porous space of the sample. For example in sample #8 the dissiminated pyrite show a volume fraction 6.35% and 4% corresponds to the HC in the porous space. The time constant of pyrite is larger than the time constant of HC, because the capacitance of the mineral carrying the charge is much stronger than that of the HC.

We should note that, the p_{gas} value in turn is directly associated with TOC in shale gas deposits. It was demonstrated [_{gas} is in 0.5 - 1 range. It was also reported close to 0.5 ratio between TOC and p_{gas} in shale gas deposits [

Sample #8 | ||||
---|---|---|---|---|

Variable | Units | Initial value | Two phases | Three phases |

ρ_{0} | Ohm-m | 39 | 37 | 30 |

f_{1} | % | 0.1 | 10 | 6.35 |

C_{1} | - | 0.1 | 0.45 | 0.27 |

τ_{1} | Seconds | 0.1 | 1.19 | 2.15 |

f_{2} | % | - | - | 4 |

C_{2} | - | - | - | 0.59 |

τ_{2} | Seconds | - | - | 0.46 |

Sample #33 | ||||
---|---|---|---|---|

Variable | Units | Initial value | Two phases | Three phases |

ρ_{0} | Ohm-m | 36 | 41 | 46 |

f_{1} | % | 0.1 | 13 | 2.4 |

C_{1} | - | 0.1 | 0.35 | 0.28 |

τ_{1} | Seconds | 0.1 | 2.93 | 8.59 |

f_{2} | % | - | - | 8.11 |

C_{2} | - | - | - | 0.43 |

τ_{2} | Seconds | - | - | 3.69 |

Sample #45 | ||||
---|---|---|---|---|

Variable | Units | Initial value | Two phases | Three phases |

ρ_{0} | Ohm-m | 70 | 78 | 89 |

f_{1} | % | 0.1 | 6.6 | 4.4 |

C_{1} | - | 0.1 | 0.42 | 0.35 |

τ_{1} | Seconds | 0.1 | 1.55 | 2.15 |

f_{2} | % | - | - | 1 |

C_{2} | - | - | - | 0.77 |

τ_{2} | Seconds | - | - | 1.29 |

samples and their complex resistivity spectra was conducted for the shale-gas and laminated shale-gas samples. The results of the study for all three samples are summarized in

The result of QEMSCan analysis have demonstrated that the shale rock samples have very complex mineral composition. For example,

Samples | QEMSCAN results, f_{pyrite}, % | Core analysis, f_{porosity}, % | GEMTIP inversion, f_{1 }and f_{2}, % |
---|---|---|---|

Shale-oil, #8 | 6.64 | 6.34 | f_{1} = 6.35 f_{2} = 4 |

Shale-gas, #33 | 1.14 | 7.98 | f_{1} = 2.4 f_{2} = 8.11 |

Lam.shale-gas, #45 | 3.53 | 1.19 | f_{1} = 4.4 f_{2} = 1 |

high frequency only (>1 kHz) [

An important result of this study is that one can observe significant induced polarization effects in shale reservoir rocks. This observation opens a possibility of direct application of the spectral IP method for exploration and monitoring of traditional and unconventional (shale gas, shale oil, tar sands etc.) energy resources. This paper also shows that the GEMTIP modeling can be used for an evaluation of the mineral composition and HC fractions in the rock samples comparable with the direct core analysis. A proper modeling and inversion with the three-phase GEMTIP model, used in our experimental study, recovers the true characteristics and structural composition of the reservoir rocks. In summary, this paper demonstrates that, the GEMTIP modeling and inversion provides a solid foundation for an application of the spectral IP method in exploration and monitoring of hydrocarbon reservoirs.

The authors acknowledge the support of the University of Utah Consortium for Electromagnetic Modeling and Inversion (CEMI) and TechnoImaging. We are thankful to TerraTek for providing the shale rock samples and core analysis.