# Prediction of Overpressure Zones in Marine Sediments Using Rock-Physics and Other Approaches

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overview

#### 2.1. Geological Setting

^{3}/d was obtained, from the interval 2006–2047 m, an oil inflow of 19.1 m

^{3}/day was obtained (productive horizon M-1).

#### 2.2. Data

_{L}[45]:

_{L}

#### 2.3. Seismic Inversion

_{p}= ρV

_{p}, the bulk density ρ, and the body wave velocity ratio V

_{p}/V

_{s}(where V

_{p}—compression wave velocity, V

_{s}—shear wave velocity), by the pre-stack amplitude inversion. From these parameters, we can calculate the dynamic elastic moduli such as bulk and shear moduli, Young’s modulus, and Poisson’s ratio.

_{s}= (E/2ρ(1 + v))

^{0.5},

_{p}/V

_{s}. The low-frequency models and the results of the seismic pre-stack inversion are shown in Figure 2. These results are further used for the pore pressure inversion.

#### 2.4. Model of Mechanical Properties

^{3}. The density of fluid is equal to 1.024 g/cm

^{3}that is the sea water density. The porosity, bulk modulus, and Poisson’s ratio along the project well are shown in Figure 3. Note that the Poisson ratio is rather high varying from 0.493 to 0.498 that is very close to the sea water value (0.5). These values are much greater than those obtained in the laboratory test on Liquidity index (see Table 1). For these values of Poisson’s ratio, the shear modulus does not exceed 0.08 GPa that is comparable to the experimental error of its determination. This forced us to assume that this modulus may have higher values than provided by the seismic data.

_{n}= C + µ

_{f}σ

_{n},

_{n}and σ

_{n}are the tangential and normal stress leading to the failure, C is the inherent shear strength (cohesion), and µ

_{f}is the internal friction coefficient (tangent of internal friction angle φ

_{i}).

## 3. Results

#### 3.1. Pore Pressure Prediction from Void Ratio

_{0}− C

_{c}logσ

_{V},

_{0}is the void ratio at a vertical effective stress of unity (1 MPa), C

_{c}is the specific compression index describing deformation along the yield surface, and σ

_{V}is the effective vertical stress. Proper rearrangement of this equation provides the following dependency for the pore pressure P

_{por}:

_{por}(z) = S

_{V}(z) − 10

^{–(e(z) − e0)/Cc},

_{V}is the total stress, z is the depth below the seafloor. If the sea depth is known alongside with the density profile, the total stress can be obtained as:

_{w}is the water density, h

_{w}is the sea depth, and ρ(z) is the estimated density profile. With all these parameters described in the previous sections, the total vertical stress reconstruction is a straightforward procedure. It is worth mentioning that effective horizontal stresses for these unconsolidated sediments tend to be close to the vertical effective stress, due to both high Poisson’s ratio and considerable elasto-plastic deformation.

_{c}= 0.18, e

_{0}= 0.88, typical of the considered site at the Black Sea. The analogous values for the Gulf of Mexico were reported to be C

_{c}= 0.54 and e

_{0}= 0.47 [18].

#### 3.2. Pore Pressure Prediction from Rock-Physics Modeling

_{0}is the critical porosity, K and µ are the bulk and shear moduli of the grain material, K

_{HM}and µ

_{HM}are the bulk and shear moduli of the dry granular medium calculated with the help of the Hertz–Mindlin (HM) method. According to the HM method, these moduli are calculated by the formulas:

_{0}is the critical porosity; $\tilde{C}$ is the average number of contacts per grain (so-called coordination number). Definitely, φ

_{0}≥ φ. If φ

_{0}= φ, then the soft-sand model is reduced to the Hertz–Mindlin model.

_{0}and K

_{fl}are the bulk moduli of the grain material and fluid. After the effective moduli of the saturated rock are found, the elastic wave velocities Vp and Vs are calculated by the formulas:

^{*}is the rock density. The rock density is calculated by the exact formula

_{fl}is the density of fluid.

^{3}), we also chose rather high values of the grain material for the rock-physics modeling: the bulk and shear moduli equal to 52 GPa and 32 GPa, respectively. These moduli are close to the Voight–Reuss–Hill average of the stiffness matrices of illite, chlorite, and kaolinite addressed in the work of Katahara [56]. The corresponding density of these clay minerals are 2.79, 2.69, and 2.59 g/cm

^{3}which, on average, gives the value close to the measured density of the grain material.

_{0}= 0.76. The respective increase in the velocities is 50 m/s for Vp and 150 m/s for Vs at the critical porosity φ

_{0}= 0.5.

_{0}. Then, for every combination, we found a set of pore pressure values satisfying the above conditions. To do this, we applied the n-dimensional mesh method. This method assumes that the range of possible values of every unknown parameter is divided into intervals. The forward problem on the determination of P- and S-wave velocities was solved for each node. Then, “good” solutions, i.e., the solutions satisfying the accepted misfit between experimental and theoretical velocities were collected. Among the “good” solutions, the most probable solution was chosen. The most probable solution is the solution having the minimum value of “misfit measure”.

_{V}. The “misfit measure” was chosen to be the relative difference between the theoretical and experimental P-wave velocity. A workflow for the inverse problem solution on the pore pressure estimation is shown in Appendix A (Figure A3).

_{0}show different solutions for the behavior of pore pressure along the project well. Among all combinations of these two parameters, we chose the combination providing the “reference” pore pressure 1.2 MPa at the depth 20 mbsf. These values are $\tilde{C}$ = 12 and φ

_{0}= 0.76. Note that without the knowledge of a “reference” value, the solution for pore pressure is rather uncertain and may exhibit different values between the hydrostatic pressure and overburden stress. This fact should be taken into account when inverting the pore pressure with the use of similar approaches.

#### 3.3. Pore pressure Prediction Comparison

## 4. Discussion

_{V}turns into σ

_{V}+ Δσ, where Δσ is an extra stress caused by the drilling operation, the weight of the drilling rig can be a simple source of this extra load), with the horizontal stress σ

_{H}remaining untouched. The Mohr–Coulomb failure criterion (1) can be rearranged for this case of triaxial loading to the following form:

_{i}is the internal friction angle (its tangent is equal to the internal friction coefficient). The horizontal stress can be estimated as:

_{H}= vσ

_{V}/(1 − v),

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 1.**The 2D seismic profile along the project well (X-proj is the projection of the engineering well X). The 1D model of the bulk density measured in the laboratory for the well X is shown on the seismic profile and on the right.

**Figure 2.**The low-frequency and the inverted models of S-wave velocity, density, and acoustic impedance along the project well. The seismic section in the vicinity of the well is shown on the right.

**Figure 3.**Porosity, bulk modulus, and Poisson’s ratio along the project well calculated from the seismic data (P- and S-wave velocities and density) and density of solid grain material and sea water.

**Figure 6.**Comparison of seismic data (exp), results of rock-physics modeling (theor), and laboratory data (lab): (

**a**) velocities of P- and S-waves and (

**b**) Poisson’s ratio.

**Table 1.**Description of engineering geologic elements identified at the research site. The depth and thickness ranges are given according to several engineering wells.

Engineering Geologic Element (EGE) | Depth (from the Seafloor), m | Thick-Ness, m | Description | Poisson’s Ratio | Den-sity, g/cc | Young’s Modulus, MPa |
---|---|---|---|---|---|---|

EGE 1 | 0.15–1.7 | 0.15–1.80 | Silt | - | 1.54 | 1 |

EGE 2 | 4.65–5.50 | 3.0–3.90 | Fluid-saturated plastic clay with an admixture of organic matter | 0.43 | 1.87 | 3 |

EGE 3 | 5.90–6.20 | 0.40–1.55 | Fluid-saturated plastic clay loam with an admixture of organic matter | 0.46 | 1.86 | 6 |

EGE 4 | 14.75–15.40 | 8.80–9.40 | Calcareous fluid-saturated plastic clay with an admixture of organic matter | 0.40 | 1.81 | 4 |

EGE 5 | 24.50–24.90 | 9.40–10.15 | Calcareous high-plastic clay with an admixture of organic matter | 0.28 | 1.85 | 7 |

EGE 6 | 41.25 | 16.55 | Calcareous high-plastic clay with an admixture of organic matter | 0.31 | 1.90 | 9 |

EGE 7 | >50.5 | >9.25 | Calcareous high-plastic clay with an admixture of organic matter | 0.30 | 1.91 | - |

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**MDPI and ACS Style**

Dubinya, N.; Bayuk, I.; Hortov, A.; Myatchin, K.; Pirogova, A.; Shchuplov, P.
Prediction of Overpressure Zones in Marine Sediments Using Rock-Physics and Other Approaches. *J. Mar. Sci. Eng.* **2022**, *10*, 1127.
https://doi.org/10.3390/jmse10081127

**AMA Style**

Dubinya N, Bayuk I, Hortov A, Myatchin K, Pirogova A, Shchuplov P.
Prediction of Overpressure Zones in Marine Sediments Using Rock-Physics and Other Approaches. *Journal of Marine Science and Engineering*. 2022; 10(8):1127.
https://doi.org/10.3390/jmse10081127

**Chicago/Turabian Style**

Dubinya, Nikita, Irina Bayuk, Alexei Hortov, Konstantin Myatchin, Anastasia Pirogova, and Pavel Shchuplov.
2022. "Prediction of Overpressure Zones in Marine Sediments Using Rock-Physics and Other Approaches" *Journal of Marine Science and Engineering* 10, no. 8: 1127.
https://doi.org/10.3390/jmse10081127