Keywords

1 Introduction

The evaluation of pore pressure in an area of exploratory interest is important for optimizing the well design, such as correctly programming the casings, shoe setting, and appropriate well completion, to not waste resources and preserve safety all involved.

In these predictions, the oil industry applies the Eaton’s Method [1], an empirical and deterministic method that infers the formation overpressure from compressional wave velocity, resistivity logs or even drilling parameters.

This modeling is interpretative since the modeler should propose a normal compaction trend, needed to detect overpressure zones. In many cases, the dataset needed to confirm the models is unavailable. Besides that, there is no way to quantify the variance or uncertainty of a model easily.

In order to reduce part of this interpretative aspect, and to be able to use more available data and give a statistical weight to the models, it was proposed to estimate the pore pressure in a portion of the eastern margin of the Brazilian coast via Sequential Gaussian Cosimulation [2, 3] with Intrinsic Colocated Cokriging [4].

2 Theoretical Foundations and Definitions

The used geostatistical modeling basically involves three steps that must be carefully evaluated to correctly calculate its probabilities. They are the variogram, the supersecondary variable [5] and the geostatistical simulation.

3 Data Presentation and Interpretation

As a region for the modeling, a recent exploratory frontier area was chosen due to its high-pressure domains and plane-parallel seismic facies.

Eight hundred eighty-three static pressure data from 24 wells were obtained, generating post-drilling models built from measured pressures, well logs and drilling reports.

To reduce the computational effort, we have delimited the modeling interval between the top of the Upper Campanian and the top of the Aptian. The histogram can be seen in Fig. 1.

Fig. 1
figure 1

Pressure data (in psi) histogram from selected wells

Full size image

The experimental variograms, as shown in Fig. 2, were obtained in the 0° and 90° azimuth directions and in the vertical direction respectively and were modeled from the Table 1. These variograms seem to be non-stationary, so the maximum search radii were limited.

Fig. 2
figure 2

Experimental and modeled variograms. On the left, 0° azimuth with 35,000 m range. Centred is 90° azimuth with 50,000 m range and on the right, vertical with 900 m range

Full size image
Table 1 Modelled variogram parameters
Full size table

Some 3D data from petroleum systems modeling were tested, such as sedimentation rate, organic matter transformation rate and porosity. Although some of these three-dimensional models correlate well with the primary data, their low resolution negatively impacted our final model. Therefore, these data were not included.

The supersecondary variable (Fig. 3) was obtained from the composition of the most recent models of seismic velocity (v) and temperature (T) according to the equation

Fig. 3
figure 3

Sectional views of the supersecondary variable in-depth, on the left, and the x-axis, on the right

Full size image
$${S}_{s}=-0.2v+0.9T$$
(1)

Sixteen realizations were calculated in the Sequential Gaussian Co-Simulation with Intrinsic Collocated Cokriging. Some of these realizations can be seen in Fig. 4.

Fig. 4
figure 4

Depth slices of realizations 1 and 2, showing higher pressures in the NW region

Full size image

Figure 5 is possible to compare histograms of each realization, showing good agreement with the well data.

Fig. 5
figure 5

CDF reproduction over all realizations

Full size image

It was possible to obtain a basic statistic from all realizations, like mean values and standard deviation (Fig. 6) and percentiles like 10, 50 and 90 (Fig. 7) of the pore pressure in each cell grid.

Fig. 6
figure 6

Mean value (left) and standard deviation (right) of the modeled pore pressure over all realizations

Full size image
Fig. 7
figure 7

Percentiles 10, 50 and 90 of the modeled pore pressure

Full size image

Finally, the workflow presented permits extraction of the pressure log in any desired coordinate for a detailed evaluation Fig. 8.

Fig. 8
figure 8

Modeled pressure log after simulation in a pair of coordinates. All realizations, percentiles 10 (blue), 50 (orange) and 90 (green) and their standard deviation are displayed

Full size image

4 Conclusions

The motivation of this work is to use cosimulation with intrinsic collocated cokriging to model a pore pressure–volume in a region of the Brazilian coast.

Post mortem pore pressure values in 24 recently drilled wells, limited between the Upper Campanian and Aptian horizons, were used as primary data. The secondary data were obtained from a composition of two variables: temperature modeled via calibrated finite elements and the seismic velocity updated until the last well drilled in the area.

After the cosimulation, 16 realizations were obtained, and it was possible to see the wide spatial variability of pore pressure, with values within the range usually found in the region. These achievements honored the histogram and the original data and the modeled variogram, demonstrating the usefulness and applicability of the proposed workflow.

The presented geostatistical workflow demonstrates its applicability in future studies of pore pressure modeling, as they can generate different scenarios that are likely to be obtained at each realization, using a wider range of data available, and different well design strategies can be probabilistically defined.

5 Benefits Promoted by This Work

One of the main issues in using the Eaton’s method is determining a normal compaction trend. This trend is quite interpretive, varying according to the modeler. In order to reduce this subjectiveness, and mainly to include, in a statistical way, other variables that may be related to pore pressure, the workflow in this article was proposed using different exhaustive variables, from different models.