Calibration of 3D P&T Basin Modelling Using Sensitivity Analysis

Paolo Ruffo¹, Giovanni Scrofani¹, Anna Corradi¹, Domenico Grigo¹, and Ulisses Mello²
¹Eni – E&P Division, Milan, Italy
²T.J.Watson IBM Research Center, Yorktown Heights, NY, USA

Introduction
Modelling of Basin Pressure and Temperature evolution is an inversion process where the only available calibration data refer to the final result of Basin evolution, which actually is a combination of geological processes. These are non-linear, non-smooth, some of them dissipative, and unfortunately only their cumulative and combined effects at present-day are known.

The solution of this inversion process is therefore non-unique and the inversion problem is ill-posed. Although the inversion is based on an advanced mathematical description of the geological processes affecting Basin Pressure and Temperature evolution, it requires also the “a priori” knowledge of an expert who reduces the solution space of all the possible answers to a reduced space of potential, acceptable, realistic geological solutions, or scenarios, to the inversion problem.

In practice the inversion modelling is performed generally as a series of deterministic runs of forward modelling, calibrated to available data through an iterative by trial and error procedure controlled by a basin modelling expert.

The risk of this approach is oversimplification, for example: the use of a 1D modelling instead of a full 3D simulation thus neglecting lateral effects, or the application of a pure conductive approach to temperature modelling evolution, or under-sampling of complex geological details. In addition to these limitations, one should have to take into account the uncertainty of data, processes and methodologies. This means that the calibration process claims for a robust statistical approach in order to evaluate and manage the uncertainty of the possible solutions to the inversion.

Finally, even if it is common practice to focus the calibration process on some specific “parameter”, it is worth remembering that the searched result of the calibration (inversion) process is the Basin Pressure and Temperature evolution as a whole, including the boundary and initial conditions.

Proposed Methodological Approach
In this work, we concentrate on the calibration of the heat flux in order to obtain one or more heat flux histories that best match the temperature and maturity measured values.

This kind of calibration has been traditionally applied mostly with 1D modelling because of the high computational cost to do it in 3D. The results of 1D calibrations obtained for several wells separately can be extrapolated to obtain a single heat flux map (for each time-step) that can be used in a 3D basin model.

This approach can be applied, for example, when small lateral variations of the thermal properties within the basin are expected to occur, or when the basement is very smooth and the same behaviour is predicted for the heat flux map.

However, in complex geological settings, which became increasingly frequent in today exploration activity, the 1D calibration may fail to produce a correct evaluation of the heat flux history. A typical example where the 1D calibration fails is when isolated salt structures are present in the basin. These structures present strong lateral heterogeneity in both thermal and permeability properties and hence important deviations from the local temperature trend are associated to these structures. If a well is located in the nearby area, the measured temperatures are significantly affected by these thermal anomalies, which cannot be taken into account by a 1D basin modelling simulation. In such cases, heat flux maps obtained by the extrapolation from a multi-1D calibration will be characterized by severe localized effects, which are geologically unrealistic.

In the last few years, increasingly availability of computational power and advances in basin modelling techniques have made 3D calibration an affordable task. Despite the fact that one should be able to perform a 3D calibration in complex geological settings to take into account the 3D nature of the basin, this does not exclude the use of a first learning phase in which a multi-1D approach is used, together with advanced geostatistical heat flux mapping in order to get an estimate of an “initial value” for the 3D inversion approach of the heat flux history.

The availability of a robust 3D geological restoration is a critical step of the calibration process as the structural and tectonic evolution has a fundamental impact on heat flux main events.

For example, in the case of presence of salt structures, the movement of salt, due to its thermal properties, can have a significant effect on the temperature regime, as indicated in the case study presented in this work.

Once the structural and tectonic evolutions are described with enough confidence, it is possible to specify distinct Scenarios for heat flux maps (at basement, for each time-step) from the initial multi-1D calibration phase.

The final calibration step makes use of a 3D Basin Pressure and Temperature modelling, using each Heat Flux Scenario, not only to find the best possible match with the available well data (e.g., temperature and vitrinite reflectance) but also to simultaneously assess the uncertainty of the solution and its sensitivity to input parameters.

As among input parameters there are also the heat flux maps, specific techniques need to be applied to perturb these maps in order to search for a better match with well data. While this could also be done manually, with a trial and error approach, which would be very time-consuming, our proposed technique is semi-automatic as the modeller controls the calibration process while all the necessary computations are executed in parallel.

The sensitivity analysis on the different runs provides valuable information for the modeller to understand what are the most important parameters and/or the most critical geological areas, so he or she can guide the calibration process and search for a set of potential “best match” solutions.

In this context, the importance of the proper modelling of complex geological setting can also be assessed, thanks to the possibility to use two different Basin Pressure and Temperature modelling techniques: a simpler one based on an hexahedral mesh and a more refined one based on a tetrahedral mesh.

Case Study
The area under study is characterized by the presence of post-salt source rocks in different layers that are producing hydrocarbons at various rates due to the heat flux gradients, the degree of compaction and burial depth. It can be seen that salt diapirism has greatly affected post-salt sediment thicknesses and sediment trapping in salt withdrawal basins. Therefore the resulting complexity of the Petroleum System in the area, and particularly the control that heat flux has on maturation, is directly influenced by salt distribution and its thermal effects.

The geological model has been described by 13 layers (14 horizons) and up to 15 wells in the area of interest have been used in the modelling, plus other 5 wells nearby. A structural and tectonic study allowed to obtain the Basin evolution in time.

We started the Basin Pressure and Temperature study using initial heat flux time-series maps which produce a 3D temperature field. In Figure 1 it is shown the temperature profile related to a well nearby a salt structure together with the measurement data and the match is clearly poor.

Then we performed a sensitivity analysis by introducing several local variations on the initial heat flux time-series maps and we checked the effects of these variations on the control wells. Finally, we used an optimisation strategy to modify the initial time-series maps and obtain a better fit with the measured data.

In Figure 2 it is shown the temperature profile calculated with the heat flux time-series maps obtained with the optimization described above for the same well shown in Figure 1, where a better fit can be observed.

In Figure 3 it is displayed an iso-temperature surface and the calibration well used in the previous figures. This visualization allows to clearly see the strong temperature anomaly induced by a salt body and how this anomaly propagates laterally in the nearby area drilled by the well.

Conclusions
Basin Pressure and Temperature modelling is a fundamental step of Petroleum System Modelling as it determines the conditions for the generation and expulsion of hydrocarbons.
More recently, modelling is increasingly gaining more importance as a tool to:
a) assess the risk of overpressure (used in combination with seismic data);
b) better evaluate porosity spatial distribution and
c) understand the evolution of reservoir and the potential fracturing in fault zones or in caprocks.

It is therefore worthwhile to improve the current methodology of calibration of Basin Pressure and Temperature modelling. Here we proposed the use of a full 3D calibration approach, which combines sensitivity analysis, a more refined geological modelling, and expert judgement to increase both the quality of the modelling and the uncertainty assessment simultaneously.

Figure 1. It is shown the temperature profile related to a well nearby a salt structure together with the measurement data and the match is clearly poor.