|Thesis abstract: |
The reservoir characterization is a delicate and challenging activity which provides the description of a reservoir model that incorporates all the characteristics related to its ability to store hydrocarbons and also to produce them. The problem of reservoir characterization is of significant economic nature to the oil companies, since the capability of estimating the oil and gas saturations allows to reduce the costly drilling of un-productive reservoir. The reservoir characterization can be performed by using various exploration techniques such as: seismic, electromagnetic sounding and well log data, depending on the peculiarity of the sediment lithology, and the cost of the exploration campaign. The present study faces the problem of the reservoir characterization through an original formulation of the inverse problem. The thesis is structured into two parts since two different geophysical exploration techniques are employed in the characterization of the subsurface media.
First, I study the petrophysical properties of the reservoir in-situ, through the integration of heterogeneous well log data for improving the estimation of the petrophysical properties of the reservoir. On this framework I formulate the joint inversion of well log data, p-velocity, electrical conductivity and density, for estimating porosity, water, oil and gas saturation. This approach allows recovering complementary information for improving the estimation of the petrophysical model, exploiting the strengths of each different geophysical data types. The analyses involves the joint inversion of experimental constitutive equations, also called rock physic models, which represent a proper link between the rock parameters and the geophysical measurements. I firstly investigate the rock parameter observability through a visual analysis of the constitutive equations. Then I explain that the existence of a common set of rock properties, (cross-properties), that influence different geophysical measurements, makes it possible to reduce the ambiguities of the interpretation. The rock cross-property concept represents the kernel of the inversion algorithm that I propose to estimate the petrophysical model of the reservoir. I formulate a Bayesian joint inversion procedure starting from the well known nonlinear relation d=g(m), where well log measurements represent the input data while the fluid saturation levels and porosity represent the model parameters. Prior to perform the model estimation it is furnished a sensitivity analysis of the model parameters based on the analysis of the Jacobian matrix through the Singular Value Decomposition technique (SVD). Finally I show that the iterative joint inversion procedure is able to control the conditioning problem, to efficiently take into account input data and model uncertainty, and to provide a confidence interval for the solution. Moreover, the inverse analysis offers a clear view of the regularization effect due to the setting of the model covariance matrix. Finally, the inversion procedure is validated on a real well log dataset. Results obtained highlight the importance of integrating heterogeneous dataset, in a systematic Bayesian joint inversion procedure, for improving the characterization of the reservoir.
The second part of the study aims to characterize the reservoir by formulating the inverse problem of Controlled Source Electromagnetic (CSEM) data for 2.5D geometry. The CSEM
method is an emerging offshore geophysical technique which employs the electromagnetic remote-sensing technology, based on the induction principle. Since that CSEM data are sensitive to the variations of the electrical resistivity of the subsurface media I focus on the characterization of the reservoir in terms of electrical resistivity. I firstly investigate the electromagnetic propagation into the subsurface medium in order to comprehend the peculiarity of the technique in terms of resolution, data sensitivity and system noise. The parameterization of the CSEM system entails the discretization of the subseafloor through the introduction of a regular grid. This straightforward approach consists of defining the electrical macroregions needed to cover the entire subsurface medium. The problem formulation is based on the nonlinear relation d=g(m), where the input data are represented by the electromagnetic components Ex, Ez, Hy in magnitude and phase, while the model parameters consist of the set of the electrical resistivity values which are associated to the macroregions. Since electric and magnetic fields have a wide dynamic range, regularization strategies have been applied on data input for reducing the ill conditioning of the problem. The driving forward model consists of an ad-hoc electromagnetic simulator based on the Finite Element Method (FEM). As in the previous part, the inversion procedure is based on the Bayesian approach. The sensitivity analysis is performed through the SVD decomposition of the Jacobian matrix. The inversion procedure is then tested on a realistic synthetic scenario in order to investigate the robustness of the algorithm. The iterative inversion algorithm provides the estimation of the model with a measure of the uncertainty associated to their parameters. Results show how the use of the Bayesian inversion can be applied to CSEM data in order to characterize the reservoir in terms of electrical resistivity allowing the discrimination of oil form water. To notice the novelty represented by the FEM forward involved in the inversion of the CSEM data.
The entire study presents useful applications for performing the characterization of the subsurface media through the Bayesian inversion of well log and CSEM data. Finally, in this study is explained how to analyse the multi-dimensional residuals, with a one-dimensional `distance¿ functional, in order to depict their topology and to appreciate visually the effect of the regularization.