Joint Inversion of Crosswell and Surface-to-Borehole Electromagnetic Data Constrained by Fluid-Flow Simulator
Authors: Abubakar Aria , Liang Lin , Habashy Tarek 
Published: March 2015

Abstract
We present a multi-physics inversion approach for improving crosswell and surface-to-borehole electromagnetic data interpretations. The inversion is constrained by a multiphase fluid-flow simulator that models the fluid flow in the reservoir and reconstructs spatial distributions of the water saturation and salt concentration, which are in turn transformed into the formation resistivity. Instead of inverting the resistivity distribution, we invert the porosity distribution assuming the existence of an empirical relationship between permeability and porosity. We employ a Gauss-Newton inversion method. The historical injection/production data are used to control the fluid-flow simulation, which provides constraints to the inversion. Hence, we obtain a resistivity distribution that is consistent with the fluid-flow physics. Additionally, we also obtain a water saturation distribution, which is a direct and explicit indication of the fluid movement. The tenth SPE comparative solution project model is employed to show advantages of our approach over the traditional approach.

Introduction
Electromagnetic methods can be used to determine subsurface saturation distribution. To characterize the reservoir beyond the welllog scale, the crosswell electromagnetic method has been developed to obtain the interwell resistivity; see Spies and Habashy (1995); Abubakar et al. (2005). The system operates similarly to the single-well induction logging tool except that sources and receivers are deployed in separate wells and are operated at a lower frequency. Another deep measurement, which employs a lower frequency, is the surface-to-borehole electromagnetic, where galvanic sources are deployed on the surface and receivers are located in the wellbore. Compared with crosswell measurement, surface-to-borehole configuration reduces the well intervention since it only needs minimum one well for operation.
Traditionally, the subsurface resistivity distribution is interpreted from electromagnetic data by using an inversion process. For example, Torres-Verdin and Habashy (1994); Abubakar and van den Berg (2000); Zhdanov and Yoshioka (2003); Abubakar et al. (2005, 2008b) developed pixel-based inversion approaches for crosswell electromagnetic data interpretations. By observing the resistivity changes over time, one can monitor the fluid-front movement and saturation changes in the reservoir. In some cases, the inverted resistivity maps are transformed to saturation maps using a correlation acquired from well logs (Hoversten et al., 2004) or using a resistivity-saturation formula (Marsala et al., 2008). These approaches may not be accurate without the knowledge of the salinity distribution, which can be disturbed by the waterflooding process. It is well-known that this inverse problem is ill-conditioned and highly nonunique that requires heavy regularization. Furthermore, the pixel-based inversion approach is usually underdetermined, so it will provide only a qualitative resistivity map of the subsurface. The quality of the inversion heavily depends on the accuracy of the initial model and the complexity of the geology. Different methods have been explored to improve the interpretation of the crosswell electromagnetic data. For example, Ali et al. (2009) incorporated geological data derived from seismic attributes, core analysis, and detailed log analysis into the initial model, hence improving the resolution of the inverted image. Hoversten et al. (2004) and Hu et al. (2009) combined crosswell seismic and crosswell electromagnetic data to achieve more physically consistent results. Li et al. (2009) developed a model-based inversion approach that significantly reduced the number of unknowns, hence obtaining more accurate inversion results than the pixel-based inversion. However, the model-based inversion approach relies on the a priori information obtained from other measurements or from the pixel-based inversion results.