Rock physics theory and analysis for fractured carbonate reservoirs

Abstract

The analysis of a geological reservoir's elastic and electrical properties forms the cornerstone of geophysical reservoir characterisation. These properties are significantly influenced by a reservoir's pore and fracture geometry. A multitude of pore shapes occurs in carbonate rocks, making their electrical and elastic properties particularly challenging to model, especially by first principles physics. In addition to this, many of the world's carbonate reservoirs are located beneath salt diapirs, which can alter the path of incidental seismic waves and impede seismic reservoir characterisation. Thus, developing new rock physics theory and methods for fractured carbonate reservoirs may serve to advance reservoir characterisation efforts. Many rock physics models assume pore and fracture shape is constant with varying pore volume fraction, however carbonate porosity is highly susceptible to diagenesis and other physical changes in reality. In this thesis, I show a systematic change in pore shape with porosity exists in many carbonate rocks, even when measured at constant effective pressure. By accounting for this changing pore shape, electrical and elastic rock physics modelling errors are reduced on seven public domain, laboratory data sets, and two well logs from a carbonate reservoir, while new calcite Vp - Vs and Vp=Vs - Ø relationships are derived from first principles. This proposed porosity-pore shape relationship leads to alternative models for Archie's first law, the Humble equation, the Castagna and Pickett relations, and the Focke and Munn relations, while being correct in the porosity asymptotes. Unlike these empirical relations, the proposed model may extrapolate to other rock and fluid types as it is derived from first principles. Reservoir characterisation uncertainty can be reduced using analysing both electrical and elastic measurements. Transforming from one physical property to the other, however, typically involves estimating reservoir porosity as an intermediate, bridging parameter. By integrating existing electrical and elastic differential effective medium models, I obtain new cross-property differential effective medium (DEM) expressions which have no explicit mathematical porosity dependence, allowing elastic moduli to be estimated directly from electrical measurements without estimating porosity intermediately. This new DEM method models public domain, electrical-elastic laboratory measurements from wet, mixed sandstones, and predicts synthetic velocity from resistivity well logs with lower error than the typical method, which estimates porosity logs as an intermediate step. Fracture characterisation in Pre-salt reservoirs can be challenging by walkaround vertical seismic profile (VSP) analysis, as algorithms often assume a simple overburden or separable S-waves. I extend the spectral ratio method to estimate interval relative azimuthal attenuation in a reservoir beneath arbitrarily complex overburden given VSP receivers in an arbitrarily deviated well. Characterising a Brazilian Pre-salt reservoir's fracturing using a pre-existing, multifluid, fractured, viscoelastic model, it seems there are two non-orthogonal, vertical fracture sets present, with a depth-dependent fracture density and orientation. Estimating tilted transverse isotropy (TTI) parameters using the slowness-polarisation method given walkaway VSP measurements shows the Brazilian Presalt reservoir interval has negative Thomsen's parameters, ε and δ. These findings are not contradictory to those of the fracture characterisation study, as a negative ε in a vertical or TTI system could be linked to (sub)vertical fracturing.