Application of Gassmann’s equation for laboratory data from carbonates from Austria

Abstract

Gassmann's "fluid substitution" equations belong to the most popular approaches to calculate velocities for rocks saturated with one fluid (1) and substituted with another fluid (2). Due to the limitations, the equations can hardly be used for carbonate samples. Different carbonate samples (limestone and dolomite) from Austria are selected for testing Gassmann's equation and modifications, and compressional and shear wave velocity for dry and saturated samples as well as porosity and density were determined in the laboratory. The next step was the calculation of the compressional and shear wave velocities for brine saturated samples using Gassmann's equation as a first approach. The second approach was to directly use the modulus k calculated from dry measured 1 data rather than the compressional modulus k for the dry rock frame, and in the third approach the Lamé parameter λ was used dry for k . λ was also calculated directly from the measured dry data and covers the pure incompressibility. These three approaches were 1 not only tested for the Austrian carbonates, where the porosity is very low, but also for a data set from chalk limestone samples with high porosity. The best results can be observed using k directly. Additionally using k leads to an underestimation of the data. dryThere is no difference between using k or λ for the low porous Austrian carbonates. In contrast, the high porous chalk limestone 1 samples show hardly any difference between the k and λ approach for the highest porosities, but a scatter when using λ for the 1 lower porosities. In summary it can be said that Gassmann's equation directly using k from the measured data or λ deliver good 1 results for low and high porous carbonate laboratory data.Gassmann's "fluid substitution" Gleichungen gehören zu den meist genutzten Anwendungen um Geschwindigkeiten für ein gesättigtes Gestein (Fluid 1) zu berechnen, welches mit einem Fluid (2) ersetzt werden soll. Durch ihre Einschränkungen, kann diese Gleichung kaum für Karbonate angewandt werden. Um diese Gleichungen trotzdem zu testen und um zu versuchen sie zu modifizieren, wurden unterschiedliche Karbonate (Kalkstein und Dolomit) aus Österreich ausgewählt. Es wurden Kompressions-und Scherwelle von trockenen und gesättigten Proben, ebenso wie Porosität und Dichte im Labor bestimmt. Der nächste Schritt war die Berechnung der Kompressions-und Scherwelle mit der Gassmann Gleichung als ersten Ansatz für gesättigte Proben. Für die zweite Methode wurde anstatt des Kompressionsmoduls k für das "trockene Gesteinsgerüst" direkt der Modul k , aus den Mes-

Negative Unjacketed Pore Modulus in Limestones? Critical Examination of a Peculiar Laboratory Observation

“…The current data set does not allow us to investigate this aspect in more detail since the undrained bulk modulus has not been measured. However, in agreement with previously reported doubts on the applicability of the Gassmann theory to rocks with complicated micro‐structure, in particular carbonates (Adam et al., 2006; Gegenhuber, 2015), our modeling for the three limestones with double‐porosity structure also put a question‐mark on how to perform fluid‐substitution in such rocks.…”

Seismic Velocity Characterisation of Geothermal Reservoir Rocks for CO2 Storage Performance Assessment

“…For future studies, it is advised to investigate alternative theoretical frameworks for modelling seismic velocities, as a function of pore fluid, for rock formations that do not obey Gassmann's assumptions. An example of an adapted version of Gassmann's theory, derived for carbonates, is presented in [71]. Figure 17.…”

Elastic Properties of Pannonian Basin Limestone under Different Saturation Conditions

“…To understand and interpret the elastic property of the samples, we performed Gassmann fluid substitution using directly the dry rock results and compared them to results of saturated samples. Gegenhuber (2015) [31] presented the direct implication of dry rock laboratory results into the Gassmann formula for Austrian carbonates. The bulk modulus resulting from the test on dry samples (Table 1) was used directly in the Gassmann equation.…”