Macro-flow and Velocity Dispersion - SEG Digital Library

Macro-flow and Velocity Dispersiondetermined by opening and closing micro-valves in thepore fluid lines.Measured Low Frequency DataWe have observed this flow effect in the Rim Sandstonewith partial saturation. In this case, the rock is measureddry and completely brine saturated (Figure 3). Atultrasonic frequencies, we see the expected effect of brinesaturation: a substantial increase in the compressionalvelocity with brine saturation. When the valves are open,fluid motion in and out of the pore system can occur at lowfrequencies. This results in a 'drained' case, or a conditionwhere pore pressure will not change with the deformationresulting from the elastic wave. Hence, the bulk moduluswill not increase. However, density is increased because ofthe water saturation. Thus the velocity is lower than for thedry case.VELOCITY (km/s)3.53.02.52.01.51.00.5RIM SANDSTONE,Pd = 2000 psi0.00 1 2 3 4 5 6 7LOG 10 FREQUENCY Log(Hz )Figure 3. Rim Sandstone, dry and saturated with brine. I nbrine saturated case, the microvalves in the pore fluidsystem are open allowing fluid moving in and out ofsample. At low frequency, the sample acts at ‘drained’condition. As results, the compressional velocity is lowertha dry case due to density effect.An injection process can be used to produce aheterogenious fluid distribution. Two cubic centimeters ofliquid butane are injected into the brine saturated sample.This results in a hydrocarbon saturation of 20%. As we cansee in Figure 4, the effect is small at ultrasonic frequencies,and increases with decreasing frequency. This is what wewould expect for fluid motion and pressure equilibrationbetween the two regions. The butane, although liquid, stillhas a very low modulus. This keeps the pore pressurechange small with deformation. At lower frequencies, thebrine-saturated zone is more strongly influenced by thispressure equilibration. Applying the flow model (with theadjustable parameters) gives the red line fit to thecompressional velocity. Note that the dispersion in shearmodulus must also be included in this model calculation.VsVpFigure 4. Brine saturated and partially butane saturatedRim sandstone. At lower frequencies, the brine can comeinto pressure equilibrium with the more compressiblebutane. The macro flow model fit is shown in red.ApplicationHere we are interested in the effects of fluid flow on themoduli and velocities, through the fluid mobility anddistance from a gas saturated zone.As an example of a logging application, we can apply therelaxation relation to the case of a porous and permeablesand. This model consists of a thin gas saturated layer ontop of a brine saturated zone. A uniform shale surroundsthe sand. The use of the Cole-Cole relation aids us sinceboth the low frequency and high frequency moduli can beestimated from the log. The 'low frequency' modulus ispresumed to be that of the gas sand (3 GPa). The infinitefrequency limit will be the modulus of the brine saturatedzone as measured as an isolated, homogeneous system (7.5GPa). These values were chosen to match values observedin a Gulf of Mexico log. The log in Figure 6 shows a sandwith a gas cap over a brine saturated zone in Figure 6.Under the correct conditions of high fluid mobility and lowfrequency, we can see that the nature of the gas-watercontact can be changed substantially. What appears as asharp contact at high (logging) frequencies, is smeared intoa gradational contact at seismic frequencies (right side ofFigure 6).