Why the Fluid Matters

Part 3, Part 3: The Fluids

Learning objectives

Name the only two properties, bulk modulus and density, through which a pore fluid reaches a saturated rock
Explain from the zero fluid shear modulus of Part 1 why a fluid moves K but never mu
Read the fluid-modulus ladder: gas, oil, and brine spanning about two orders of magnitude
Predict when a stiff frame hides its fluid and when a soft frame is ruled by it

Two Doors Into the Rock

Part 1 left a fact that now goes to work: a fluid has a shear modulus of exactly zero, because it flows to relieve any change of shape. A pore fluid therefore has only two ways to reach the seismic response. It can resist being squeezed, through its own bulk modulus $K_{fl}$ fl, and it can add mass, through its density $\rho_{fl}$ fl. It touches the rock's bulk modulus $K$ and it touches the rock's density $\rho$ ; it never touches the shear modulus $\mu$ . The whole of Part 3, and the whole of Gassmann in Part 4, is bookkeeping on those two doors, and the first of them is the one that carries the signal.

The Ladder

Fluid detection is possible at all because the first door opens onto an enormous range. Order the three pore fluids by bulk modulus and they do not merely differ, they span two orders of magnitude. Gas is the soft floor, with $K_{fl}$ fl around 0.02 to 0.1 GPa depending on depth. Oil sits in the middle, roughly 0.5 to 1.5 GPa, a live 40-API oil reading about 0.72 GPa at reservoir conditions and a dead one about 1.35 GPa. Brine is the stiff top, near 2.5 to 3.3 GPa, a 100,000 ppm brine reading 3.03 GPa at 50 degrees Celsius and 25 MPa. From gas to brine is a factor of roughly fifty, and that gulf is the entire reason a fluid change can move a seismic amplitude.

Slide the temperature and pressure and every rung shifts, but the ordering never scrambles and the gulf never closes: gas stays soft, brine stays stiff, oil stays in between. The three sections that follow give each rung its real physics; here the point is only the size of the range.

Stiff Frame, Soft Frame

A large fluid range does not guarantee a large seismic effect, because the fluid competes with the frame. Read the saturated bulk modulus as a sum of what the dry frame supplies and what the fluid adds. In a stiff, well-cemented, low-porosity rock the frame supplies a large modulus of its own, and the fluid term is a small correction: swap gas for brine and $K$ barely moves. In a soft, high-porosity, poorly consolidated rock the frame supplies little, and the fluid term dominates: the same swap moves $K$ a great deal. This is the language of Part 2 read forward. A rock near the stiff upper bound is nearly fluid-blind; a rock near the compliant lower bound is fluid-loud. Which one you have decides whether a fluid is visible, and only a model of the frame can say so in advance.

The exact accounting, how much the fluid adds for a given frame and porosity, is Gassmann's theory, and it is the whole of Part 4. Before a fluid can be substituted its own properties have to be known, and those are the work of the next three sections. We start at the stiff end of the ladder, with the fluid that fills most of the subsurface and that every fluid substitution takes as its starting point: brine.

References

Mavko, G., Mukerji, T., & Dvorkin, J. (2009). The Rock Physics Handbook (2nd ed.). Cambridge University Press.
Batzle, M., & Wang, Z. (1992). Seismic properties of pore fluids. Geophysics, 57(11), 1396-1408.