The T2 Cutoff: BVI and FFI

One Line Through the Spectrum

The T2 distribution of Section 10.2 becomes an answer the moment you draw one vertical line on it. The line is the T2 CUTOFF. Fluid that relaxes faster than the cutoff, in the small pores, is held by capillary forces and is called bound: its volume is the bulk-volume irreducible, $\text{BVI}$. Fluid that relaxes slower is called free: its volume is the free-fluid index, $\text{FFI}$, which Looyestijn (2001) describes as "mobile water and/or hydrocarbons". The two add to the NMR porosity, $\phi = \text{BVI} + \text{FFI}$.

The figure draws that line on a spectrum for one half foot of Ogbon-1. At 5890 ft, in the upper oil sand, the rock is 23.2 % pore space; split at 33 ms, BVI is 4.2 % of the rock and FFI 19.0 %. Ogbon-1 has no NMR log, so the spectrum is a what-if, the same as Figure 9.5's, built to hold the well's irreducible water in a bound peak at 4 ms. What that does and does not prove is set out below.

Irreducible Water Without Resistivity

The split hands over a saturation that no resistivity went into:

read from the relaxation times alone, with no Archie and no $R_w$. At 5890 ft it reads 18.0 %. It can feed the Timur permeability of Section 9.2, which needs an irreducible water, and it can be set beside the resistivity saturation of Chapter 7. The two are not the same quantity: the resistivity gives the water in the rock now, $S_w$, and the bound fluid gives the water the pores hold against the capillary pressure the cutoff stands for. Far above the free-water level they nearly agree. At 5890 ft, 360 ft above it, the well's water saturation is 18.9 %, 0.9 points above its irreducible 18 %, at a capillary pressure of 39.0 psi.

The Cutoff Is a Default

The one discipline NMR demands is the cutoff itself. The sources call 33 ms for a sandstone and 92 ms for a carbonate the "well-known industrial standards" and say in the same sentence that they "are not always applicable" (Chen, Ostroff and Georgi, 1998). Rocks differ in surface relaxivity, and a pore of radius $r$ relaxes at $T_2 = r/(3\rho_2)$ (Section 10.2), so a rock of lower relaxivity puts the same pores at longer T2. The figure's limestone is drawn that way, with a relaxivity 0.36 times the sandstone's, so that its 92 ms falls where 33 ms falls in a sandstone. That is the figure's own assumption; the sources give the two cutoffs and do not say they mark one pore size.

Choose the wrong line and the answer moves. Raise the cutoff on the upper oil sand from 33 ms to 92 ms and the spectrum has not changed, but BVI rises from 4.2 % to 5.0 % of the rock, FFI falls from 19.0 % to 18.2 %, and BVI over the porosity reads 21.6 %, 3.6 points above the well's 18 %. That is more bound water than the 18.9 % the well holds at that depth, which is how a cutoff that is too high gives itself away, and 0.8 pu of rock that the well says is free has been called bound: the producible-fluid call is that much low. The reverse error is smaller in this model. The sandstone's 33 ms in the tight limestone, where the bound peak sits at 11.2 ms, reads 17.0 %, 1.0 points below the well's 18 %, against 18.0 % at its own 92 ms.

Those errors are small because the figure's peaks are narrow and far apart. Widen each peak to 0.50 decades and 33 ms reads 19.7 % in the sandstone, and the cutoff that would read 18 % is 23.6 ms, not 29.7 ms. A real carbonate's spectrum is not a sandstone's moved along the axis, so the figure shows which way a wrong cutoff pushes the answer, not by how much.

Looyestijn (2001) gives the reason: bound water "is not an absolute quantity, but related to capillary pressure", and a single cutoff amounts to choosing a single capillary pressure. That is why a cutoff is calibrated to the formation, against core NMR and core capillary-pressure data, as Chen and co-authors do, and why the textbook values are only where to start.

What Ogbon-1 Can and Cannot Show

Ogbon-1 states one irreducible water, 18 %, the same in its sandstones and its limestone, and a capillary drainage curve that sets its water saturation above the free-water level. It has no T2, no pore size, no irreducible saturation that depends on the rock, and no clay-bound water in its shales. So the split returns 18.0 % at 33 ms only because the what-if spectrum was drawn to hold 18 %: the agreement is built in. What the figure shows is what a wrong cutoff does to a number the well fixes, not how well NMR would measure the irreducible water of Ogbon-1.

What the Cutoff Does Not Say

The line separates bound from free; it does not say what the free fluid is. Below the oil-water contact at 6230 ft the main sand is 25.7 % pore space and 100 % water: split at 33 ms, FFI is 21.1 % of the rock and all of it is water, so the movable water is 21.1 %. At 5890 ft the same line gives an FFI of 19.0 % of which only 0.2 % of the rock is water. Telling them apart is the work of Section 10.4, T1, T2, and Fluid Typing.

References

• Chen, S., Ostroff, G. and Georgi, D. T. (1998). Improving estimation of NMR log T2cutoff value with core NMR and capillary pressure measurements. Society of Core Analysts, paper SCA-9822. www.ux.uis.no/~s-skj/ipt/Proceedings/SCA.1987-2004/1-SCA1998-22.pdf
• Looyestijn, W. J. (2001). Distinguishing fluid properties and producibility from NMR logs. Proceedings of the 6th Nordic Symposium on Petrophysics, Trondheim, 15-16 May 2001. www.ipt.ntnu.no/nordic/Papers/6th_Nordic_Looyestijn.pdf