Tapered Cutoffs for Magnetic Resonance Bound Water Volume
Authors: Kleinberg R.L. , Boyd A. 
Published: December 2007

Abstract
In standard magnetic resonance processing, the porosity is partitioned into free fluid and bound fluid volumes. All components in the T2 distribution less than a lithology-specific T2 cutoff are assigned to the bound fluid, while all components greater than that cutoff are assigned to the free fluid. It has been observed that this method sometimes predicts no bound water, where in fact there is a bound water volume. The cutoffs are determined by a laboratory method in which the porosity of a core is measured by magnetic resonance, the Archimedes method, or both, and its T2 distribution determined in the fully saturated state. The core is then centrifuged to the desired air-brine capillary pressure and the bound water determined by magnetic resonance and/or by weight. The T2 distribution of the fully saturated rock is integrated from T2min to T2cutoff, so that the integral equals the volume of water remaining in the rock after centrifugation.
This method assumes that bound water occupies small pores and free fluid occupies large pores, and that centrifugation completely empties large pores. This is only an approximation. In fact, after centrifugation a layer of water is left on the surfaces of all pores. The thickness of this layer depends on the pressure generated by the centrifugation and the capillary pressure of the film. Generally speaking, the larger the pore, the larger the proportion of water that will be lost.
We have developed an algorithm that explicitly includes water lining large pores in an estimate of bound water, based on a computation of capillary forces in the pores. A tapered cutoff is employed in which the bound water is found from a weighted sum of amplitudes in the magnetic resonance T2 distribution. The algorithm has been tested on a number of well logs. Often, the tapered and sharp cutoffs give the same answer, but in formations with large pores the tapered cutoff gives a better indication of bound water saturation.

Introduction
In standard NMR processing, the porosity is partitioned into a free fluid volume (FFI) and a bound fluid volume (BFV). All components in the T2 distribution less than a lithology-specific T2 cutoff are assigned to BFV while all components greater than that cutoff are assigned to FFI. The cutoffs are nominally 30 msec for sandstones and 100 msec for carbonates, but these are sometimes changed based on laboratory measurements on core, or at the discretion of the log interpreter.
Bound fluid volume can be determined by laboratory measurements. The porosity of the core is determined by NMR techniques or by the Archimedes method, or both, and its T2 distribution determined in the fully saturated state. The core is then centrifuged to the desired air-brine capillary pressure and the bound water determined by NMR and/or by weight. Then T2cutoff, used to partition the porosity into free and bound fluid volumes, is determined: the T2 distribution of the fully saturated rock, m(T2i), is summed from T2min up to a value, T2cutoff, at which the sum equals the volume of water remaining in the rock after centrifugation:
(1)
where
(2)
is the porosity. In current practice, the T2i are logarithmically spaced. This method assumes that the centrifuging process completely drains large pores, leaving the water in small pores unaffected, see Figure 1. This technique has been found to work well for many, but not all, rocks.
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