The Influence of Instrument Design on Neutron Lifetime Measurements
Authors: Youmans Arthur H. , Hopkinson Eric C. 
Published: December 2007

Abstract
Commercially available logging services provide a measurement of the lifetime of thermal neutrons in formations adjacent to a borehole. This lifetime provides a measure of the macroscopic thermal neutron-capture cross-section S of the formation. which in turn is functionally related to the abundance and constituency of the rock matrix and contained fluids. Because the measurement is extremely sensitive to an abundance of trace elements like boron and gadolinium, it is very difficult to find rock formations with an accurately known value of S, which is required for the accuracy of the measuring system to be experimentally tested. Various theoretical studies published suggest that errors in the determination of S may occur because of the influence of borehole parameters and the effects of neutron diffusion. Experimental results are reported that demonstrate that the design of the instrument is crucial to the validity of any theoretical treatment of the subject. The influence of neutron diffusion and borehole effects can be overcome by optimal selection of spacing and shielding parameters.

INTRODUCTION
The lifetime of thermal neutrons in formation materials is a measure of the thermal neutron-capture cross-section of the bulk materials comprising the formation. This parameter, S, is quantitatively related to the elemental constituency of the medium. As such, a log based on the measurement of neutron lifetime1 can be used for identifying fluids in porous rocks when there is a contrast between the values of S for the respective fluids. Where formation waters are saline, the log has been used with great success to detect and evaluate oil-bearing zones behind casing. If S is accurately measured, it may be used to compute an unknown parameter with commensurate accuracy using the following relations.2Equation 1
whereEquation 2
The basic assumption of the logging method is that a population of neutrons in a formation will obey the simple relation N = Noe−Svt if the medium is homogeneous. In a medium penetrated by a borehole, it is assumed that the same kind of relation holds true after some time t1:Equation 3
From this equation, the value of S may be derived by measuring N1 and N2 at two times, t1 and t2.Equation 4
This theory requires two assumptions: that neutrons die or disappear only because of capture in the formation, and that it is possible to measure N, the number of live neutrons at any given time (or rather, the ratio of N1 to N2).
About 10 years of commercial logging experience have established that S is, to all intents and purposes, accurately and reliably measured3 by the Neutron Lifetime Log (NLL). * This is true even though the foregoing assumptions are not rigorously true. Neutrons do diffuse4 during the measurement interval, with the result that some leave the formation and enter the borehole where their remaining lifetime is dependent on borehole parameters rather than on the formation. Also, the problem of sampling the neutron population is complicated by the fact that the spatial distribution of neutrons changes during the measurement interval, so that any sampling technique designed to measure N is prone to error, or at least subject to doubt.