Question 1 of 12: Neutron Detectors and the Static SP

Question 1: Neutron Detectors and the Static SP (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) The three detector types used in neutron logging

A neutron tool emits fast (≈ 4.5 MeV) neutrons from a chemical source, and everything it can measure is decided by which product of the slowing-down and capture sequence the detector responds to. Neutrons leaving the source are slowed by elastic collisions — overwhelmingly with hydrogen, because a neutron and a proton have almost the same mass — passing through the epithermal band (about 0.1 to 100 eV) into thermal equilibrium (≈ 0.025 eV), after which they diffuse until they are captured by a nucleus, which promptly emits a capture gamma ray. The three detector families intercept that sequence at its three distinct stages.

1. Capture-gamma-ray detectors (neutron–gamma tools). The oldest arrangement, used by the GNT tool referred to in Question 3, does not detect neutrons at all: a scintillation crystal — typically NaI(Tl) coupled to a photomultiplier, or in the earliest tools a Geiger–Müller counter — counts the high-energy gamma rays released when thermal neutrons are captured, chiefly by chlorine in the borehole and formation waters, and by hydrogen. The measurement is cheap and robust, and it works through casing, but it is doubly indirect: the count rate depends on the capture cross-section of the medium as well as on its hydrogen content, so salinity, borehole fluid, and casing all bias the reading. This is why GNT porosities require large environmental corrections and why the tool is non-directional, unfocused, and cannot be pad-mounted.

2. Thermal-neutron detectors. These count neutrons that have already reached thermal energy, using a gas-filled proportional counter charged with ³He (or, historically, BF₃). The reaction ³He(n,p)³H releases 764 keV of charged-particle energy inside the counter, giving a large, easily discriminated pulse; the counter is essentially blind to gamma rays, which removes the main interference suffered by type 1. Thermal-neutron detection gives the high count rates and good statistics of the modern compensated neutron log (CNL), and dual spacing allows a ratio measurement that cancels much of the borehole effect. Its weakness is that thermal neutrons are strongly absorbed by high-capture-cross-section nuclei — chlorine, boron, gadolinium, and rare-earth-bearing clays — so a salt-water-filled or shaly formation reads an apparent porosity that is too high.

3. Epithermal-neutron detectors. These count neutrons in the epithermal band before thermal capture can bias the answer, and are the basis of the sidewall neutron porosity (SNP) tool used in Question 7. The detector — a ³He proportional counter, or a ⁶Li-loaded glass or ZnS(Ag)/⁶LiF scintillator — is wrapped in a thin cadmium or gadolinium shield that absorbs every thermal neutron, so only epithermal neutrons register. Because slowing down to the epithermal band is controlled almost purely by hydrogen concentration, the epithermal measurement is nearly independent of formation salinity and of thermal absorbers, and it is therefore the most direct hydrogen-index measurement of the three. The price is a much lower count rate (poorer statistics, slower logging speed), which is why the SNP is skid-mounted and pressed against the borehole wall.

(b) Static SP of the clean water sand

Given.

Find. The static spontaneous potential $E_{SSP}$ that a fully developed, thick, clean bed would produce opposite this sand.

Approach. Convert both resistivities to formation temperature with the Arps relation, recognise that "predominantly NaCl" makes the equivalent resistivities equal to the actual ones, then evaluate the electrochemical SP equation with the temperature-dependent coefficient from the formula sheet.

1. Move both resistivities to formation temperature. The Arps conversion supplied on the formula sheet is $$R_2 = R_1\,\frac{T_1 + 6.77}{T_2 + 6.77}$$ with $T$ in °F. Substituting the mud filtrate, $$R_{mf@180} = 0.29 \times \frac{68 + 6.77}{180 + 6.77} = 0.29 \times \frac{74.77}{186.77} = 0.116\ \Omega \cdot \text{m}$$ and the formation water, $$R_{w@180} = 0.048 \times \frac{74.77}{186.77} = 0.0192\ \Omega \cdot \text{m}$$
2. Form the resistivity ratio. Because both fluids are carried to the same temperature by the same factor, the ratio is independent of temperature — a useful check that no arithmetic slipped: $$\frac{R_{mf}}{R_w} = \frac{0.116}{0.0192} = \frac{0.29}{0.048} = 6.042$$
3. Replace equivalent resistivities by actual resistivities. The SP equation is written in terms of the NaCl-equivalent resistivities $(R_{mf})_{eq}$ and $(R_w)_{eq}$, which differ from the measured values only when divalent ions matter. Both fluids here are stated to be predominantly NaCl, so $(R_{mf})_{eq} = R_{mf}$ and $(R_w)_{eq} = R_w$, and the R_weq chart on page 18 is not needed.
4. Evaluate the SP coefficient at formation temperature. From the formula sheet, $$K = 61.3 + 0.133\,T_f = 61.3 + 0.133(180) = 85.24\ \text{mV}$$
5. Compute the static SP. Substituting into the electrochemical SP equation, $$E_{SSP} = -K \log_{10}\!\left[\frac{(R_{mf})_{eq}}{(R_w)_{eq}}\right] = -85.24 \times \log_{10}(6.042) = -85.24 \times 0.7812$$ $$\boxed{E_{SSP} = -66.6\ \text{mV}}$$

The sign is negative because the mud filtrate is fresher than the formation water, so the SP curve deflects to the left of the shale base line — the normal appearance opposite a clean, permeable, water-bearing sand.