THE USE OF THE MCNP CODE FOR THE QUANTITATIVE ANALYSIS OF ELEMENTS IN GEOLOGICAL FORMATIONS

THE USE OF THE MCNP CODE FOR THE QUANTITATIVE ANALYSIS OF ELEMENTS IN GEOLOGICAL FORMATIONS Cywicka-Jakiel T. 1), WoŸnicka U. 1) and Zorski T. 2) 1) The Henryk Niewodniczañski Institute of Nuclear Physics, ul. Radzikowskiego 152, PL-31-342 Kraków, Poland 2) University of Mining and Metallurgy, Faculty of Geology, Geophysics and Environmental Protection, al. Mickiewicza 30, PL-30-059 Kraków, Poland Abstract The Monte Carlo modelling calculations using the MCNP code have been performed, which support the spectrometric neutron-gamma (sngl) borehole logging. The sngl enables the lithology identification through the quantitative analysis of the elements in geological formations and thus can be very useful for the oil and gas industry as well as for prospecting of the potential host rocks for radioactive waste disposal. In the sngl experiment, gamma-rays induced by the neutron interactions with the nuclei of the rock elements are detected using the gamma-ray probe of complex mechanical and electronic construction. The probe has to be calibrated for a wide range of the elemental concentrations, to assure the proper quantitative analysis. The Polish Calibration Station in Zielona Góra is equipped with a limited number of the calibration standards. An extension of the experimental calibration and the evaluation of the effect of the so-called side effects (for example the borehole and formation salinity variation) on the accuracy of the sngl method can be done by the use of the MCNP code. The preliminary MCNP results showing the effect of the borehole and formation fluids salinity variations on the accuracy of silicon (Si), calcium (Ca) and iron (Fe) content determination are presented in the paper. The main effort has been focused on a modelling of the complex sngl probe situated in a fluid filled borehole, surrounded by a geological formation. Track length estimate of the photon flux from the (n,γ) interactions (Tally F4) as a function of γ-rays energy was used. Calculations were run on the PC computer with AMD Athlon 1.33 GHz processor. Neutron and photon crosssections libraries were taken from the MCNP4c package and based mainly on the ENDF/B-VI, ENDF/B-V and MCPLIB02 data. The results of simulated experiment are in conformity with results of the real experiment performed with the use of the main lithology models (sandstones, limestones and dolomites). 1

Introduction Different methods using neutron sources are applied in geophysical prospecting. Neutrons from isotopic or accelerator sources penetrate a geological formation and the neutron transport process and/or specific nuclear reactions are detected. The detector response is sensitive to physical parameters of the investigated medium and their knowledge is of the great importance in geophysical interpretation of the measurements and in the description of the properties of geological formation. The information on porosity of rocks, on the water or another fluid (gas or oil) content, and on the mineral or elemental composition can be obtained from such a type of measurement. The interpretation of the detector response is very difficult and depends on many parameters usually known with insufficient accuracy. The sensitivity of the geophysical tool (generally consisting of the complete measuring instruments which include a neutron source, detectors and a transmission device) depends on the construction parameters, for example on the source - detector distance which is a very important parameter determining measuring abilities of the tool. The examination of the tool capability requires many dedicated test measurements made in wellknown laboratory conditions or theoretical approach to the whole physical processes of the neutron transport from the source to the detector. The geophysical tool is frequently used in drilled boreholes therefore the analytical solutions of the neutron transport in such a complicated medium as the geological formation with a hole filled by brine, are always approximate. Numerical methods used to simulate the particle transport in heterogeneous medium are very useful. It is possible to simulate exact history of particles and γ-rays in the complicated system and thus to simulate in details the neutron well-logging tool. The composition of the geological formation, parameters of the borehole, materials used for a tool construction can be changed easily. Numerical methods are very powerful tool in geophysical application. In the present paper an example of the application of numerical simulations is presented for a spectrometric neutron-gamma (sngl) welllogging tool. Such a tool is used for the quantitative analysis of some elements in underground geological formations. The spectrometric neutron-gamma borehole logging (sngl) based on detection of gamma rays created by thermal neutron capture and inelastic scattering of fast neutrons is very useful for lithology interpretation. Therefore the sngl play an important role in the oil and gas prospecting for the detailed mineralogy identyfication. Also the sngl can be used in the investigation of geological formations suitability for radioactive waste repository. The properties of geological formations should be well recognize before selection of suitable sites. The potential geologic repository sites as salt, granite, clay and basalt are the preferred potential host rocks having low permeability. Using neutron-gamma spectrometer consisting of Am-Be source and efficient BGO detector it was shown [1] that concentration of elements: Al, Si, Ca and Fe, which are the main constituents of many minerals, can be obtained from the sngl measurements. Concentration of aluminium (wt.%), well correlated with clay content was evaluated from the concentration of Si, Ca, Fe. The quantitative elemental analysis based on sngl needs the geophysical neutron-gamma spectrometer to be calibrated. Introduction of the environmental corrections reducing the effect of the disturbing factors is necessary for the fully effective calibration procedure. Factors such as the borehole fluid salinity, formation salinity, borehole diameter or temperature affect the accuracies of the measurements. The experimental investigation of the formation salinity problem is difficult, expensive and destructive for the used models. The Polish Calibration Station in Zielona Góra (Geofizyka Ltd.) is equipped with a limited number of the calibration standards. Therefore the main 2

purpose of this work was to simulate the sngl experiment for evaluating the expected influence of chlorine in a borehole and formation fluids on the accuracy of determination of Si, Ca and Fe content. Calculations have been carried out by the use of the Monte Carlo code MCNP4c [2], which is very useful for simulating neutron-gamma transport in media of complex geometry. High correlations between the results of real and simulated experiments were obtained. Experiment for calibration of the sngl sonde SO-5-90-SN type The feasibility study has been done for evaluating possibility of the quantitative analysis of elements H, Si, Ca and Fe in geological formations by the use of the spectrometric neutron-gamma borehole logging sngl [3]. The borehole spectrometer SO-5-90-SN, which belongs to Faculty of Geology, Geophysics and Environmental Protection (University of Mining and Metallurgy in Kraków, Poland) was applied for measurements at the calibration station in Zielona Góra (Geofizyka Kraków Ltd.) [4] using major lithology standards i.e. sandstones, limestones and dolomites of variable porosities. Models were situated inside the basin of water (100 cm layer of water above the rock) on a 50 cm thick concrete floor. The holes drilled in the centre of the rocks have diameters from the range 215 to 220 mm and were filled by water. The density and chemical compositions of the rock matrices were tested by four laboratories. Average elemental composition was established for every standard. In Table 1 the concentrations of the main elements i.e. H, Si, Ca and Fe are listed together with porosities and matrix densities ρ matrix. Table 1. The calibration models concentrations of H, Si, Ca, Fe elements, porosity and rock matrix density. The name and lithology H Si Ca Fe porosity r matrix of calibration standard (wt%) (wt%) (wt%) (wt%) (%) g/cm 3 Biala Marianna 2 - limestone 0.004 1.301 37.635 0.075 0.100 2.714 Morawica 2 - limestone 0.109 1.142 38.517 0.125 2.570 2.674 Jozefow 2 - limestone 0.704 0.685 36.161 0.079 15.240 2.659 Pinczow 2 - limestone 1.813 0.446 32.546 0.068 34.460 2.828 Libiaz 2 - dolomite 0.664 0.252 20.694 0.115 15.240 2.697 Mucharz 2 - sandstone 0.326 28.073 6.127 1.202 2.600 2.710 Brenna 2 - sandstone 0.484 34.700 1.923 1.667 7.670 2.648 Radkow 2 - sandstone 0.784 39.831 0.223 0.238 14.700 2.620 Zerkowice 2 - sandstone 1.307 39.250 0.442 0.362 24.870 2.640 The geophysical tool consisted of aluminium pipe which included two Am-Be sources (coupled together) in a special source-housing made of steel and the BGO (φ 40x60 mm) detector separated from the source by the lead (Pb), aluminium (Al) and polyamide shields. Pb protected the BGO cristal from the direct 4.43 MeV source photons. The resolution (FWHM) of BGO crystal was about 23 % for photons of energy 0.662 MeV from 137 Cs source. Two Am-Be sources used in experiment gave totally 1.32 10 7 n/s. The gamma-rays spectra were measured for all standards in 100 energy channels (104 kev/channel). 3

Calibration procedure for determination of H, Si, Ca and Fe content, based on measured intensities of major γ-rays from (n,γ) reactions i.e. 2.22 MeV for H, 3.54 MeV and 4.93 MeV for Si, 6.42 MeV for Ca and 7.631 MeV and 7.645 MeV for Fe. Because of not well-resolved gamma peaks in spectra measured by the BGO detector, the gross gamma counts from the selected energy windows E γ surrounded the major peaks were used. The ranges of the windows and energies of main gamma lines are listed in Table 2. The concentrations of H, Si, Ca, Fe (wt.%) in calibration standards were known from chemical analyses and were treated as reference values ( true values). Table 2. The most intensive gamma lines from (n,γ) interactions with H, Si, Ca and Fe and the range of energy windows E γ. Element E g [ MeV ] DE g [ MeV ] H 2.22 2.001 2.521 Si 3.54; 4.93 2.625 5.228 Ca 6.42 5.332 6.789 Fe 7.631; 7.645 6.893 8.975 For obtaining the calibration equation for determination of H, Si, Ca and Fe content the multiple linear regression was used for both: the gamma counts in the windows and reference elemental contents. The calibration equations have been used of the form: H = a 11 +a 12 IH + a 13 ISi + a 14 ICa + a 15 IFe (1) Si = a 21 +a 22 IH + a 23 ISi + a 24 ICa + a 25 IFe (2) Ca = a 31 +a 32 IH + a 33 ISi + a 34 ICa + a 35 IFe (3) Fe = a 41 +a 42 IH + a 43 ISi + a 44 ICa + a 45 IFe (4) where IH, ISi, ICa, IFe are gross numbers of counts in the selected energy windows, a 11, a 12... a 45 - coefficients determined by multiple linear regression. Introduction of the mentioned earlier environmental corrections is necessary before the application of the above equations in a field practice. Most prominent environmental correction for sngl concerns the reduction of the effect of formation and hole fluid salinity on the quality of measured γ-ray spectra. The influence of borehole salinity on the accuracy of elements determination has been investigated using single Mucharz 2 calibration standard. The concentration of NaCl in borehole was changed gradually i.e.: 4, 8, 17 and 50 kppm. The experimental results were in conformity with the MCNP simulations. The investigation of formation salinity problem which is experimentally difficult, expensive and leads to the lack of the used model was done on a base of MCNP simulations only. Monte Carlo simulations of the experiment. The Monte Carlo methods are very useful for the simulation of the radiation transport through matter, particularly when the complicated geometry occurs. Furthermore the existence of accurate cross-section data enables the simulation of chemically complex medium. The main effort of calculations has been focused on a modelling the complex sngl tool placed in a borehole, surrounded by a geological formation, to obtain well correlated experimental and simulated results. 4

MCNP simulations of the mentioned above sngl experiment run on the PC computer with AMD Athlon 1.33 GHz processor. In Fig. 1 the simplified scheme of the experimental arrangement used for the MCNP input is depicted. Fig. 1. The simplified scheme of the sngl experimental arrangement. The calibration standards listed in Table 1. were simulated by a regular cylinders (φ 160x150 cm) with the vertical hole in the middle, where the tool was inserted. Boreholes of diameter about 220 mm were filled by water. The matrix density and chemical composition of calibration standards were assumed to be homogeneous in volume of the models. The bulk densities of the formations were calculated knowing the porosity values. Detailed elemental compositions of the rocks were introduced for simulations, including: H, C, O, Na, Si, Ca, Mg, Al, K, Mn, Fe, Rb, Cd. No rare earth elements and 10 B were taken into account, their admixtures were expected for Mucharz 2 and Brenna 2 sandstones and have been confirmed by laboratory analysis. Some of rock elements lack their gamma production cross sections (Cd, Rb) - they were not present in cross section libraries included in MCNP4c. Neutron and photon cross-sections libraries taken from the MCNP4c package based mainly on the ENDF/B-VI, ENDF/B-V and MCPLIB02 data. The S(α,β) treatment was used for the H cross section. The BGO Bi 4 Ge 3 O 12 - scintillator of density 7.13 g/cm 3, diameter 4 cm and length 6 cm was surrounded by aluminium casing and the layer of teflon (3 mm). The photomultiplier and electronic were simulated by a diluted aluminium having density of 1.35 g/cm 3. Similar approach can be found in [5] where the photomultiplier was treated as a 30 mm aluminium disk. Following 5

experimental arrangement detector was separated from the source by the lead (Pb), aluminium (Al) and polyamide shields. The cross sections data for Ge were not included in MCNP4c package, they were kindly obtained from CSIRO Division of Mineral Engineering in Australia [6 ]. Volume distributed 241 Am-Be sources were simulated using Dependent Source Distribution Card. The sources in two locations along vertical axis of the probe (one by one) were picked with the same probability. Each location had the same energy spectrum. Neutrons were emitted isotropically. In simulations the track length estimate of the γ-flux, (tally F4) was used as a function of energy of γ-rays resulting from the neutron interactions: F V E t fi dv F ( E, r, t) dedt V 4 = = fi ) WT / V l where F ( E, r, t is the γ-flux in a cell (BGO) volume (V), W is photon weight and T l is track length. Fm4 card was introduced to obtain the photon rates in BGO material in photons/cm 3 (per one source neutron) which correspond to measurable γ-count rates. This number of photon collisions has form: C f ( E) Rm ( E) de where f(e) is energy-dependent flux (neutrons/s cm 2 ), R m is the microscopic reaction cross section (in barns) for m type reaction taken from the MCNP libraries and C constant is used for normalization (C= -1 was used for atomic density in atoms/(b cm)). The number of histories equal to 100 millions was taken to obtain relative errors of photon rates in a range 1 2.6 %. Calibration standards - comparison of experimental and simulated results. The photon rates in BGO obtained by the use of Fm4 card have units photons/cm 3 per one source neutron and per energy bin. To obtain the results in counts (cps) per energy bin, factor N= 995.25624 10 6 (cm 3 n/s) was used which is the product of the sources strengths equal to 1.13 10 7 n/s and the volume of the BGO crystal amounted to 75.3982 cm 3. The MCNP calculated spectra do not ideally respond to that from experiment. There are some limitations in capability of MCNP as well as remarkable errors of elemental compositions and porosities due to assumption of homogeneity of geological standards. In the case of simulation of sngl experiment the limitations of MCNP concern: - the lack of delayed gamma-rays from Al(n,γ)Al producing 1.78 MeV γ-line - the lack of modelling the interaction between the current in the PMT tube and impedances of the external electronic circuit. 6

- the lack of cross section data for (n,γ) interaction with some rock elements (Cd, Rb) and the imperfect quality of the (n,γ) cross sections from the existing libraries [7]. The new, improved library has been announced for (n,γ) processes [8]. From the above reasons simulated spectra are normalized to the experimental data. Using multiple linear regression equations of type (1) (4) the concentrations of H, Si, Ca and Fe in calibration standards were calculated from real ( meas ) and simulated ( MCNP ) experiments. The results were compared with reference (chem) H, Si, Ca and Fe concentrations. The comparison for Ca element is presented in Figs.2 and 3. The complete results are listed in Table 3. Ca (wt.%) from sngl experiment 40 MO2 Jo2 BM2 30 Y 1 =0.5976 + 0.9691*X PI2 Y: Ca meas (wt.%) 20 10 0 ZE2 R=0.984 rms = 2.85 wt. % RA2 BR2 MU2 LI2 Y 1 Y=X -10 0 10 20 30 40 X: Ca chem (wt.%) Fig. 2. Comparison of Ca concentration obtained from sngl experiment with reference Ca (wt%). Ca (wt.%) from simulated sngl experiment 40 MO2 Y: Ca MCNP (wt.%) 30 20 10 Y 1 =0.5906 + 0.9695*X R=0.984 rms=2.83 wt.% MU2 LI2 PI2 Y=X Y 1 JO2 BM2 0 ZE2 RA2 BR2-10 0 10 20 30 40 X: Ca chem (wt.%) Fig. 3. Comparison of Ca (wt.%) predicted from MCNP simulations with Ca (wt.%) from chemical analysis. 7

As can be seen in Figs. 2 and 3 Ca concentrations calculated on a base of simulated and experimental data are in good conformity with reference concentration of Ca. The departure of result for Li 2 (Libiaz 2) has the same character for simulations and experiment and is probably caused by the enhanced heterogeneity of this calibration model. Table 3. Parameters of multiple linear regression: correlation coefficients R and rms errors for: (1) correlation between simulated and reference concentrations of H, Si, Ca and Fe, (2) correlation between experimental and reference elemental concentrations. Simulations Measurements Configuration of standards Multiple linear regression R rms error (wt.%) R rms error (wt.%) H =H(IH,ISi,ICa,IFe) 0.965 0.14 0.964 0.14 Si =Si(IH,ISi,ICa,IFe) 0.986 2.89 0.990 2.47 Ca =Ca(IH,ISi,ICa,IFe) 0.984 2.83 0.984 2.85 Fe =Fe(IH,ISi,ICa,IFe) 0.986 0.10 0.946 0.18 From Table 3 can be seen that correlation coefficients R and rms error being the measure of goodness for linear dependence between predicted and reference ( true ) concentrations are nearly identical for real and simulated experiment. Small discrepancies can be seen for dependence Si MCNP (Si chem ) as two calibration sandstones -Mucharz2 and Brenna2 were simulated without the rare earth elements (Gd, Sm, Eu) and 10 B in a rock matrix. Their existence has been already analysed and they are included in going on simulations. The higher rms error in a case of Fe meas (Fe chem ) is probably caused by electronic instabilities. Simulation of Cl influence on the results of sngl borehole loging. Cl element can be a component of the used borehole fluids. This fact causes that γ-lines from Cl(n, γ)cl reaction interfere with γ-lines from Si, Ca and Fe and quality of spectra is worse. Cl lines cover predominantly the part of spectra above 5 MeV where the lines 6.42 MeV from Ca(n, γ)ca and 7.631 and 7.645 MeV from Fe(n, γ)fe are located. 8

NaCl in borehole fluid The calculations were performed for the Mucharz 2 sandstone with borehole salinities: 4, 8, 17 and 50 kppm NaCl. No rare earth elements (Gd, Sm, Eu) and 10 B were included in a rock matrix from the mentioned earlier reason. The simulated γ-rays spectra are presented in Fig.4 for Mucharz 2 sandstone with both: waterfilled and brine-filled (50 kppm NaCl) borehole. These spectra were not folded with resolution function of detector. The experimental spectrum with is included for comparison. 10000,0 Mucharz 2 sandstone Simulation (Mch2_2d) - water filled borehole Simulation (Mk2_16) - brine in borehole (50 kppm NaCl) Experiment - water filled borehole count rate (cps) 1000,0 100,0 10,0 H: 2,223 MeV Si: 3,539 MeV Si: 4,934 MeV Cl: 4.98 MeV Cl: 6.111 MeV Si: 6,38 MeV Ca:6,418 MeV Cl: 6.620 MeV Cl: 7.414 MeV Fe: 7,632 MeV Fe: 7,646 MeV Al: 7,724 MeV Cl: 8.579 MeV 1,0 1,06 1,27 1,48 1,69 1,90 2,10 2,31 2,52 2,73 2,94 3,15 3,35 3,56 3,77 3,98 4,19 4,40 4,60 4,81 5,02 5,23 5,44 5,64 5,85 6,06 6,27 6,48 6,69 6,89 7,10 7,31 7,52 7,73 7,93 8,14 8,35 8,56 8,77 8,98 9,18 9,39 Gamma-rays energy (MeV) Fig.4. Comparison of MCNP- simulated γ-ray spectra for Mucharz 2 sandstone with water filled borehole and with brine in borehole (50 kppm NaCl). The experimental γ-ray spectrum for water filled borehole (points) is included. Following the experimental situation the simulated spectra are binned in 104 kev-wide energy channels over the energy range E γ = 0.25-10 MeV. The major γ lines from (n,γ) reactions with H, Si, Ca, Fe and Cl nuclei are indicated. From Fig.4 is visible that the contributions of Cl γ-lines are remarkable in Ca and Fe windows. Therefore the main influence of Cl on the accuracy of Ca and Fe determinations is expected. Correlation coefficients R and rms errors for multiple linear regression used for Ca and Fe calculations (equations 3 and 4) are presented in Table 4. 9

Table 4. Dependence of Ca and Fe content on simulated and measured gamma counts, obtained according to equations 3 and 4 for calibration standards with water-filled and brine-filled (Mucharz 2) boreholes. Parameters of multiple linear regression: correlation coefficients R and rms errors. N is the number of measurements. Simulations Measurements Configuration of standards Multiple linear regression R rms error (wt.%) R rms error (wt.%) water-filled and brinefilled borehole N=14 water-filled and brinefilled borehole N=14 Ca =Ca(IH,ISi,ICa,IFe) 0.984 2.83 0.984 2.85 Ca =Ca(IH,ISi,ICa,IFe) 0.978 3.0 0.976 3.25 Fe =Fe(IH,ISi,ICa,IFe) 0.986 0.1 0.946 0.18 Fe =Fe(IH,ISi,ICa,IFe) 0.895 0.25 0.892 0.26 It can be seen from the Table 4. that the presence of NaCl (4-50 kppm) in a borehole fluid of Mucharz 2 sandstone, causes the remarkable decrease of linear correlation coefficient R and the accuracy of Ca and Fe determination. MCNP simulations are in conformity with measurements. As mentioned the lack of the rare earth elements and 10 B in simulations contribute to discrepancies between MCNP and experimental results. Also remarkable errors of the elemental compositions and porosities introduced for simulated models, cause additional differences as well as the electronic instabilities from the experimental side. As it concerns the influence of Cl present in geological formation on the accuracy of interesting elements, the MCNP simulations have been done for different formation salinities (17, 45 and 80 kppm of NaCl) and different salinities of the borehole fluid (0, 8, 17, 25 kppm NaCl). Standard Miocene formation of SE Poland was used with porosity of 25 %. Additionally twelve artificial rocks were used which composed of SiO 2, CaCO 3 and Fe 2 O 3 of different proportions. Porosity of the rocks was equal to 35 %. The preliminary results for Ca determination are listed in Table 5. The results for nine calibration standards are included. 10

Table 5. Parameters of multiple linear regression for Ca (wt. %) determination - correlation coefficients R and rms errors. N is the number of models. Configuration of standards calibration standards calibration standards + 20 artificial rocks with formation salinity 0-80 kppm NaCl. Water-filled and brine-filled borehole N=29 Simulations R rms error (wt.%) Ca =Ca(IH,ISi,ICa,IFe) 0.984 2.83 Ca =Ca(IH,ISi,ICa,IFe) 0.952 3.9 As can be seen from Table 5 the presence of Cl in borehole and formation fluids caused the worsening of parameters of multiple linear regression. The new calibration for 29 geological models, gives evaluation of Ca to within 3.9 wt. % i.e. relatively 38 % less accurate than for models without Cl. For accurate and reliable prediction of Cl influence on elements determination, the suitable corrections can be done evaluating the increase of gamma counts in selected energy windows. The MCNP support can be valuable. Summary The obtained results showed that the MCNP code is a very useful and effective tool for modelling the spectrometric neutron-gamma (sngl) experiments performed in the borehole surrounded by geological formations. The sngl well logging is a very important method for determination of the elements Si, Ca, Fe which are the main constituents of numerous minerals. Therefore sngl can contributed to the prospecting of the potential geologic repository sites as well as to oil and gas prospecting. The described sngl experiment performed at the Polish Calibration Station in Zielona Góra, using SO-5-90-SN spectrometer, showed that for calibration standards with the borehole diameter of 220mm Si, Ca and Fe concentrations can be measured to within 2.47 wt%, 2.85 wt.% and 0.18 wt.% respectively. This results are in conformity with results of simulated experiment (Tabele 3) even though in the MCNP simulations no rare earth elements and 10 B were taken into account. Already analysed Mucharz 2 and Brenna 2 sandstones showed remarkable amounts of Sm, Gd, Eu and 10 B which are introduced to the present calculations. Better correlations between Si MCNP and Si chem as well as between Fe MCNP and Fe chem are expected. The influence of Cl, present in a borehole fluid on the quality of γ-ray spectra and in consequence on accuracy of elements determination has been evaluated using results of the simulated experiment. The obtained data are well correlated with experimental results. Also preliminary evaluation of summation effect of Cl presence in borehole and formation fluids on determination of Ca in geological models has been done. Acknowledgements This work has been done under research projects of the State Committee for Scientific Research (KBN grants No: 8T12B 046 21 and No 3113/CT12-6/2002) 11

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