**6. Quantitative Mineral Analysis by FTIR Spectroscopy**

**Zhiyong Xu, ^{a} Bahne C. Cornilsen,^{a} **

Domenic C. Popko,^{b} Wayne D. Pennington,^{b}

James R. Wood,^{b} and Jiann-Yang Hwang ^{c}

^{a}Department of Chemistry,

^{b}Department of Geological Engineering and Sciences, and

^{c}Institute of Materials Processing

Michigan Technological University

Houghton, MI 49931

USA

Email: zhxu@mtu.edu or bccornil@mtu.edu

**Introduction
**

Traditionally, X-Ray Diffraction (XRD) has been used to identify minerals in oil well core samples [1]. Quantitative XRD analysis is limited to minerals with good crystallinity. For amorphous and poorly crystallized minerals, XRD cannot provide accurate quantitative information. At the same time, even for well crystallized minerals, XRD is a time-consuming technique.

FTIR spectroscopy is a potential alternative method for rapidly acquiring quantitative mineralogy. Infrared spectroscopy has not been utilized extensively for quantitative analysis of oil field minerals. Rather, its main uses have been for mineral identification and structural study [2-4]. Typical mixture spectra display characteristic features which can be quantitatively related to variations in the constituent minerals. FTIR spectroscopy has more recently received attention for use in quantitative mineral analysis, including oil well cores [1,2,4-10].

FTIR spectroscopy relies on the detection of vibrational modes, *i.e.*, lattice vibrations and/or molecular group vibrational modes. Mineral identification is possible because minerals have characteristic absorption bands in the mid-range of the infrared (4000 to 400 cm^{-1}). The concentration of a mineral in a sample can be extracted from the FTIR spectrum because the absorbance of the mixture is proportional to the concentration of each mineral. This is given by Beer’s Law (equation 1), where A is the absorbance of a mineral mixture at a given wavenumber, a is the number of mineral components, e_{j} is the absorptivity of component *j*, *l* is the absorption path length (pellet thickness), and *c _{j}* is the concentration of component

*j*. All multicomponent analyses are based on Beer’s law, and the absorbance at a specific wavenumber is the sum of the absorbance of all sample components that absorb at that wavenumber.

**(1)**

Before the recent technological advances of computer equipment, the measurement of peak heights or peak areas was the common technique for quantitative analysis. A suite of chemometric approaches, including multiple linear regression, principal component regression, classic least squares, partial least squares, wavelets, and factor analysis provide choices for quantitative FTIR analysis [11-17]. Among these methods, the least squares fit is the most widely used. Unfortunately, when using the least squares model to fit the spectra of unknown samples with the standard matrix, the analysis can fail and negative coefficients may appear. Negative coefficients are physically meaningless, because it is impossible to have negative mineral concentrations. Recent work has focused on the development of a Non-Negative Least Squares (NNLS) method for use with FTIR to overcome this limitation [6,10]. NNLS is a promising deconvolution algorithm, which is based on the non-negative least squares matrix inversion. This project will apply the NNLS algorithm to calculate the mineral composition of core samples.

The basis of the quantitative IR analysis of minerals is the availability of a standard matrix of mineral spectra. This standard matrix is different from the common IR spectra of minerals, which only provide qualitative information for identification of the minerals. This standard matrix contains quantitative information for each mineral standard, *i.e.*, the absorbance at each step in the spectrum for each mineral at the given concentration in the KBr pellet (0.11 wt. %). To obtain this matrix, systematic, reproducible procedures are required for pellet sample preparation and collection of the spectral data. These will be outlined in the experimental section.

It is well known that in the linear region of Beer’s law, the mixture spectrum is a linear combination of the component mineral spectra. This combination or summation is carried out at each step or wavenumber in the spectrum, including steps or regions where there is no absorption due to vibrational modes. Such absorbance is “background.” It can be observed that this background can vary from sample to sample, independent of overall sample absorption. Therefore, in this study, the background has been removed to find out if its removal allows better precision or accuracy. However, in the references related to FTIR quantitative analysis, discussion about background subtraction techniques is seldom found. In addition to removing the background, it is also possible to ignore spectral regions where there are no peaks. In this project, “the Linear Background Subtraction Procedure” (LBSP) for FTIR spectra, including omission of empty spectral regions, is used to minimize the adverse effect of variable backgrounds.

**Experimental
**

Spectra for 13 standard minerals, the predominant minerals in oil well cores, were collected. These include illite, kaolinite, quartz, opal-A, opal-CT, oligoclase, albite, microcline, chlorite, dolomite, calcite, gypsum, and barite. These were carefully selected and characterized using SEM, ICP, and XRD analytical techniques [18]. FTIR spectra were collected in the mid-IR range (4000 – 400 cm^{-1}) for these 13 mineral standards, a core sample (1725.6 ft) from McKittrick Front well #418 in the Cymric Oil Field, and a core sample (2860 ft) from well KCL 44-375X in the Pioneer Oil Field (both in Kern County, CA, USA). Analysis of a synthetically prepared mixture demonstrates the accuracy of the LBSP and NNLS algorithms.

Sample preparation is critical to the successful quantitative analysis. The sample to KBr ratio used is 0.33 mg sample/300 mg KBr. This ratio was chosen so that the absorption bands are in the linear region of Beer’s Law, and so that the signal-to-noise ratio is maximized. Reliable quantitative analysis depends on precise and reproducible sample preparation. For an accurate quantitative IR analysis, the particle size should not exceed 2.5 mm [6]. This limit coincides with the shortest wavelength radiation used in the mid-IR. Particles that are comparable in size to the wavelength of the light interact with the light, and lead to broadened peak shapes and sloped baselines [1]. When particle size is larger than or equal to the wavelength of the incident infrared radiation, there can be a decrease in the intensity of the absorption band and an increased background. Particle size reduction and sample preparation, therefore, are very important. Particle sizes of less than 2.5 mm for all samples, both standards and oil well samples, were obtained using the following procedures:

- The core samples containing hydrocarbons were ground with organic solvent to remove the organic matter.
- The sample mineral mixtures, both standards and unknowns, were ground in a puck mill with absolute ethanol for 5 minutes, and then the resulting solution was centrifuged at 750 rpm for 3 minutes to remove larger particles, above 2.5 mm. The remaining suspended material in the solution was of 2.5 mm particle size or less. This was confirmed by examination with a Microtrac II particle-size analyzer (Leeds & Northrup Company).
- This suspension from procedure 2 was then centrifuged at 4000 rpm for 5 minutes to collect all remaining material. The resulting powder was dried at 105ºC for 24 hours to assure that water and ethanol were expelled. The dried powder was used to make a KBr pellet for the FTIR scan.
- 900 mg of KBr (IR grade, Fisher Scientific) were mixed with 1 mg of sample for 45 seconds in a Crescent Wig-L-Bug™ (International Crystal Laboratories) to homogeneously distribute the sample in the KBr. The mixture was then split into three, 300 mg aliquots to make three transparent KBr pellets under vacuum, and 10K psi pressure for 10 minutes.
- The samples were scanned using a Perkin-Elmer model 1600 FTIR spectrometer. Spectra were collected in the mid-IR region (4000-400 cm
^{-1}) at 4 cm^{-1}resolution (2 cm^{-1}steps) with 16 scans. A blank KBr pellet or air background was used when scanning the reference spectrum, and all samples were scanned in KBr pellets. An air background was used for the oil well core sample spectra.

The sample preparation method for the standard and unknown mineral samples is shown in Figure 1.

**Figure 1. **The sample/KBr pellet preparation flow chart.

**Data Analysis
**

The LBSP for FTIR spectra was developed in this project. An EXCEL™ spreadsheet macro method was used. First the minimum absorbance in a spectrum was found, and this minimum was adjusted to zero over the entire spectral range. The remaining background was removed linearly. Tangent lines were successively drawn between the non-zero peak minima and the lowest background point, and then subtracted, as demonstrated in Figure 2. The use of the LBSP, together with omission of spectral regions containing no sample absorbance, is expected to improve the quantitative analyses.

The NNLS algorithm (equation 2) solves a set of simultaneous, linear equations (equation 3) in matrix form, with non-negative constraints, where *b _{i}* is the absorbance at point

*i*. x

_{j}is a vector giving the concentrations of the a different minerals in the unknown sample. b

_{i}is the unknown mixture absorbance vector (containing b data points). A

_{ij}is the standard spectral

A_{ij} * x_{j} = b_{i } **(2)**

**(3)**

**Figure 2. **The Linear Background Subtraction Procedure (LBSP) used to remove FTIR spectral background.

matrix (equations 2 and 4) which contains absorbances (*A _{ij}*) for a standard minerals (at b data points). This is a straightforward application of a complicated, pre-existing, constrained linear algebra algorithm that was first developed by Lawson and Hanson [19]. Matlab™ is used to solve this deconvolution algorithm with the NNLS matrix inversion. It implements the matrix calculation algorithm, x

_{j}= NNLS (A

_{ij},b

_{i}), to allow NNLS to deal with a very large amount of data in a short running time. Therefore, equation 2 is solved for each spectral data point (

*b*) in a least squares sense, subject to the constraint that the solution vector x

_{i}_{j}has non-negative elements

*x*³ 0,

_{j}*j*=1, 2,…a. Values for

*x*are calculated to fit the observed

_{j}*b*absorbance values using equation 5.

_{i} ** (4)**

** (5)**

Spectra were collected with 4 cm^{-1} resolution. Therefore, with 2 cm^{-1} steps there are a total of 1801 data points (b) for each spectrum from 4000 to 400 cm^{-1}. Then according to Beer’s law, the quantitative analysis for a mineral requires solution of 1801 equations (for the 1801 data points in each spectrum) to obtain the 13 unknown concentrations *x _{j}* (

*j*=1,2,…a).

**Results & Discussion
**

The FTIR absorption spectra of thirteen mineral standards (illite, kaolinite, quartz, opal-A, opal-CT, oligoclase, albite, microcline, chlorite, dolomite, calcite, gypsum, and barite) and of a synthetic mixture were scanned. The calculated results (with and without background removal and for different wavenumber ranges) are listed and compared to the weighed amounts in Table 1.

MINERAL STANDARDS |
ACTUAL | Calculated (MATLAB) | ||||

before subtraction |
after subtraction* |
|||||

4000-400 | 4000-400 | 1600-400 | ||||

SHEET SILICATES |
CLAYS | Illite | 0.06 | |||

Kaolinite | 0.30 | 0.32 | 0.27 | |||

CHLORITE | Chlorite | 0.29 | ||||

FRAMEWORK SILICATES | SILICAS | Quartz | 0.30 | 0.11 | 0.28 | 0.28 |

Opal-CT | ||||||

Opal-A | 0.09 | |||||

FELDSPARS | Oligoclase | 0.17 | ||||

Albite | ||||||

Microcline | ||||||

CARBONATES | Dolomite | 0.29 | ||||

Calcite | 0.40 | 0.40 | 0.40 | |||

SULPHATES | Gypsum | 0.06 | ||||

Barite |

Weighed (actual) and measured compositions (wt. fraction) for a synthetic mixture, with and without background subtraction.

* Background area removed with the LBSP (Linear Background Subtraction Procedure), as defined in Figure 2.

**Table 1**

The mineral percentage of the synthetic mixture is first calculated “without background removal.” The result is not in good agreement with “actual” weighed amounts (see Table 1, 4000-400 cm^{-1}, “before subtraction” of background). The disagreement is great, and the specific minerals are not distinguished.

To determine how the non-zero, variable backgrounds influence the calculated percentages, the calculated composition for the spectrum with a non-zero background is compared with those calculated for spectra which have had the background removed (see Table 1, 4000-400 cm^{-1}). The calculated percentages “after background subtraction” using the LBSP are in good agreement with the actual percentages (within 2% to 3%). These are much more accurate than the initial analysis where the background was not removed. The individual minerals have now been distinguished. Therefore, application of the LBSP procedure to remove all background allows a more accurate quantitative analysis.

The compositions were also calculated using only the spectra within the 1600-400 cm^{-1} region. These results, also calculated after LBSP, are compared with those from the 4000-400 cm^{-1} region in Table 1. The results for these two regions are very similar. The accuracy is clearly improved by eliminating the background. Omitting the 4000-1600 cm^{-1} spectral region does not significantly improve the results. Values calculated after omitting only the 3000-1600 cm^{-1 }region (using the data from 4000-3000 cm^{-1} and 1600-400 cm^{-1 }after subtraction) are not included here, because these are similar to those reported for the 1600-400 cm^{-1} region alone.

The experimental FTIR spectra and calculated spectra (using LBSP and NNLS algorithms) for a sample (2860 ft) from well KCL 44-375X in the Pioneer Oil Field, and a sample (1725.6 ft) from McKittrick Front well #418 in the Cymric Oil Field, both in Kern County, CA, USA, are shown in Figures 3 and 4. For these two samples, the LBSP and the 1600-400 cm^{-1} region have been used for FTIR quantitative analyses. The resultant mineralogical analyses for these two samples are shown in Table 2. Visual inspection of the two spectra in each figure allows one to see the quality of these fits. This comparison demonstrates how well the actual experimental spectrum and the calculated spectrum agree.

**Figure 3. **Comparison of experimental and calculated FTIR spectra for well KCL 44-375X, in the Pioneer Field, Kern Country, CA, USA.

**
Figure 4. **Comparison of experimental and calculated FTIR spectra for McKittrick Front well #418, in the Cymric Field, Kern County, CA, USA.

Minerals |
McKittrick 1725.6 ft. |
Pioneer 2860 ft. |

ALBITE BARITE CALCITE CHLORITE DOLOMITE GYPSUM ILLITE KAOLINITE MICROCLINE OLIGOCLASE OPAL-A OPAL-CT QUARTZ |
0.0 0.0 0.0 4.8 6.1 6.6 0.0 1.2 0.0 0.0 0.0 81.4 0.0 |
0.0 0.0 6.5 0.0 4.6 0.7 3.5 10.6 12.8 6.7 0.0 26.7 27.8 |

**
Table 2. **FTIR mineralogical analyses (wt. %) for McKittrick Front well #418, in the Cymric Field, and well KCL 44-375X in the Pioneer Field, both in Kern County, CA, USA.

In order to examine the accuracy of the FTIR quantitative analysis for a core sample, the powder XRD patterns were also obtained for these two samples [18]. Then area fit software was used to fit the XRD patterns for opal-CT and quartz, and the ratio of opal-CT and quartz was obtained [18]. The comparison of results from FTIR analysis and this XRD fit are shown in Table 3. In the Pioneer 2860 ft sample, for opal-CT, the result is 49.1% by FTIR analysis and 49.4% by XRD peak area fit. For quartz, the result is 50.9% by FTIR analysis and 50.6% by XRD peak area fit. These are in excellent agreement. In the McKittrick 1725.6 ft sample, FTIR does not observe any quartz, but the XRD measurement shows 2.5% quartz. XRD is expected to be most sensitive to the more crystalline phases and less sensitive to the less crystalline phases. If it underestimates the opal-CT, the quartz content can be exaggerated. Most importantly, these results obtained by FTIR and XRD are completely consistent with each other, within an experimental precision of ± 2% to 3% each. This agreement substantiates the successful application of FTIR for these analyses. It also defines the reproducibility of each of these two methods (± 2-3%), which is consistent with the analysis of the synthetic mixture.

Percentage relative to total SiO_{2} |
||||

McKittrick 1725.6 ft. | Pioneer 2860 ft. | |||

opal-CT | quartz | opal-CT | quartz | |

FTIR | 100.0 | 0.0 | 49.1 | 50.9 |

XRD | 97.5 | 2.5 | 49.4 | 50.6 |

**Table 3. **Comparison of FTIR and XRD analyses for quartz and opal-CT.

**Conclusions**

Using 13 mineral standards in a “standard mineral matrix” and the Matlab™ NNLS function, the composition of mineral mixtures has been determined rapidly and accurately using FTIR spectroscopy. Using the synthetically prepared mixture, removal of background using a “linear background subtraction procedure” (LBSP) is shown to substantially improve the analyses, *i.e.*, improve agreement with the specific minerals and weighed amounts. Without background removal, the agreement is not acceptable. However, with the LBSP, agreement is good to ± 2.5%. Therefore, removing the background of a spectrum is a key factor for successful quantitative analysis. The LBSP is then applied to analyze two oil well core samples. Comparison of the FTIR results with the XRD analyses shows good agreement, again ± 2-3%. These results demonstrate the power and potential of FTIR spectroscopy for quantitative mineral analysis. The FTIR spectroscopic method is expected to be superior to XRD because it is sensitive to amorphous, as well as crystalline phases.

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**

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*Originally printed 12th February 2001.*

**REF:** Z. Xu, B.C. Cornilsen, D.C. Popko,W.D. Pennington, J.R. Wood

& J-Y Hwang, *Internet J. Vib. Spec*.[www.irdg.org/.ijvs] **5**, 1, 4 (2001)

Received in revised format 27th June 2001, accepted 13th August 2001.

**
REF:** Z. Xu, B.C. Cornilsen, D.C. Popko,W.D. Pennington, J.R. Wood

& J-Y Hwang,

*Internet J. Vib. Spec*.[www.irdg.org/ijvs]

**5**, 4, 6 (2001)