Simple MATLAB and Python scripts for multi-exponential analysis.

Multi-exponential decay is prevalent in magnetic resonance spectroscopy, relaxation, and imaging. This paper describes simple MATLAB and Python functions and scripts for regularized multi-exponential analysis methods for 1D and 2D data and example test problems and experiments. Regularized least-squares solutions provide production-quality outputs with robust stopping rules in ~5 and ~20 lines of code for 1D and 2D inversions, respectively. The software provides an open-architecture simple solution for transforming exponential decay data to the distribution of their decay lifetimes. Examples from magnetic resonance relaxation of a complex fluid, a Danish North Sea crude oil, and fluid mixtures in porous materials-brine/crude oil mixture in North Sea reservoir chalk-are presented. Developed codes may be incorporated in other software or directly used by other researchers, in magnetic resonance relaxation, diffusion, and imaging or other physical phenomena that require multi-exponential analysis.

Kinetics of Calcite Dissolution and Ca-Mg Ion Exchange on the Surfaces of North Sea Chalk Powders.

Calcite dissolution and Ca-Mg ion exchange on carbonate rock surfaces have been proposed as potential mechanisms occurring during smart waterflooding in carbonate reservoirs. However, there is still a lack of fundamental understanding of these reactions to quantitatively evaluate their effects in the reservoir flooding process. Especially, the data on precipitation and dissolution kinetics are insufficient. In this work, the equilibration kinetics of calcite dissolution and Ca-Mg exchange was experimentally studied. The behavior of three powders was compared: pure calcium carbonate, Stevns Klint outcrop chalk, and North Sea reservoir chalk. It was found that the equilibration time for calcite dissolution was of the order of seconds for a given surface-area-to-liquid-volume ratio. The existing theory of calcite dissolution could well reproduce our observations. The Ca-Mg exchange showed two-step kinetics: the first step was fast, and it dominated the process within the first hour of reaction; the second step was slow, and it continued longer than the time of observation (2 weeks). Characteristic times for the two steps were extracted by fitting the experimental curves. A two-layer adsorption model was proposed to characterize the kinetic process and successfully matched with experimental data. The findings were further extended to flow-through scenarios. By comparing with literature data and surface complexation models, it was concluded that calcite dissolution alone was unlikely to be able to explain the additional recovery reported in the literature. The Ca-Mg exchange process could dominate the fluid-rock interactions at a high temperature in pure calcium carbonate rocks, while competitive adsorption of cations appeared to control the process at a lower temperature. Different carbonate rocks possess different properties with regard to the ion-exchange process.

Electrical Double-Layer and Ion Bridging Forces between Symmetric and Asymmetric Charged Surfaces in the Presence of Mono- and Divalent Ions.

An atomic force microscope, employing the colloidal probe technique, was used to study the interactions between six different combinations of silane-functionalized silica surfaces in NaCl and CaCl2 solutions. The surfaces consisted of monolayers of the apolar trimethoxy(octyl)silane, the positively charged (3-aminopropyl)trimethoxysilane, and the negatively charged (3-mercaptopropyl)trimethoxysilane. The interactions between the three symmetric systems, as well as between the three asymmetric combinations of surfaces, were measured and compared to calculated electrical double-layer forces. The results demonstrated that the long-range interactions between the surfaces in all cases were dominated by double-layer forces, while short-range interactions, including adhesion, were dominated by ion bridging forces in the cases where both interaction surfaces favored adsorption of calcium ions. The study thus also demonstrates how surface force studies in mono- and divalent salt solutions can be used as an analytical tool for probing specific functional groups on heterogeneous surfaces.

13C, 18O, and D fractionation effects in the reactions of CH3OH isotopologues with Cl and OH radicals.

A relative rate experiment is carried out for six isotopologues of methanol and their reactions with OH and Cl radicals. The reaction rates of CH2DOH, CHD2OH, CD3OH, (13)CH3OH, and CH3(18)OH with Cl and OH radicals are measured by long-path FTIR spectroscopy relative to CH3OH at 298 +/- 2 K and 1013 +/- 10 mbar. The OH source in the reaction chamber is photolysis of ozone to produce O((1)D) in the presence of a large excess of molecular hydrogen: O((1)D) + H2 --> OH + H. Cl is produced by the photolysis of Cl2. The FTIR spectra are fitted using a nonlinear least-squares spectral fitting method with measured high-resolution infrared spectra as references. The relative reaction rates defined as alpha = k(light)/k(heavy) are determined to be: k(OH + CH3OH)/k(OH + (13)CH3OH) = 1.031 +/- 0.020, k(OH + CH3OH)/k(OH + CH3(18)OH) = 1.017 +/- 0.012, k(OH + CH3OH)/k(OH + CH2DOH) = 1.119 +/- 0.045, k(OH + CH3OH)/k(OH + CHD2OH) = 1.326 +/- 0.021 and k(OH + CH3OH)/k(OH + CD3OH) = 2.566 +/- 0.042, k(Cl + CH3OH)/k(Cl + (13)CH3OH) = 1.055 +/- 0.016, k(Cl + CH3OH)/k(Cl + CH3(18)OH) = 1.025 +/- 0.022, k(Cl + CH3OH)/k(Cl + CH2DOH) = 1.162 +/- 0.022 and k(Cl + CH3OH)/k(Cl + CHD2OH) = 1.536 +/- 0.060, and k(Cl + CH3OH)/k(Cl + CD3OH) = 3.011 +/- 0.059. The errors represent 2sigma from the statistical analyses and do not include possible systematic errors. Ground-state potential energy hypersurfaces of the reactions were investigated in quantum chemistry calculations at the CCSD(T) level of theory with an extrapolated basis set. The (2)H, (13)C, and (18)O kinetic isotope effects of the OH and Cl reactions with CH3OH were further investigated using canonical variational transition state theory with small curvature tunneling and compared to experimental measurements as well as to those observed in CH4 and several other substituted methane species.

Relative tropospheric photolysis rates of HCHO and HCDO measured at the European Photoreactor Facility.

The relative photolysis rates of HCHO and HCDO have been studied in May 2004 at the European Photoreactor Facility (EUPHORE) in Valencia, Spain. The photolytic loss of HCDO was measured relative to HCHO by long path FT-IR and DOAS detection during the course of the experiment. The isotopic composition of the reaction product H(2) was determined by isotope ratio mass spectrometry (IRMS) on air samples taken during the photolysis experiments. The relative photolysis rate obtained by FTIR is j(HCHO)/j(HCDO) = 1.58 +/- 0.03. The ratios of the photolysis rates for the molecular and the radical channels obtained from the IRMS data, in combination with the quantum yield of the molecular channel in the photolysis of HCHO, Phi(HCHO-->H(2)+CO) (JPL Publication 06-2), are j(HCHO-->H(2)+CO/jHCDO-->HD+CO) = 1.82 +/- 0.07 and j(HCHO-->H+HCO/(jHCDO-->H+DCO + jHCDO-->D+HCO)) = 1.10 +/- 0.06. The atmospheric implications of the large isotope effect in the relative rate of photolysis and quantum yield of the formaldehyde isotopologues are discussed in relation to the global hydrogen budget.

Relative tropospheric photolysis rates of HCHO, H13CHO, HCH18O, and DCDO measured at the European photoreactor facility.

The relative photolysis rates of HCHO, H13CHO, HCH18O, and DCDO were studied in pseudo-natural tropospheric conditions in July 2003 at the European Photoreactor Facility (EUPHORE) in Valencia, Spain. The photolytic decay of HCHO, H13CHO, and HCH18O is measured relative to DCDO by long path FT-IR detection during the course of about 3 h of sunlight. The relative photolysis rates obtained are as follows: JH13CHO/JHCHO = 0.894 +/- 0.006, JHCH18O/JHCHO = 0.911 +/- 0.011, and JDCDO/JHCHO = 0.597 +/- 0.001. The errors represent 1sigma and do not include possible systematic errors. The atmospheric implications of the large isotope effects in the photolysis of formaldehyde are discussed.

Relative rates of reaction of 13C16O, 12C18O, 12C17O and 13C18O with OH and OD radicals.

A relative rate experiment is carried out for four isotopomers of carbon monoxide (CO) and their reactions with OH and OD radicals. The relative reaction rates of 13C16O, 12Cl8O, 12C17O and 13C18O with OH and OD radicals are measured at 298 +/- 2 K and 1013 +/- 10 mbar. The OH/OD source in the reaction chamber is photolysis of ozone to produce O(1D) in the presence of molecular hydrogen: O(1D) + H2/D2 --> OH/OD + H/D. The relative reaction rates are determined as: k(OH) + 13C16O/k(OH) + 12C18O = 0.98 +/- 0.01, k(OH) + 12C17O/k(OH) + 12C18O = 0.990 +/- 0.008, k(OH) + 13C16O/k(OH) + 13C18O = 0.98 +/- 0.01, k(OD) + 13C16O/k(OD) + 12C18O = 0.99 +/- 0.01, k(OD) + 12C17O/ k(OD) + 12C18O = 1.000 +/- 0.008, k(OD) + 13C16O/k(OD) + 13C18O = 0.98 +/- 0.01. The errors represent 2sigma from the statistical analyses and do not include possible systematic errors. These are novel results for the kinetic isotope effects in the reactions of CO isotopomers with OD radicals. The results for the reactions of CO isotopomers with OH radicals constitute a repeat and a re-analysis of experimental data previously published by this group which have been found to be partly erroneous. This communication serves as a correction to the following paper: K. L. Feilberg, S. R. Sellevåg, C. J. Nielsen, D. W. T. Griffith and M. S. Johnson, Phys. Chem. Chem. Phys., 2002, 4, 4687.