OR/21/006 Mineral composition analysis by linear inversion of log data

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Newell, A J, Woods, M A, Graham, R L, and Christodoulou, V. 2021. Derivation of lithofacies from geophysical logs: a review of methods from manual picking to machine learning. British Geological Survey Open Report, OR/21/006.

Contributor/editor: Kingdon, A

4.1 BACKGROUND The volumetric determination of mineral composition from petrophysical logs has a long history originating in efforts to estimate reliable porosity values from rocks with variable mineralogy and associated log responses (Doveton, 2018). By (mathematically) generating mixtures of mineralogical components with known petrophysical properties (Table 3) and comparing their calculated log response against the observed values it was possible to inverse model the likely composition of the rock by solving a system of linear equations.

Table 3. Table showing a section of the library of petrophysical properties used in the inverse modelling process. (DENS density, DT Compressional Delta Time (Slowness), DTS Shear Delta Time, VP P-Wave velocity), VS S-Wave velocity, PE Photoelectric Index (barns/electron)

Mineral DENS(g/cc) DT(μsec/ft) DTS(μsec/ft) VP(m/s) VS(m/s) PE Quartz 2.65 43.90 88.80 6037.62 4120.82 1.82 Shale 2.60 62.50 150.00 2559.92 1129.87 3.42 Calcite 2.71 47.20 89.90 2559.92 3436.29 5.09 Clay 2.65 64.30 98.90 5966.29 3079.51 3.03 Dolomite 2.87 43.90 74.80 7346.57 3959.73 3.13 Anhydrite 2.95 50.00 85.00 6105.55 3366.50 5.08 Gypsum 2.35 52.40 85.40 6513.39 3603.75 4.04 Muscovite 2.83 47.20 91.10 5773.50 3342.19 2.40 Biotite 3.20 55.50 100.60 5374.84 3027.65 8.59 Kaolinite 2.64 64.30 101.70 5637.62 2995.90 1.47 Glauconite 2.83 55.50 157.40 3257.57 1935.28 4.77 Illite 2.77 64.30 98.90 5966.29 3079.51 3.03 Chlorite 2.87 55.50 61.30 9268.86 4969.11 4.77 Orthoclase 2.54 68.90 84.90 4926.98 3586.24 2.87 Siderite 3.91 43.90 84.90 6957.66 3588.70 14.30 Pyrite 5.00 39.60 55.90 8429.07 5448.05 16.40 Halite 2.03 66.70 114.50 4594.68 2661.45 4.00 FreshWater 1.00 205.00 -999.25 1482.00 -999.25 0.36 Brine 1.10 188.00 -999.25 1522.00 -999.25 0.81 Oil 0.85 238.00 -999.25 1280.00 -999.25 0.12 Since the log response is a product of both the rock matrix and the fluid fill of the pore space, the fluid composition and their variable petrophysical properties must be taken into account (Table 3). The method works as an iterative search procedure. The input logs and the output mineralogical components (and pore-space filling fluid) are first defined and an initial composition is estimated. A series of intermediate solutions is calculated each comparing the input log responses with those predicted from the computed mineral proportions. The process terminates when convergence has been reached and there is no appreciable difference between successive solutions. The appropriate logs for this method are those that discriminate well between the various mineralogical components under consideration. The method traditionally uses those logs which are indicative of porosity (density, neutron porosity and sonic) but today can include resistivity, spectral gamma-ray and geochemical logs. The number of available logs has a direct limiting effect on the number of mineralogical components that can be distinguished. This method is useful for carbonate rocks of mixed calcite-dolomite composition and a wide range of other lithologies, although shales, mudstones and clay minerals can present problems because of their compositional variability. The method can generate reproducible solutions that are entirely erroneous if the initial mineral component model is incorrectly specified. Meaningful results are thus best obtained with as much a priori knowledge of the rock formation under consideration as possible. Careful geological evaluation of a range of possible solutions is a good approach together with pre-model calibration and post-model validation against cored intervals and cuttings where possible.

4.2 PRACTICAL APPLICATION Functionality to estimate mineral composition from petrophysical logs is a standard feature in many log analysis software packages and has also been implemented within Excel spreadsheets. Amosu and Sun (2018) provide an openly available MATLAB program (MinInversion) for petrophysical composition analysis of geophysical well log data that features an easy-to-use graphical user interface, a selection of inputs that include LAS and a choice of

three inversions methods. The underpinning table of mineral/fluid components and their petrophysical values is user editable.

Table 4. Graphical user interface of MinInversion with input data and results from the Mercia Mudstone Group of the Winterborne Kingston Borehole. The availability of only two input logs (Density and Sonic) restricts the analysis to two specified mineralogical components (halite and clay) and inverted porosity.