The effect of accumulation in 2D estimates in phosphatic ore

Diego Machado Marques et al. Mining Mineração The effect of accumulation in 2D estimates in phosphatic ore http://dx.doi.org/10.1590/0370-44672014670179 O efeito da acumulação em 2D em estimativas de minério fosfático Diego Machado Marques Abstract Mining Engineer, MsC, PhD, Mining Engineering Department, UFRGS, Porto Alegre, Rio Grande do Sul, Brasil Ricardo Hundelshaussen Rubio Industrial Engineer, Msc, PhD Candidate, Mining Engineering Department, UFRGS, Porto Alegre, Rio Grande do Sul, Brasil João Felipe Coimbra Leite Costa Mining Engineer, Msc, PhD. Mining Engineering Department, UFRGS, Porto Alegre, Rio Grande do Sul, Brasil Evangelina Maria Apparicio da Silva Mining Engineer, Msc, Vale S.A, Belo Horizonte, Minas Gerais, Brasil The geological modeling of stratiform deposits can become very complex, often making use of geological envelopes of small thickness and requiring the use of subblocks (based on Cartesian coordinates) to produce a coherent block model. However, geological events after the formation of the deposit (folds, faults, etc.) can change the direction of spatial continuity of certain attributes, with the mixing of samples belonging to different formation eras (in the case of stratiform deposits) in the same elevation. This study presents a solution for deposits with stratigraphic grades combined with samples of different origins. The solution is a two-dimensional estimate obtained by accumulating the thicknesses of P2O5 in a phosphate deposit (as compared to traditional statistical analysis in three dimensions). Keywords: accumulation, ordinary kriging, phosphate. Resumo A modelagem geológica de depósitos estratiformes pode-se tornar muito complexa, muitas vezes fazendo uso de envelopes geológicos de pequena espessura e exigindo o uso de sub-blocos (com base em coordenadas cartesianas) para produzir um modelo de blocos coerente. No entanto, eventos geológicos após a formação do depósito (dobras, falhas, etc.) podem mudar a direção da continuidade espacial de certos atributos, com mistura de amostras pertencentes a épocas de formação geológicas diferentes (no caso de depósitos estratiformes) na mesma elevação. Esse estudo apresenta uma solução para depósitos com teores estratigráficos combinados com amostras de diferentes origens. A solução é uma estimativa bidimensional obtida pela acumulação da espessura de P2O5 em um depósito de fosfato (em comparação com a análise estatística tradicional em três dimensões). Palavras-chave: acumulação, krigagem ordinária, fosfato. 1. Introduction The estimate of an attribute (grade, thickness, etc.) using geostatistical data requires certain assumptions, and among them is the assumption that the attribute presents autocorrelation in time and/or space. These estimates are based on temporal/spatial continuity for the attribute, which in turn is based on the sample values of the attributed model. In many cases, the database is geo-positioned using a Cartesian coordinate system. However, the con- tinuity of the phenomenon may not be compatible with this type of coordinate. At the time of formation of mineral deposits, the minerals are crystallized or deposited in positions consistent with an active geological process, and this process determines the continuity of attributes related to the constitution of the rocks (e.g. mineral grades). Geological events subsequent to the formation of the deposit, such as folding, can change the direction of continuity of certain at- tributes (Koppe et al., 2006). There are some ways around this issue, such as coordinate transformations (McArthur, 1987; Deutsch, 2002) and accumulation in two dimensions (2D) (Krige, 1981). In cases where one dimension is much smaller than the others (stratiform deposits), it is usual to use the accumulation method of grades by the layer thickness, where the estimate of the grades is obtained indirectly. This process cannot be considered a simplification because REM: R. Esc. Minas, Ouro Preto, 67(4), 431-437 jan. mar. | 2014 431 The efect of accumulation in 2D estimates in phosphatic ore it adds complexity to the estimation process. Besides requiring additional steps to obtain the final grades, it can generate inconsistencies if not executed properly, with, for example, extreme values exceeding the minimum and maximum grades of the original data. This article aims to present the steps in the estimation of a phosphatic deposit (P2O5) through the accumulation process in 2D, showing all the necessary steps for its implementation. In addition, the reasons for choosing to perform the estimation in 2D rather than the conventional three dimensions (a) Figure 1. Theoretical example of how folds in the geological phenomenon (a) may affect the analysis of spatial continuity, and (b) how unfolding of the layer can reduce the problem. It can be noted in (a) that, independent of the orientation of the ellipsoid search of samples, those of the same geological (3D) are shown. The deposit studied had several layers of phosphatic ore interspersed with layers of waste rock. The positions of the Highwall and the Footwall were determined using data from drillholes. The results of the modeling showed almost horizontal layers, with a slight folding, and large variations in thickness The determination of the spatial continuity of the deposit could be undermined by mixing samples of the same level (elevation), Z, belonging to a different geological formation era (distinct stratigraphic levels), correlating samples that may be on the Highwall in a drillhole at one given Z coordinate and on the Footwall in another drillhole at the same Z coordinate, as shown in Figure 2(a) (holes A, B, C and D). In view of this, the unfolding (transformation of Cartesian coordinates to stratigraphic coordinates) of the deposit could be a way of improving the results of the analysis of spatial continuity, given that in deposits of sedimentary origin, the values from sediments of the same geological age (stratigraphically on the same horizon) tend to have high spatial correlation (Figure 1 (b)). (b) Figure 1 era (1, 2 and 3) will be the same, if properly analyzed. After the transformation (b), samples of the same geological era (1, 2 and 3) have the same orientation and coordinates in the search plan. Finally, in certain cases, the Euclidean distance is an inadequate measure (as in the Figure 2) and should be replaced by, for example, a "curved" distance measurement in layers with folds (Dagbert et al. 1984). To determine whether the study should be performed in 3D with support, or in 2D, accumulating grades by the thickness, the series of tests presented below were performed. Elevation (m) -20 -30 -40 -50 -60 8000 7000 6000 5000 4000 3000 2000 1000 Isatis NE (m) Figure 2 Cross section of interest layer (north–south) 2. Methodology The sample data from a drilling campaign were obtained from d r i l l c ore s of d i f f ere nt le n g t h s (different base (...truncated)