Simulation of cement raw material deposits using plurigaussian technique

Tayfun Yusuf Yünsel

doi:10.1515/geo-2018-0070

Article Open Access

Simulation of cement raw material deposits using plurigaussian technique

Published/Copyright: December 31, 2018

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From the journal Open Geosciences Volume 10 Issue 1

Abstract

Plurigaussian simulation is a powerful and very effective technique for modelling subsurface rock type domain distribution and in-situ mining reserve analysis. Modelling of subsurface to reveal the rock type distribution plays a key role for raw material extraction planning and plant operations such as extraction, transportation and comminution strategies. Because, the raw material distribution defines the plant operations and final product quality (cement modulus). This study addresses the application of plurigaussian simulation technique to reveal the subsurface rock type distribution of a cement raw material deposit in Turkey. The rock type domains include the limestone, clayey limestone, marl and sandstone which are the basic four rock type classes effecting the cement modulus in the field. The simulation process is carried out using these four rock type data on a determined grid system. A series of tests are made for the validation of the plurigaussian simulation. As a result, the rock type distributions are presented as both 2D-3D graphics and tabulated. The limestone is found as a dominant rock type in the deposit. The marl – a natural clinker - is another widespread raw material in the field and is found interbedded with limestone across the study field. The unwanted sandstone existence exhibited a sparse distribution in reserve body. The results indicated that, the deposit can provide the required raw material for the plant, showing the localised rock type distribution. A detailed raw material extraction planning and scheduling may be made using the results of this study.

Keywords: Plurigaussian simulation; rock type domain; cement raw material; sedimentary modelling

1 Introduction

Decision making for a mining engineer or a geologist about an underground value relies hardly on the field experience, knowledge and quality of sample data. Inability to construct a realistic underground model or insufficient geo-information may lead high financial loss. Thus, a deterministic approach with a suitable instrument to reveal the subsurface structure plays a very important role in the future planning for a plant [1].

A cement factory production planning starts at the raw material deposit. Thus, the necessary underground rock type modelling is carried out by Plurigaussian simulation for further mine planning. Geostatistical simulation procedures provide a solution for this as incorporating multiple simulations at once for the mineral types [2]. Although the main concept for the simulations includes a single variable application, extended implementation of the algorithm allows realizations of multiple categorical variables simultaneously. This aspect of the application of the simulations dealing with geological domains requires an exhaustive data process and simulation procedure. The geological domains here stand for the precisely and carefully defined rock types. Dealing with the geological domains by simulation techniques is carried out using categorical variables called “rock types” or “lithofacies”. There are several types of simulation techniques applied to characterize the geological domains. Gaussian-based methods are well-developed techniques and they include the advanced utilisation of the previously developed Truncated Gaussian Simulations techniques [1, 3, 4]. Plurigaussian simulation, the extension of Truncated Gaussian Simulation, exhibits better results in domain modelling of interrelated rock types by complex transitions and is becoming more popular in recent years [1, 2, 5, 6, 7, 8, 9].

2 The Study Area

The study area is located on the 10km southeast of Adana province and Adana Cement Factory (ACS) (Figure 1). The area spreads out approximately 461,000m² area. A typical Mediterranean climate prevails all over the region with an annual precipitation rate of about 600 mm. Transportation is available four seasons. The run of mine raw material is transported by rubber-wheel trucks to the plant. A significant amount of precipitation may obstruct the transportation and can decrease the crush and mill’s performance by smearing.

Figure 1

Location map of the study area.

The study area and environment are studied in detail by different researchers [10, 11, 12, 13, 14, 15]. According to observations in the field, the northern part of the area consists of Tertiary-aged rocks and pinky-red, sometimes yellowish-orange pebble stone, sandstone and clay stone formation start with Oligocene-lower Miocene aged Gildirli formation. The region exhibits a very flat topography and sedimentary formation occurrence.

A sedimentary deposition take place in the study field including the formations of limestone, clayey limestone, marl and sandstone. These lithological units are aged in Upper Miocene. The most widespread and abundant rock is clayey limestone across the study area. Its thickness exhibits a distribution as a variable manner and interbedded formation with other formations. The limestone is formed as fine grained and contains microcrystalline calcite and clay minerals quartz crystals, in addition to complementary fossil fragments. The most wanted formation in the field is marls which is a perfect raw material for cement production. Because it has a naturally ready-to-use chemical composition and easy to operate in the both field and plant. The marls are a variant of limestone having an admixture of clay and iron oxide. Chemical contents of the marls define its colour varying from yellowish-green to blue-grey-black. In terms of chemical content there is a little difference among the marl variants. A representative stratigraphy of the study field is presented in Figure 2.

Figure 2

A representative regional stratigraphy of the field.

3 Materials and Methods

3.1 Materials

The data is collected from the 43 vertical drilling hole samples (Figure 3). The average depth of drilling holes is about 30m, and rock samples were collected by a 3-4m interval for entire drilling holes. The drilling borehole data includes drilling coordinate, hole depth, sample lengths, lithological classification and chemical analysis (Al₂O₃, SiO₂, CaO, Fe₂O₃, Aluminium modulus, Silica Modulus and Lime standard). Lithological classes (such as marl, limestone) can be distinguished according to the chemical and physical differences. Thus, not only chemical analyses but also the distribution of rock types strongly affect the ratio of raw material to be fed to the cement factory. Primary target is to keep cement modulus’ between particular limits by mixing different rock types in accordance with their chemical contents. Therefore, a good cement production requires a good blending of lithological units according to their chemical contents and keep them in a specific interval.

Figure 3

Drilling hole locations in the study field.

Lithological classification is made for each sample in the drilling bore holes, and the categorised lithological units were used as input data for the Plurigaussian simulations. The lithology is classified into four lithological units according to the hand specimen, petrographic and chemical analyses. The classes are Marl, Limestone, Clayey limestone and Sandstone although numerous subclasses of these four main lithological units in the field. Percentages of the categorised lithological units are presented in Table 1.

Table 1

Individual rocktype percentages in the drilling well log.

Rock Type	Count of samples	Percentage (%)
# Marl	92	47.18
# C_Limestone	37	18.97
# Limestone	42	21.54
# Sandstone	24	12.31

3.2 The Method

3.2.1 The Plurigaussian Simulation

It is necessary for a lithological assessment to transfer the underground geological structure data to a digital media. There are a few methods used for this transferring process such as multipoint simulation with training image [16, 17, 18], multivariable stochastic model for indicator simulation [5, 19], co-simulation [20], truncated Gaussian simulation [21, 22]. Joint simulation also has superiorities on other techniques. However, it conducts the analyses in the similar Plurigaussian framework. Thus, the latest technique, Plurigaussian simulation, is used in the study. Especially, truncated Gaussian simulation remained as a context for the later derived subsurface modelling methods. When subsurface rock type distribution is simulated according to these methods, lithotypes’ (individual rock types in interested reserve) complex relations are reproduced as a single organisation of lithotypes. In addition, early times of truncated Gaussian modelling is developed from 2D to 3D lithotype ruling [23]. Easy visual modelling of facies, being an improved method for categorical simulations are a few superiorities of this simulation method among other techniques.

For the complex lithotype organisation, it is necessary to consider several Gaussian random functions in a single model. This complex transition modelling is the latest method called Plurigaussian Simulation [9, 24]. In this method, every lithotype is defined by its category along each Gaussian random functions. It means that each lithotype modelling is collected under one defining lithotype rules. As a result, exhibiting linked lithotype characteristics facies can create some dependencies among Gaussian random functions (correlation).

Plurigaussian simulation application is based on the idea of simulations of Gaussian random function in the field of domains to attribute the rock-type on the simulated values of each sample point. Truncation handles this operation. Using multigaussian random function, this operation’s conditions becomes much more complex and requires determination of rock-type transitions orders graphically called “lithotype ruling” [25].

The process of the plurigaussian simulation has four steps as follows:

Discretization and flattening is used to describe variables and the working grid system. Available data coordinates are migrated to a working grid system to work in a referenced level.
The drill hole data statistics is used to calculate the vertical proportion curves (VPC). These statistics are mainly utilised by reference surface which governs the modelling of deposition of domains in the working grid system. Thus, the drill hole data is then converted into a flattened space where the reference surface stands for zero elevation. The transferring the of simulation results to a real stratigraphic grid is the last step after employing simulations in a flat space [25].
Next step consist of deciding the lithotype ruling. The modelling is carried out in accordance with the correlation among the Gaussian variables, and their variogram models.
The lithotypically ruled Gaussian variables are simulated. The simulation results are then ported to real scale grid system called “structural grid”.

The previous model is used as complementary to the geological information in accordance with [26]:

Gaussian functions count;
Their correlation;
Domaining proportions for calculation of thresholds;
The domaining information data normalisation;
Lithotypical ruling.

External information such as stratigraphic domain sequence can be integrated into defining the proportion curves or grade proportion matrix. As a result, Plurigaussian simulation technique does not seek for reproducing input data variability structure, tries to mimic the real underground image.

This study is implemented by software ISATIS [27]. The lithotypes in the study area are split into four main groups although many subclass for each lithological unit.

The sample colours are assigned in accordance with the sample length in the drill hole logs.

# Blue: Marl

# Yellow: Clayey Limestone

# Green: Limestone

# Red: Sandstone

3.2.2 Application of the Plurigaussian Simulation

Figure 4 shows the rock type distribution in a single drilling well as a pie chart. Pie charts depict the rational rock type distribution for a single drill hole log data across the study field. Especially, rock-type locations and their ratios give information to the user for a good judgement of distribution. But, vertical change is not taken into account.

Figure 4

Pie chart of the rock type ratios in the related drill holes.

Before studying on vertical proportion curves (VPC) it is necessary to estimate rock types at each cell by an edition of the proportions of drilling rock-type data. In this way, the domain transitions are interconnected horizontally in the vertical direction. VPCs are created by counting the number of occurrences of each rock type distribution and used for validation of the geological interpreting of boreholes. After creating polygons on the field, vertical proportions curves are assigned to every polygon area representing domaining information. Study field is separated 6x6 polygon area. Polygon dimension is created according to drill hole spacing and the geometrical position of drill hole distribution. Figure 5 shows approximate rock type transitions at the individual polygons. These VPCs will be used for the later combination of the rock type domaining.

Figure 5

Vertical proportion curves of individual drill holes.

Next stage consists of defining the lithotypical ruling or truncation. As indicated previously four rock type domains are available in the field. Lithotype ruling is carried out in two-dimension on the basis of the sequencing probabilities of the lithological units. The transition probabilities of lithological units in both and upward direction is given in Table 2. The table says which lithological unit intersected with other units how many times. For example, Marl intersected with others, but with a low probability for sandstone in downward direction. Detailed information about lithotype ruling is well documented in the literature [23, 28]. According to Figure 6, limestone domains are crosscut the other two domains. Lithotype ruling or truncation is decided completely by the mining or geological engineer’s experience in the field. Because lithotype ruling is the key definition of domain’s transitions and it is necessary to have a basic knowledge about the manner of rock type distribution in the field.

Table 2

Transition statistics of the lithological units (downward and upward probability matrix).

		Number	#Marl	#Limestone	#Cl_ Limestone	#Sand
Downward	# Marl	738	0.93	0.031	0.027	0.012
	# Limestone	356	0.053	0.924	0.003	0.02
	# Cl_ Limestone	520	0.05	0.004	0.933	0.013
	# Sand	112	0.161	0.009	0.009	0.821

Upward	# Marl	749	0.916	0.025	0.035	0.024
	# Limestone	355	0.065	0.927	0.006	0.003
	# Cl_ Limestone	507	0.039	0.002	0.957	0.002
	# Sand	115	0.078	0.061	0.061	0.8

Figure 6

Lithotype ruling for the rock type domains.

Final analysis stage is the plurigaussian variogram fitting prior to Plurigaussian simulation. Figure 7, 8 and 9 show the indicator semivariograms of the easting, northing and vertical direction respectively. The related variogram parameters of the theoretical variograms of the lithological units are presented in Table 3. It can be seen on the table that all variograms are fitted as Spherical model. Because, the best representative lithological unit transitions are obtained by Spherical model. Fitting theoretical variograms to experimental variograms requires an exhaustive modelling process. It should be stressed that prior data process affects the variogram process strongly. In other words, an incorrect relation between domains will raise difficulties at fitting stage.

Figure 7

Easting projected multiple integrated variogram analyses.

Figure 8

Northing projected multiple integrated variogram analyses.

Figure 9

Vertical projected multiple integrated variogram analyses.

Table 3

Plurigaussian variogram parameters of lithological units.

	Nugget (C_o)	Sill (C)
	Nugget (C_o)	Easting	Northing	Vertical

Variogram Model		Spherical	Spherical	Spherical
# Marl	0.02	0.24	0.24	0.247
# Limestone		0.21	0.21	0.217
# Cl_ Limestone		0.17	0.17	0.158
# Sand		0.06	0.06	0.058

Lag (m)		14	15	0.5
No of Lag		28	30	25
Range (m)		250	350	12

4 Validation of the Results

Although there is no obligation, the Plurigaussian simulation results can be validated by a number of tests. They are based on comparison of input and simulated data results including visually examination, basic statistics and spatial structure reproduction. Plurigaussian simulations are carried out on a grid system given in Table 4.

Table 4

Grid design for the simulation process.

	Origin (m)	Number of Grid	Grid Size (m)
Easting, X (m)	718150	175	4
Northing,Y (m)	4092000	375	4
Elevation, Z (m)	35	45	1

In terms of statistical reproduction, the Table 1 shows the rock type domain percentages for input data. The simulated rock type histogram is presented in Table 5 and it reflects close values according to input data statistics (Table 1). In addition, this relation can be observed clearly from histogram comparison of input and simulated data (Figure 10). Again, the simulated rock type domain distribution histogram (Figure 10b) mimics the distribution behaviour of input rock type domain percentages.

Table 5

Individual rock type percentages in the simulated resource body.

Rock Type	Count of samples	Percentage (%)
# Marl	197166	44.09
# C_Limestone	97667	21.84
# Limestone	124932	27.94
# Sandstone	27443	6.14

Figure 10

Rocktype domain percentages: a) Drilling well log data result, b) Simulated resource body result.

Another validation technique consists of the reconstruction of the spatial structure from the simulated data. The simulation success should be supported by a good reproduction of spatial distribution of input data spatial distribution in addition to histogram and statistics. Figure 11a and 11b exhibit the analysis of variogram in three main directions (E-W, N-S and Vertical) for input and simulated data, respectively. The figure comparison concludes that the simulation algorithm satisfactorily reproduced the input variogram model of rock types. It should be noted that lithotype variogram modelling is a very exhaustive and time consuming process since multivariable spatial structure is defined by a single model.

Figure 11

Variogram reproduction in three main directions for the simulation results: a) Input data variogram, b) Simulated data variogram.

Visual examination of the drilling log data versus simulated structures is another method for judging the efficiency of the simulation results. Figure 12 presents the 3D visualization of the drilling wells within the sliced simulation results. The simulated resource is sliced so as to place next to drilling hole. The harmony between lithotype sequence in drilling holes and simulated resource can be seen clearly. Therefore, the figure indicates that the simulation in the field is reasonably confirmative because that the study field is very closely simulated in accordance with the drilling hole rock type data. The defined rock type units in the drill hole are conformably covered by simulated rock type units.

Figure 12

Visual examination of simulation result.

5 Mapping and Assessment

Mutually contacted rock type domains are simulated in accordance with the specific lithotype ruling (thresholds and Gaussian random fields) and the variogram models. The threshold values are determined as consistent with the domain proportions at the drilling log data. Also, the variograms are modelled by using the domain indicator data obtained from the drilling logs. To get a consistency in the contacts among the domains, the spherical variograms were used.

The simulation maps are presented in Figure 13, 14 and 15. Z-axis scale is increased by 7 fold because of shortness of vertical axis in comparison to horizontal axis’s length. Isometric view of the deposit (Figure 13) suggests that dominant rock type domain in the field is limestone and clayey limestone as expected through the drilling log data. Also, it is evident that sandstone distribution in the field is not local, rather distributed in small quantities across the field in both horizontal and vertical direction. It means that, it obstacles the selectivity to eliminate the undesired silica content in raw material to be extracted. In addition, it can be clearly said that the marl and the limestone domains exhibit a local distribution as illustrated in Figure 14. The figure gives relevant information about domaining distribution at different levels. Especially sequential domain transition structures in the vertical direction can be observed clearly. The cross-sections from west to east part of the study area (long axis of the deposit, exhibiting clearer domain transitions) are depicted as three cross-sections (A-A_′, B-B_′, C-C^′) in Figure 15. Figure 15b, 15C, 15d are the cross-sections of the traces indicated in Figure 15a. Topographic elevation change to east can be observed obviously. In addition, the Figure 15b, 15c, 15d implies that marl is much more abundant in the west-side region of the deposit, and east side of the deposits exhibits much more stratified structure (e.g. limestone) than the west side. Also, an important point here is revealed that the marl layers sink to east direction and limestone covers the marl (Figure 15c). Last but not least, the Figure 15 confirms that the sandstone distribution in the field is not regular, randomly distributed in small quantities.

Figure 13

Simulated 3D view of rock type distribution in the field.

Figure 14

Simulated horizontal section view of rock type domains distribution at different levels in the field. a) 49.5m, b) 52.0m, c) 54.5m, d) 57.0m.

Figure 15

Simulated vertical section view of rock type domains distribution in Y-Z plane in the field. a) X=718200m(A-A′), b) X=718500m(B-B′), c) X=718850m(C-C′).

6 Conclusions

Cement raw material deposit in the field has enough capacity and quality for a successful mining operation for the factory. Because the most valuable rock type domain marl – “having a natural clinker content” and limestone derivations distributed together in the field as expected. On the other hand, sandstone occurrences also distributed unevenly but in a narrow location.

As a result of this study, the produced rock type distribution maps enable a user (geological, mining or plant engineer) to plan and schedule the run of mine operations much more effectively and may help to tune up the cement modulus variation. A subsequent study may be implemented to observe the effects of the production planning and scheduling according to the chemical content or cement modulus variations from this plurigaussian simulation result.

This study is thought to be another proof of applicability of plurigaussian simulation for subsurface geological rock type domain simulation. A healthy and satisfactory geological interpretation of underground is found very limited with known techniques such as seismic analyses, magnetic surveying, and induced polarisation method. However, the best way to know the underground is drilling logs preserving in situ conditions. An underground modelling can be best achieved by co-initializing the robust drilling logs in a geostatistical simulation framework. Anyway, an experienced geologist is a key person in this kind of geostatistical simulation modelling study.

In addition, some aspects of the Plurigaussian simulation such as Lithotypical ruling and variogram modelling have a strong effects on the final model. Thus, modelling parameters should be cross-checked by final simulated image. Analysing of the modelling parameters of Plurigaussian simulations may be conducted under a further study.

Acknowledgement

The author would like to extend his sincere gratitude to Adana Cement Factory Administration providing data and logistics for this study.

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Received: 2018-09-18

Accepted: 2018-11-22

Published Online: 2018-12-31

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Articles in the same Issue

https://doi.org/10.1515/geo-2018-0070

Keywords for this article

Plurigaussian simulation; rock type domain; cement raw material; sedimentary modelling

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