Açık ocak üretim yöntemi ile üretim yapacak olan bir maden ocağının üretim planlamasının optimizasyonu
Production scheduling optimisation of an open pit mine
Yazar: KÜRŞAT HASÖZDEMİR
Danışman: PROF. DR. SELAMET GÜRBÜZ ERÇELEBİ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Maden Mühendisliği Ana Bilim Dalı / Maden Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2019
Konu: Maden Mühendisliği ve Madencilik = Mining Engineering and Mining

Özet:
Günümüzde yüksek tenörlü cevher yataklarının tükenmesi ile birlikte madencilik
işlerinin ekonomik açıdan güvenli bir şekilde yürütülebilmesi stratejik bir planlama
evresi gerektirmektedir. Bu anlamda açık ocak üretim planlaması, üretilmesi sonucu
kar elde edileceği düşünülen cevher bloklarının maksimum net bugünkü değeri elde
edeceğimiz şekilde hangi sırayla üretilmesi gerektiğini bulmaktır. Bu çözüme
ulaşmak pek çok kısıtı ve karar değişkeni olan büyük bir optimizasyon probleminin
çözülmesini gerektirir. Bu boyutlarda bir problemin eldeki teknolojik imkanlarla
çözülebilmesi adına araştırmacılar problemi daha küçük alt problemlere bölerek
çözmeyi hedeflemişlerdir. Geleneksel yöntem olarak tabir edeceğimiz bu
yöntemlerde önce nihai ocak sınırı belirlenir, daha sonra bu sınır içerisinde kalacak
şekilde alt ocak sınırları oluşturulur ve planlama işlemi bu alt ocak sınırları üzerinden
devam eder. Bu metodun dezavantajları şu şekilde ifade edilebilir. Problemin alt
parçalarına ait optimum sonuçlar bir araya geldiklerinde ana problem için optimum
bir sonuç üretmiyor olabilirler ve bu yöntemin paranın zaman değerini hesaba
katmıyor oluşudur. Bu duruma bir alternatif metod ise Johnson tarafından ortaya
atılmıştır. Bu metoda göre cevher ve topoğrafyayı temsil eden bir blok modeldeki
blokların direk olarak sıralanması ile yapılan direk blok planlaması metodudur.
Problemi alt problemlere bölmek yerine tek bir adımda çözmesi ve paranın zaman
değerinide hesaba katması bu metodun avantajlarıdır. Bu metodun dezavantajı ise
büyük maden yataklarına uyarlamadaki eksikliklerdir. Bu dezavantaj ise
bilgisayarların artan işlemci kapasiteleri ve araştırmacaların daha pratik algoritmaları
sayesinde bertaraf edilmeye çalışılmaktadır. Bu çalışmanın amacı bu 2 farklı
metodun aynı bakır cevheri yatağına uygulanması ile elde edilen sonuçları ortaya
koymak ve kıyaslamaktır. Bu kapsamda, yapılan arama çalışmaları ve laboratuvar
analizleri sonucu elde edilen sondaj verilerinin bilgisayar ortamına taşınması ile 3
boyutlu olarak modellenmiş bir cevher yatağı kullanılmıştır. Bu cevher yatağı,
boyutları x:10m, y:10m, z:10m olan madencilik bloklarına bölünmüştür. Bu bloklara
3 boyutlu semi-variogram analizlerine dayalı olarak krigging metodu ile tenör
ataması yapılmıştır. Tenör atamaları yapılan blokların ekonomik değerleri, cevher
satış fiyatı, satış maliyeti ve tesis geri kazanım oranına göre hesaplanmıştır.
Ekonomik değerleri hesaplanmış olan bloklar, uzun vade üretim planlaması
yapılabilmesi için hem geleneksel yöntemle (alt-açık ocak sınırları üretme) hem de
direk blok planlaması yöntemiyle planlama işlemine tabi tutularak sonuçları
karşılaştırılmıştır. Bu bağlamda, geleneksel yöntemlerle planlama yapabilmek için
Micromine isimli yazılım kullanılırken direk blok planlaması metodu içinse
SimSched isimli yazılım kullanılmıştır. Bahsi geçen yazılımlar önce nihai açık ocak
sınırlarının optimizasyonu için kullanılmıştır. Ardından bu sınırlar içerisindeki
blokların hangi sırayla üretilecekleri, mevcut üretim ve tesis kapasitesine göre,
şevlerin fiziksel kısıtlamalarına göre, düşey ilerleme hızı ve madencilik
faaliyetlerinin yürütüleceği  minimum genişliğe göre, üretilecek cevherin cut-off
tenörüne göre ve atığa gönderilecek malzemenin maksimum tenörüne göre istenilen
sınırlar içerisinde kalacak şekilde simüle edilerek optimum üretim planı yapılmış ve
karşılaştırılmıştır.

Abstract:
Nowadays, the strategic mine planing has become very crucial for the sustainability of mining investments because of the lack of high grade ore reserves. In this sense, the mine production scheduling assists to solve a very complex optimization problem in order to identify the production sequence of the mining blocks which is profitable after mining activities. In order to be able to solve this complex problem with the technological capability of their time, researchers divided the master problem into the sub-problems. These sub-problems can be listed as, determination of the annual production capacity according to the total ore reserve and ore type, determination of the cut-off value according to the economical parameters obtained from economical and physical analysis, designation of the ultimate pit limit, pushback generation according to the ultimate pit limit and selling price of the ore and creating the production schedule throughout the life of mine. The designation of the cut-off value is not mentioned in this study. First of these sub-problems is determination of the ultimate pit limit. In order to obtain the ultimate pit limit, either Lerch and Grossman(1965) method which is based on graphic theory or maximum flow algorithm which is proposed by Johnson and Barnes(1988) can be used. The aim of the both methods is the maximization of the undiscounted cashflow. In this study, both softwares use the LG method in order to define the ultimate pit limit. Firstly, an economic block model should be created for the LG method. In order to be able to create an economic block model, the ore grades must be assigned to all blocks. The krigging interpolation method is used for grade assignment to the blocks. The krigging method requires nugget effect, sill and range values which can be obtained through semi-variogram analysis. In this context, geostatistical analyzes have conducted in order to define nugget effect, sill and range values. Before the variogram analyses, the grade values of the drill hole data analysed by histograms and their suitability to the normal distribution has investigated. The descriptive statistical analyses show that, using the ln values of the copper grades instead of the actual values will increase the statistical accuracy of the variogram analyses and krigging method. Down-the-hole variograms have been analysed in order to obtain the nugget effect (C0) of the log data which is  Co= 0,0438. In order to  investigate directional anisotropy of the grade values of drill hole data, omni-directional and multi directional variograms also analysed. According to the variogram analyses the sill value of the grade values is defined as 1 and the range value is defined as 25. In addition, the  highest directional anisotropy of the grade values can be seen on these directions:  azimuth 120o and dip angle -40o. Last step before the grade assignment by krigging method, the dimensions of the search elipsoid are defined. According to the JORC, the dimensions of the search elipsoid defined as 90m,70m,40m respectively. In addition to dimensions, the azimuth, incline and dip values of the search elipsoid also defined according to the 3D model of the mineralized region which is created by Micromine software. The search elipsoid has 4 regions in it. After grade assignment, the reserve estimation study is conducted. According to reserv estimation result, there are 91.8 millions ton of copper reserve which has overall grade of %0.28. Before the designation of the ultimate pit limit, all block values should be calculated in terms of block volume, ore grade, recovery of the processing plant, density of the materials, selling price of the ore, mininig costs, processing cost and selling cost. The economic blok model used as an input for the pit optimization process for both softwares (Micromine and SimSched). According to the pit optimization results, undiscounted cashflow of the ore reserve is 508.3 M$ and 505.9 M$ respectively. In addition to the undiscounted cashflow, destination of the blocks (process plant or waste dump) also designated. After defining the ultimate pit limit, the pit volume divided into sub pit limits which is called push-backs. In the process of the push-back generation, the selling price of the ore is multiplied by a revenue adjustment factor. The aim of the revenue adjustment factor is designation of the largest pit limit which has the minimum ore grade and the smallest pit limit which has the maximum ore grade. After push-back generation the ore and waste amounts of the generated pit limits are defined. The traditional mine production scheduling process uses those pit limits as inputs and production scheduling studies are conducted according to those push-backs. Proper pit limits selected according to the yearly production capacity as yearly production plans. The disadvantages of this method can be expressed by the criteria followed: the optimal solutions of the sub problems may not generate an optimal solution for the master problem when we combine them and the time value of the money is not considered in this method. An alternative method for production scheduling of an open pit mine is direct block sequencing  which is proposed by Johnson (1968). According to this method, all blocks in a block model which shows the ore body and the topography above the ore body can be sequenced in one step unlike the traditional methods. The advantages of this method can be expressed as: instead of dividing the master problem in to sub problems, this method solves the problem in one step. In addition, this method is also considers the time value of the money. Disadvantage of this method is its inapplicability to the complex block models. Thanks to technological advances, increasing computational capacity of the computers and practical algorithms of the researchers is facing with these disadvantages today. Optimising the production scheduling can be explained as the maximization of the Net Present Value of a mining operation for both methods. Basically both methods are facing with the same problems within the scheduling process. Those problems can be listed as: in-situ grade uncertainity, ambiguity of the operational and physical constraints and uncertain mining and processing costs. In order to be minimally affected by those uncertainities while planing the production schedule of a mining operation, those parameters must be considered carefully. Drilling operations which is done in order to explore valuable ore reserves must be well organized and should follow the proper standarts according to the ore type. In addition, laboratory works while analyzing the core samples from drilling operations in order to define grades, must obey international standarts. Lastly, the geo-statistical analyzes which defines the economical and physical charactheristics of a valuable ore reserve should be conducted meticulously.  The purpose of this study is: to apply both methods to the same block model and show the results and make a comparison of the solutions. For application of the traditional methods, the Micromine software was used and the SimSched software was used for direct block sequencing method. Both softwares are used for determination of the ultimate pit limit first then the production schedule is obtained according the phsyical and economical constraints. The comparison of the results are also given. The results of the production scheduling made by two methods compared in terms of, annual ore productions, annual waste removals, grades of the annual ore productions, annual strip ratios, annual Net Present Values and cumulative Net Present Values. The constraints used for both pit optimization and production scheduling can be listed as: yearly production capacity, recovery of the processing plant, selling price of the ore, selling cost, processing cost, mining cost, yearly discount rate, mining with, minimum bottom width, vertical rate of advance and cut-off grade. The physical and economical constraints of the scheduling process can be seen on (Table 3.1). According to the  production scheduling results, Net Present Value of the mineralized region identified as 341.9 M$ by the traditional methods and 301.8 M$ by the direct block sequencing method after 22 years of production. Both methods tries to produce the high grade blocks within the early stages of production in order to maximize the Net Present Value of the operation. In this context, the ore grades of the traditional scheduling methods varies between 2000 ppm and 6000 ppm, while the grades of the direct block seqeuncing method varies between 2000 ppm and 5000 ppm (Figure 3.24). Both methods have different strip ratios throughout the life of mine which varies between 0.4 and 2. We should consider the effects of the uncertanities on the scheduling process and should repeat the scheduling processes according to the re-created economic block models. By doing so we can minimize the effects of uncertanities and can observe the degree of the possible effects of uncertanities. In this context, repeating the production scheduling processes wtih the traditional methods will be more challenging than the direct block sequencing.  Micromine software is an important study in terms of providing the suitable work platform for traditional mine planing processes. SimSched, on the other hand, is an important study in terms of giving the opportunity to the mine planner to apply direct block sequencing method to the complex mine projects. Another advantage of the SimSched software is that it gives the planner the chance of investigating the different constraints and their effects on the production schedule.