Grade-Tonnage Curves – Worthy of a Good Look

Most of us have seen the typical “grade-tonnage” table or graph, showing ore tonnes and grade at varying cutoff grades. It is usually part of every 43-101 technical report in Section 14.  We may glance at it quickly and then move on to more exciting chapters. Section 14 (Mineral Resources) can be a very complex chapter to read with statistics, geostatistics, and mathematical formulae.  However the grade-tonnage curve aspect isn’t complicated at all.
The next time you see the grade-tonnage relationship, I suggest taking a few seconds to study it a bit further.   There might be some interesting things in there.

Typical Grade-Tonnage Information

Typically, one will see grade-tonnage data in 43-101 Technical Reports towards the back of Section 14 "Mineral Resources".  The information is normally presented in either of two ways; (i) a grade-tonnage table or (ii) a grade tonnage graph.  Examples of each are shown below.  The grade tonnage graph typically has the cutoff grade along the bottom x-axis and the two separate y-axes  representing the ore tonnes above cutoff and the average ore grade above cutoff.
typical grade tonnage table
typical grade tonnage curve
Rarely do you see both the table and curve in the report, although ideally one would want to see both.  Given the option, I would prefer to see the graph more than the table of numbers.  The trend of the grade-tonnage information is just as important as the values, maybe even a bit more important.  Unfortunately, a data table by itself doesn’t illustrate trends very well.

Useful Grade-Tonnage Curve Information

mining grade tonnage curveWhen I am undertaking a due diligence review or working on a study, very early on I like to have a look at the grade-tonnage information.  This could be for the entire deposit resource, within a resource constraining shell, or in the pit design.
The grade-tonnage information gives an understanding of how future economics or technical issues may impact on the mineable tonnage.
An example of a typical grade-tonnage curve is shown here.
The cutoff grade along the x-axis will be impacted by changes in metal price or operating cost. The cutoff grade will increase if metal prices decrease or if operating costs increase.
The question is how sensitive is the mineable tonnage to these economic factors. The slope of the tonnage and grade curves will help answer this question.
In the example shown, the tonnage curve (blue dots) is fairly linear, meaning the ore tonnage steadily decreases with increasing cut-off grade.  That is expected and is reasonable.
mining grade-tonnage curveHowever, if the tonnage curve profile resembled the light blue line in this image, with a concave shape, the ore tonnage is decreasing rapidly with increasing cutoff grade.   This is generally not a favorable situation.
It indicates that a significant portion of the tonnage has a grade close to the cutoff grade.  If that’s the situation, the calculation of the cutoff and the inputs used to generate it are important and worthy of scrutiny.  Are they reasonable?  Over the long term, is the cutoff grade more likely to increase or decrease?
The same logic can be used with the ore grade curve in the graph.  As  shown in this example, the ore grade increases steadily as the cutoff is raised.  This is because lower grade ore is being shifted from ore to waste, and hence the remaining ore has better quality.  If the cutoff is raised from 0.4 g/t to 0.5 g/t, then some material with a grade of about 0.45 g/t is moved from ore to waste.
I also like to compare the ratio of the average grade to the cutoff grade.  Its nice to see a ratio of 4:1 to 5:1 to ensure the overall average grade isn’t close to the cutoff.  In this example, the cutoff grade is 0.5 g/t and the average grade is 4.5 g/t, a ratio of 9:1.
The tonnage curve and grade curve provide information on the nature of the mineral resource. Study them both.

Reporting Waste Within a Shell

One complaint I have about reporting mineral resources inside a resource constraining shell is the lack of strip ratio information. This applies whether disclosing a single mineral resource estimate or variable grade-tonnage data.
In my view, the strip ratio is even more important to be aware of when looking at grade tonnage data.
The strip ratio within a shell will climb as an increasing cutoff grade results in a decreasing ore tonnage.  Sometimes the strip ratio will increase exponentially. The corresponding amount of waste remaining in that pit shell increases, hence the ratio of the two (i.e. strip ratio) can escalate rapidly.
mining strip ratio curveRegarding mineral resources, one should be required to disclose the waste tonnage and strip ratio when reporting resources inside a constraining shell. The constraining shell and cutoff grade are both based on defined economic factors such as unit mining costs, processing cost, process recoveries, and metal prices.  With respect to the mining cost component, the strip ratio is a key aspect of the total mining cost, yet it normally isn’t disclosed.
Its common to see mention that the mining cost is (say) $2.50/t, but if the strip ratio is 10:1, that equates to an effective mining cost of $27.50 per tonne of ore.   That’s an important cost to know, especially if one is pushing a pit shell deep to maximum the mineral resource tonnage.
Each mineral deposit resource model can behave differently.  Hence, in my view, the waste tonnage should be included when reporting mineral resource tonnages (or presenting grade-tonnage data) within a constraining shell.  This waste tonnage or strip ratio can be in the footnotes to the mineral resource summary table.

Spider Diagram Downsides

In 43-101 technical reports, the financial Chapter 22 normally presents the project sensitivities expressed in a spider diagram or a table format.
In a previous blog post I had discussed the flaws in the spider diagram approach.  That article link is at “Cashflow Sensitivity Analyses – Be Careful”.  The grade-tonnage curve helps explain why that is.
In the spider diagrams, we typically see sensitivities related to +/- 20% on metal prices and operating costs.    If either of these factors change, then in reality the cutoff grade would change.
If the metal price decreases by -20%, or the operating cost climbs by +20%, the cutoff grade must increase.  This adjustment is normally not made in the sensitivity analysis because it requires a lot of re-work.
Elevating the cutoff grade would shift the pit ore tonnage towards the right on the grade-tonnage curve, showing a decrease in mineable tonnes.   However, in the spider diagram logic, the assumption is that production schedule in the cashflow model is unchanged and simply the metal prices or operating costs are adjusted.  Therefore, the spider diagram can be a misleading representation of the downside risk, showing a more positive situation than in reality.

Conclusion

The grade-tonnage information is always presented in technical reports. It examines the sensitivity of the orebody size to changes in cutoff grade. The next time you see grade-tonnage data, don’t skip over it.  Take a minute to study it further to see what can be learned.
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NPV One – Cashflow Modelling Without Excel

NPV One mining software
From time to time, I encounter interesting software applications related to the mining industry.  I recently became aware of NPV One, an Australian based, cloud hosted application used to calculate mineral project economics. Their website is https://npvone.com/npvone/
NPV One is targeting to replace the typical Excel based cashflow model with an online cloud model. It reminds me of personal income tax software, where one simply inputs the income and expense information, and then the software takes over doing all the calculations and outputting the result.
NPV One may be well suited for those not comfortable with Excel modelling, or not comfortable building Excel logic for depreciation, income tax, or financing calculations. These calculations are already built in the NPV One application.
I had a quick review of NPV One, being given free access to test it out. I spent a bit of time looking at the input menus and outputs, but by no means am I proficient in the software after this short review.
Like everything, I saw some very good aspects and some possible limitations. However, my observations may be a bit skewed since I do a lot of Excel modelling and have a strong comfort level with it. Nevertheless, Excel cashflow modelling has its own pro’s and con’s, some of which have been irritants for years.

NPV One – Pros and Cons

NPV One mining softwarePros

  1. NPV One develops financial models that are in a standardized format. Models will be very similar to one another regardless of who creates it. We are familiar with Excel “artists” that have their own modelling style that can make sharing working models difficult. NPV One might be a good standard solution for large collaborative teams looking at multiple projects while working in multiple offices.
  2. NPV One, I have been assured, is error free. A drawback with Excel modelling is the possibility of formula errors in a model, either during the initial model build or by a collaborator overwriting a cell on purpose (or inadvertently).
  3. With NPV One, a user doesn’t need to be an Excel or tax modelling expert to run an economic analysis since it handles all the calculations internally.
  4. NPV One allows the uploading of large input data sets; for example life-of-mine production schedules with multiple ore grades per year. This means technical teams can still generate their output (production schedules, annual cost summaries, etc.) in Excel. They can then simply import the relevant rows of data into NPV One using user-created templates in CSV format.
  5. As NPV One evolves over time with more client input, functionality and usability may improve as new features are added or modified.

Cons

Like anything, nothing is perfect and NPV may have a few issues for me.
  1. Since I live and breathe with Excel, working with an input-based model can be uncomfortable and take time to get accustomed to. Unlike Excel, in NPV One, one cannot see the entire model at once and scroll down a specific year to see production, processing, revenue, costs, and cashflow. With NPV jump to. If you’re not an avid Excel user, this issue may not be a big deal.
  2. In Excel one can see the individual formulas as to how a value is being calculated.  Excel allows one to follow a mathematical trail if one is uncertain which parameters are being used. With NPV One the calculations are built in. I have been assured there are no errors in NPV One, so accuracy is not the issue for me. It’s more the lack of ability to dissect a calculation to learn how it is done.
  3. With NPV One, a team of people may be involved in using it. That’s the benefit of collaborative cloud software. However that means there will be a learning curve or training sessions that would be required before giving anyone access to the NPV One model.  Although much of NPV One is intuitive, one still needs to be shown how to input and adjust certain parameters.
  4. Currently NPV One does not have the functionality to run Monte Carlo simulations, like Excel does with @Risk. I understand NPV One can introduce this functionality if there is user demand for it. There will likely be ongoing conflict to try to keep the software simple to use versus accommodating the requests of customers to tailor the software to their specific needs.

Conclusion

The NPV One software is an option for those wishing to standardize or simplify their financial modelling.
Whether using Excel or NPV One, I would recommend that a single person is still responsible for the initial development and maintenance of a financial model. The evaluation of alternate scenarios must be managed to avoid it becoming a modelling team free for all.
Regarding the cost for NPV One, I understand they are moving away from a fixed purchase price arrangement to a subscription based model. I don’t have the details for their new pricing strategy as of May 2023. Contact Christian Kunze (ck@npvone.com) who can explain more, give you a demo, and maybe even provide a trial access period to test drive the software.
To clarify I received no compensation for writing this blog post, it is solely my personal opinion.
Regarding Excel model complexity mentioned earlier, I have written a previous blog about the desire to keep cashflow models simple and not works of art. You can read that blog at Mine Financial Modelling – Please Think of Others”.
As with any new mining software, I had also posted some concerns with QP responsibilities as pertaining to new software and 43-101. You can read that post at the appropriately titled “New Mining Software and 43-101 Legal Issues”.

 

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Steeper Pit Slopes Can Save Money

We likely have all heard the statement that increasing pit wall angles will result in significant cost savings to the mining operation.
What is the potential cost saving?
The steeper wall angles reduce waste stripping volumes, which also provide other less obvious benefits.
I was recently in a situation where we undertook some comparative open pit designs using both 45 and 50 degree inter-ramp angles (“IRA”). I would like to share some of those results and discuss where all the benefits may lay.

Comparative Pit Designs

In this project, four separate open pits were designed with 45 and 50 degree IRA’s in an area with hilly topography. Some of the pits had high walls that extended up the valley hillsides. Its not hard to envision that waste stripping reductions would be seen along those areas with steepened walls.
The results of applying the increased  inter-ramp angle to each of the four pits is shown in the Bar Chart. Note that the waste reduction is not necessarily the same for each pit.  It depends on the specific topography around each pit.
However, on average, there was an overall 15% reduction in waste tonnage.
The Table shown below presents the cumulative tonnage for all four pits. The 50 degree wall results in a waste decrease of 25.4 million tonnes (15%), with a strip ratio reduction from 5.8:1 to 5.0:1.
There is also a very minor decrease in ore tonnage. This is because the 50 degree slopes did lose some ore behind the walls that is being recovered by the 45 degree slope.
In both scenarios the project life would be about 10 years at an assumed ore processing rate of 3 Mtpa.

4 Positive Impacts of Steeper Walls

In general one can typically see four positive outcomes from adopting steeper pit walls. They are as follows:
1. Cost Savings: The waste tonnage reduction over the 10 year life would be about 25.4 million tonnes. At a mining cost of $2.00/tonne, this equates to $50.8 million tonnes spent less on stripping. This could move the project NPV from marginal to profitable, since most waste is normally stripped towards the front part of the mining schedule with less discounting.
The next time you are looking at the NPV from an open pit project, take a quick look to see if the pit slope assumptions are conservative or optimistic. That decision can play a significant role in the final NPV.
2. Equipment Fleet Size: Over the 10 year life, the average annual mining rate would range from 20.5 Mtpa (45 deg) to 18.1 Mtpa (50 deg). On a daily basis, the average would range from 56,100 tpd (45 deg) versus 49,700 tpd (50 deg). While this mining rate reduction is not likely sufficient to eliminate a loader, it could result in the elimination of a truck or two.   This would have some capital cost saving.
3. Waste Dump Size: The 15% reduction in the waste tonnage means external waste dumps could be 15% smaller. This may not have a huge impact but could be of interest if waste storage sites are limited on the property. It could have a more significant impact if local closure regulations require open pit backfilling.
4. Pit Crest Location: The steeper wall angles result in a shift in the final pit crest location. The Image shows the impact that the 5 degree steepening had on the crest location for one of the pits in this scenario.
Although in this project the crest location wasn’t critical, there are situations where rivers, lakes, roads, mine facilities, or public infrastructure are close to the pit.  A steeper wall could improve ore recovery at depth while maintaining the same buffer setback distance.

Conclusion

Steeper pit walls can have multiple benefits at an open pit mining operation. However, these benefits can all be negated if the rock mass cannot tolerate those steeper walls. Pit wall failures could be minor or they could have major impacts. There are the obvious worker safety issues, as well as equipment damage and production curtailment concerns with slope failures.  Public perception of the mining operation also comes into play with dangerously unstable slopes.
Steepening of the pit walls is great in theory, but always ensure that geotechnical engineers have confirmed it is reasonable.
It is relatively easy to justify spending additional time and money on proper geotechnical investigations and geotechnical monitoring given the potential slope steepening benefits.
When designing pits, there is some value in looking at alternate designs with varying slope angles to help the team understand if there are potential gains and how large they might be.
In closing, I previously wrote a related blog post about how pit walls are configured to ensure safe catch bench widths and decisions as to whether one should use single, double, or triple benching. That earlier post can be read at this link. Pit Wall Angles and Bench Widths – How Do They Relate?
Feel free to share your personal experiences if you are aware of other benefits (or even downsides) to steeper pit walls that I did not mention.
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Clays and Mining – Friends or Foes?

Overburden is a generalized termed used to describe unconsolidated material encountered at a mine.  It can consist of gravels, sands, silts, and clays and combinations of each. Usually overburden is not given much focus in many mining studies. Very often, the overburden as a unit, is not adequately characterized.
This blog will explain why proper characterization can be an important issue,  particularly the clay component.
I also want to share some personal mining experiences with clays, all types of clays.  There is more to them than meets the eye; a fact often not apparent to those involved only in hard rock mining.
Clays have unique geotechnical properties that can make for challenging situations and require special consideration in project design.   Many simply view clay as a sticky cohesive material – no big deal. So let’s examine this a bit further. I tried to avoid geotechnical lingo where possible, since this blog isn’t being written for geotechnical engineers.
There are several types of clays, or clay-like materials that can be encountered in mining. Here are the ones that I have been lucky (or unlucky) enough to have dealt with over the years.
  • Normally consolidated clays
  • Over-consolidated clays
  • Sensitive (or quick) clays
  • Swelling clays
  • Saprolite clays
  • Kimberlite clays (muds)

What are the challenges?

Each of the clays listed above can be found in different locations, have unique properties, will behave differently, and can create specific mining challenges.   Clays can also cause problems in process plant circuits, but that is a subject outside my area of expertise.

Normally consolidated clays

These are the clays most people are familiar with, i.e. a sedimentary deposit of very fine particles that have settled in a calm body of water.   Normally consolidated clays are generally not a problem, other than having a high moisture content.  As such, they can be very sticky in loader buckets, truck boxes, and when feeding crushers.
When wet, they can become sloppy and difficult to handle efficiently.  They can creep and run when placed into waste dumps.  For these reasons, engineers must be aware if a large proportion of the overburden will consist of clays so they can avoid surprises.

Over-consolidated clays

These clays have undergone greater vertical compression in their history than in their current condition.  For example, perhaps they were once pre-loaded and compressed by a mile of glacial ice sheet during an ice age, which has subsequently melted.
Clays in general consist of very fine plate like particles, as shown in this sketch.   In over-consolidated clays, these particles have been flattened and tightly compressed as in the right image.   The result is that the clay may be dense, have a good cross bedding shear strength, but very low shear strength along the plates.  This characteristic is analogous to the lubricating properties of graphite, which is facilitated by sliding along graphite plates.
My experience in working with over-consolidated clays was at the Fort McMurray oil sands mining operations.  In that region the Clearwater clays formed part of the overburden sequence above the oil sands.  Stripping these clays with trucks and shovels was not exceptionally challenging.  They had low moisture content and were stiff.   The challenge really came when needing to build on top of them, for example building a waste dump or tailings dam.
The cross-bedding shear strength was good, with peak friction angles exceeding 25 degrees.  However after any creep or deformation, the peak shear strength was gone and the residual friction angle would now control stability.   The residual friction angles could drop as low as 6 degrees (very weak) and, upon surcharging the clay could maintain high internal pore pressures.   Due to these factors it was not uncommon to see tailings dams or waste dumps with 15:1 (H:V) downstream slopes.  This compares to the 3:1 slopes one may normally see at hard rock mine sites.
Building a 15:1 dam or dump is much less volume efficient than building a 3:1 embankment.  It also doesn’t take much instability to cause an embankment to creep along a foundation with only a 6-degree friction angle.  Hence the over-consolidated clays presented a unique engineering challenge when working in the oil sands.

Sensitive (quick) clays

Referring to the clay particle sketch shown above, quick clays represent a card house structure (on the left image).  These clays were often deposited in a quiet marine environment, where electrical charges prevented the clays from settling uniformly.  Instead, the clay particles tend to stack up like a house of cards.  The large void spaces are filled with water, whereby moisture contents can exceed 100% by weight.
When these clays are disturbed by vibration or movement, the house of cards structure collapses.  Combined with the excess void water, these clays will flow…. and flow a lot.   This video shows a slope failure in quick clays in Norway.  Try to stop that failure once it has initiated.
My experience with sensitive clays was at the former BHP bauxite mining operations along the northern coast of Suriname.   There were Demerara clay channels up to 20m thick over top of many of their open pits.   The bucketwheel excavators used for waste stripping would trigger the quick clay slope failures, sometimes resulting in the crawler tracks being buried and unfortunately also causing some worker fatalities.
I recall walking up towards a bucketwheel digging face as the machine quietly churned away.   About 70 metres from the machine, we would see cracks quietly opening all around us as the ground mass was starting to initiate its flow towards the machine.   Most times the bucketwheel could just sit there and dig.  Instead of the machine having to advance toward the face, the face would advance towards the machine.
To address the safety issue, eventually mine-wide grids of cone penetration tests were used to define the Demerara clay channels.  Dredges were then brought in to remove these channels before allowing the bucketwheels to strip the remaining sands and normally consolidated clays.

Swelling clays

In some locations, mines may contain swelling clays.  The issue with these clays is that they can absorb water rapidly, swell by 30%, and become extremely soft to operate on.  If they form part of the ore zone and find their way to the tailings pond, one may find they don’t want to settle out in the pond. Water clarification and clean water recycle to the plant can become an operational issue.   Mineralogy tests will indicate if one has swelling clays (smectites, montmorillonites, bentonite).  The swelling clays do have a functional use however, discussed later.

Kimberlite clays (muds)

The formation of the diamond deposits in northern Canada often involved the explosive eruption of kimberlite pipes under bodies of water. The lakebed muds and expelled kimberlite by the eruption would collapse back into the crater, resulting in a mix of mud and kimberlite (yellow zones in the image).   This muddy kimberlite could be soft, weak, and difficult to mine with underground methods.
Normally as one descends deeper into the kimberlite pipe,  the harder primary kimberlite dominates over the muddy material.   An upside is that the muddy kimberlite can be scrubbed fairly easily during processing, with the very fine clay particles being washed away.

Clays can’t be all bad?

Encountering clays at a mine site can’t be always negative?  There must be some benefits that clays can provide?   Well there are a few positive aspects.

Saprolite clays 

At many tropical mining operations (west African gold projects for example) the upper bedrock has undergone weathering, resulting in the fresh rock being decomposed into saprolite.  This clay-rich material can exceed 50 metres in thickness, can be fairly soft and diggable without blasting.   This is an obvious mining cost benefit.
As well, grinding circuits can easily deal with saprolite.  For example, if a 1000 tpd grind circuit is designed for the underlying deeper bedrock, it may be able to push through 1400 tpd of saprolite.   This would yield a 40% increase in mill throughput for little added cost.  This will boost early gold production.  However as the blend of saprolite to fresh rock declines over the years as the pit deepens, the plant throughput will decrease to the original design capacity.
One concern with saprolite sometimes is its sticky nature.   A truck load of saprolite ore dumped on a crusher grizzly may just sit there.  Possible some prodding or water flushing may be required to get it moving.  Nevertheless, this is normally an easily resolvable operating issue.

Clay core dams

One of the ways miners build water retention or tailings dams is to use mined waste rock.   The issue with this is that a dam built solely with waste rock will leak like a sieve, which can lead to piping failure.  One solution is to build an internal clay core in the center the dam to act as a seepage barrier.   Having on-site access to good quality clean clay fill is a benefit when such dams are required.   If the clay fill isn’t available at site, then more complex synthetic liners or internal seepage control measure must be instituted.
Compacted clay fill can also be used as a pond liner material for water retention ponds.
One can also purchase rolls of geosynthetic clay liners (GCL), whereby a thin layer of dried swelling clay is encapsulated between two sheets of geotextile.  Once the liner is laid out and re-hydrated with water, the clays swell and will act as an impervious liner.   The installation approach is somewhat simpler than for HDPE liners and such liners can be self-healing if punctured.  A downside is that the transport weight of these GCL liners can be significant.
See, there are some positives with having clay at site.

Conclusion

All clays are not the same.  The mining of clays can create unique challenges for mining engineers and operating personnel.   Whenever I see study happily mention that their open pit mine waste consists of “free digging overburden”, I say to myself “Be careful what you wish for”.
One must ensure that the overburden is properly characterized, even though it may be viewed as an unimportant or uninteresting material.  Determine whether it consists of gravels, sands, silts, tills, or clays, or combinations thereof.   It can make a big difference in how it is mined, disposed of, and whether it can have any secondary uses on site.  In many studies that I have reviewed, the overburden tends to be forgotten and does not get the technical respect it deserves.
Please feel free to share any thoughts on your experience in working with clays.
We had to build mine haul roads across large swamps underlain by soft clays.   One option was to use geo-textiles or swamp vegetation to assist us.  Another option was to place the sand fill hydraulically.  You can read how we did this at the following blog post “Using Pumped Sand to Build Mine Roads“.
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Let A.I. Help Target Your Infill Drilling

From time to time I come across interesting new tech that I like to share with colleagues.  The topic of this blog relates to solving the problem of defining an optimal infill drill program.
In the past I have worked on some PEA’s whose economics were largely based on Inferred ore.  The company wanted to advance to the Pre-Feasibility (PFS) stage. However, before the PFS could start they would need additional drilling to convert much of the Inferred resource into Measured and Indicated resources.
I’ve seen similar experience with projects that are advance from PFS to FS where management has a requirement that the ore mined during the payback period consist of Measured classification.

The Problem

In both cases described above, it is necessary for someone to outline an infill drill program to upgrade the resource classification while also meeting other project priorities.  The goal is to design an infill drill program with minimal time and cost yet maximize resource conversion.  Possibly some resource expansion drilling, metallurgical sampling, and geotechnical investigations may be required at the same time.
I’m not certain how various resource geologists go about designing an infill drill plan.  However, I have seen instances where dummy holes were inserted into the block model and then the classification algorithm was re-run to determine the new block model tonnage classification.   If it didn’t meet the corporate objectives, then the dummy holes may be moved or new ones added, and the process repeated.
One would not consider such a trial & error solution as optimal. It may not necessarily meet the cost and time objectives although it may meet the resource conversion goals.

The Solution

The DRX Drill Hole and Reporting algorithm developed by Objectivity.ca uses artificial intelligence to optimize the infill drilling layout.  It intends to match the QP/CP constraints with corporate/project objectives.
For example, does company management require 70% of the resource in M&I classifications or do they require 90% in M&I?  Each goal can be achieved with a different drill plan.
The following description of DRX is based on discussions with the Objectivity staff as well as a review of some case studies.  The company is willing to share these studies if you contact them.
The DRX algorithm relies on the resource classification criteria specified by the company QP.  For example, the criteria could be something like “For a block to qualify as Measured, the average distance to the nearest three drill holes must be 30 m or less of the block centroid. For a block to qualify as Indicated, the average distance from the block centroid to the nearest three holes must be 50 m or less. For a block to qualify as Inferred it will generally be within 100 m laterally and 50 m vertically of a single drill hole.
The DRX algorithm will use these criteria to optimize drill hole placement three dimensionally to deliver the biggest bang for the buck.   Whatever the corporate objective, DRX will attempt to find an optimal layout to achieve it.  The idea being that fewer well targeted holes may deliver a better value than a large manually developed drill program.
The DRX outcome will prioritize the hole drilling sequence in case the drill program gets cut short due to poor weather, lack of funding, or the arrival of the PDAC news cycle.
The DRX approach can also be used to optimally site metallurgical holes and/or geotechnical holes in combination with resource drilling if there are defined criteria that must be met (by location, ore type, rock type, etc.).   The algorithm will rely on rules and search criteria developed by experts in those disciplines.  It does not develop the rules, it only applies them.
DRX can also help optimize step-out drilling, such that the step-out distance will not be beyond the range that negates the use of the hole in a resource estimate.  It can also consider geological structure in defining drill targets.

By optimizing the number of drill holes and their orientation, the company may see savings in drill pad prep, drilling costs, field support costs, and sample assaying.
One can even request drilling multiple holes from the same drill pad to minimize drill relocation costs and safety issues in difficult terrain.
A large benefit of DRX is to be able to examine what-ifs.  For example, one may desire 85% of the resource to be M&I.   However, if one is willing to accept 80%, then one may be able to save multiple holes and associated costs.   Perhaps with the addition of just a few extra holes one could get to 90% M&I.   These are optimizations that can be evaluated with DRX.

An Example

In the one case study provided to me, a $758,000 manually developed drill program would convert 96.6% of the Inferred resource to Indicated.  DMX suggested that they could achieve 96.7% for $465,000. Alternatively they could achieve 94% conversion for $210,000.  These are large reductions in drilling cost for small reductions in conversion rate.  This may allow the drill-metres saved to be used for other purposes.
For that same project, a subsequent study was done to convert Indicated to Measured in a starter pit area. DRX concluded that a 5000-metre program could convert 62% of Indicated into Measured.  A 12,000-metre program would convert 86%,  A 16,000-metre program would achieve 92%.
So now company management can make an informed decision on either how much money they wish to spend or how much Measure Resource they want to have.

Conclusion

Although I have not yet worked with DRX, I can see the value in it.   I look forward to one day applying it on a project I’m involved with to develop a better understanding of what goes in and what comes out.   DRX hopes to become to resource drilling what Whittle has become to pit design – an industry standard.
The use of the DRX algorithm may help mitigate situations where, moving from a PEA to PFS, one finds that the infill program did not deliver as hoped on the resource conversion.  Unfortunately, this leaves the PFS with less mineable ore than anticipated and sub-optimal economics.
New tech is continually being developed in the mining industry.  Hopefully this is one we continue to see forward advancement. It makes sense to me and DRX could be another tool in the geologist toolbox.  Check out their website at objectivity.ca
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Mining Financial Modeling – Make it Better!

In my view one thing lacking in the mining industry today is a consistent approach to quantifying and presenting the risks associated with mining projects. In a blog written in 2015 titled “Mining Cashflow Sensitivity Analyses – Be Careful” I discussed the limitations of the standard “spider graph” sensitivity analysis  often seen in Section 22 of 43-101 reports.
This blog post expands on that discussion by describing a better approach. A six-year time gap between the two articles – no need to rush I guess.
This blog summarizes excerpts from an article written by a colleague that specializes in probabilistic financial analysis. That article is a result of conversations we had about the current methods of addressing risk in mining. The full article can be found at this link, however selected excerpts and graphs have been reprinted here with permission from the author.
The author is Lachlan Hughson, the Founder of 4-D Resources Advisory LLC. He has a 30-year career in the mining/metals and oil gas industry as an investment banker and a corporate executive. His website is here 4-D Resources Advisory LLC.

Excerpts from the article

Mining can be risky

“The natural resources industry, especially the finance function, tends to use a static, or single data estimate, approach to its planning, valuation and M&A models. This often fails to capture the dynamic interrelationships between the strategic, operational and financial variables of the business, especially commodity price volatility, over time.”
“A comprehensive financial model should correctly reflect the dynamic interplay of these fundamental variables over the company life and commodity price cycles. This requires enhancing the quality of key input variables and quantitatively defining how they interrelate and change depending on the strategy, operational focus and capital structure utilized by the company.”
“Given these critical limitations, a static modeling approach fundamentally reduces the decision making power of the results generated leading to unbalanced views as to the actual probabilities associated with expected outcomes. Equally, it creates an over-confident belief as to outcomes and eliminates the potential optionality of different courses of action as real options cannot be fully evaluated.”

Monte Carlo can be risky

“Fortunately, there is another financial modeling method – using Monte Carlo simulation – which generates more meaningful output data to enhance the company’s decision making process.”
Monte Carlo simulation is not new.  For example  @RISK has been available as an easy to use Excel add-in for decades. Crystal Ball does much the same thing.
“Dynamic, or probabilistic, modeling allows for far greater flexibility of input variables and their correlation, so they better reflect the operating reality, while generating an output which provides more insight than single data estimates of the output variable.”
“The dynamic approach gives the user an understanding of the likely output range (presented as a normal distribution here) and the probabilities associated with a particular output value. The static approach is relatively “random” as it is based on input assumptions that are often subject to biases and a poor understanding of their potential range vs. reality (i.e. +/- 10%, 20% vs. historical or projected data range).”
“In the case of a dynamic model, there is less scope for the biases (compensation, optionality, historic perspective, desire for optimal transaction outcome) that often impact the static, single data estimates modeling process. Additionally, it imposes a fiscal discipline on management as there is less scope to manipulate input data for desired outcomes (i.e. strategic misrepresentation), especially where strong correlations to historical data exist.”
“It encourages management to consider the likely range of outcomes, and probabilities and options, rather than being bound to/driven by achieving a specific outcome with no known probability. Equally, it introduces an “option” mindset to recognize and value real options as a key way to maintain/enhance company momentum over time.”

Image from the 4-D Resources article

“In the simple example (to the right), the financial model was more real-world through using input variables and correlation assumptions that reflect historical and projected reality rather than single data estimates that tend towards the most expected value.”
“Additionally, the output data provide greater insight into the variability of outcomes than the static model Downside, Base and Upside cases’ single data estimates did.”
The tornado diagram, shown below the histogram, essentially is another representation of the spider diagram information. ie.e which factors have the biggest impact.
“The dynamic data also facilitated the real option value of the asset in a manner a static model cannot. And the model took less time to build, with less internal relationships to create to make the output trustworthy, given input variables and correlation were set using the @RISK software options. This dynamic modeling approach can be used for all types of financial models.”
To read the full article, follow this link.

Conclusion

image from 4-D Resources article

Improvements are needed in the way risks are evaluated and explained to mining stakeholders. Improvements are required given increasing complexity in the risks impacting on decision making.
The probabilistic risk evaluation approach described above isn’t new and isn’t that complicated. In fact, it can be very intuitive when undertaken properly.
Probabilistic risk analysis isn’t something that should only be done within the inner sanctums of large mining companies. The approach should filter down to all mining studies and 43-101 reports.
It should ultimately become a best practice or standard part of all mining project economic analyses. The more often the approach is applied, the sooner people will become familiar (and comfortable) with it.
Mining projects can be risky, as demonstrated by the numerous ventures that have derailed. Yet recognition of this risk never seems to be brought to light beforehand.
Essentially all mining projects look the same to outsiders from a risk perspective, when in reality they are not. The mining industry should try to get better in explaining this.
Management understandably have a difficult task in making go/no-go decisions. Financial institutions have similar dilemmas when deciding on whether or not to finance a project.   You can read that blog post at this link “Flawed Mining Projects – No Such Thing as Perfection
UPDATE:  For those interesting in this subject, there is a follow up article by the same author published in January 2022 titled “Using Dynamic Financial Modeling to Enhance Insights from Financial Reports!“.
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Pit Optimization – More Than Just a “NPV vs RF” Graph

In this blog I wish to discuss some personal approaches used for interpreting pit optimization data. I’m not going to detail the basics of pit optimization, assuming the reader is already familiar with it .
Often in 43-101 technical reports, when it comes to pit optimization, one is presented with the basic “NPV vs Revenue Factor (RF)” curve.  That’s it.
Revenue Factor represents the percent of the base case metal price(s) used to optimize for the pit. For example, if the base case gold price is $1600/oz (100% RF), then the 80% RF is $1280/oz.
The pit shell used for pit design is often selected based on the NPV vs RF curve, with a brief explanation of why the specific shell was selected. Typically it’s the 100% RF shell or something near the top of the NPV curve.
However the pit optimization algorithm generates more data than just shown in the NPV graph.  An example of that data is shown in the table below. For each Revenue Factor increment, the data for ore and waste tonnes is typically provided, along with strip ratio, NPV, Profit, Mining cost, Processing, and Total Cost at a minimum.
Luckily it is quick and easy to examine more of the data than just the NPV curve.

In many 43-101 reports, limited optimization analysis is presented.  Perhaps the engineers did drill down deeper into the data and only included the NPV graph in the report for simplicity purposes. I have sometimes done this to avoid creating five pages of text on pit optimization alone, which few may have interest in. However, in due diligence data rooms I have also seen many optimization summary files with very limited interpretation of the optimization data.
Pit optimization is a approximation process, as I outlined in a prior post titled “Pit Optimization–How I View It”. It is just a guide for pit design. One must not view it as a final and definitive answer to what is the best pit over the life of mine since optimization looks far into the future based on current information, .
The pit optimization analysis does yield a fair bit of information about the ore body configuration, the vertical grade distribution, and addresses how all of that impacts on the pit size. Therefore I normally examine a few other plots that help shed light on the economics of the orebody. Each orebody is different and can behave differently in optimization. While pit averages are useful, it is crucial to examine the incremental economic impacts between the Revenue Factor shells.

What Else Can We Look At?

The following charts illustrate the types of information that can be examined with the optimization data. Some of these relate to ore and waste tonnage. Some relate to mining costs. Incremental strip ratios, especially in high grade deposits, can be such that open pit mining costs (per tonne of ore) approach or exceed the costs of underground mining. Other charts relate to incremental NPV or Profit per tonne per Revenue Factor.  (Apologies if the chart layout below appears odd…responsive web pages can behave oddly on different devices).

Conclusion

It’s always a good idea to drill down deeper into the optimization output data, even if you don’t intend to present that analysis in a final report. It will help develop an understanding of the nature of the orebody.
It shows how changes in certain parameters can impact on a pit size and whether those impacts are significant or insignificant. It shows if economics are becoming very marginal at depth. You have the data, so use it.
This discussion presents my views about optimization and what things I tend to look at.   I’m always learning so feel free to share ways that you use your optimization analysis to help in your pit design decision making process.
As referred to earlier, there is a lot of uncertainty in the input parameters used in open pit optimization.  These might include costs, recoveries, slope angles and other factors.  If you would like to read more, the link to that post is here.  “Pit Optimization–How I View It”.
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O/P to U/G Cross-Over – Two Projects into One

Over the years I have been involved in numerous mining tradeoff studies. These could involve throughput rate selection, site selection, processing options, tailings disposal methods, and equipment sizing. These are all relatively straightforward analyses. However, in my view, one of the more technically interesting tradeoffs is the optimization of the open pit to underground crossover point.
The majority of mining projects tend to consist of either open pit only or underground only operations. However there are instances where the orebody is such that eventually the mine must transition from open pit to underground. Open pit stripping ratios can reach uneconomic levels hence the need for the change in direction.
The evaluation of the cross-over point is interesting because one is essentially trying to fit two different mining projects together.

Transitioning isn’t easy

There are several reasons why open pit and underground can be considered as two different projects within the same project.
There is a tug of war between conflicting factors that can pull the cross-over point in one direction or the other. The following discussion will describe some of these factors.
The operating cut-off grade in an open pit mine (e.g. ~0.5 g/t Au) will be lower than that for the underground mine (~2-3 g/t Au). Hence the mineable ore zone configuration and continuity can be different for each. The mined head grades will be different, as well as the dilution and ore loss assumptions. The ore that the process plant will see can differ significantly between the two.
When ore tonnes are reallocated from open pit to underground, one will normally see an increased head grade, increased mining cost, and possibly a reduction in total metal recovered. How much these factors change for the reallocated ore will impact on the economics of the overall project and the decision being made.
A process plant designed for an open pit project may be too large for the subsequent underground project. For example a “small” 5,000 tpd open pit mill may have difficulty being kept at capacity by an underground mine. Ideally one would like to have some satellite open pits to help keep the plant at capacity. If these satellite deposits don’t exist, then a restricted plant throughput can occur. Perhaps there is a large ore stockpile created during the open pit phase that can be used to supplement underground ore feed. When in a restricted ore situation, it is possible to reduce plant operating hours or campaign the underground ore but that normally doesn’t help the overall economics.
Some investors (and companies) will view underground mines as having riskier tonnes from the perspective of defining mineable zones, dilution control, operating cost, and potential ore abandonment due to ground control issues. These risks must be considered when deciding whether to shift ore tonnes from the open pit to underground.
An underground mine that uses a backfilling method will be able to dispose of some tailings underground. Conversely moving towards a larger open pit will require a larger tailings pond, larger waste dumps and overall larger footprint. This helps make the case for underground mining, particularly where surface area is restricted or local communities are anti-open pit.
Another issue is whether the open pit and underground mines should operate sequentially or concurrently. There will need to be some degree of production overlap during the underground ramp up period. However the duration of this overlap is a subject of discussion. There are some safety issues in trying to mine beneath an operating open pit. Underground mine access could either be part way down the open pit or require an entirely separate access away from the pit.
Concurrent open pit and underground operations may impact upon the ability to backfill the open pit with either waste rock or tailings. Underground mining operations beneath a backfilled open pit may be a concern with respect to safety of the workers and ore lost in crown pillars used to separate the workings.
Open pit and underground operations will require different skill sets from the perspective of supervision, technical, and operations. Underground mining can be a highly specialized skill while open pit mining is similar to earthworks construction where skilled labour is more readily available globally. Do local people want to learn underground mining skills? Do management teams have the capability and desire to manage both these mining approaches at the same time?
In some instances if the open pit is pushed deep, the amount of underground resource remaining beneath the pit is limited. This could make the economics of the capital investment for underground development look unfavorable, resulting in the possible loss of that ore. Perhaps had the open pit been kept shallower, the investment in underground infrastructure may have been justifiable, leading to more total life-of-mine ore recovery.
The timing of the cross-over will also create another significant capital investment period. By selecting a smaller this underground investment is seen earlier in the project life. This would recreate some of the financing and execution risks the project just went through. Conversely increasing the open pit size would delay the underground mine and defer this investment and its mining risk.

Conclusion

As you can see from the foregoing discussion, there are a multitude of factors playing off one another when examining the open pit to underground cross-over point. It can be like trying to mesh two different projects together.
The general consensus seems to be to push the underground mine as far off into the future as possible.  Maximize initial production based on the low risk open open pit before transitioning.
One way some groups will simplify the transition is to declare that the underground operation will be a block cave. That way they can maintain an open pit style low cutoff grade and high production rate. Unfortunately not many deposits are amenable to block caving.  Extensive geotechnical investigations are required to determine if block caving is even applicable.
Optimization studies in general are often not well documented in 43-101 Technical Reports. In most mining studies some tradeoffs will have been done (or should have been done).  There might be only brief mention of them in the 43-101 report. I don’t see a real problem with this since a Technical Report is to describe a project study, not provide all the technical data that went into it. The downside of not presenting these tradeoffs is that they cannot be scrutinized (without having data room access).
One of the features of any optimization study is that one never really knows if you got it wrong. Once the decision is made and the project moves forward, rarely will someone ever remember or question basic design decisions made years earlier. The project is now what it is.

 

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Pre-Concentration – Maybe Good, Maybe Not

A while back I wrote a blog titled “Pre-Concentration – Savior or Not?”. That blog was touting the benefits of pre-concentration. More recently I attended a webinar where the presenter stated that the economics of pre-concentration may not necessarily be as good as we think they are.
My first thought was “this is blasphemy”. However upon further reflection I wondered if it’s true. To answer that question, I modified one of my old cashflow models from a Zn, Pb project using pre-concentration. I adjusted the model to enable running a trade-off, with and without pre-con by varying cost and recovery parameters.

Main input parameters

The trade-off model and some of the parameters are shown in the graphic below. The numbers used in the example are illustrative only, since I am mainly interested in seeing what factors have the greatest influence on the outcome.

The term “mass pull” is used to define the quantity of material that the pre-con plant pulls and sends to the grinding circuit. Unfortunately some metal may be lost with the pre-con rejects.  The main benefit of a pre-con plant is to allow the use of a smaller grinding/flotation circuit by scalping away waste. This will lower the grinding circuit capital cost, albeit slightly increase its unit operating cost.
Concentrate handling systems may not differ much between model options since roughly the same amount of final concentrate is (hopefully) generated.
Another one of the cost differences is tailings handling. The pre-con rejects likely must be trucked to a final disposal location while flotation tails can be pumped.  I assumed a low pumping cost, i.e to a nearby pit.
The pre-con plant doesn’t eliminate a tailings pond, but may make it smaller based on the mass pull factor. The most efficient pre-concentration plant from a tailings handling perspective is shown on the right.

The outcome

The findings of the trade-off surprised me a little bit.  There is an obvious link between pre-con mass pull and overall metal recovery. A high mass pull will increase metal recovery but also results in more tonnage sent to grinding. At some point a high mass pull will cause one to ask what’s the point of pre-con if you are still sending a high percentage of material to the grinding circuit.
The table below presents the NPV for different mass pull and recovery combinations. The column on the far right represents the NPV for the base case without any pre-con plant. The lower left corner of the table shows the recovery and mass pull combinations where the NPV exceeds the base case. The upper right are the combinations with a reduction in NPV value.
The width of this range surprised me showing that the value generated by pre-con isn’t automatic.  The NPV table shown is unique to the input assumptions I used and will be different for every project.

The economic analysis of pre-concentration does not include the possible benefits related to reduced water and energy consumption. These may be important factors for social license and permitting purposes, even if unsupported by the economics.  Here’s an article from ThermoFisher on this “How Bulk Ore Sorting Can Reduce Water and Energy Consumption in Mining Operations“.

Conclusion

The objective of this analysis isn’t to demonstrate the NPV of pre-concentration. The objective is to show that pre-concentration might or might not make sense depending on a project’s unique parameters. The following are some suggestions:
1. Every project should at least take a cursory look at pre-concentration to see if it is viable. This should be done on all projects, even if it’s only a cursory mineralogical assessment level.
2. Make certain to verify that all ore types in the deposit are amenable to the same pre-concentration circuit. This means one needs to have a good understanding of the ore types that will be encountered.
3. Anytime one is doing a study using pre-concentration, one should also examine the economics without it. This helps to understand the  economic drivers and the risks. You can then decide whether it is worth adding another operating circuit in the process flowsheet that has its own cost and performance risk. The more processing components added to a flow sheet, the more overall plant availability may be effected.
4. The head grade of the deposit also determines how economically risky pre-concentration might be. In higher grade ore bodies, the negative impact of any metal loss in pre-concentration may be offset by accepting higher cost for grinding (see chart on the right).
5. In my opinion, the best time to decide on pre-con would be at the PEA stage. Although the amount of testing data available may be limited, it may be sufficient to assess whether pre-con warrants further study.
6. Don’t fall in love with or over promote pre-concentration until you have run the economics. It can make it harder to retract the concept if the economics aren’t there.

 

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Climbing the Hill of Value With 1D Modelling

Recently I read some articles about the Hill of Value.  I’m not going into detail about it but the Hill of Value is a mine optimization approach that’s been around for a while.  Here is a link to an AusIMM article that describes it “The role of mine planning in high performance”.  For those interested, here is a another post about this subject “About the Hill of Value. Learning from Mistakes (II)“.
hill of value

(From AusIMM)

The basic premise is that an optimal mining project is based on a relationship between cut-off grade and production rate.  The standard breakeven or incremental cutoff grade we normally use may not be optimal for a project.
The image to the right (from the aforementioned AusIMM article) illustrates the peak in the NPV (i.e. the hill of value) on a vertical axis.
A project requires a considerable technical effort to properly evaluate the hill of value. Each iteration of a cutoff grade results in a new mine plan, new production schedule, and a new mining capex and opex estimate.
Each iteration of the plant throughput requires a different mine plan and plant size and the associated project capex and opex.   All of these iterations will generate a new cashflow model.
The effort to do that level of study thoroughly is quite significant.  Perhaps one day artificial intelligence will be able to generate these iterations quickly, but we are not at that stage yet.

Can we simplify it?

In previous blogs (here and here) I described a 1D cashflow model that I use to quickly evaluate projects.  The 1D approach does not rely on a production schedule, instead uses life-of-mine quantities and costs.  Given its simplicity, I was curious if the 1D model could be used to evaluate the hill of value.
I compiled some data to run several iterations for a hypothetical project, loosely based on a mining study I had on hand.  The critical inputs for such an analysis are the operating and capital cost ranges for different plant throughputs.
hill of valueI had a grade tonnage curve, including the tonnes of ore and waste, for a designed pit.  This data is shown graphically on the right.   Essentially the mineable reserve is 62 Mt @ 0.94 g/t Pd with a strip ratio of 0.6 at a breakeven cutoff grade of 0.35 g/t.   It’s a large tonnage, low strip ratio, and low grade deposit.  The total pit tonnage is 100 Mt of combined ore and waste.
I estimated capital costs and operating costs for different production rates using escalation factors such as the rule of 0.6 and the 20% fixed – 80% variable basis.   It would be best to complete proper cost estimations but that is beyond the scope of this analysis. Factoring is the main option when there are no other options.
The charts below show the cost inputs used in the model.   Obviously each project would have its own set of unique cost curves.
The 1D cashflow model was used to evaluate economics for a range of cutoff grades (from 0.20 g/t to 1.70 g/t) and production rates (12,000 tpd to 19,000 tpd).  The NPV sensitivity analysis was done using the Excel data table function.  This is one of my favorite and most useful Excel features.
A total of 225 cases were run (15 COG versus x 15 throughputs) for this example.

What are the results?

The results are shown below.  Interestingly the optimal plant size and cutoff grade varies depending on the economic objective selected.
The discounted NPV 5% analysis indicates an optimal plant with a high throughput (19,000 tpd ) using a low cutoff grade (0.40 g/t).  This would be expected due to the low grade nature of the orebody.  Economies of scale, low operating costs, high revenues, are desired.   Discounted models like revenue as quickly as possible; hence the high throughput rate.
The undiscounted NPV 0% analysis gave a different result.  Since the timing of revenue is less important, a smaller plant was optimal (12,000 tpd) albeit using a similar low cutoff grade near the breakeven cutoff.
If one targets a low cash cost as an economic objective, one gets a different optimal project.  This time a large plant with an elevated cutoff of 0.80 g/t was deemed optimal.
The Excel data table matrices for the three economic objectives are shown below.  The “hot spots” in each case are evident.

hill of value

hill of value

Conclusion

The Hill of Value is an interesting optimization concept to apply to a project.  In the example I have provided, the optimal project varies depending on what the financial objective is.  I don’t know if this would be the case with all projects, however I suspect so.
In this example, if one wants to be a low cash cost producer, one may have to sacrifice some NPV to do this.
If one wants to maximize discounted NPV, then a large plant with low opex would be the best alternative.
If one prefers a long mine life, say to take advantage of forecasted upticks in metal prices, then an undiscounted scenario might win out.
I would recommend that every project undergoes some sort of hill of value test, preferably with more engineering rigor. It helps you to  understand a projects strengths and weaknesses.  The simple 1D analysis can be used as a guide to help select what cases to look at more closely. Nobody wants to assess 225 alternatives in engineering detail.
In reality I don’t ever recall seeing a 43-101 report describing a project with the hill of value test. Let me know if you are aware of any, I’d be interested in sharing them.  Alternatively, if you have a project and would like me to test it on my simple hill of value let me know.
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