You have, by now, learned some things about “peak oil”, the notion that the production of oil is at or near a peak and will decline in the future, forcing us to conserve more and shift to other sources for our energy needs in the future. The goal of this activity is to explore this notion of peak oil in a bit more depth, to understand how it is a natural consequence of supplies, demands, prices.
In this activity, we’ll be using computer models created in a program called STELLA. STELLA models are simple computer models that are perfect for learning about the dynamics of systems — how systems change over time. Systems, in this case are sets of related processes that are involved in the transfer and storage of some quantity. For example, the global water cycle is a system that involves processes like evaporation, precipitation, surface water runoff, groundwater flow, moving water from one place to another. Earth’s climate system is set of related processes involved in the absorption, storage, and radiation of thermal energy. In fact, you can think of the whole Earth as one big, complex system. Through the use of computer models, we can learn some important things about how they work, how they react to changes; this understanding can then help us make smart decisions about how to respond and adapt to a changing world.
A STELLA model is a computer program containing numbers, equations, and rules that together form a description of how we think a system works — it is a kind of simplified mathematical representation of a part of the real world. Systems, in the world of STELLA, are composed of a few basic parts that can be seen in the diagram below:
A Reservoir is a model component that stores some quantity — thermal energy in this case.
To construct a STELLA model, you first draw the model components and then link them together. Equations and starting conditions are then added (these are hidden from view in the model) and then the timing is set — telling the computer how long to run the model and how frequently to do the calculations needed to figure out the flow and accumulation of quantities the model is keeping track of. When the system is fully constructed, you can essentially press the ‘on’ button, sit back, and watch what happens.
In this course, the models have all been made; you will interact with the models by changing variables with a user interface that has knobs and dials and then running the models to see how they change over time.
We will start with the simplest model we can imagine that represents the consumption of oil and gas, and then we will work with progressively more complex versions of the model.
This assessment is broken into five sub-parts, with questions related to each part. Separate web pages have been provided for each part to reduce scrolling. We have also provided the activity as a worksheet that you can download and even print if you prefer. You may find downloading or printing the complete worksheet easier to work with as you prepare your answers to submit to the Mod 3 Summative Assessment (Graded) quiz.
Download the worksheet [1]. Completing the 'Practice' and 'Graded' versions of the exercise, in the following pages or on the attached worksheet, is required before submitting your assignment.
Once you have answered all of the questions on the worksheet, go to the Module 3 Summative Assessment (Graded) quiz, in which you will see the worksheet link again and the Graded Assessment. The worksheet has practice questions with answers provided, and then graded versions of similar questions. Use the practice questions to make sure you are running the model correctly and reading the graphs properly, then do the graded questions, writing down your answers. The questions listed in the worksheet are repeated in the Canvas Assessment, so all you will have to do is read the question and select the answer that you have on your worksheet. You should not need much time to submit your answers since all of the work should be done prior to logging into clicking the assessment quiz.
This assignment is worth a total of 19 points -- the questions are all multiple choice.
Oil and gas form at extremely slow rates — 10’s of millions of years — so we can consider the oil and gas present now to be all that is available. We can wait around all we want and there will be no significant increase in the oil and gas. The total amount of oil and gas in existence on Earth is sometimes called the oil in place. We can only guess at this (somewhere around 6 trillion barrels of oil equivalent), but regardless of its size, we can probably only get about 50% of it out of the ground (this recovery factor ranges from 10% to 80% for individual oil fields). The recoverable oil and gas can be divided into two types of reserves — proven and unproven. Proven reserves are the oil and gas that we know about (which means we have a 90% confidence level about them), while unproven reserves are the oil and gas that we are less certain of, but we have some indication of their existence. These reserves are usually expressed in terms of barrels of oil equivalent and include both oil and natural gas.
It is estimated that our proven reserves are on the order of 1.5 trillion barrels of oil, and unproven reserves are thought to be in the range of 3 trillion barrels. Last year, we consumed 31 billion barrels of oil, and at this rate of consumption, we’ve got less than 50 years worth of oil in the proven reserves, and about 97 years worth in the unproven reserves. Now, move onto the first part of this assessment 1. The Simplest Case.
In this first case, we’ll just consider the proven reserves, and we’ll assume that the oil produced is a constant percentage of how much remains in the proven reserves. The logic here is very simple — if there is more oil, you can produce more in a period of time, while if there is less oil, you produce less in the same time period — but the percentage remains the same.
Here is what the system looks like as a STELLA model:
Since this model is simply meant to illustrate the general pattern of oil/gas production resulting from an assumption of how production works, we’re not going to worry about the actual values, but you can think of the starting amount of Proven Reserves as 100% of what we have. Every year, we produce oil/gas at the rate of 2% of however much remains in the Proven Reserves reservoir. The production flow transfers oil/gas into the Produced Oil reservoir, so we can keep track of the total amount of oil/gas produced over time.
Let’s see if we can predict what will happen by doing a few simple calculations. When the model first begins:
Proven Reserves = 100
production = 100 x 0.02 = 2
This will reduce the Proven Reserves by 2, so it becomes 100-2=98. Then, in the next year:
Proven Reserves = 98
production = 98 x 0.02 = 1.96
This will reduce the Proven Reserves by 1.96, so it becomes 98-1.96=96.04. So, in the next year:
Proven Reserves = 96.04
production = 96.04 x 0.02 = 1.92
Notice that the production is declining as time goes on, and the amount of decline is getting smaller. If this pattern continues, the production will follow an exponential decline curve — like this:
Take a few minutes to watch the following video and learn about the browser-hosted STELLA model interface, before running the model.
PRESENTER: This is actually the cover of a piece of sheet music that was published in 1864 in New York. This is "The American Petroleum Polka," or charge, or gallop, or waltz, or march. And it has a picture of a beautiful Pennsylvania scene, the oil well spouting its oil. Now, oil was black back then. Oil is still black. But you couldn't have black oil falling on the lady's pink dress, so they made the oil white.
And then bragging, "This oil well threw pure oil a 100 feet high." people understood the value that you get from oil, from petroleum. And they celebrated that.
Now, let’s run the model and see what happens. Follow this link to the Peak Oil Model [4] which should be set up exactly the same as the diagram above. Answer the questions either on the worksheet you downloaded or on a piece of paper to be submitted later to the Module 3 Summative Assessment (Graded) quiz. If you didn't download the worksheet on the main page of this assessment, do it now.
1A. Does the production history agree with our simple calculations (position the cursor on the graph, and it will show you the values at different times)?
Oil and gas companies have certainly become better at what they do over time. Originally, they drilled near natural oil seeps and hoped for the best, but now, a good team of geoscientists can “see” exactly where the oil/gas is, and engineers can drill with great precision and then “stimulate” the oil/gas-bearing rock formations to squeeze as much oil/gas as possible out of the rocks.
One way to incorporate this into the model is to change the rate of oil/gas production, r, so that it increases as time goes on. To do this, we make a simple equation that says r = 0.0005 x TIME, so then when TIME is 10 years, r will be 0.005 and when TIME is 100 years, r will be 0.05. Other than this change, the model is the same as in experiment 1. The value 0.0005 is called tech rate in the model, and we’ll see what happens if we change it.
Let’s see how this change affects the history of oil/gas production. Click this link to run the model [5] and then answer the following questions on your worksheet or on a sheet of paper to be submitted to a Canvas Assessment later. As you can see, the production of oil peaks in this case. It rises because r is increasing, but as r increases, the Proven Reserves is decreasing and eventually a point is reached where the product of these two numbers (the production) starts to decline.
- | Practice | Graded |
---|---|---|
Tech Rate | 0.0002 | 0.0004 |
2A. When does the production reach its maximum (peak) value?
2B. What is the magnitude of the peak in production?
In addition to technology, economics also plays a role in the production of oil/gas, in the sense that higher prices will motivate greater production. Let’s assume that the as the supply of proven reserves drops, the price will rise. As long as there is a demand for oil and gas, as it becomes more scarce, it will become more valuable. This is a pretty simplistic view of what determines the price of oil and gas — reality is much more complex, which is why prices fluctuate quite a bit over time. But it is hard to escape the basic reality that as a desirable commodity becomes scarce, its value goes up.
To make this change in the model, we need to add something that will calculate the price. This new model looks like this:
As before, production is defined as Proven Reserves x r, and r in this case is defined as price x tech_slope x TIME, so it once again has the increase over time that our previous model had, but it also increases as the price goes up. The tech_slope is just the slope of the increase in technology over time and the default value is 0.0002. Price here is defined as 0.01 + price_slope x (100 – Proven Reserves); price_slope is the slope of price increase relative to change in Proven Reserves, and is originally set to 0.05. At the beginning, Proven Reserves is 100, so this gives a price of 0.01 — very small. But, when Proven Reserves has declined to 50, we get a price of 2.51. This equation is not meant to be anything more than a way to make the price increase as the Proven Reserves get smaller. The value 0.01 at the front end of this equation is just there so that the price is not 0 at the beginning, which would then make r be 0 and no oil would ever get produced.
What we have created here is a system with a feedback mechanism. Here is how it works:
If the production increases, then the proven reserves must decrease; this triggers an increase in price, which in turns triggers an increase in production. Notice that the starting point (production increase) and the ending point (production increase) are the same. In other words, the change at the beginning of the mechanism promotes more of the same — this is what is known as a positive feedback mechanism. Positive feedback mechanisms tend to cause an acceleration of change, sometimes resulting in runaway behavior. In contrast, the are other feedback mechanisms that tend to counteract change, encouraging stability; these are known as negative feedback mechanisms. Note that in this context, positive is not necessarily good, and negative is not necessarily bad.
Take a few minutes to watch the video below to learn more about the positive feedback mechanism the oil production model before running the next model.
NARRATOR: This simple diagram is meant to represent the positive feedback mechanism that we've put into the model. So if you imagine that we begin with a production increase. That's the initial change. Let's say something happens and we increase production. That is going to cause the proven reserves to decrease, right, because production drains that reservoir. So as that goes down, the commodity becomes more scarce and because of that, the price goes up. So that's another effect here that's triggered by the production increase. And as the price is increased, that will then encourage us to do even more to try to produce more of the oil that's out there. It's an incentive to produce more oil.
So that leads to an increase in production again. So the initial change that began this was the production increase and that has ended up triggering a series of responses in the model that lead to a further increase in price, and so when that happens, this is called a positive feedback mechanism. It's kind of like a cause and effect loop, right. So here's a cause, it makes in effect, it makes an effect, makes another effect that comes back on that cause and enhances it. So that's going to really change the way that this model behaves.
This model has two pages of graphs to look at; the first one shows the Proven Reserves, Produced Oil, price, and production, and r (which combines price and tech slope), while the second one shows just the production. The second graph retains the results from previous model runs, allowing you to make comparisons as you make changes to some of the adjustable model parameters. If you want to clear this graph, hit the Restore Graphs button.
- | Practice | Graded |
---|---|---|
Tech slope | 0.0001 | 0.0002 |
Price slope | .05 | .07 |
3A. First, run the model as it is, with the price slope set to 0.05 and the tech slope set to 0.0002. Note the time and magnitude of the peak in production. Then alter the tech slope or price slope as prescribed, using the new values provided. Run the model and compare the peak time and magnitude with the original case (use page 2 of the graph pad). Use “sooner” or “later” and “greater” or “smaller” to describe how your alterations changed the timing and magnitude of the peak in production.
Change in time of peak =
Change in magnitude of peak =
For our next experiment, we’ll try a different assumption about what drives oil/gas production — demand. The demand for oil and gas has risen over time due to an increase in the global population and an increase in the per capita energy consumption. Here is what this modified version of the model looks like:
The image is a diagram titled "Carbon Reservoirs and Fluxes in a Forest Ecosystem." It shows how carbon moves and is stored within a forest environment.
Here, the population increases according to pop pct, which is the net growth percentage per year derived from historical data and then extrapolated into the future — so it is a graphical function that changes over time. The population starts at the 1800 level of 1 billion; the net growth % drops to 0 in 2100, and at that point, the population will stabilize.
The demand for oil/gas is represented here by per capita demand, which is essentially a percentage of the proven reserves per billion people. The per capita demand is another graphical function of time, patterned after actual history up until 2010 and then extrapolated to 2100 — optimistically assuming that the per capita energy demands will level off at about 2100. Multiplying the population times the per capita demand gives us r, the fraction of the proven reserves produced in a given year, and then r multiplied by the Proven Reserves gives us the production. The fraction r will increase as the population grows and as the per capita demand grows, and if population and per capita demand level off, so will r. Recall from experiment 2 that if r is increasing over time, a peak in production is inevitable.
Because we are using real population values and real values for the per capita demand, it makes sense to use real numbers for the Proven Reserves. At the present time, the best estimates are that there are 1.5 trillion barrels of oil as proven reserves (this number includes natural gas too), and we have consumed about 1.2 trillion barrels from about 1900 to the present. This means that at the beginning of time, our Proven Reserves will be 2.7 trillion barrels.
This model also includes a component called per capita oil that keeps track of how much oil is actually available per person, by taking the production and dividing it by the population. As per capita oil increases, we can use more and more oil for our energy needs, but as it decreases, we will have to either reduce our energy consumption or turn to other sources to meet our energy demands.
4A. Can you guess what will happen? Remember that r here is just like r in the earlier models, and you’ve seen what happens to the production history when r increases over time. Which of the following represents your approximate prediction?
Now run the model by clicking this link [8], and see what happens. We will consider this as the “control” for the next experiment.
- | Practice | Graded |
---|---|---|
Initial proven reserves | 2.0 | 3.5 |
(above numbers refer to trillions of barrels of oil)
4B. How will changing the initial size of the Proven Reserves reservoir affect the history of production? Set the initial Proven Reserves to 2.0 for the Practice Assessment (3.5 for the Graded Assessment) and then run the model and see what happens; choose the response below that best represents how your altered model compares with the control. Page 2 of the graph pad will be useful in making this comparison.
Oil per capita in 2100 = _______ (within 0.1 barrels/person)
Previous time in history with same oil per capita = _______ (within 10 years)
For our last experiment, we’ll see what happens when we add two more reservoirs, Unproven Reserves (the oil and gas that, we think, is likely to be discovered in the future) and Unknown Oil (the oil and gas we don’t know about, but might be there). Discovery adds Unproven Reserves to the Proven Reserves reservoir, and another flow called discovery adds Unknown Oil to the Unproven reservoir. An example from the Arctic Ocean region helps us get a grasp of these unknown reserves. In this frontier region, less than half of the offshore sedimentary basins have been explored, but based on what is known from more serious exploration off the coast of Alaska, the USGS estimates that there might be ~130 billion barrels of oil and gas — so this is a resource that, we think, might exist, but not enough is known about it yet to put it into the unproven reserves category, which applies to oil reserves that we know exist, but we don’t know enough about them to put them into the proven reserves. For perspective, this Arctic Ocean oil might represent 10-15% of all the unknown oil/gas that remains, and it would be enough to last for 4 years at the current rate of global use.
The discovery of these new resources is a function of a rate constant that increases over time, dictated by something called the exploration slope. The discovery flow that leads from Unknown to Unproven Reserves is set to be 1/5 the rate of the other discovery flow, reflecting the fact that it is much harder to discover something we know little about. Both of the discovery flows are controlled by switches (they can be turned on or off) and they begin (if the switch is on) at a time that can be set using the explor start time control knob. Here is what this new model looks like:
The image is a diagram titled "The Global Carbon Cycle with Human Perturbations." It shows how carbon moves through Earth’s systems, with a focus on how human activities affect this cycle. The diagram is a flowchart with black boxes and arrows on a white background, using red text to highlight human impacts.
At the top, a box labeled "Atmosphere" contains "CO₂" (carbon dioxide), representing the air where carbon dioxide collects. Below it, the diagram splits into natural and human-altered components:
A key feature is a red arrow labeled "Deforestation" pointing from "Terrestrial Biosphere" to "Atmosphere," highlighting how cutting down trees releases stored carbon as carbon dioxide. All arrows are straight and black, except for "Combustion" and "Deforestation" in red, emphasizing human impacts. The layout is clear, with text labels on or beside each arrow and box, showing both the natural cycle and how human actions—like burning fossil fuels and deforestation—add extra carbon to the atmosphere.
5A. How will these new sources of oil/gas change the production history? The total amount of produced oil obviously must be greater than in our model from experiment 4, but how about the shape of that production curve? Will there be a peak, as before? If so, what will that peak look like?
Before launching the model and experimenting with it, take a few minutes and watch the video that explains how to operate the switches that can turn the discovery flows on and off.
NARRATOR: This last model has some new features added to it. And so I want to explain these before you play with this model. It includes two new reservoirs, unproven reserves, and unknown oil here. And these can be tapped into through a process of discovery and eventually flow into the proven reserves, here.
These two discovery flows here are controlled by switches. And I'll show you those switches in a second. You can turn them on or off. And they're also controlled by a timer, here, that controls when we really tap into these other potential sources of oil. Other than that, it's quite similar to the other model.
Here's what it looks like when you interact with the model. You open the model, you'll see this. You can turn on these switches here, there's the unproven switch, and here's the unknown switch. Now, we're set to tap into those two new sources of oil.
And then down here, we control the time when we would start to produce that oil. So let me turn these things off first, the switches. There's one switch turned off. There's another one off.
I'm just going to go ahead and run this model. It's running now from 1800 to the year 2600, and here it shows the production peaking here at about the year 2000, then dropping off. Here's the population leveling off at-- I got it leveling off at 11.7 billion here, in this case almost 12 billion.
Now, watch this, if I turn on this unproven switch here, and run the model, you can see the production curve changes. See that? Gets bumped out. Basically, because of the addition of this oil here produced by discovery.
So then if we put this one on here, turn that on, then we can even make a more gradual decline in this production curve. So we're tapping into these new sources, and it makes that decline from the peak here, much more gradual.
Now, there are lots of things you can change here. You can change how much is in the unproven reserves and how much is in the unknown oil reservoir. You can control the rate at which those new sources are tapped into. You can control the timing of when we really aggressively start this exploration to tap into these new resources.
So this is just a little bit more optimistic model.
Open the model here [10], and first make sure the switches are in the off position (down), disabling the two discovery flows. Run the model and you should see exactly the same thing you saw in experiment 4B, with the difference that it runs for a longer period of time. If you study the graphs #3 and #7 show comparative plots of the production (in billions of barrels per year) and oil per capita (in barrels). Make sure you watch the video above to get a general sense of what happens when you turn on the switches.
You will be presented with one of the following 4 sets of initial conditions. Your answers to the following 3 questions will depend on which case you are presented.
- | Practice | Graded |
---|---|---|
Initial unproven reserves | 1.5 | 3.5 |
Initial unknown reserves | 2.0 | 2.5 |
Explore start time | 1980 ± 1 | 2000 ± 1 |
5B-D. Set the model up using the initial values provided. Use the slider bars at the top to set the initial unproven reserves and the initial unknown oil, and use the dial near the lower right to set the explore start time (the time when we begin to develop and produce the unproven reserves and unknown oil. This dial is a bit hard to adjust precisely, but if you are within a year or two of the specified date, it will be fine. Then run the model with both switches off, then run it again with the unproven switch turned on and then one more time with both switches turned on. Evaluate the differences between these three model runs in terms of the production (graph #3) and the oil per capita (#7). There are many ways to evaluate the effects of adding these new sources of oil, but we’ll focus on the size and timing of the production peak, and the oil per capita in the year 2100.
5B. Oil per capita in 2100 with Unproven Reserve switch on (± 0.1)
5C. Oil per capita in 2100 with both switches on (± 0.1)
5D. Peak in production with both switches on compared to control (with no switches on).
5F. Can a peak in oil production be avoided? In other words, is it possible to find some combination of model parameters that results in more of a plateau in oil production? To figure this out, try changing the exploration slope (this will control that rate that the discovery flows increase), and the exploration start time. We’ll leave the unproven and unknown reserves at 3.0 because this is already a very optimistic outlook.
6. In your own words, summarize the effects of 1) improving technology (of oil production); 2) the price-production feedback; and 3) growing population on the history of oil production.
We’ve just completed quite a few experiments, so it is a good idea to try to summarize a few important points.
Links
[1] https://www.e-education.psu.edu/earth104/sites/www.e-education.psu.edu.earth104/files/Unit1/Mod3/Earth104SAMod3_Peak_Oil_worksheet%2009162024.docx
[2] https://www.youtube.com/@duttoninstitute
[3] https://www.youtube.com/watch?v=-Sa0nvcbafY
[4] https://exchange.iseesystems.com/public/davidbice/earth-104-mod-31
[5] https://exchange.iseesystems.com/public/davidbice/eaeth-103-mod-32
[6] https://www.youtube.com/watch?v=Mat7w1AfTIE
[7] http://exchange.iseesystems.com/public/davidbice/earth-104-mod-33
[8] https://exchange.iseesystems.com/public/davidbice/earth-104-mod-34
[9] https://www.youtube.com/watch?v=Uuww4L0Iaso
[10] https://exchange.iseesystems.com/public/davidbice/earth-104-mod-35