 So in this case, we're going to be talking about hyperbolic decline. There's a couple other declines, there's harmonic decline, exponential decline. The difference between them is how conservative they may be, maybe like exponential is the most conservative estimate. You would use that in volumetric reservoirs. Hyperbolic, which we're going to be talking about, you'd use in non-volumetric reservoirs. And harmonic is more theoretical. It's not likely, it's like the best payout if possible, but we really don't see that. So we're going to be talking about hyperbolic in this case. So we're going to have three parameters here. We're going to have QOI, which is your initial production of oil, which is 2,000 STV per day. We're going to have a DI coefficient, which is 0.50 per year, and then we're going to have a B value, which is 0.9. This B really is what differentiates your curves for exponential, your harmonic, and hyperbolic. So there's a couple of equations we're going to be using to do this. So what we're trying to do is we're going to be finding future production rates at different times, and also at the same time, finally, what our cumulative production is and all that. And so for the first thing, this is like initially, so we're going to be using two different equations. We're going to be using equation 4.73 and 4.74. So equation 4.73 is this. So it's going to be your production of oil is equal to your initial production of oil. And this equation at work is for hyperbolic. B, DI, T, where T is time over B, and where T will be in terms of years. Another equation we're going to be dealing with is QO1-B equals QOI1-B minus your cumulative oil production up to a certain time times your DI1-B over QOI to the power of B. So with these equations, we can predict future flow rates, knowing that B equals 0.9 and DI equals 0.5 per year, and also that initial production of oil is 2,000 STB per day. So the first thing we're going to do is we are going to calculate QO for year 1. So we're going to be doing that by using... It's going to be the equation right here just rearranged a little bit. So the first equation I listed rearranged a little bit. So it's going to be QO. So this is going to be for, let's see, year 1. It's going to equal to 2,000 because this is our QOI. So I'll put... We're going to be using this equation, so it's going to be 2,000 divided by 1 plus B, which is 0.9 times D, which we know is 0.5. And then T is in terms of years, which is why this is in terms of year, so they cancel. So this is going to be 1 because we're interested about year 1, or it's a one-year time step anyway. That's why we're going to be using a 1 here. And then this is going to be the 1 over B power, so just 1 over 0.9. And when you do this, you're going to find that your oil production after one year is going to be 1,323.5 STB per day. And then if you want to find what your cumulative oil production is at this point, you're going to be rearranging this equation to solve for NP. So NP is going to equal... I'll rearrange it for you so it's easier to follow. So NP is going to equal QOIB divided by DI 1 minus B. And this is all going to be multiplied by QOI to the power of 1 minus B minus QO, which we just found, 1 minus B. So then we solve for NP. So QOIB, that's going to be just the 2000. So DI is 0.5, 1 minus 0.9. So we're going to have QOI, which I said is 2000. This is going to be to the 0.1 power because 1 minus 0.9 will be 0.1. Minus QO, which we just found, is 1,323.5 to the 0.1 power. Okay, so this should be QOI to the power of B, not subscript B. So 2000 will be to the 0.9 power. So it's 2000 to the 0.9 power divided by 0.5 times 1 minus 0.9 times this quantity here. And so when you do this math, you're going to find that your cumulative oil production after one year is going to be 1,617.84, and that's going to be STB per day. And since this is a cumulative oil production, we're going to want this in terms of STB. We're going to try to get rid of that time. So what we do is we multiply this by 365 because we are just interested in the cumulative oil. So 1617.84 times 365 will give us a cumulative oil production of 590,485.7 STB. And so this is what our cumulative oil production is after one year and our flow rate after one year is 1,323.5 STB per day. And now we can just move on to year two and it's going to be the same process. So the first thing you're going to do is you're going to find your QO for year two. So to do that, you're now going to have, excuse me, going to be equal to the same equation we have up here. But now the T, since it's two years, is going to be two instead of one. So that's the difference here. So it's going to be 2,000 divided by 1 plus 0.9 times 0.5 times 2 because it's two years. And this is going to be to the 1 over 0.9 power. This is going to give you 980.2 STB per day. And the same thing with the equation up here for NP. We can just solve that real quick. So it's just going to be still 2,000 because it's QOI to the B power. So it's still to 0.9 divided by 0.51 minus 0.9. Then it's going to be multiplied by 2,000 because it's like I said, it's QOI to the 1 minus B. So it's going to be to the 0.1 minus our flow rate we just found. So it's going to be 980.2 to the 0.1 power. So as I was working up here earlier, so this is what you get for NP. But keep in mind your units of NP, your production of oil will be a volume. So it'll just be STB. So I just have this as a rate because I need to convert it to how much it would be in a year just because we're looking for cumulative production in terms of years. So I had to multiply this by 365. And so now using doing for year two, I get a flow rate of 980.2 STB per day. And so I'm solving for my cumulative production of oil. In terms of if I look at in terms of rate per day, I'm going to have, this is going to be 2753.24. This is going to be STB per day. But I want this in terms of for one year. So I'm going to multiply this by, I'll just do that here. So I'm going to multiply this 2753.24 times, so this is STB per day. I'll multiply this by 365 days in one year. So this is going to get me 1,004,968 STB. So this will be my cumulative production of oil. And so if I want to get a yearly production for year two. So this is going to be my total production so far for combining year one and year two. So if I wanted to just look at year two, I would multiply, let's say this is MP2 and this is MP1. I would multiply, or I'm sorry, I subtract MP2 minus MP1. And this will give me my yearly production in year two. So that will just be 1,004,968 minus 590,485. And that will equal, should equal about 414,000 STB or so. And so you can keep doing this process. So if we were to do it for year three, it would be very similar. So QO for year three is going to be 2,000 divided by 1 plus 0,9 times the D, which is 0.5 times 3 because we're dealing with three years now. And this would all be, so 1 over 0.9 power. And so QO for year three would equal 774 STB per day. And using this QO and the equation we have to solve for MP, just doing the same process would get our NP to equal 1,322,292.6 STB per day. And so if we wanted to find the cumulative production in just year three alone, we would subtract the 1.3 million by the 1.004 million. That would give us a yearly production in year three. Note how in year one it increased by about almost 600,000. Year two, it increased 414,000. Year three, it only increased by 318,000 or so. So as time goes on, your rate or your cumulative production each year is going to fall off. And that's why the B value matters because say if you were to have one, for example, like I believe it would just be a constant. So you're going to have like the same change in your cumulative production each year. Or like for exponential, for example, when your B is very low, like zero, it's going to fall off very quickly, which is why it's the most conservative. So you can keep doing the same process for multiple years and to see what your production may be, your cumulative production may be in five years from now. And so it helps you forecast maybe like the life of a well maybe worth it or not to drill. So I just noticed this should have an extra zero right here for 414,000. And like I said, your cumulative production of oil will be in terms of STB. It's a volume, not a rate. Rate is going to be like flow rate, where it's volume over time. Where in this case, this is just volume, like NP and they all have units of STB because you're talking about oil. Now if you're talking about gas, you might have like GGP, which is going to be like SCF. You could also be dealing with water, but it's going to be terms of volume and not STB per day. And that will be it for this problem.