 So here we're going to be working on question two for the midterm review. In this case we're going to be finding a stock tank oil in place for a reservoir. We're going to be basically given four different data points in the reservoir regions A, B, C, and D. The values are listed here. So you have the saturation of oil, which is SO. You have your net pay zone, which is HN. You have your gross pay zone, which is HG. You have your oil formation volume factor, which is BO, and you have your porosity, which is Fee. So in this case, we're going to be doing two different methods. We're going to be doing volumetric method, which you'll see first, and then you're going to see isocontor method. And this will give you an example of why one way may be better than the other way and how to approach a problem like this. And this is a very common problem in reservoir engineering because you're not able to drill a well in every single location you want to. It costs money. And so you have to work with data that you already have in the reservoir. And so you have to make sure you understand how to use those values properly. So in this case, like I said, we have these values given. And so what I'm going to do first is calculate the average values. So basically for saturation of oil, for example, I would add all the SOs up and just divide by four because there's four regions. And it's the same thing for each property. So I'm just going to give you those averages right here. So the saturation of oil average is going to be 70%. Our net pay zone average is going to be 72.5 feet. Our gross pay zone average is going to be 112.5 feet. Our formation volume factor of oil average is going to be 1.2. And our porosity average is going to be 16.2%. Using these values, we can then find what our stock tank oil is in place using a few equations. So the first equation I want to talk about is equation 4.03 that you'll find in your notes. This is the gross volume of your pay zone. So, which is going to be and 43.560, what I'm about to write, is just a unit conversion to go from acres to feet. So one acre equals 43,560 feet squared. So we have 43.560. And then we're multiplying by our area of our reservoir, which is 40 acres. So basically this is like for agent A, B, C, and D, it's encompassed within that. And so we multiply that by here because we basically want to get that into feet squared. So we can calculate the volume and then we're going to multiply by our gross pay zone. You might ask like what's the difference between gross pay zone and net pay zone? You'll notice that you'll learn like in classes like 440, PNG 440 for example. You may have like a certain water saturation and part of your pay zone, which really you won't be able to get much production from or it's not very good to recover from. So you don't really include that in your net pay zone, but it's included in your gross pay zone. And so we multiply by our gross pay zone average, which is the 112.5. So when we do that we are going to get 43,560 times 40 times HG average, which is 112.5. Now we will be using this. I'm just going to keep it as it is so I can show you how things cancel. We're going to then plug this in to an equation that solves for our stock tank oil in place, which this is going to be equation 4.04A in your notes. So that equation is this, which this is what we just found. And then we're going to have our net pay zone average divided by our gross pay zone average, multiplied by our porosity average, multiplied by our oil saturation average. And then we're going to divide this all by 5.615. Like I said, because this right here, when you solve for this, this will be units of feet cubed. And so when we find stock tank oil in place, we want it in terms of barrels. Or in this case, it would be stock tank barrels because as you see, I'll divide by a BO. So this will be our BO average. So when you multiply or divide by your BO average, you're basically converting your barrels to like stock tank barrels. So you basically want what it would be at your production facility, how much oil you'd have. So this is just going to be this equation right here divided by this. It's a little looks a little off, but it's just your gross volume of your rock times your average of net pay zone divided by gross pay zone times porosity average times oil saturation average divided by 5.615 times formation volume factor average. And when we do this calculation, like I said, these values right here are just these values right here just plug it in for them. We find that and another reason why I kept it like this, as you'll see this HG right here is the same thing as this HG. So I'll cancel. So basically this right here and this right here cancel. So that's why I kind of want to show it like that. And so when I write this out, we're going to have 43, 5, 60 times our area in acres, which is 40 times. We're going to have our net pay zone average, which is going to be 72.5. And then we're going to be multiplying this all by porosity average and oil saturation. So our porosity average is 0.162 or oil saturation average is 0.7. And we're dividing this by 5.615. Like I said previously, you're using the 5.615 to convert from cubic feet to barrels. And then the BO's to convert from barrels to stock tank barrels. So then you have 5.615 times your BO average, which is 1.2. And when we do this calculation, we find that N is going to be equal to 2,132,584.59 STB. This can also be written as 2,132.584 MSTB or 2.132584 MMSTB. So our M is million, M is a thousand. And so this is basically what our original oil would be in place if we used volumetric method. And now, since we did this, we can talk about isocontor method, which is our other method of approach for evaluating different points in the reservoir. So for this, we're going to have an equation 4.05. It's going to be a little bit different. In this case, we're going to ignore gross volume and gross pay zone. Just because, like you said, it cancels anyway. And because how this approach works, it's a little weird in terms of having different HGs because we're not averaging A, B, C, and D anymore. We're actually going to find a value for an isocontor of region A, region B, region C, region D individually. And so the equation for this will be the following. So this could be G or O. This is just in terms of the phase you're working with. So in this case, we're just working with oil. So we're going to have porosity times the net pay zone times SO divided by BO. As you can see, it's very similar to what N is. It just doesn't include the VGRV or the HD, like I said. So in this, we can calculate this for region A, B, C, and D. So basically, I'll just show you how you'd calculate for region A and then it'll be the same way for the other three regions. So for ICOA, just going to equal like the porosity of A is 0.10. The net pay zone for A is 75 feet. The oil saturation is 0.6. And the formation volume factor is 1.2. When you do this calculation, you're going to get that ICO for region A is 3.075. And now for B, it's going to be the same way, just using B's values. Now it's going to be 10.046. For C, it's going to be 5.250. And for region D, it's going to be 8.727. And so these are just, we look at them as constants. So it's a parameter for that region. And so once we have these values, we can actually average them together, kind of like what volumetric did, but now we're doing each region individually instead of connecting them. So when we do that, let's sit over here. We're just going to add all four of these values up, divide by four, and we get 6.745. And similar to how we solved for the N, which is original sock tank oil in place, we had all this information times the VGRV. And so like I said, like the HN or HG, porosity, SO, BO, it's all part of the ICO, except for like the HG because it cancels. And so basically what we can do with this right here is just plug it in for in the N equation. So N is going to equal 43, 560 times 40, because our area is still 40 acres, times our ICO average, which is the 6.7745. And then we're going to divide by 5.615, because everything else that's not included here is already calculated for when you compare it to N. So this is going to equal 2,102,206.38 STB. Or you can write it as 2,102.206 MSTB or 2.102 MSTB. And so as you can see, these values are very close to each other, but there is a main reason why Isocontour method is preferred. And you're going to see that with the next example, because one of each property in each of these regions is going to be very low to where it's not really shown when you're taking the averages, when you're doing the volumetric method. So you're going to be getting a lot more oil than what you would if you do the Isocontour method. And so I'm going to write those values up now. Okay, so in this case, we have three regions now. And I'm going to show you why the Isocontour method is a lot better than the volumetric method. So in the last case, the numbers were somewhat close. I think there's about 20,000 STB or so difference. But in this case, it'll be a lot bigger difference. So we're given region A, B, and C. And if you notice like region A, for example, its porosity is approximately 0%. And region B will have the oil saturation approximately equal to 0%. And region C will have the net pay zone equal to approximately zero feet. And so we can like just think about it in terms of like very small, like say your porosity is like times one times 10 to the negative 12 or something like that. Like there may be a little bit of porosity, but it's going to be so little that there'd be such little oil in that area. And you can look at that for all three regions because each have a property of zero. But when you're taking the average of all three properties, as you'll see, it doesn't really mimic or show that you have a zero property in one of your regions. And so for when we do our averages just like before, it'll be the same way. Just add all three up and divide by three. So our oil saturation will be 0.50. Our net pay zone average will be 51.67 feet. Gross average is going to be 113.33 feet. Our BO average is going to be 1.23 BBL per STB. And our porosity average is going to be 0.117. So 11.75%. And like using the equations showed earlier, let's solve the volumetric of oil first. So first like we can use the VGRV, which is going to be somewhat similar to this last case. So we're going to have the unit conversion again of 43.560 times our area, which is 40 acres. So our area is staying the same for this case, still 40 acres. And then our gross pay zone is going to be 113. Our average gross pay zone is 113.33 feet. And so then when we solve for N, just like before, we're going to use the average properties again. So we have the VGRV. And then we're going to multiply this by our net pay zone average by gross pay zone average. So like the 113.33 will cancel. So I'll just like cancel them right now. And then we're going to multiply by the average porosity and then average oil saturation. So times 0.50. And then just like before, we're going to divide this by the unit conversion of feet cubed barrels, which is 5.615 when you divide by 5.615 anyway. And then we're going to multiply by our BO average, which is going to be 1.23. And when you do this calculation, you find that your original oil, original stock tank oil in place is going to be 762,583.35 STB, which before is around 2 million or so. So let's say like maybe a third or so, or two thirds less than what it was originally. Now we'll see here in the ISO contour method. When you take each region individually, you'll get a value that's negligible, basically zero. So let's do ICO of A. Just like before, it's going to be like the same process for A, region A, B and C. So I'll just show the calculations for A. So for A, it's going to be 70. Yep, it's going to be 1070 times our porosity, which is approximately zero. So like very small, multiplied by our oil saturation, which is going to be 0.75. And then we're going to divide that by our formation volume factor of oil, which is 1.2. And so like I said, zero, it's approximately zero for your porosity. So this is going to end up being zero. And it'll be the same thing for region B and C. Because as I said, like with B, your oil saturation is approximately zero. So you can say this is also zero and same thing with C. Your net pay zone is approximately zero. So we can say it's about zero. And so when you calculate N using the average of your ISO contour, you find that the average of this is just zero plus zero plus zero all divided by three, so it's just zero. So when you're calculating your oil in place using the ISO contour method, you're going to have N times your average ICO, which is just zero times like the VGRV term, which is the 43, 560 times 40. And like I said, before the HGs cancel, so we can just ignore that in this case. And then that's just going to be divided by 5.615. So as you can see, this is zero. And this makes sense too. This is what you should expect for your oil in your reservoir, just because if region A, neither of these regions have the capability of having any oil present. Because in region A, your porosity is approximately zero percent, so there will be no room for any fluid volume at all. In region B, the oil saturation is approximately zero, so it may be all water. So that porosity is 20 percent. So the water saturation may be 100 percent, or like 99.99 percent and so on. And in region C, our net pay zone is zero feet, so there is no actual region where there's going to be any oil in terms of produceable oil anyway. And so, as you can see, the zero is very different than 762,000 stock tank barrels. And so that's why the isocontor method is a lot more accurate, because by doing the average volumetric method, you're going to find that there will be oil in this reservoir, but as you can see in each region, there wouldn't be any oil. So that's why the isocontor method is better.