 First what we're going to actually find is the density of your dead oil So I don't know if this is covered in the notes or not But if you define a density of a dead oil what you do so your row So are you like standard? conditions Is going to equal it's sixty two point four, but if you want to like be more specific it'll be sixty two point three six eight Times specific gravity of your oil So in this case like our specific gravity of our oil is 0.81556 which will give us a density of 50.86 And that should be pounds per cube Using this we can find what BO is Formation volume factor above bubble point. So we're going to be using this equation right here so for BO It's going to equal your BO at your bubble point So it can be BOB and then it's going to be When it's simplified you're gonna have it to be one minus CO P minus PB so you can use this equation to find your Formation volume factor of your oil above bubble point and So for below bubble point you're going to be using Equations three point four four and three point four five And you can also use this equation to find your BO at bubble point as well So for these equations you're going to have So this is going to be Above PB and for below PB you're going to have the equations BO is going to equal to 0.9 759 Plus 12 Times 10 to negative fifth And then times C BO to the 1.2 power and to find CBO CBO is going to equal RSO so your RSO at your pressure of interest times Gamma G over gamma O So this is 0.5 power plus 1.2 5 times your temperature which in this case 120 degrees Fahrenheit and So for this we already know what our RSO is at bubble point like I said because you can use this And below Bubble point so RSO in this case was is going to be 900 our gamma G is going to be 0.7 our gamma O is going to be 0.81 And our temperature is 120 so we can calculate with CBO is real quick. So that's gonna be so our CBO is going to equal 983 point 803 and now plugging that in to the equation right here so we're going to have 0.9 759 plus 12 Times 10 to the negative fifth Times your CBO, which we just calculated is 983 point eight zero three to the one point two power And we get that BO at bubble point is going to equal So BO at PB so all point is going to equal 1.44 For BBL For STB if you think about it it makes sense your BO should never be less than one because you can't have a volume of barrel of oil in which is going to be of Greater volume than what your stock tank barrel of Volume of oil would be and so your stock tank barrel is going to be like your oil at standard conditions So it's going to be expanded as much as possible to where your Reservoir barrel of oil is going to be a lot smaller. It's going to be compressed. So And so to find the BO At above bubble point. I said we're going to be using this equation right here And now that we have our BO PB we can use that equation to find that so our BO 4,000 psi It's going to equal 444 That was one of my eyes and the compressibility of the oil for because we're doing this at 4,000 psi I Have it on my notes Presently the oil is going to be 1.208 times 10 negative 5 which we found earlier. So Great to put that in real quick and then the P in this case is going to be 4,000 And PB is just gonna be a bubble point pressure which we found was 2,634 And so our BO above bubble point is going to equal 1.420 179 this is good because your BO above bubble point should always be below what your BO is at bubble point So if you actually look at a graph for BO with respect to pressure So you can have pressure here be over here. It's gonna look something similar to this So like similar to that and so this right here Is going to be your PB and this right here will be your BO B and so as your pressure increases toward bubble point gas will dissolve in solution which allows The oil to take the place of the gas in the reservoir So your volume of your oil is going to be increasing in the reservoir and once you reach bubble point There's no more gas to dissolve and so it's as much volume as you can possibly have but as your pressure increases even more The forces because of your pressure is increasing your actual fluid is going to actually be decreasing in size Which causes your BO to actually drop at pressures above your bubble point pressure and so once we have that we can also find what our BO is at 2000 psi and like according to this graph as you can see our BO Should still be less than what our BO is at bubble point because like our BO bubble point should be your maximum Formation volume factor. So your BO at 2000 psi is going to equal so we're going to be using this equation again for Below bubble point and so the only thing that's going to be changing and this equation is your RS value And so as you can see over here our S value for 2000 psi 648 point 145 Which will give us a different CB value CBO value, and so let's do that real quick. So you're 648 So our new CBO value is going to be 750.47 and then we're just going to plug that back into this equation up here for CBO So we're going to get a zero point So our BO value is going to be 1.3 1.4 BBL per STB and Like I said, like you expected a lower value just because you're not at the bubble point yet So there's still free gas in the reservoir where oil has not taken up that volume yet So once you get to that point where it will then like I said, you'll have your maximum BO value So once we have these three BO values the next thing we can do is define the density of our oil At bubble point or above bubble point below bubble point, which is where we're going to be actually using this relationship at and So I'll just I'm going to erase this real quick and then have some new workspace So now to find the density of your oil at bubble point below bubble point We're going to be using equation 3.51 to do this, which is going to be equals Which is just this that right there which the RSO is going to be your pressure of interest for your density and so as I said earlier, so the BO for 2000 psi was 1.3144 so that's what's going to be used here. So And like our RSO since this is going to be below bubble point or at bubble point So first one will do below bubble point So our BLB 1.3144 BBL per STB our RS will be 648.145 in a row ST will be 50.865 So this will give us a value So this will give us a density of 43.3 6 Pounds per foot cubed. This is for 2000 psi Now to do it at bubble point same equation the only thing that's going to be changing is your RS value and your BO value So your RS value at bubble point is going to be 900 and your BO value at both points can be 1.44 So doing that we'll get we'll get a density of 41.114 pound per foot cubed at bubble point now to find the density of Your oil above bubble point You're going to be using an equation similar to what it was for BO So it's going to be ROW equals ROWB Which is just going to be This right here One plus Your compressibility of your oil at bubble point. I'm sorry the compressibility of your oil at your pressure of interest So it's going to be P minus PB and so like I said we're going to do this for 4,000 PSI because it's for above bubble point So this will turn into 41.114 One plus which are CO at 4,000 PSI was 1.208 times 10 to the negative 5 and Times our pressure, which is going to be 4,000 that's the pressure. We're doing it for Minus our bubble point pressure, which is going to be 2,634.4 and this will give us our density of our oil at 4,000 PSI Which is going to be 41.7 9 pounds per foot cubed Once we find our density of our oil We can then move on to the viscosity of our oil, which is going to be using Few equations going to be using equation 3.53, 3.54 and 3.55 and so Our viscosity of our oil so the main equation Is going to be going to be a times The viscosity of the oil It's going to be to the B power This is going to be valid for Below bubble point pressure and at bubble point pressure and so What we can do is Our a constant Is going to equal 10.7 15 Times RSO Plus 100 to the negative 0.515 power and B is going to equal 5.44 Times RSO Plus 150 to negative 0.338 power Okay, so for solving this equation You're going to need a B and also mu o d to solve mu o d. You're going to be using equation 3.52 in the notes Which? write it out here It's going to be log base 10 of log base 10 of mu o d plus 1 It's going to equal to one point eight six five three minus zero point zero two five zero eight six Times your API of your oil, which is forty two minus zero point five six four four Times log base ten Of your temperature in Fahrenheit, which is going to be 120 so just During that calculation beforehand your viscosity of your dead oil It's going to be 1.512 Center poise so that's going to be plugged in right here so then we can finish calculating what a and b is and Yeah, so a is going to equal This is going to be for pressures below bubble point, so I'm going to be doing this for 2000 psi at first So at 2000 psi we see our solution gas solar ratio is 648. So 10.715 times So we get the a is equal to 0.354 7 and when we solve for B we get we get B Is equal to 0.5 684 So then using this equation we can solve for the viscosity of oil at 2000 psi So our viscosity of our oil will be So our viscosity of our oil is going to be 2000 psi a it's going to equal 0.4 486 Center poise and then we can also find what the viscosity of the oil is above bubble point Which is going to be using equation 3.56 I'll just re-erase this and do that then And we're going to calculate the viscosity of the oil bubble point We also need to find what the viscosity of the oil is at bubble point So using these equations I'll just find what the viscosity of the oil is at bubble point So I'll just do that up in this workspace up here because it's pretty crammed around here So your viscosity of your oil at bubble point It's you're still going to be using like your a B in your dead oil viscosity the only thing that's changing here is your RSO value which RSO and I'll be 900 So our a is going to Equal So a will equals zero point three zero five B will equal you will equal zero point five one eight and so Mu o d will still be one point five one two and so plugging that in we get zero point three zero five Times their viscosity of dead oil, which is one point five one two to the power of B Which is power of B just zero point five one eight So we get that our viscosity of our oil Just want to check Yeah, viscosity of our oil at bubble point is going to be zero point 3778 Which I'm going to read over here So viscosity of the oil at bubble point You go this is a center poise zero point three seven seven eight center poise and Then for our next calculation, we're just going to find with the viscosity of the oil is above bubble point So we'll do four thousand psi