 Okay, so for this case, we're going to be working with flow rates into a well. So we're going to be given some different parameters to do this. We're going to be using variations of Darcy's law for single phase calculating these properties. So let's start with our bubble point pressure. This reservoir is going to be 2,634 psi. And we're going to be at that or above. If we're just at that, it's going to be maybe one gas bubble or so, which isn't going to affect anything in terms of this problem. So our well bore, PWF states for like well bore flowing pressure, bottom hole pressure, that's going to be, we're going to say this is just at like bubble point, maybe a little bit above bubble point. So that's 2,634 psi. This is just so we don't have like gas coming out of the oil and therefore you'd have different equations you'd use for two phase. So for our actual reservoir itself, our external radius, our ease a thousand feet, our thickness is going to be 200 feet, our permeability is going to be 2 milli Darcy's, our well bore radius, our W is going to be 0.5 feet, our skin factor is going to be 3.5, which is dimensionless. Skin factor is a way of measuring near well bore damage, so which may affect your flow rates for example. So you may have heard of fracking, fracking typically will give you a very low skin value and negative skin value, which in turn will improve your recovery or flow rates. And so when you have a positive skin in this case, it means there's damage, so there may be something like blockage or there's different reasons why you may have skin. So we have different properties from a PVT report, which will be in question one which you may have seen or may see later. So our, we have two different pressure ranges, we have 4,000 psi for this case and we also have 2,635 psi for this case, which is just one psi above bubble point. I kind of want to show you how pressure in your reservoir, when it's different in your well bore pressure, how that will affect flow rates. So this pressure you see here is going to be your average reservoir pressure. And do take note in the notes, you may see PE or P bar, there is a difference and you'll see that in your equations for like pseudo steady and steady state. So make sure if you're using, you're using the right P value and you're using the right equation and what it's asking for. So in this case, it'll be P bar that we're going to be talking about. The other one is external pressure, which is like at your boundaries. And so our formation volume factor of oil at bubble point is going to be 1.444. At 4,000 psi, it's going to be 1.42, 07. Our viscosity at bubble point is going to be 0.3785 and it's going to be center poise, CP. And then our viscosity at 4,000 psi is going to be 0.4367. We'll start with solving for a steady state. First, we're going to be talking about pseudo steady state and steady state for this question. So for steady state, we're going to be using equation 4.34 in your notes. And this is as follows, right over here. So you're going to have Q equals your permeability in millidarcy's times your height in feet times your average reservoir pressure, which is like P bar, like I said, in PSIA minus your well more pressure, which is also in PSI. And so this is a pressure differential, which that's how Darcy's law works. It's based off pressure. Deference is why we say flow is occurring, why there's movement of fluids. So that's necessary in order for there actually to be flow in our case. And then we have 141.22, which is just a unit conversion to get your answer in terms of stock tank barrels per day. So we're going to have viscosity of oil, our formation volume factor of oil. And this is going to be all multiplied by the natural log of your external radius of your reservoir divided by your well bore radius minus 1 half plus s, which is your skin. So do you take note, like if you have a PE, for example, up there, based off what I believe you won't have a negative 1 half at all, just be plus s. So based off what you're using, it is a different value. So this would be for steady state. And our other equation we'll be working with is pseudo steady state. So a big difference with these steady states, a lot less likely to occur in your reservoir, pseudo steady states more common. So do not try to get into too many details. Pseudo steady state is basically the time where you're saying your external, basically after your pressure propagation from your well bore, what you feel, hits your external boundaries of your reservoir and then it goes into pseudo steady state. And don't worry about that too much for right now. Just know that there is a difference between pseudo steady state and steady state and they have different equations. So it's going to be basically the same thing. Permitability, milled-darsie times height in feet times your pressure in your reservoir minus your well bore pressure. Got it by 141.22 times viscosity of the oil times the formation volume factor of oil times the natural log of your external radius divided by your well bore radius minus, in this case it'll be minus 3 fourths plus your skin factor S. So we're going to be doing both steady state and pseudo steady state for 4,000 psi and 2,635 psi. So you'll get a total of four different flow rates for this question. So let's start with doing steady state for 4,000 psi. So we'll have Q and this will be in stock tank barrels per day. We're going to equal our permeability which is 2 times our thickness which is going to be 200 times our differential, our difference in pressure. You can look, this is also called draw down pressure. So you have your P minus PWF which is just going to be 4,000 minus 2,634. And this is going to be divided by 141.22. So since we're dealing with 4,000 psi here, we're going to be using these two properties here, formation volume factor of 4,000 and viscosity of 4,000. So this is going to be times 1.4207 times 0.4367. It's also going to be multiplied by the natural log of RE over RW, which that would just end up being 2,000. It's 1,000 divided by 0.5, which would just be 2,000. And this is going to be minus 1.5 because we're dealing with steady state here. Plus your skin factor, which is 3.5. And by looking at this equation, your higher your skin factor, your lower your Q. So like I said, that deals with damage. So when you do this out and you solve for this, you're going to get a flow rate of 588.283 STB per day. Now using the same pressure, now we're going to use pseudo steady state. So it's going to be the same equation. The only thing that's changing is the minus 1.5 to a minus 3.4. So that's the only difference between for the 4,000 psi. So it's going to be the same equation pretty much. So it's going to be 200 times 4. And like I said, it's going to be the same thing. You have the 141.22, let's see 1.4, 0.43, just to shorten it up a little bit. But it's going to be the same values as here. And then it can be the natural log of 2,000 minus 3.4 this time plus 3.5. When you do this, you get Q to be 602.401 STB per day. So as you can see, having that greater negative value in the denominator will increase your flow rate. And like I said, with skin factor, that's a negative value. It's going to also increase your flow rate. So these are for steady state. Well, this one's for steady. This one's for pseudo steady. Now, doing the same exact equations, but now we're doing it for 2,635 psi. So a few things will change here. One thing will change is your average reservoir pressure, P bar, which is listed here. That would become 2,635. The other thing that will change is your viscosity of your oil. And that would be for at bubble point because we're just saying that's the property we're using for. So at bubble point, our viscosity of oil is 0.375 formation volume factor, bubble point is 1.444. And so basically doing steady state, we're going to have the equation of 2 times 200, 2,635 minus 2,634. Because the pressure is 2,635 and the wall bore pressure is 2,634. So there's only one psi difference. So you can think about what kind of number you should expect then if it's going to be higher or lower. So like I said, it's going to be for round bubble points. So we're just going to use the bubble point values. So for viscosity of 0.785, for Bo, BoB, BoB just following formation factor at bubble point, MuOB of viscosity at bubble point, 1.444 times the natural log of 2,000 minus, like I said, we're doing this for steady state. So we're going to have a minus one half plus 3.5. So at 2,635 psi, our flow rate for steady state will be 0.4888 STB per day. So as you can see, just by looking at this equation for even doing pseudo-steady state, the closer your pressure and your reservoir is to your wall bore pressure, the less potential fluids will have to move. So you're going to have a lower flow rate. So now using 2,635 psi to calculate for pseudo-steady state, just going to be like the same equation as this for except the only difference is going to be changing the negative one half to a negative three-fourths. So your flow rate for that will be 0.50067 STB per day. So as you can see, the flow rates are a lot lower when your pressure and your well bore is closer to reservoir pressure, which why reservoir engineers, production engineers, they want to optimize your production, but at the same time, you don't want to produce too much all at once. So it's really a game to what you want your well bore pressure to be. You can manipulate it in different ways. You can use things called artificial lift, which can like simulate different bottom hole pressures. You can have like a well head pressure that might be different than your bottom hole pressure that will drive fluids through the well bore. There's a variation of different ways. But basically pressure is the key component here of why you're having flow into your well bore and eventually into your production facilities. So it is important property and to understand it. So pretty good. So that's it for this problem.