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welcome back in five days I'm Brendon Tolbert and today we're talking to natural gas engineering decline curve analysis it's one of the most important fundamental building blocks of petroleum engineering you can use decline curve analysis to forecast reserves predict the URS and even determine original gas in place today we're going to start with the most fundamental aspect of decline curve analysis the rate time interpretation although it's not widely used today if you understand the fundamentals of this you are well-equipped to understand more complicated interpretations so guys let's get started welcome guys today we're going to determine the reserves and estimated ultimate recovery of a well using great time decline curve analysis so rate time decline curve is represented by this graph right here you have your production rate on the y-axis and you have your production time on the x-axis and so these dots right here blue dots blue circle dots represents the gas production rate at a given time and you can see it declines over time and so we fit a curve to this data and then we forecast it with the red line to determine reserves Andy you are so that's what we're going to do today we're going to actually take gas production data and do this and so the key concepts and want you to think about as we do this is the Arps rate decline equation this is the most fundamental equation of decline curve analysis and a lot of other more complicated interpretations built off of this so kind of understand this also minimizing the sum of squared errors so in order to fit our curve we're gonna have to apply the minimization of the sum of squared errors to forecast and then you need to know what reserves are which is basically what is left to produce from a well it considers the economic limit or the economic rate and also estimated ultimate recovery is how much gas you produce over the life of a while so before we get started let's kind of look at the theory and don't get caught up in the equation so much it's not that important what is important is the logic you go through so this is the Arps equation this is the main equation right here and so you have the initial producing rate the initial decline and then the time and then you have a B exponent the exponent is basically a decline constant the larger it is the longer your well produces there's smaller it is well you're you don't produce well doesn't produce as long and you get smaller EU RS but this is the fundamental equation and so our equation covers basically three different types of well behavior you have exponential flow harmonic flow and hyperbolic flow and so that's not too important but just remember that what you have here is for B values greater than zero you can apply this equation so this is the equation you're going to use for B values equal to zero you can reduce this equation right here to this equation using calculus but it's derived this equation is derived from here and so you have two equations you can apply it to determine rate that's it no more and so now another thing you want to do to forecast reserves is to calculate the kuna of gas production so that's simply just the integral of the rate right our flow rate times time equals Q moon of gas produced so it's the area under this curve and so what you get here is you get this equation right here and so once again when you only need two equations this one right here for when B values don't equal one and then this equation right here can be derived from calculus two from the above equation when B equals one this is highly unlikely to happen but we're actually going to code this in Excel VBA using these two equations to in these two equations to determine human of gas production but we're more than likely never going to encounter this case I'm gonna include it anyways and then the nominal decline is the instantaneous decline at a specific point in time so you're gonna need this because if you look at this graph over here the way we forecast reserves is we basically apply the minima minimization of the sum of squared errors of the Arps equation right here these two equations right here we get our best fit line through the production data and then we stop okay so now that we have our last point in time we know how much gas we produced up to this point in time we can calculate that in Excel now we need a forecast so now we forecast to the economic limit which is going to be determined by your economic analysis and then you determine the reserves by taking the integral under this curve which is simply this equation so you basically take the rate at this point Qi right here and then your rate at the last point the economic limit and then you'd have your B value that's you determine from your best fit line and then your instantaneous decline would be your instantaneous decline at this point and then you can determine your cumulative reduce which is your reserves so that's how we do it it's not that complicated but just keep that in mind you're fitting this data right here and then you're using your equation to forecast from the last data point and beyond so that's really what it is so these are the steps you need to go through to fit your decline curve and forecast your well or determine your e you are in reserves and I'm not going to go through this if you're interested pause the video read through this it's pretty self-explanatory so I'm gonna move on so now I had to talk I talked about earlier or introduced this concept is in that we don't really apply this rate time the client curve analysis anymore why well these are the reasons because a lot of times these days we have the wells have flow regime changes what does this mean this means like you well can go from producing linear flow to boundary dominated flow that there's just different flow regimes and I'm not gonna get into too much detail but basically if you fit your rate time decline curve to a well that's exhibits flow regime changes you're gonna overestimate your reserves another reason we don't like to use great time decline curves is because it's affected by shut-ins so if I showed it in the well over a period of time and then I turn on the well full choke down the line well my entire fit is gonna be screwed up I'm gonna overestimate reserves so that's really the reason we don't want to use this rate time interpretation because it overestimates reserves because it neglects flow regime changes and shut-ins and so but I'm gonna demonstrate it anyways because you're gonna use these same concepts for radio flow interpretations and linear flow interpretations so let's go ahead and step over to excel get started okay guys so let's start this so what I've done is I pulled in production data from a gas well and so what I pulled in is the cumulative guess produced a time at which the time and also the rate at that given time so these are the three pieces of information I need to do great time decline so what I want to do so you can see this production data it's plotted on this graph this is a rate time graph this is what it looks like we start off with a high rate and see it slowly decline over time so the objective is to fit this early production data with our Arps equation and then forecast from our last point and beyond it to determine EU are in reserves and so before we get started let's go look into the code what you have here is the equations we used in the slides basically slide two this is our arcs rate let's see so what you have here is you have the logic to determine Arps rate so if B equal to C if B is equal to 0 then you have exponential decline else you have hyperbolic and harmonic decline which can just be described with one equation so these are the two equations in the slide that's all you need okay and you can see that our variables we need our initial rate initial decline rate the B value and also time and so this is our exponential rate equation that I called up here the next thing we want to do is to determine cumulative gas produce so these are the other two equations in the slides so if B equals the one you have one equation if B is not equal to one then you have another equation so the last equation we need is nominal decline because we want to forecast reserves at our last data point using our fit so this is what you need so this is that equation in the slide di is initial decline rate is the decline exponent T is time and so this is it so these are the only equations you need to do rate time analysis not too much right I like it easy and simple man I'll take it any day of the week it's so the first thing we want to do is determine our Arps rate and plot it on this graph so let's use our Arps rate equation and so what you have here it takes in Qi which I've put up here you're going to need qi d ib to determine Arps right that sort of the inputs of the ARP equation you're going to need these and I'm going to make these absolute or freeze them and then the time so our time is zero initially bang so I'm going to copy that all the way down our production data and I made a mistake this should not be frozen bang copy it all the way down okay so now I've plotted this on the graph already okay so this is our Arps decline equation right here plotted on this plot so the next thing we want to do is calculate the difference so I met I mentioned earlier to use the minim a minimization of squared errors goodness but I'm actually gonna do something easier I'm gonna do the absolute relative error okay it's pretty much the same thing it's a little bit easier so what I'm gonna do is take the absolute value of our actual rate minus our predicted rate divided by our actual rate okay bang and I'm gonna carry that all the way through our data and so that goes all the way down here to our last data point and so I sum these right here because we're gonna need to do regression or apply an optimization algorithm to get our data fit close to the data and so I've some the errors the next step is we want to put our forecasts on here okay and so what you do to do that is I've take your last data point okay which is gonna be the maximum of the rate column so it's gonna take our last data point at this point okay it's actually the maximum of our time call in my bad so it's going to take the last point in time and then I just went ahead and just forecasted a few days ahead in time so I could show the forecast on this graph and so we're gonna have to calculate our pea rate okay our P rate and so that's going to take into account q I di be and time I'm gonna freeze these right there whoops and carry this down so now we have shown our forecast on the pot and so what we're trying to do guys if you recall in the slides what I was trying to point out is in order to forecast we need our last point in time right here our rate at this point in time using our Arps equation and also the nominal decline at this point and then we need our rate at the economic limit so we need four pieces of information the rated at the economic limit our instantaneous decline at the last production point in time and also the time and also the rate so guys that's what we're doing here so we just read need the instantaneous rate at our last point right here so it's gonna take the I B and time okay so that's really all we need okay so now let's go ahead and put in our reserves equation which is just going to be our cumulative production from this point and beyond so this is why we calculated all this right so we need this point and Beyond okay so what we take into this is Q I at this point right here so that would be our last data point so bang and then di at our last point right here so right there and then B and then our economic right economic limit rate so bang there we have it okay and then re you are simply to sum of these two numbers and the reason this is negative right here is because our forecast isn't right okay so basically I've chosen a point in this region right here on this this curve but once we get closer you'll see that change next we want to do next thing we want to do is we want to minimize the sum of errors with solver if you haven't used solver before you need to learn how to use it because it's very useful for engineers but before I minimize this with solver I want to at least get this a close fit you know just in the ballpark solver will give you a better result if you get a close fit initially so let's do that let's get a little closer so let's go change the parameters right here that we're gonna optimize off of so our initial rate let's change that to around 400 okay so now our decline is a little bit too steep so I'm going to reduce the decline a little bit change that to 0.04 okay we're getting close okay and so this was we can mess around with this say 0.6 that's a little high let's change it to 0.5 that looks like a pretty darn good fit so you can see here our reserves have updated to positive values because our forecast here 30 right here falls over here instead of on our curve right here and so it falls on the forecast curve and so let's change this or let's go ahead and forecast so let's minimize this with solver to get a better solution so what I'm going to do is I'm going to this is my objective I want to change these values to minimize the objective so if we solve this and we get a sum of errors of 97% which is better than what we did by hand and you can see the curve right here that is a nice clean fit you know somebody who could look at this and say yeah I agree with that that's a great fit and so what we've done here is we have our fit so now we have our reserves right there in our EU r so now if our economic limit changes say we want say our economic limit is going to be 50 in CF per day so our Reserve should decrease and they do Bank so we only have two hundred thousand m/s CF to produce left what if it's 15 it should increase and yes it does so you can see this as right here so guys that's it we were able to forecast production data using rate time interpretation using Excel VBA and the Arps equations so that's it and if you liked the video please subscribe and I'll catch you next time adios