4

12.2.4 Oil Well Drilling Costs Estimating the costs of drilling oil wells is an important consideration for the oil industry DS 12.2.1 contains the total costs and ...

Question

12.2.4 Oil Well Drilling Costs Estimating the costs of drilling oil wells is an important consideration for the oil industry DS 12.2.1 contains the total costs and the depths of 16 offshore oil wells located in the Philippines (taken from "Identifying the major determinants of exploration drilling costs: A first approximation using the Philippine case' by Gary $. Makasiar, Energy Exploration and Exploitation, 1985). (a) Fit a linear regression model with cost as the dependent variable

12.2.4 Oil Well Drilling Costs Estimating the costs of drilling oil wells is an important consideration for the oil industry DS 12.2.1 contains the total costs and the depths of 16 offshore oil wells located in the Philippines (taken from "Identifying the major determinants of exploration drilling costs: A first approximation using the Philippine case' by Gary $. Makasiar, Energy Exploration and Exploitation, 1985). (a) Fit a linear regression model with cost as the dependent variable and depth as the explanatory variable (b) What does your model predict as the cost increase for an additional depth of 1000 feet? (c) What cost would you predict for an oil well of 10,000 feet depth? (d) What is the estimate of the error variance? (e) What could you say about the cost of an oil well of depth 20,000 feet? (This problem is continued in Problems 12.3.3,12.4.4, 12.5.3,12.6.5,12.7.1,and 12.9.3.)



Answers

The marginal cost of drilling an oil well depends on the depth at which you are drilling: drilling becomes more expensive, per meter, as you dig deeper into the earth. The fixed costs are 1,000,000 riyals (the riyal is the unit of currency of Saudi Arabia), and, if $x$ is the depth in meters, the marginal costs are $$ C^{\prime}(x)=4000+10 x \quad \text { riyals } / \text { meter } $$ Find the total cost of drilling a 500 -meter well.

Okay, here we have a problem of the depletion of natural resource is we have our tea, which is the rates in which a nation extracts oil and we have 10 to the power of seven. The actual problem is actually gonna have are zero e r of negative, Katie, but I'm replacing Upset seven because our zero is equal to 10 7 for our purposes. 10 to the power of seven. For our purposes, we also have to assume that we have in the reserves of oil two times since the bottom line or two billion. We're gonna find Q t to find q t. We are going to just find the integral for this. So if we find the anti derivative all right, find the total oil consumed are extracted. We get 10 7 get one minus e negative. K t over. Okay, the reason we have the came the nominator here is because we have the k here. So that's what we get from that. Now what it asks us to do next and asks us to figure out if we have t to the power of infinity. What do we get so e to the power of infinity, Our sorry teacher, the part infinity. If we have teaching part infinity, this part here goes to zero because negative infinity, each of our mega Nefertiti becomes one over eats of our affinity. And if one is being divided by something incontestable, it approaches zero. With that, we get 10 to the power of seven times one over K. So the total amount of barrels of oil extracted over an infinitum of time we get 10th with 57 over K. That's the meaning of the limit. So I means the nation has to have at least this much oil unreserved. So if we want to figure out for the next part, how much oil do we need? What does they have to be for us? Toe Have unlimited oil, basically. So we want 10 to the power of seven over Kate to be equal to two times 10 to the power of nine. To do that, some of the K over here of our seven equals two times tends bar of nine. Okay, so we gets If we divide this, this comes zero. This becomes too. And we get, um, one over 200 which is a good 2000.5 Okay. Lastly, it asks us, what if our of zero is in sad equal to two times 10 to the power of So So we have two times 10 to the power of seven year, and instead and we have k changed that a bit. K is equal 2.5 once again. As we figured out in the last problem, we're gonna try to figure out when will we run out of oil? If we have this, remember, it would. 10 to the part of seven. It's unlimited oil if we have 70.5 But this is different. We If we want to figure out when it runs out, we need to figure out When does it become 10 to the power of seven. So when does this? If we this times this we wanted to be equal 10 to the power of seven. Because when we do tend to over seven divided by this, we're going to get two times, sends apart nine. So we need to figure out what does this value have to be the valley? It has to bees, of course, half because too time sensitive are some toe to extending far. So? So we're gonna do that equals 1/2. We get you negative. 0.5 t is equal to 1/2 but yeah, and if we calculate this out, we'll figure out that T is equal to 138. What? Six years? And if you wanted to figure that out, you would have to get the natural log of 1/2 is equal 2.5 t the natural log of 1/2. He's equal to negative 0.69 If we divide that point negative 0.0.5 we get 138.6 and we're done.

Problem 71. We are given this oil consumption word problem. So for part A, it asks us to write c prime of tea for the oil company Leading T equals zero. So for part A, we would just rewrite this except Artie would be zero would be c prime of tea because so the cave value is 1.2 I was given in the problem. That would be 1.2 e to the and the R value is 0.4 and t you would just have here and for part B. It asks us to set up a definite inter grow for the amount of oil that the company will sell in the next 10 years. So that means our inner girl bounds would be 0 to 10. This is going up to 10 years, and we would just have the sea of tea inside, so 1.2 into the point before T d. T and part bees just asking us to set it up, so this would be a sufficient answer. So part see asks us to evaluate this in a girl. So to do that, we will just we don't we don't need any u substitution. We just look at this and the integral off e to the point. 04 t would just be need to the point. 0 40 over point. 04 So, me to the point, 04 t over 0.4 And don't forget to bring down the 1.2 and this would be evaluated from 0 to 10 which really does make it easier, because if you plug in 10 you get a value. But if you plug in zero, the top would cancel out. So just be one over 0.4 So we have 1.2 times e to the 0.4 times 10 over to your point here for and then if you plug in the zero, you would get one over I know for and this gives us about 14.7. This is in billions and for party. It asks us to do everything the same. Except now it goes up to um so now it has 20 billion barrels of oil. So it has. We have to find the tea value. So we have to find this t value. So 1.2 you toothy you know for team, and it says it adds up to 20 billion. So we can we know what we got for the integral, which was this value over here. So if he's if you, um if you simplify this, you would have gotten 30 times me to the point for T minus one. So now you can just go ahead and solve for tea. So if you saw for tea we get t equals approximately 15 years and finally for part E. We're asked to do the same thing that we did for party. Except we have to assume that our equals 0.2 instead of 0.4 So we do the same thing. Except this would be 0.0 two. So if you do the exact same thing letting t letting Ari quotes point or two. You can again Saul for tea, and you get a new value for Team, which is approximately, or tea

Okay, We'll come back. New raid. Here we go. Alright. We're in Chapter five. Section one of Thomas's captains. 14 Tradition. We're on page 2. 58 number 19. Now, we're not giving a function or a graph this time to estimated area were given a table of values. F zero is 55. 1 is 70. It increases our way to FF 87 26 An increasing function. So right. Three months, some would be an underestimate and a love three months, um, would be an underestimate. They're asking us to give over a number under estimates for five hours worth. Let's see. What is this? This is, um this table has given its time and ours, and the function value is leakage of oil tanker leaking oil in gallons per hour. Okay, so I'm going to say that the total amount of oil lost is now, let's make this easy. They want five rectangles. They went from the first five hours. Right. So I'm gonna say Delta X of one, and then f of one, which is 70 was up to which is 97 plus f of three, which is 1 36 less effort forward just 1 90. Is that not? This will be my underestimate. And F five was 2 to 65 and I punches up in my calculator already. I got 758 gallons of oil leaked in the first five hours of the leak. All right, because, uh, taxes in hours and the white values in gallons per hours of the units were getting here in gallons. Alright, what's my overestimate? That would be my left. Some, which is gonna be dealt X is one times f of zero, which is 50. So we're just shifting to the left f of one percent of to puts up of three plus f of my rights. My rights, um, isn't over. So this is my underestimate, okay? And f of four, we just 1 90. So we're using a lot of the same membership were dropping off, dropping the 2 56 and adding the fifties were using a zero none of five Here. We're using f of 12 ff 50 f before, and that's some I got e got 543 gallons. Alright, so that's over. The first five hours with the dubbed X of one. They didn't give us a dubbed X eso. I just made that up. Okay. Now, for not part, that's part of the part B is Can you do this with for eight hours? Okay. So stood up for eight hours. So my overestimate Marie, three months. Um, you give me the same thing. Really? Don't. Tax of one times f of one concept of two. What's up for three plus four? I'm just reading off the table. That's given a page to 38. Number 19 after five. We gotta go away to a debate, which is a whole table rates of close to 56 30 65 plus it for six because for seven. Sorry, plus up of eight. So this uses that won't separate from may. Overestimate. Alright. Already punched this up. I got about what I get. This works out to 23 2363 counts and my underestimate using my left sums So we're starting with f of zero the approximate it has detected just one times. The first time, which is f of zero, is 50. What's up? One is 70% to 97 except for three is one and 1 36. So we're going from F zero f of seven instead of it for one that made so 1 36 plus 1. 90 after four is 1. 90 of course, of five was stupid to 65. You keep on doing that. What? Sets of sixes. 3. 96 3 69. And then the eighth height is every 75 16, And one times that is that. And add it all up. And I got what I get 1600 93 girls they actually answers. Suck somewhere between sandwich. Their, um, stuff hasn't goes to infinity. Let someone write some shit boat approached. The correct answer is somewhere around traps. Um, all right, now, the tanker leaks 720 gallons per hour after the eighth hour, so it stays at 7. 20. If the tanker originally had 25,000 gallons of oil, Approximately how many more hours will collapse in the worst case? And in the best case, All right, well, let's see. Let's say we lost 2363 gallons. So let's say I have so time right. How much longer it takes for the spill toe stop. I guess so. My time estimate after the eighth hour is, um I'm using approximations. Right. So let's say we lost 23 63. All right, So I'll be 25,000 minus 23 63 over 720. So there was this. A number of gallons divided by gallons per hour will give you ours. Mhm. Right. There's gonna be gallons divided by gallons per hour. Remember he divided by a fraction you don't You multiplied by the reciprocal, so multiplying by hours per gallon, gallon canceling to get ours. Yeah, and I didn't punch the stuff on the Calculate. Let's do that. All right, so it's quantity or parentheses. 25,000 minus our overestimate 23. So this will be an understand how long it takes to finish leaking because they've lost a lot of ready quantity. Divided by 7. 20. This about 31.440 if you run with the nearest 1000. So what do we got here? 31 point or 40 hours. Okay. And that would be Let's see, that would be my underestimate has already lost a lot of stuff. Okay, so my overestimate, the time it's gonna take to finish leaking. Let's say, is 25,000 how much I started with minus 1693. Underestimate that. We had over 7. 20 and that's gonna work out Toe wash. All right, look, it's my calculator. I'm just gonna type over the 23 63 with the 16 93. And if you're under this afternoon's thousands of an hour, it's 32.371 So there's my overestimate. There's my unrest mint of the amount of time it will take to finish the leak. All right, there you go. So there's five our estimates over over and under estimates. There's the eight hour estimates over and under estimates. And then let's see estimate of how much time is gonna take the leak beyond the first eight hours. And there you go. So that was helpful, right? Have a nice day. Because look what your homework. See you next time. Bye bye.


Similar Solved Questions

5 answers
Infrared - worksheetCompoundCumpouma HCompuundCompunu DCwmnpoundCUMIICompunaCompatind [[ComjumdCmmnounU]Cumpuuna(umnounuCuMnamanal BComDMComnoumlCompoumlCompounCompel R(UMIOIIACumpaund |
Infrared - worksheet Compound Cumpouma H Compuund Compunu D Cwmnpound CUMII Compuna Compatind [[ Comjumd CmmnounU] Cumpuuna (umnounu CuMnamanal B ComDM Comnouml Compouml Compoun Compel R (UMIOIIA Cumpaund |...
5 answers
Propose Structure for the Following Molecules1H NMR for C12ll,aSinglet; 9H4H, Doublet Triplet Triplet DoublelTriplel , 3HQuarlet, 2HPPMIH NMR for CmHm4OzDoublet, 6HTriplel,Doublet, 2H1Doublet; 2H Seplel, 1HDoublet, 2HPPM
Propose Structure for the Following Molecules 1H NMR for C12ll,a Singlet; 9H 4H, Doublet Triplet Triplet Doublel Triplel , 3H Quarlet, 2H PPM IH NMR for CmHm4Oz Doublet, 6H Triplel, Doublet, 2H1 Doublet; 2H Seplel, 1H Doublet, 2H PPM...
5 answers
~/2.5 pointsLarCalc11 2.1.038_Find an equation of the line that is tangent to the graph of and parallel to the given line _ Function Line f(x) 2x2 2X Y + 4
~/2.5 points LarCalc11 2.1.038_ Find an equation of the line that is tangent to the graph of and parallel to the given line _ Function Line f(x) 2x2 2X Y + 4...
5 answers
Use the concept of Implicit Derivative to find dy or Y' () of the following dx
Use the concept of Implicit Derivative to find dy or Y' () of the following dx...
5 answers
Use logarithmic differentiation to find the derivative of y with respect to the given independent variable:y = (t)t + 3)(+ 6).Take the logarithm of both sides of the equation and expand it using the product rule of logarithms (#)t + 3)(t + 6) Iny : =In ((t)(t + 3)(t+ 6))Now find the derivative of y with respect to
Use logarithmic differentiation to find the derivative of y with respect to the given independent variable: y = (t)t + 3)(+ 6). Take the logarithm of both sides of the equation and expand it using the product rule of logarithms (#)t + 3)(t + 6) Iny : =In ((t)(t + 3)(t+ 6)) Now find the derivative of...
2 answers
Point) Find the maximum and minimum values of the functionf(c,y)522 18ry 5y2 + 1on the disk €2 + y2 < 1.MaximumMinimum
point) Find the maximum and minimum values of the function f(c,y) 522 18ry 5y2 + 1 on the disk €2 + y2 < 1. Maximum Minimum...
5 answers
1. y = -2 + sin(x -5Functlonsin(x~2 + sin(xGraph:
1. y = -2 + sin(x -5 Functlon sin(x ~2 + sin(x Graph:...
1 answers
State the transversal that forms each pair of angles. Then identify the special name for each angle pair. $\angle 3$ and $\angle 6$
State the transversal that forms each pair of angles. Then identify the special name for each angle pair. $\angle 3$ and $\angle 6$...
5 answers
Consider the following system of equations411 + T2 11 + 512 11 1 2122Do two iterations of Gauss-Seidel to solve the system. Start with an initial guess of [1 0.5 OJT . Compute the approximate relative error at each iteration.21310r3
Consider the following system of equations 411 + T2 11 + 512 11 1 212 2 Do two iterations of Gauss-Seidel to solve the system. Start with an initial guess of [1 0.5 OJT . Compute the approximate relative error at each iteration. 213 10r3...
5 answers
Comment on the following statement: Exothermic reactions are spontaneous, but endothermic reactions are nonspontaneous.
Comment on the following statement: Exothermic reactions are spontaneous, but endothermic reactions are nonspontaneous....
5 answers
Preblem twoMark the following true or false. Correct_the_false_statement:(a) The union of two subgroups of n group G is pot subgroup'(6) Every group isomorphism is VCTHtation
Preblem two Mark the following true or false. Correct_the_false_statement: (a) The union of two subgroups of n group G is pot subgroup' (6) Every group isomorphism is VCTHtation...
5 answers
Question 3 [30ptsk: Given the function f (x) = 4x5 10x4 160x3 + 25Find the critical point(s)b) Determine the intervals of increase and decreaseFind the local (relative) maximum r minimum point(s).
Question 3 [30ptsk: Given the function f (x) = 4x5 10x4 160x3 + 25 Find the critical point(s) b) Determine the intervals of increase and decrease Find the local (relative) maximum r minimum point(s)....
5 answers
(Bonus) Show the electron pushing mechanism for the following of (racemic) isoborneol to the major product of the reaction_ (E1) dehydration camphene _H3C CH36M HzSO4Hsc H3CrefluxOHHzcH3C
(Bonus) Show the electron pushing mechanism for the following of (racemic) isoborneol to the major product of the reaction_ (E1) dehydration camphene _ H3C CH3 6M HzSO4 Hsc H3C reflux OH Hzc H3C...
5 answers
0 Check Biyandtd Geeas United Ivthegeni 1 1 Ito 4 1 1 covlatlon 1 33.65 11 1 iV Unlted 1 JistrIbutlons L 6 essnd 3 cowntrles and thatthe W 1 Drobabilit thatthe 1 = 1
0 Check Biy andtd Geeas United Ivthegeni 1 1 Ito 4 1 1 covlatlon 1 33.65 1 1 1 iV Unlted 1 JistrIbutlons L 6 essnd 3 cowntrles and thatthe W 1 Drobabilit thatthe 1 = 1...
5 answers
4 A coin is tossed twice and let X be thenumber of heads Then, the coin will be tossed two more times and let Y be the number of heads that observed this time. Find the probability P(x<1 and y>2) . Hint a test of independence.
4 A coin is tossed twice and let X be the number of heads Then, the coin will be tossed two more times and let Y be the number of heads that observed this time. Find the probability P(x<1 and y>2) . Hint a test of independence....
4 answers
(20 points Evaluate the integral6' [' cos(r?) dz dyby reversing the order of integrationWith order reversed,L" K" cos(e') dyds,wereand dEvaluating the integral, Jcos(z? ddyNete: You can ear partial credit On [his problem
(20 points Evaluate the integral 6' [' cos(r?) dz dy by reversing the order of integration With order reversed, L" K" cos(e') dyds, were and d Evaluating the integral, Jcos(z? ddy Nete: You can ear partial credit On [his problem...

-- 0.059624--