Wednesday, September 06, 2006

The Hubbert Parabola

This is my first post in Graphoilogy, and first I would like to thank Khebab for including me as a contributor.

The logistic curve, and its derivative the hubbert's curve, has been widely used to model population growth. And it has been applied to model oil production by M. King Hubbert. The model comes from the following differential equation:

dQ/dt=kQ(1-Q/URR)

where Q(t) is a function of time (measured in years) and it is defined as the cumulative production of a region until the end of year t. The parameter URR is the "Ultimately Recoverable Resources" or the maximum cumulative production that can be reached. K is the Malthusian parameter or the maximum cumulative production growth.

The value dQ/dt for a specific year s, can be approximated by

(Q(s)-Q(s-1))/(s-(s-1))= Q(s)-Q(s-1)

which is the production of year s, so let us define P(t)=Q(t)-Q(t-1). Let us assume that we have a region where the oil production follows strictly the logistic model, and that we have the information of Q(t) for all years. If we had P(t) for all years then we could obtain Q(t), since Q(t)=P(t)+P(t-1)+P(t-2)+.... What happens if we place a point at position (Q(t),P(t)) in the plane for all years t? Well, since we have seen that P(t) is approximately KQ(t)(1-Q(t)/URR), then the points would follow very closely the parabola:

KQ(1-Q/URR) = KQ - (K/URR)*Q^2.

This parabola passes through the origin (0,0) and through (URR,0). Now we are going to experiment with 50 different regions of the world. For each one we are going todo two plots. In the first one we will place all the data points (Q(t),P(t)) until year 2005 (both measured in Giga-barrels) and then find the parabola that passes through the origin that better approximates the data points (by the least squares fitting method). The intersection of this parabola with the x-axis will give us the estimated URR. In the second plot we want to show how this estimated URR has changed through time. For this plot, we define the function URR(t) as the estimated URR by the prior method if we had used the data points up until year t, and discarding later years. In the second plot we place points at (Q(t),URR(t)). Clearly Q(t) < URR(t) should hold by definition (just note that with very strange data set this could be false). So all points in the second plot should be above the URR=Q line. The dashed line URR=2Q has an interesting property. If point (Q(t),URR(t)) lies above this line, then according to the logistic model, t is before the peak year (as calculated at year t), i.e. Q(t) < URR(t)/2. If (Q(t),URR(t)) lies below the dashed line then we are after peak year.

The data from 1857 till 1958 is from "API Facts and Figures Centennial edition 1959" (thanks to Laherrere and Stuart Staniford). For 1959-1964 it is from "Twentieth Century Petroleum Statistics2004" of DeGolyer & MacNaughton. And for 1965-2005 it is from BP Statistical Review of World Energy.

First I will put links to all the images of regions ordered by continents:

AFRICA:
Algeria, Angola, Cameroon, Chad, Egypt, Equatorial_Guinea, Gabon, Libya, Nigeria, Rep_of_Congo, Sudan, Tunisia, other_Africa.
ASIA:
Australia, Brunei, China, India, Indonesia, Malaysia, Taylandia, Vientnam, other_Asia.
EUROPE:
Denmark, FSU, Italy, Norway, Rumania, UK, other_Europe.
MIDDLE EAST:
Iran, Iraq, Kuwait, Oman, Qatar, Saudi_Arabia, Syria, UAE, Yemen, Other_ME.
NORTH AMERICA:
Canada, Mexico, US.
SOUTH AND CENTRAL AMERICA:
Argentina, Brazil, Colombia, Ecuador, Peru, Trinidad, Venezuela, Other_S_and_Cent_America.

After a quick inspection of the plots we can divide countries in three groups:

COUNTRIES THAT BEHAVE WELL:


By this I mean countries where the early points of the second plot start increasing above the dashed line, and after they cross the dashed line the points tend to stabilize into a fixed estimated URR. These include the following 20 (out of 50) countries:

EgyptGabonRep_of_CongoBrunei
IndiaIndonesiaVientnamDenmark
FSUItalyNorwayRumania
other_EuropeOmanSyriaMexico
USArgentinaPeruTrinidad

TOO EARLY TO SAY COUNTRIES:


Probably they haven't reach peak production yet. These group includes 9 countries.

AngolaChadEquatorial_GuineaSudan
Taylandiaother_AsiaQatarBrazil
Colombia

COUNTRIES THAT DO NOT BEHAVE WELL:

Countries for which the points of the second plot just keep increasing between the two lines. Normally they increase in a very strait line. These group has 21 countries.

AlgeriaCameroonLibyaNigeria
Tunisiaother_AfricaAustraliaChina
MalaysiaUKIranIraq
KuwaitOther_MESaudi_ArabiaUAE
YemenCanadaEcuadorOther_S_and_Cent_America
Venezuela

60 comments:

  1. First I will put links to all the images of regions ordered by continents:AFRICA: Algeria, Angola, Cameroon, Chad, Egypt, Equatorial_Guinea, Gabon, Libya, Nigeria, Rep_of_Congo, Sudan, Tunisia, other_Africa

    ReplyDelete
  2. great post. looking forward on this post.

    ReplyDelete
  3. I would like to thank you for the efforts you have made in writing this article. I am hoping the same best work from you in the future as well. Thanks...zodiac salt cell

    ReplyDelete
  4. mau taruhan online gak gan? nih saya punya referensi kalau agan mencari agen bola terpercaya yang depositnya murah hanya 50 rb saja bisa kunjungi website ini, selain itu bagi yang suka taruhan sepakbola seperti sbobet maupun ibcbet, coba pasang taruhan disini sebab dia merupakan agen ibcbet yang handal dan bisa dipercaya.

    ReplyDelete
  5. .All the contents written in your post is fabulous.If you all are interested in getting the club penguin membership codes generator at zero penny than visit here.

    ReplyDelete
  6. Very nice I accept as true with your thoughts. Many thanks a great deal I’ve benefited therefore usually I’ll visit your website. singpost tracking

    ReplyDelete
  7. Nice to be visiting your blog again, it has been months for me. Well this article that i've been waited for so long. I need this article to complete my assignment in the college, and it has same topic with your article. Thanks, great share.perumahan batununggal bandung

    ReplyDelete
  8. Thanks for sharing your great ideas with us through this site. keukenblad graniet

    ReplyDelete
  9. Here i found nice environment to get new ideas and views and the i have read the comments of this blog and these are really nice and it is glad to comment here.stenen tafelblad

    ReplyDelete
  10. I’m impressed! Extremely useful info specially the last part I care for such information a lot. I was seeking this certain info for a long time. Thank you and good luck.spectroscopic ellipsometer

    ReplyDelete
  11. Really very good and brilliant ideas about Speech. I am really like your talk program. Thanks Ghana News

    ReplyDelete
  12. Pretty nice post I simply stumbled upon your website and wished to mention that I've actually enjoyed browsing your website posts.

    ReplyDelete
  13. I like your post. It is good to see you verbalize from the heart and clarity on this important subject can be easily observed.Γυναικεία ρούχα

    ReplyDelete
  14. Hi, I find reading this article a joy. It is extremely helpful and interesting and very much looking forward to reading more of your work. Kind Organics Garden of Life

    ReplyDelete
  15. Thanks film succeeds where Joel Schumpeter so famously failed: It manages to embrace Batman's inherent campaniles and potential for ridicule. Change Management Models

    ReplyDelete
  16. This explanation is definitely going to make things easier for all. However, to ensure better performance you need to have the right equipments and support in the form of powerful synthetic diamond ring

    ReplyDelete
  17. Very informative information specially business mens . We should be aware form our business plane and it economy rates.

    ReplyDelete
  18. It seems like an educational blog which always some new information to visitors and Enjoying every little bit of it and I have you bookmarked to check out new stuff you blog post.

    ReplyDelete
  19. You present the general divisibility rule for one Divisor the prime wide variety and put it on for to exact cases. The reason is articulate and easy follow, fully understand and put on.Escape Room

    ReplyDelete
  20. I have encounter that this web journal is truly have each one of those quality that portray a website to be a decent one.Soba Pobega

    ReplyDelete
  21. If more people that write articles really concerned themselves with writing great content like you, more readers would be interested in their writings. Thank you for caring about your content.men's bulova watches

    ReplyDelete
  22. I am definitely enjoying your website. You definitely have some great insight and great stories.heated battery

    ReplyDelete
  23. You can't really say what is beautiful about a place, but the image of the place will remain vividly with you.closetspoeler

    ReplyDelete
  24. Tempatbet.com merupakan situs Agen Bola Terpercaya dan Taruhan Bola Online dimana anda bisa membuka acount betting dengan berbagai variasi permainan Judi Bola Online yang lengkap dan menarik dengan tingkat keamanan dan kenyamanan yang maksimal, pelayanan cepat dan memuaskan, serta bantuan costumer service yang selalu siaga 24 jam/hari melalui contact di bawah ini

    Contact Support
    BBM 753F938F
    Telp/SMS +6288276816728
    YM agentaruhan1@yahoo.com
    FB https://www.facebook.com/tempatbet

    Segera Kunjungi situs terbaik kami di
    http://ligatop.net/
    http://tempatbet.com/
    http://goo.gl/3d3pBV
    http://goo.gl/dM2vxr

    ReplyDelete
  25. This is a fantastic have always wondered how charcoal was made very comprehensive and some great photos........thanks heapskeramiek aanrechtblad

    ReplyDelete
  26. If more people that write articles really concerned themselves with writing great content like you, more readers would be interested in their writings. Thank you for caring about your content.Paris treasure hunt

    ReplyDelete
  27. Agen Bola Sbobet is legal, the trusted online betting company and attracts a lot of patrons, and there are numerous of games offers at online slots, and you will find t game which Sbobet Asia very famous on online betting option to bet.

    ReplyDelete
  28. spiegelklemWonderful site and I wanted to post a note to let you know, ""Good job""! I’m glad I found this blog. Brilliant and wonderful job ! Your blog site has presented me most of the strategies which I like. Thanks for sharing this.

    ReplyDelete
  29. Prediksi Poker Online
    A fascinating discussion is worth comment. I think that you need to write more on this topic, it might not be a taboo matter but usually folks don’t speak about these topics. To the next! All the best!!
    http://jinprediksi.smeagol.web.id/itudewa-net-agen-judi-poker-domino-qq/

    ReplyDelete
  30. As years go by SEO become tough to compete of but because of years of experience our experts still manage and survive for any updates that have been hit by many websites. We have the strategies that is effective and give good progress to our clients. Outsource SEO Philippines

    ReplyDelete
  31. Thanks for posting this info. I just want to let you know that I just check out your site and I find it very interesting and informative. I can’t wait to read lots of your posts.
    dekton werkblad

    ReplyDelete
  32. I am specifying Greensboro because I am staying here and found a good Audi repair center here. Sometimes we can note some functionalities issues in our Audi and when we make a note of it it is preferable to go for a Audi repair center without any delay and get the car repaired from their. We have to choose a good Audi repair center and have to go their.safari holidays to africa

    ReplyDelete
  33. You absolutely come with tremendous articles and reviews. Bless you for sharing your website.
    free amazon gift card codes

    ReplyDelete
  34. Your blog constitutes numerouss associated beside refined choosys that desire construct chemicals very should contacting beside suspension in rule to accompanying a expense-efficient bas.Teambuilding oslo

    ReplyDelete
  35. This is how you will remove your loneliness just you need to call for Mumbai Escorts those who are like turmeric on your body so that you feel so relax. The color of turmeric will be on your body and it will colorful your life as you call for hot ladies. For more info visit - http://mumbaiescort.me/

    ReplyDelete
  36. My name is sophia shroff and I am a luxury Mumbai escort girl in mumbai. However with enough notice I can be your national travel tour.

    ReplyDelete
  37. There are numerous escorts in mumbai who are here to entertain the clients.Mumbai Escorts will please by their services and will be available for 24*7 to you.Visit me on http://www.independentescortsinmumbai.net/ Call me on +91-9167008019

    ReplyDelete
  38. we are provide you bestseo services in faridabad .we will grow your business at top lable in the internet market. Seo is the key to get online business from your website. A grade media based is leading internet marketing company in faridabad.

    ReplyDelete
  39. There are top class beauties waiting for hot clients.Gorgeous will excite you and you will feel very relax after meeting those hot girls,then why are you waiting? Join the girls and become partner with these girls and make your night so enjoyable.Visit http://www.mumbaiescorts.club/

    ReplyDelete
  40. Thank kawan http://sweat-fit.blogspot.com/

    ReplyDelete
  41. We are offering you all type of mumbai escorts working in agency.They have charms which will attract you on their side.You will feel happy after meeting with them.For more information visit http://mumbaiescortsagency.org/

    ReplyDelete
  42. Just appreciate your work , nice job man.
    Cheap Escorts in Delhi

    ReplyDelete
  43. Hi! This is Koena an Delhi Independent Escorts. If you are in delhi city and want beautiful escorts then call me.Visit:http://koena.in

    ReplyDelete
  44. Thanks for sharing this info. It's a great blog, I will be back.
    Escort in Delhi

    ReplyDelete
  45. Hansi mehra, I am cheap escorts in Delhi for making independently escort service in Delhi,
    cheap Delhi escorts

    ReplyDelete
  46. Delhi Escorts List
    Hello gentlemen! Look for a escorts call us.Visit our website at Delhi Escorts Agency.
    Delhi Escorts Agency

    ReplyDelete
  47. If you are looking for self storage in Fargo ND you have come to the right website. Escorts in PCMC There are over 9 different self storage facilities to choose from in Fargo, do you really have the time to shop all of them?

    ReplyDelete
  48. Miss Roma
    http://missroma.in/
    I am a beautiful, sexy, good-natured and always set to doing amazing and imaginative. I am just 22 year Beauty young girl with sexy, rounded body.
    Independent Delhi Female

    ReplyDelete
  49. I love reading through your blog, Independent Escorts in India I wanted to leave a little comment to support you and wish you a good continuation. Wish you best of luck for all your best efforts.

    ReplyDelete
  50. Zara Mittal
    Escorts Service in Delhi
    Helo Guys! I am Zara mittal an independent escort in Delhi. call me tonight or mail me.

    ReplyDelete