Archive for June, 2007

A (Very) Simple Oil Field

Tuesday, June 19th, 2007

Assume and are the amount of oil in the ground and the production rate respectively. We model the behaviour of the oil field with a system of linear ordinary differential equations (ODEs).

In clear text, this means that the amount of oil in the ground decreases by the amount produced, and the production capacity increases if it is small compared to the amount of oil left in the field, and decreases if it is large compared to this amount.

Now, the system is easily transformed into a single ODE by differentiating the second equation and inserting for from the first equation. This gives

which is has a simple analytical solution. The general solution is

Now we impose the initial conditions

which translates to some finite amount of oil in the reservoir, and the production capacity 0 at the time we start. These two conditions are used to determine the coefficients and . The solution is then

This solution reveals that the model has some obvious flaws. The first thing that becomes apparent when plotting the solution (or simply noticing the sine factor), is that the production becomes negative at times. Another flaw, is that if we integrate the production from the start to the time it becomes negative, the amount of oil extracted is larger than the amount that was originally in the field. Clearly, some modifications to the model are needed. A fix is to replace the first equation by

This new equation makes the system a lot harder to solve by hand. Using a computer program and Euler’s method for explicit time-integration, it was easy to plot the result, however.

This time, the integral is 1 (at least with numeric integration), and the production is never negative.

Compared to real-life oil fields, the model production is ramped up too fast. The model does not incorporate the effects of limited manpower, investment and equipment. A sharp cliff is present where the technical production capacity exceeds the geological capacity of the field. This cliff should not be observed in any well-planned oil project, since no-one would invest in bringing production capacity beyond what the field can handle.

Social Networking With a Purpose

Saturday, June 16th, 2007

Today, I stumbled upon the page, which is a social networking site with slightly better terms of usage than But the real reason I got interested in this site is that it facilitates easy borrowing of items between friends and neighbors.
In order to protect the planet, it is essential to optimize the use of its limited resources. If you’re like me, you probably have a whole lot of books, games, computer accessories, tools and equipment just hanging around being used infrequently at most. But your friend or neighbor might be in need of that component. Most people never ask their neighbor if they happen to have an old LPR cable stuffed away somewhere. And it would be very ineffective to brute-force search for the part by asking all your friends, compared to instantly finding that one right friend who has the item listed in his inventory on
As of today, the site is in its alpha stage, which means there are obvious bugs and flaws. There are only a handful of users yet. I still encourage you to take a look at it and join, to show your support to the developers. If the user base can reach a ‘critical mass’, then it could turn out to be an incredibly useful online community.
PS. Join the private group ‘Geirs Venner’ if you feel eligible. The password is geb, as it should be.

Why I Left Facebook

Saturday, June 16th, 2007

An extra entry for you today, since Facebook decided to respond so viciously to my note there. In the note, I complained about how imbalanced its terms of use are. You’re likely to be a Facebook user, but you’re not likely to be a Facebook terms of use reader, so let me enlighten you a bit:

By using Facebook, you agree to grant Facebook an irrevocable, perpetual right to use any material you post there for any purpose they wish. This was all fine with me, since they also have a moderation clause: You can revoke the irrevocable right (makes sense eh?) by terminating your account. This provides you with a sort of backup escape route if hell breaks lose and Facebook starts using your content or your information in ways you don’t like.
But like many big American companies who like to think they’re morally justified to act as God, they have a ‘We pwn all you noobs’ clause as well. Facebook reserves the right to change the terms of use at any time with no prior warning. You automatically accept such new terms by continuing to use the site. There is no visible warning that the terms have changed when they change, you have to click your way to the terms page again (yeah, lots of people do that, LOL). By the way, in civilized countries, such as Norway, contracts that reserve the right for one of the parts to unilaterally change the contract are illegal. However, Norwegians are still bound by the terms, since this is an an American company.
Today, just for fun, I checked the terms of use page, since I don’t want to be pwned. And guess what, the terms had changed on May 11. The bastards removed my emergency escape clause. There and then, I was left with the choice of immediately leaving Facebook, or be pwned forever. I left.
I don’t think it’s likely that Facebook will abuse my info in any way, but I’m not willing to take the chance. And I get really mad when companies throw terms at me that are so wildly imbalanced. To illustrate, assume you were playing cards with someone. But that someone you’re playing with reserves the right to change the rules at will. You on the other hand can’t suggest rules, and you automatically agree to new rules by continuing to play. The rules start out saying that he scores a point whenever he gets a spades, clubs or hearts card. You only get half a point if you happen to get the queen of spades. After a while, you grow tired of this game (your odds of winning are pretty low, and the game is pretty boring). But your friend likes the game so much (because he’s winning big time), and he senses you’re about to leave. He thus invents a new rule that prohibits you from ever leaving, and you automatically agree by picking up the next card. What do you do?