Reserves types in VEDA

[mresende]

Hi!
 I have a model in which we represent some different kinds of oil reserves, such as developed, undeveloped and proved oil reserves. Each of them is a different "MIN" process, with a "CUM" attribute that defines the amount of each type of reserve. TIMES can invest on these processes in order to make these reserves available for exploration. For example, it can invest in proved reserves, and this reserves will be promptly available. But, in real life, exploration investment are made in order to turn proved reserves into undeveloped reserves, and then into developed reserves. My question is: is there anyway to represent this in TIMES? For example, a way to transform "CUM" of proved reserves into "CUM" of undeveloped reserves? Or a way to represent an investment to increase "CUM" of a process?

Thank you!

[Antti-L]

I would say that most certainly there should be a way to represent that in TIMES, if it can be represented with linear equations. But at least for me it is not at all clear what the formulation you would like to have would look like. Maybe you could write down the equations first?

Perhaps you are mainly looking for a way to introduce a delay for the utilization of the cumulatively constrained resource, such that it cannot be actually consumed in the period "produced", but only later, after some predefined delay? There are several ways to introduce such delays (e.g. lagged commodity flows, inter-period storage, capacity-related flows), but I am not at all sure which approach would correspond to your desired formulation. For example, it is not clear to me what kind of a time profile you would be expecting to have for the "undeveloped reserves" that are produced from the resource by the "exploration investments", in comparison with the lifetime of those exploration investments.

[mresende]

Actually, I am also not sure about the mathematical formulation we should employ, because I believe there may have many ways to represent this. Although I have not explicitly said this, a delay between investment and utilization of reserves is desirable, but is not the only thing I want here. I would appreciate if you can briefly describe each of these possibilities (lagged commodity flows, inter-period storage, capacity-related flows).

In terms of equation, I was thinking on something like CUM(t) = CUM(t-1)+NCUM(t), where CUM is the reserve of a specific commodity and process and NCUM would be the new reserves of that commodity/process in period t. And we would associate this NCUM(t) to an investment cost made one or two periods before. I don't know if there is this variable "NCUM" or something similar.

Let me know if my point is not clear yet. Thank you once more

[Antti-L]

Yes, it is quite easy to make dynamic equations like that, for example, saying that

VAR_X(t) = VAR_X(t–1) + C×VAR_NCAP(prc,t–lag)

such that VAR_NCAP(prc,t–lag) refers to the amount of new capacity of some process prc installed in a certain user-defined number of years earlier than t. A constant could also be easily added as a "default" or exogenous value for VAR_X(t), if there are no investments into new capacity prc in years t' such that t'+lag ≤ t.

However, as such that equation does not constrain anything; it only defines a new model variable VAR_X(t) for each period t, setting it equal to the cumulative sum of the term C×VAR_NCAP(prc,t–lag) corresponding to those previously installed new capacities. I think you should also formulate some other equation(s) that make use of that variable for some constraint. Can you give me an example, how you would use the variables VAR_X(t) in other model equations?

[Antti-L]

Ok, as you did not provide any example, I will not try to refine the idea further.

But for any other potentially interested users, I attach a very simple test model where I define a constraint on the oil reserve utilization based on previously made cumulative exploration investments, with a lag time of 11–15 years, plus a small exogenously available amount. The exploration investments have five different cost categories, and each with a cumulative bound. As far as I can see, the basic idea works reasonably well, but the coarseness of model periods makes the timing of the investments only approximate.

  CUMOIL.zip (Size: 99.11 KB / Downloads: 18)