multivariate production systems optimization - Stanford University

At the end of each time step, the well model gives the cumulative production that
occurred during a time step. Specifically, the well model will yield a stream of n
production quantities, C1 , C2 , ..., Cn, where n is the number of time steps occurring over
the life of the project. These production quantities are discounted back to the present by
assuming the production is constant over the time step and discounting from the midpoint
of the time step (see Figure 7.12).
t = 0
Δt Δt Δt Δt Δt
C1 C2 C3 Cn-1 Cn
Figure 7.12: Revenue Stream is Discounted from Center of Time Step.
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t = T
For instance, if the time step is one year, then the cumulative production produced over the
first year will be discounted as if it were sold in one discrete quantity at six months’ time.
Thus, the present value of the production stream for n time steps of length Δt may be
expressed as
PV =
n
∑
T=1
Cn Pn
1+R 2n-1 2 Δt
where P n is the real price of the production at the nth time step.
(7.3)
The present value calculation determines only the positive effects of the decision
variables, namely the revenue stream. The concept of present value is easy to conceptualize
since it is simply the gross value of the revenue stream. To change the objective criterion
from present value to net present value, the negative effects of the decision variables must
be included. For instance, the negative effects may include capital expenditure, tax
payments, royalty payments, labor cost, and corporate overhead contribution just to name a
few. Since the purpose of the research was to demonstrate the effective application of
optimization techniques and not to concoct an elaborate economic model, present value was
made the objective criterion. However, to use this technique in the design or analysis of an
actual well system, the objective criterion should be made to reflect the financial