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# Depletion and Decline Curve Analysis in Crude Oil Production

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35
(4.2.7)

Simplifying yield a depletion rate which is decreasing with time:
(4.2.8)
The hyperbolic depletion rate also approaches zero as time increases, since the depletion rate function
is strictly decreasing as t. This is a very interesting property as it implies that a maximum depletion
rate
must be reached before the field reaches the onset of decline in the general case. Typically the
maximum depletion rate occurs just before the onset of decline, provided that the URR estimate is accu-
rate. This is illustrated in Figure 4.6.
Figure 4.6. Theoretical field with hyperbolic decline behaviour. The depletion rate reaches a maximum value when
the onset of decline is reached, before slowly decreasing asymptotically towards zero with decreasing production.
The existence of a maximum depletion rate for individual fields also indicates the existence of a
maximum depletion rate on a regional or global scale. Over recent decades various models and studies,
which all use some limit for the depletion rate or the RPR of a resource, have been made by Flower
(1978), Wood et al. (2004) and Campbell and Heapes (2008). The fundamentals behind this approach
have been analyzed in more detailed by Jakobsson et al. (2008), which also coined the name maximum
depletion rate modelling
to describe this type of forecasting methodology.
The depletion-at-peak (DAP) parameter is the depletion rate of remaining reserves that occurs when
the production peaks or the point at which production lastingly leaves the plateau phase. Closer discus-
sion and examples of this can be found in paper II. This is often the highest depletion rate that occurs in
the entire production profile, provided that the URR estimate is reasonably accurate and realistic. DAP
may also be seen as the point in time when depletion-caused decline in reservoir pressure and/or flows
will begin to dominate over other factors, thus forcing the field into a stage of predominantly depletion-
driven decline.

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Summary :

## 35 (4.2.7) Simplifying yield a depletion rate which is decreasing with time: (4.2.8) The hyperbolic depletion rate also approaches zero as time increases, since the depletion rate function is strictly decreasing as t.

Tags : decline,maximum,decreasing,production,which,field,occurs,time,before,onset,existence,dap,hyperbolic
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