Compute rates, cumulative production values, and instantaneous nominal declines for Arps harmonic decline curves (i.e. hyperbolic with b = 1).
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initial rate [volume / time], i.e. q(t = 0).
initial nominal Arps decline exponent [1 / time].
time at which to evaluate rate or cumulative [time].
Assumes consistent units of time between
t. To convert, see the decline-rate conversion functions referenced below.
harmonic.q returns the rate for each element of
in the same units as
harmonic.Np returns the cumulative production for each element of
t, in the same units as
qi * t.
harmonic.D returns the nominal instantaneous decline for each
t. This can be converted to effective decline and
rescaled in time by use of
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## qi = 1000 Mscf/d, Di = 95% effective / year, t from 0 to 25 days harmonic.q(1000, as.nominal(0.95, from.period="year", to.period="day"), seq(0, 25)) ## qi = 500 bopd, Di = 3.91 nominal / year, t = 5 years harmonic.Np(rescale.by.time(500, from.period="day", to.period="year"), 3.91, 5) ## Di = 85% effective / year, t = 6 months harmonic.D(as.nominal(0.85), 0.5)
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