# harmonic: Arps harmonic declines In aRpsDCA: Arps Decline Curve Analysis in R

## Description

Compute rates, cumulative production values, and instantaneous nominal declines for Arps harmonic decline curves (i.e. hyperbolic with b = 1).

## Usage

 ```1 2 3``` ```harmonic.q(qi, Di, t) harmonic.Np(qi, Di, t) harmonic.D(Di, t) ```

## Arguments

 `qi` initial rate [volume / time], i.e. q(t = 0). `Di` initial nominal Arps decline exponent [1 / time]. `t` time at which to evaluate rate or cumulative [time].

## Details

Assumes consistent units of time between `qi`, `D`, and `t`. To convert, see the decline-rate conversion functions referenced below.

## Value

`harmonic.q` returns the rate for each element of `t`, in the same units as `qi`.

`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 element of `t`. This can be converted to effective decline and rescaled in time by use of `as.effective` and `rescale.by.time`.

`as.effective`, `as.nominal`, `rescale.by.time`.
 ```1 2 3 4 5 6 7 8``` ```## 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) ```