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

## Description

Compute rates, cumulative production values, and instantaneous nominal declines for Arps hyperbolic decline curves.

## Usage

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

## Arguments

 `qi` initial rate [volume / time], i.e. q(t = 0). `Di` initial nominal Arps decline exponent [1 / time]. `b` Arps hyperbolic exponent. `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.

When appropriate, internally uses `harmonic.q` and `harmonic.Np` to avoid singularities in calculations for `b` near 1.

## Value

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

`hyperbolic.Np` returns the cumulative production for each element of `t`, in the same units as `qi * t`.

`hyperbolic.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`.

## See Also

`as.effective`, `as.nominal`, `rescale.by.time`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## qi = 1000 Mscf/d, Di = 95% effective / year, b = 1.2, t from 0 to 25 days hyperbolic.q(1000, as.nominal(0.95, from.period="year", to.period="day"), 1.2, seq(0, 25)) ## qi = 500 bopd, Di = 3.91 nominal / year, b = 0.5, t = 5 years hyperbolic.Np(rescale.by.time(500, from.period="day", to.period="year"), 3.91, 0.5, 5) ## Di = 85% effective / year, b = 1.5, t = 6 months hyperbolic.D(as.nominal(0.85), 1.5, 0.5) ```

### Example output

``` [1] 1000.0000  991.8714  983.8869  976.0423  968.3341  960.7585  953.3121
[8]  945.9915  938.7934  931.7148  924.7525  917.9037  911.1654  904.5351
[15]  898.0099  891.5875  885.2652  879.0407  872.9117  866.8759  860.9312
[22]  855.0755  849.3066  843.6227  838.0219  832.5021
[1] 84744.78
[1] 0.783015
```

aRpsDCA documentation built on July 24, 2017, 1:03 a.m.