Decline curves can be created from the right-click menu for a curve in the **Plot Project Tree**.

Three decline curves are created, and the values for the decline curves can be inspected visually in the plot and values can be displayed using **Show Plot Data** from the menu inside the plot window.

J.J. Arps [1] concluded that the decline in oil production rate ($q_i$) over time can be described by these equations:

$$\frac{ 1 }{ q_0 } \frac{\partial q_0}{ \partial t} = -D$$

where the decline rate, $D$ is a time-dependent function:

$$D = \frac{D_i}{1+bD_i t}$$

where:

- $q_0$ is the production rate (e.g. oil production) in a unit of choice (e.g STB/day)
- $t$ is the time
- $D$ is the time dependent decline rate
- $D_i$ is the initial decline rate (constant)
- $b$ is a dimensionless constant (typically used as a tuning parameter to match actual field data) and is in the range of $ 0 <= b <= 1 $.

The equations can be used to forecast future reservoir and well production.

Based on the value of $b$ in the function, Arps classified the decline curves into three types:

- The exponential decline has $b = 0$.
- The harmonic decline has $b = 1$.
- The hyperbolic decline has $b$ ranges between 0 and 1.

It is important to note that the decline curve is an empirical model and assumes a simplified representation of the complex physical and geological factors affecting production decline.

Exponential decline is the production decline when $ b = 0 $. This gives a constant decline ($D_i = D$).

$$q_0 = q_i e^{-Dt }$$

Hyperbolic decline is the generic case where $ 0 < b < 1 $.

$$q_0 = \frac{q_i}{ (1+bD_i t )^\frac{1}{b} }$$

Harmonic decline is the production decline when $b = 1$:

$$q_0 = \frac{q_i}{ (1+D_i t ) }$$

Exponential decline is the production decline when $b = 0$. This gives a constant decline ($D_i = D$).

$$N_p = \frac{q_i - q_0}{D}$$

Hyperbolic decline is the generic case where $ 0 < b < 1 $.

$$N_p = \frac{q_i^b}{D_i(1-b)} [q_i^{(1-b)} - q_0^{(1-b)}]$$

Harmonic decline is the production decline when $ b = 1 $:

$$N_p = \frac{q_i}{ D_i } * \ln(\frac{q_i}{ q_0} )$$

The continuous decline rate ($D_i$) can be determined from production history data. Using production rate and time data the value is the slope of the straight line on a semi-log plot. Taking two points on from the data $(t_1, q_1)$ and $(t_2, q_2)$:

$$D_i = \frac{1}{t_2 - t_1} \ln(\frac{q_1}{q_2})$$

where:

- $t_1$ is the time of the first point.
- $q_1$ is the production rate in the first point.
- $t_2$ is the time of the second point.
- $q_2$ is the production rate in the second point.

[1] Arps, J. J.: “Analysis of Decline Curves,” SPE-945228-G, Trans. of the AIME (1945)