# Fetkovich-Arps Type Curves

Estimating reservoir parameter using Fetkovich-Arps Type Curves excel spreadsheet.

09-04-2021

Fetkovich (1980) developed a set of dimensionaless (log-log) type curves for production data (rate-time) analysis of wells completed in conventional reservoir.

The fetkovich type curves were developed specifically to analize vertical wells exhibiting transient flow followed by boundary-dominated flow for the case of a well placed at the center of a closed cylindrical reservoir. In order to incorporate the effects of near-wellbore stimulation/damage effects, the apparent (efective) radius concept was employed in type-curve development.

The left part when $$t_{Dd} < 0.3$$ represents the early and middle transient flow period, which is mainly affected by dimensionless reservoir drainage radius $$r_{eD}$$ and the right part when $$t_{Dd} > 0.3$$ represents the boundary-dominated flow, which is the curve cluster controlled by Arps decline exponent $$b$$

The solution for constant BHFP for a well entered in a closed circular reservoir could be regarded as an Arps exponential decline curve in the later flow period, it could be described by a general formula:

$q_{Dd}(t_{Dd})= \frac{1}{(1+bt_{Dd})^{1/b}}$

For a well entered in a closed circular reservoir a constant BHFP , the relationship between Fetkovich dimensionless decline rate function qDd and dimensionless decline time tDd is defined as:

$q_{Dd} = q_D\left[ln \left(\frac{r_e}{r_{wa}}\right)-\frac{1}{2}\right]$ $t_{Dd} = \frac{t_D}{\frac{1}{2}\left[\left(\frac{r_e}{r_{wa}}\right)^2-1\right]\left[ln \left(\frac{r_e}{r_{wa}}\right)-\frac{1}{2}\right]}$ $r_{eD} = \frac{r_e}{r_{wa}}$

Using the type-curve matching method between field data and Fetkovich-Arps type curve, the Arps decline parameters $$q_i$$, $$D_i$$ and $$b$$ could be determined by the second half of the type curve, and the value of $$r_{eD}$$ could be determined by the first half of the curves. Then the permeability $$K$$, skin factor $$S$$, reservoir drainage radius $$r_e$$, single-well original HC in place, ans the cumulative production before reaching the abandoned condition could all be determined.

Determine the initial flow rate

$q_i=\left(\frac{q}{q_{Dd}}\right)_M$

Determine the initial decline rate $$D_i$$

$D_i=\left(\frac{t_{Dd}}{t}\right)_M$

Acording $$r_{eD}$$ value and $$q_i$$ determine the value of permeability

$k = \frac{141.2B_o \mu}{h(p_i-p_{wf})}\left[ln \left(\frac{r_e}{r_{wa}}\right)-0.5\right]\left(\frac{q}{q_{Dd}}\right)_M$

Calculate the apparent wellbore radius based in the time matching point

$r_{wa} = \sqrt{\frac{0.00633k}{\phi\mu_o c_t(0.5) \left[ r_{eD}^2-1\right]\left[ln \left(r_{eD}\right)-0.5\right]}\left(\frac{t}{t_{Dd}}\right)_M}$

and then determine the skin factor $$S$$

$S = ln\frac{r_w}{r_{wa}}$

Example

Excel File

References

Sun, H. (2015) Advanced Production Decline Analysis and Application Clarkson C.R. (2021) Unconventional Reservoir Rate-Transient Analysis

### Citation

Vazquez (2021, Sept. 4). Chato Solutions: Fetkovich-Arps Type Curves. Retrieved from https://www.chatosolutions.com/posts/2021-09-04-fetarps/
@misc{vazquez2021fetkovich-arps,
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