Question 7 of 7: Skin from Formation Damage and the Productivity Gain from Stimulation

Question 7: Skin from Formation Damage and the Productivity Gain from Stimulation (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. External (drainage) radius $r_e=3000$ ft; well radius $r_w=0.3$ ft; damaged-zone radius $r_s=2$ ft; damaged-zone permeability $k_s=k/10$; steady-state radial flow (pressure has stabilized, i.e. constant $p_e$); $p_{wf}$ held the same before and after stimulation.

Find. (a) skin factor $S$ due to the damage; (b) $q_{after}/q_{before}$, assuming stimulation fully removes the damage (post-stimulation $S=0$).

Approach. Use the Hawkins formula for skin caused by a finite damaged annulus of reduced permeability, then compare the steady-state radial-flow rate equation before (with $S$) and after (with $S=0$) stimulation at the same $p_e$, $p_{wf}$.

1. Skin due to formation damage (Hawkins' formula). $S=\left(\dfrac{k}{k_s}-1\right)\ln\dfrac{r_s}{r_w}=(10-1)\ln\dfrac{2}{0.3}=9\ln(6.667)$, so $\boxed{S=17.07}$.
2. Rate ratio at fixed $p_e$ and $p_{wf}$. From the steady-state radial-flow equation $q=\dfrac{7.08kh(p_e-p_{wf})}{\mu B_o[\ln(r_e/r_w)+S]}$, everything except $S$ is unchanged between the two cases, so $\dfrac{q_{after}}{q_{before}}=\dfrac{\ln(r_e/r_w)+S_{before}}{\ln(r_e/r_w)+S_{after}}$. With $S_{after}=0$ (stimulation removes the damage) and $\ln(r_e/r_w)=\ln(3000/0.3)=\ln(10{,}000)=9.210$: $\dfrac{q_{after}}{q_{before}}=\dfrac{9.210+17.07}{9.210+0}$, so $\boxed{q_{after}/q_{before}=2.85}$.
3. Interpretation. A skin of $S\approx17$ is severe: the damaged ring alone is throttling the well nearly as much as the entire undamaged drainage area does, since $S$ is comparable in size to $\ln(r_e/r_w)=9.21$. That is exactly why the well is a good stimulation candidate — restoring the flowing radius all the way back to the undamaged permeability (acidizing the damaged annulus, or bypassing it with a perforation/fracture that reaches past $r_s$) very nearly triples deliverability at the same drawdown, whereas a well with the same $\ln(r_e/r_w)$ but little or no skin would see almost no benefit from the same treatment.