Drawdown test – permeability and skin: 24-Pet-B5 Reservoir Mechanics, December 2015, Q3

Question 3: Drawdown test – permeability and skin (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. The 9-point $p_{wf}$-vs-$t$ table above, with $q$, $h$, $B_o$, $p_i$, $\phi$, $c_t$, $\mu_o$, $r_w$ as listed.

Find. Formation permeability $k$ and skin factor $S$.

Approach. Before fitting any straight line, check the real-time trend: consecutive $dp/dt$ values fall from $-20.8$ (0.3–0.7 hr) to a constant $-1.725$ psi/hr from $t=14$ hr onward – that constant late-time slope is boundary-dominated (pseudo-steady-state) decline, not part of the semilog transient. Only the true middle-time region, before the boundary is felt, gives a valid $k$/$S$; fit the semilog straight line to the early points alone and use the late points only as a self-check.

Dashed red line: semilog straight line fit through the first 3 points (0.3, 0.7, 2 hr). Later points visibly fall below the extrapolated line as the well transitions to boundary-dominated decline.

Fit the true middle-time-region. Linear regression of $p_{wf}$ vs $\log_{10}t$ on the first 3 points ($t=0.3,0.7,2$ hr) gives $R^2=0.999999$, essentially a perfect line – confirming these three points are the genuine semilog transient, with slope $$m=22.58\text{ psi/cycle}$$ Including the $t=6$ hr point already degrades the fit ($R^2$ drops), and including all 9 points would wrongly blend the transient with the late boundary-affected decline.
Permeability. $$k=\frac{162.6\,qB_o\mu}{mh}=\frac{162.6(1000)(1.333)(2)}{22.58(32)}$$ $$\boxed{k\approx 600\text{ mD}}$$
Skin factor. Reading $p_{1hr}=2365.7$ psia from the fitted line at $t=1$ hr: $$S=1.151\left[\frac{p_i-p_{1hr}}{m}-\log_{10}\left(\frac{k}{\phi\mu c_tr_w^2}\right)+3.23\right]$$ $$S=1.151\left[\frac{2500-2365.7}{22.58}-\log_{10}\!\Big(\frac{600}{(0.15)(2)(12\times10^{-6})(0.333)^2}\Big)+3.23\right]$$ $$\boxed{S\approx 0.0\text{ (essentially undamaged)}}$$

Quantity	Result
Semilog slope, $m$	22.58 psi/cycle
Permeability, $k$	600 mD
Skin factor, $S$	≈ 0

Check: from $t\approx14$ hr onward this well's $dp/dt$ is exactly $-1.725$ psi/hr, constant – a hallmark of pseudo-steady-state (boundary-dominated) decline, well before the full 46-hr test ends. No drainage radius is given for this question, so no reservoir-limit-test estimate of pore volume is reported here (unlike Question 5, where $r_e$/OOIP is explicitly asked for); the observation is flagged only to justify excluding the late points from the $k$/$S$ fit.

Topic. Semilog (MTR) drawdown analysis and identifying its validity window.

Key relations. $m=162.6qB_o\mu/(kh)$; $S=1.151[(p_i-p_{1hr})/m-\log_{10}(k/\phi\mu c_tr_w^2)+3.23]$.

Why this works. The semilog straight line is only valid during infinite-acting radial flow; once any boundary is felt the pressure response departs from $\ln t$ behaviour, so blindly regressing all available points (rather than checking where the straight line actually holds) systematically biases both $m$ and the resulting $k$/$S$.

Common pitfall. Fitting every data point "because more data is better" – doing so here would give a much steeper apparent slope, an under-estimated $k$, and (having compared it directly) a spuriously large negative apparent skin, since the late boundary-driven pressure drop gets misread as extra near-wellbore damage-free (or even stimulated) behaviour.

Source. Lee, Well Testing, ch.1, 3 (drawdown test analysis); Earlougher, Advances in Well Test Analysis, ch.2 (validity of the semilog approximation).

Question 3 of 7: Drawdown test – permeability and skin

Question 3: Drawdown test – permeability and skin (20 marks)