Question 1 of 7: Well-testing terminology

Question 1: Well-testing terminology (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.

(a) Infinite acting reservoir. A reservoir large enough, relative to the time of the test, that the pressure transient never reaches any outer boundary – the pressure far from the well stays at its undisturbed initial value $p_i$ throughout. Every log-approximation formula on this paper's own formula sheet ($p_D=0.5[\ln t_D+0.809]$, valid for $t_D\gt 100$) assumes this regime.

(b) Non-Darcy flow. Additional, velocity-squared (turbulent/inertial) pressure loss near a high-rate wellbore that Darcy's linear rate-pressure relation does not capture, usually significant only in high-rate gas wells; it appears as an extra rate-dependent term $Dq$ added to the mechanical skin, giving an apparent (total) skin $s+Dq$ that grows with flow rate.

(c) Phase redistribution. A wellbore-storage-like distortion, seen in buildup tests on wells producing two phases, caused by the gas and liquid columns in the shut-in wellbore continuing to re-segregate (denser liquid settling, gas rising) after shut-in – it can produce a pressure hump in early-time data that mimics (and is easily confused with) a real reservoir feature.

(d) Dimensionless time. The normalized time group $t_D=0.0002637\,kt/(\phi\mu c_tr_w^2)$ (field units) that collapses the diffusivity equation's solution for any combination of $k$, $\phi$, $\mu$, $c_t$ and $r_w$ onto a single universal curve $p_D(t_D)$, which is exactly why one type curve or one $p_D$-vs-$t_D$ chart (as supplied for Q7) can be re-used for any well.

(e) Drill stem test (DST). A temporary, rig-conveyed completion run on a new well (often before permanent casing/tubing is set) that opens the formation to flow for a short, controlled period while recording downhole pressure, giving an early estimate of productivity, reservoir pressure and fluid type before committing to a full completion.

(f) Pseudo steady state (PSS). The late-time flow regime in a closed (no-flow-boundary) drainage volume, reached once the transient has swept the entire reservoir; from that point every point in the reservoir declines at the same rate $dp/dt$, and the pressure profile shape simply translates downward with time without changing form.

(g) Dual (double) porosity reservoir. A naturally fractured reservoir idealised (Warren & Root, 1963) as two overlapping, interacting continua – a low-storage, high-permeability fracture network that flows directly to the well, fed by high-storage, low-permeability matrix blocks. It produces the characteristic S-shaped Horner curve analysed in Q5: an early fracture-only line, a transition dip, and a late total-system line of the same slope.

(h) Fall-off test. The injection-well analogue of a pressure buildup test: an injector is shut in and the pressure falls from its elevated injecting value back toward reservoir pressure, analysed with the same Horner/superposition machinery (with the injection rate treated as negative) to get injectivity, skin and average pressure near the injector.

(i) Drainage area. The portion of the reservoir volume from which a given well actually withdraws fluid, bounded either by a physical no-flow boundary (fault, pinch-out) or by the pressure interference from a neighbouring well; it sets the outer radius $r_e$ used in every pseudosteady-state and reservoir-limit-test formula.

(j) Horner time. The dimensionless ratio $(t_p+\Delta t)/\Delta t$ used to plot a pressure buildup, where $t_p$ is the producing time before shut-in and $\Delta t$ is elapsed shut-in time; plotting $p_{ws}$ against $\log$ of this ratio linearises the semilog response and lets the straight line be extrapolated to a ratio of 1 ($\Delta t\to\infty$) to estimate $p^*$, the technique used throughout Q4 and Q5.