24-Pet-B5 Reservoir Mechanics · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Petroleum Engineering, 2014-Dec. 3 hours, closed book. This sitting's own cover page reads “98-Pet-B5, Well Testing,” not Reservoir Mechanics, and every question is pressure-transient/well-test analysis (radial diffusivity, drawdown/buildup, double-porosity, sealing-fault, interference). NOTES item 4/5 state that five (5) questions constitute a complete exam and only the first five as they appear are marked; all seven questions on the paper are solved in full below. Three of the seven questions (Q3, Q4, Q6) are chart-reading questions built around semilog/log-log plots with no printed data table — every plotted value used below was read from the printed figure and is flagged check where it feeds a boxed result.
Reference texts: Lee, J., Well Testing, SPE Textbook Series Vol. 1 (diffusivity equation, type curves, radius of investigation); Earlougher, R.C., Advances in Well Test Analysis, SPE Monograph Vol. 5 (Horner analysis, superposition in time, interference and reservoir-limit tests); Bourdet, D., Well Test Analysis: The Use of Advanced Interpretation Models, Elsevier (double-porosity/Warren–Root model, sealing faults); Warren, J.E. & Root, P.J., “The Behavior of Naturally Fractured Reservoirs,” SPE Journal, 1963.
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) Pseudo-steady state (PSS). The late-time flow regime in a closed (no-flow-boundary) drainage volume, reached once the pressure transient has swept the entire reservoir and the no-flow outer boundary is fully felt everywhere. From that point on, pressure declines at the same rate $dp/dt$ at every point in the reservoir – the pressure profile shape "freezes" and simply translates downward with time, which is exactly the behaviour exploited in Q5's reservoir-limit test.
(b) Radius of investigation. An estimate of how far a pressure disturbance has propagated into the reservoir at elapsed time $t$, $r_{inv}\approx\sqrt{kt/(948\phi\mu c_t)}$ (field units). It marks the boundary between the region already "feeling" the well and the still-undisturbed reservoir beyond it, and is the basis of Q3's estimate.
(c) Type curves. Pre-computed, dimensionless log–log plots of $p_D$ (or its derivative) versus $t_D$ for a family of reservoir/well models (wellbore storage + skin, boundaries, fractures, double porosity). Field data plotted in the same dimensionless form is overlaid and slid to find the best-matching curve, from which $k$, skin, and model-specific parameters (e.g. storativity ratio $\omega$) are read off the match point.
(d) Interference test. A multi-well test in which one well (the "active" well) is produced or injected at a controlled rate while pressure is measured in one or more nearby shut-in "observation" wells. The delayed, attenuated response at the observation well confirms reservoir continuity between the wells and yields an average $k$ and $\phi$ for the interwell region – the exact scenario analysed in Q7.
(e) Double porosity reservoir. A naturally fractured reservoir represented (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. On a semilog buildup plot it produces the characteristic S-shaped curve analysed in Q4 – an early fracture-only line, a transition dip, and a late total-system line of the same slope.
(f) Wellbore storage. The early-time distortion of a pressure transient caused by the wellbore itself continuing to produce (or accept) fluid, from its own compressed fluid column or a moving liquid level, for some time after the surface rate is changed – before the sandface rate has actually ramped to match. Data recorded while wellbore storage dominates cannot be used for reservoir characterisation (Q3 identifies where it ends).
(g) Sandface pressure. The pressure at the wellbore wall, i.e. at $r=r_w$ – conventionally written $p_{wf}$. It is the pressure that actually drives inflow from the formation and is what a downhole gauge measures directly (as opposed to a surface/tubing-head pressure, which needs a hydrostatic and friction correction to relate back to it).
(h) Line source approximation. Treating the producing well as an infinitesimally thin line (zero radius) when solving the radial diffusivity equation. It replaces the exact finite-$r_w$ solution with the simpler exponential-integral ($Ei$) solution, valid once enough time has passed that near-wellbore effects (storage, skin) have died away – the basis of the $p_D=0.5[-Ei(-1/4t_D)]$ formula used in Q7.
(i) Horner time ratio. The dimensionless time group $(t_p+\Delta t)/\Delta t$ used to plot a pressure-buildup test, where $t_p$ is the producing time before shut-in and $\Delta t$ is elapsed shut-in time. Plotting $p_{ws}$ versus $\log[(t_p+\Delta t)/\Delta t]$ linearises the semilog response for a well that did not produce for infinite time, and lets the line be extrapolated to a ratio of 1 ($\Delta t\to\infty$) to estimate $p^*$ – used throughout Q4 and Q6.
(j) Reservoir limit test. An extended drawdown test deliberately run long enough to reach pseudosteady state, so that the resulting linear pressure-decline rate can be inverted (via $dp_w/dt=-0.234qB_o/(c_tV_p)$) to estimate the reservoir's own pore volume – literally the method used in Q5.
