24-Pet-B5 Reservoir Mechanics · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Petroleum Engineering, 2015-Dec. 3 hours, closed book. This paper's own cover page reads “98-Pet-B5, Well Testing,” not Reservoir Mechanics, and every question below is pressure-transient/well-test analysis. 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. The one reference chart supplied with this paper (the page-7 “plot of dimensionless pressure versus dimensionless time”) is the generic exact line-source curve $p_D=0.5[-\mathrm{Ei}(-1/4t_D)]$, so every reading from it below is computed directly from that expression.
Reference texts: Lee, J., Well Testing, SPE Textbook Series Vol. 1 (diffusivity equation, radial flow, wellbore storage); Earlougher, R.C., Advances in Well Test Analysis, SPE Monograph Vol. 5 (Horner analysis, superposition in time, reservoir-limit test, multi-rate tests); Bourdet, D., Well Test Analysis: The Use of Advanced Interpretation Models, Elsevier (log-log diagnostic plots, wellbore storage); 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) Finite acting reservoir. A reservoir in which the pressure transient has already reached every outer (no-flow) boundary, so the well can no longer "see" an infinite medium; once finite-acting, the flow regime moves from transient toward pseudo-steady-state, where the whole drainage volume declines together. Question 2 below computes the exact time this well reaches that state.
(b) Extended flow test. A long-duration single-rate drawdown (days, not hours) run specifically to reach the late-time straight-line pressure decline of pseudo-steady-state flow, so that its slope $dp/dt=0.234qB_o/(c_tV_p)$ can be read directly and inverted for reservoir pore volume – the exact technique used in Question 5.
(c) Pseudo radial flow. The late-time flow regime around a stimulated or partially-completed well (fractured, horizontal, or partially penetrating) once the near-well flow geometry has "healed" and streamlines far from the well again converge radially, as if from an ordinary vertical well with an effective (often negative) skin absorbing the near-well geometry.
(d) Partial penetration. A well completed (perforated) over only part of the producing interval thickness; flow converges from the full formation thickness into the shorter completed interval, adding extra (spherical/hemispherical-flow) pressure drop near the wellbore that is normally lumped into an apparent "pseudo-skin" on top of the true mechanical skin.
(e) Pressure derivative analysis. Plotting $t\cdot dp/dt$ (or $\Delta t\cdot d\Delta p/d\Delta t$) alongside $\Delta p$ on the same log-log axes (Bourdet derivative); flat, sloped and dipping segments of the derivative curve identify flow regimes (IARF, boundaries, dual porosity) far more distinctly than $\Delta p$ alone, since the derivative of the log-approximation term $0.5\ln t_D$ is a constant, giving a flat line for infinite-acting radial flow.
(f) Gas pseudo pressure. The real-gas transform $p_p(p)=2\int_{p_0}^{p}\frac{p'}{\mu(p')z(p')}\,dp'$ that absorbs the strong pressure dependence of gas viscosity and $z$-factor into a single variable, so that the same liquid-flow diffusivity-equation machinery (semilog slope, skin formula) can be applied unchanged to gas buildup/drawdown data.
(g) Dual porosity storativity ratio. The Warren & Root parameter $\omega=(\phi c_t)_f/[(\phi c_t)_f+(\phi c_t)_m]$, the fraction of total system storage held in the high-permeability fracture network alone; it sets the vertical size of the characteristic Horner-plot dip between the early fracture-only line and the late total-system line (small $\omega$ → most storage in the matrix → a deeper dip).
(h) Interference test. A multi-well test in which one well is produced (often at a changing rate) while pressure is recorded in one or more separate, non-flowing observation wells; the pressure response at the observation well, analysed by superposition in time, confirms reservoir connectivity/communication and yields an independent estimate of $k$ and $\phi c_t$ away from the wellbore – the technique used in Question 6.
(i) Type curves. Pre-computed, dimensionless families of $p_D$ vs. $t_D$ curves (parameterized by skin, wellbore storage, or reservoir geometry) that a test's real $\Delta p$-vs-$\Delta t$ data is overlaid on (matched) to read $k$, $s$ and $C$ directly from the match point, without needing an identifiable semilog straight line; the page-7 curve supplied with this paper is the simplest such type curve (zero storage, zero skin, line-source).
(j) Stimulation. Any treatment (acidizing, hydraulic fracturing) intended to reduce the near-wellbore flow resistance, i.e. to make the mechanical skin factor $s$ more negative; a successfully stimulated well shows a measurably lower (or negative) skin on a post-job test than the same well's pre-job baseline.
