Pseudopressure Plot

Key Takeaways

• The theoretical foundation for pseudopressure was established by Al-Hussainy, Ramey, and Crawford in a landmark 1966 SPE paper that showed how the nonlinear partial differential equation governing gas flow in porous media could be linearized by the pseudopressure substitution — prior to this work, engineers either analyzed gas wells using the direct pressure method (which assumed constant gas properties and was accurate only at high pressures) or the pressure-squared method (which assumed a specific relationship between viscosity and compressibility that was accurate only at low pressures); Al-Hussainy's pseudopressure function covered the full pressure range correctly and became the standard approach, though its adoption in routine practice was slow until commercial software made the numerical integration of the gas property functions routine; the 1966 paper is one of the most cited works in petroleum engineering because it solved a problem that was central to every gas well analysis conducted anywhere in the world, and it did so with a mathematically elegant substitution that transformed a nonlinear problem into a solved linear one.
• The pseudotime function (an analogous transformation applied to the time axis) complements pseudopressure in gas well pressure transient analysis by accounting for the time-varying total compressibility of gas during a buildup or drawdown test — gas compressibility changes with pressure, which means that even when pseudopressure accounts for the spatial nonlinearity of the gas flow equation, the time derivative in the transient flow equation has a remaining nonlinearity from changing total compressibility; pseudotime replaces actual time with an integral of (1 / mu-ct) dt over the production history, where ct is the total compressibility; using both pseudopressure and pseudotime makes the gas flow equations formally equivalent to the liquid flow equations across the full pressure range, allowing analytical solutions developed for liquid flow to be applied to gas wells without approximation; the combined use of m(p) and pseudotime is the current standard for rigorous gas well pressure transient analysis in commercial software packages.
• Production data analysis (PDA) or rate-transient analysis (RTA) for gas wells requires pseudopressure transformation of the flowing bottomhole pressure data to correctly extract reservoir and fracture properties — when an unconventional gas well is produced at variable rate and flowing pressure over a period of months to years, the analysis of that production history using normalized rate (rate divided by normalized pressure drop) plotted against material balance time generates a type curve signature that can be matched to analytical models; using actual pressure rather than pseudopressure in this analysis introduces errors in the derived permeability, fracture half-length, and drainage area that can be 20-50% in magnitude for wells producing at low reservoir pressures below 2,000 psia; tight gas wells in the Western Canada Sedimentary Basin and unconventional shale gas wells in the Marcellus and Haynesville — which often start production at reservoir pressures of 3,000-8,000 psia and eventually produce at pressures below 1,000 psia — experience the full range of gas property nonlinearity over their producing life, making pseudopressure transformation especially important for accurate EUR calculation.
• Gas well deliverability testing uses pseudopressure to calculate absolute open flow potential (AOFP) — the theoretical maximum rate a gas well could produce if the sandface flowing pressure were reduced to atmospheric pressure; the back-pressure (Rawlins-Schellhardt) plot and the LIT (laminar-inertial-turbulent) deliverability analysis both use pseudopressure to account for non-Darcy turbulence effects near the wellbore that cause the pressure drop to increase faster than linearly with rate; by plotting [m(Pr) - m(Pwf)] / q (normalized pseudopressure drop) versus q (rate), the LIT method separates the Darcy (laminar) flow component (which varies linearly with rate) from the turbulent non-Darcy component (which varies with rate squared), allowing the engineer to quantify the D-factor (non-Darcy skin) and the laminar permeability-thickness product independently; this separation matters for gas well optimization because the non-Darcy component increases with rate, meaning that a gas well at high rate pays an additional turbulent friction penalty that reduces the marginal deliverability of each incremental unit of rate increase.
• Numerical reservoir simulators for gas reservoirs internally apply the pseudopressure concept through pressure-dependent PVT properties (gas viscosity, z-factor, and formation volume factor as functions of pressure and temperature) that are updated at each grid block in each timestep — the pseudopressure calculation is embedded in how the simulator computes fluid mobility and transmissibility terms rather than appearing explicitly as a separate calculation step; when a reservoir engineer compares analytical pseudopressure-based well test results to simulator output, the two approaches should give consistent reservoir descriptions if both are using the same gas PVT correlations; discrepancies between analytical and simulation results for gas wells sometimes trace back to inconsistent PVT assumptions (different correlations for z-factor or viscosity between the analytical and numerical models) rather than actual differences in reservoir model, and checking PVT consistency is a standard QC step when calibrating a gas reservoir simulation to well test and production history data.