How to Calculate Plateau Pressure for Water Influx

In water-influx and material-balance work, plateau pressure is a constant pressure assigned to a finite time interval so a measured reservoir-pressure history can be represented by discrete steps. This guide uses that reservoir-engineering meaning. For a pressure that changes approximately linearly from p_start to p_end during an interval, the usual midpoint representation is p_plateau = (p_start + p_end) / 2. The result is an average pressure for the interval, not a new pressure measurement and not a universal reservoir-pressure estimate.

The van Everdingen-Hurst constant-terminal-pressure solution describes the response to a pressure step. A real reservoir boundary pressure changes with depletion, so multiple step responses are combined by superposition. The original method and later institutional references explain why the pressure history must be converted into pressure changes with known inception times. Calculating plateau values is therefore only the data-preparation stage; a water-influx result also needs an aquifer constant, dimensionless time, dimensionless cumulative influx, geometry, rock-fluid properties, and a consistent boundary-pressure assumption.

Pressure surveys provide observations at discrete dates, while the analytical aquifer response is evaluated continuously in time. A staircase approximation bridges those descriptions by holding one representative pressure constant over each interval. The Colorado School of Mines source linked below describes this stepwise interface-pressure profile as a practical approximation when average reservoir pressure is measured only at discrete times. The approximation makes every change explicit and gives each change a defined starting time for superposition.

The plateau should represent pressure at the reservoir-aquifer interface. In many field applications that interface pressure is approximated by average reservoir pressure, but the equality is an assumption rather than a measurement. Pressure gradients, compartmentalization, delayed communication, sparse shut-in data, and survey corrections can make a field-average value differ from pressure at the contact. Record the pressure source, averaging method, datum, and basis before calculating the midpoint.

Place the observations in chronological order as pairs of time and representative reservoir pressure. For interval i, bounded by pressures p_(i-1) and p_i, calculate p_plateau,i = [p_(i-1) + p_i] / 2. This arithmetic average is appropriate when pressure is assumed to vary linearly between the two observations. Keep more decimal places during the calculation than the pressure survey supports, then round only the reported table so repeated subtraction does not accumulate avoidable rounding differences.

A pressure plateau is associated with an interval, not just a survey date. The first plateau spans the initial time to the first observation, the second spans the first to second observation, and so on. Include start time, end time, duration, start pressure, end pressure, plateau pressure, and a data-quality note in the working table. If a major shut-in, injection change, or rapid depletion event occurs inside an interval, split the interval at that event when defensible pressure information is available.

The influx calculation does not multiply every plateau pressure independently by the same response. It uses an initial pressure drop and later incremental changes. With initial reservoir pressure p_i and first plateau p_bar1, the first drop is Delta p_1 = p_i - p_bar1. For a declining history, each later increment is Delta p_j = p_bar(j-1) - p_barj. Sign convention must be consistent with the implementation: the PetroCalcHub single-step calculator expects a positive pressure-drop increment when that increment drives water into the reservoir.

Each increment begins at a different time. At a current evaluation date, the first pressure step has acted for the longest elapsed time and a recent step for the shortest. Convert each elapsed time to the dimensionless-time definition required by the selected aquifer geometry, evaluate W_eD for that elapsed time, calculate the contribution B_aq times Delta p_j times W_eD, and sum all active contributions. Reusing the current total elapsed time for every increment overstates newer contributions and breaks the superposition history.

Shorter intervals usually reproduce a curved pressure trend more closely, but they do not improve unreliable pressure data. Interval size should reflect survey frequency, the rate of pressure change, operational events, and the sensitivity of the influx result. The original van Everdingen-Hurst discussion notes that pressure or rate plateaus should be sufficiently short to reproduce the trend within engineering accuracy. A practical convergence check repeats the calculation with selected intervals divided and compares cumulative influx.

The simple midpoint is not automatically valid for every history. If pressure is known to spend most of an interval near one level and then change abruptly, a time-weighted pressure or multiple subintervals better represent the history. Any weighting must be documented from evidence rather than selected to improve a history match. The model should also use average reservoir pressure corrected to a common datum and representative condition, not an arithmetic average of unrelated flowing measurements.

For the radial field-unit form provided on PetroCalcHub, the aquifer influx constant is calculated from porosity, total aquifer compressibility, aquifer radius squared, thickness, and encroachment fraction. The single-step calculator then evaluates W_e = B_aq Delta p W_eD. These two calculators expose the dimensional multiplication, but they do not generate W_eD from geometry and dimensionless time or perform the complete multi-step superposition table automatically.

Cumulative modeled influx should be reviewed with oil, gas, and water production; formation volume factors; pore-volume changes; compressibility; pressure uncertainty; and the selected material-balance form. A visually good pressure match is not proof that aquifer size and properties are unique. Test alternative aquifer geometries and boundary conditions, compare predicted future behavior with later observations, and avoid using an unconstrained influx match as the sole reserves basis.

Is plateau pressure the same as average reservoir pressure? Not exactly. The pressure data may be an estimate of average reservoir pressure, while the plateau is the constant interval value constructed from that history for the stepwise model. Can plateau pressure increase? Yes, if injection, recharge, measurement revision, or another event raises representative pressure; the resulting increment must retain the correct sign and be handled by a model that supports that history.

Should the first plateau be averaged with zero pressure? No. Average the initial reservoir pressure and the pressure at the end of the first interval. Should all survey points be equally weighted? The midpoint formula assumes linear change between adjacent points, independent of the duration of other intervals. Should a user report only the plateau table? No. Report the original pressure data, averaging and datum corrections, interval boundaries, pressure increments, dimensionless-time method, aquifer parameters, superposition sum, and sensitivity cases so another engineer can reproduce the result.