Treat PE Petroleum preparation as decision training. For every practice problem, identify which named model the data supports before calculating: which side of the well (IPR or TPR), which inflow model (constant PI or Vogel), which estimate tool (material balance or decline curve), which Arps exponent, and which barrel unit. Build a one-page decision map, drill it until identification takes under a minute, and score yourself on decisions, not answers.
IPR versus TPR: which side of the well is the question asking about?
An inflow performance relationship (IPR) describes flow from the reservoir into the wellbore; tubing performance (TPR, or vertical lift performance) describes flow from the sandface to the surface. Locate which curve the data describes before computing anything.
An IPR plots surface rate against flowing bottomhole pressure and is governed by reservoir properties: average reservoir pressure, permeability, thickness, fluid properties, and skin. A TPR plots rate against the bottomhole pressure required to lift fluid to surface, governed by tubing size, depth, wellhead pressure, water cut, and gas-liquid ratio. In nodal analysis, the operating point is the intersection of the two curves. A quick habit: sketch both curves with labeled axes before starting any well-performance calculation.
To decide which side you are on, read the given data. Reservoir pressure, permeability, or skin signals an IPR problem; wellhead pressure, tubing size, or GLR signals a TPR problem. Also check the reference depth: pressures quoted at sandface and at wellhead belong to different curves, so trace which curve each quoted pressure sits on before substituting it. Mislabeling the side of the well produces a number that looks reasonable and answers a different question.
Vogel or constant PI: is the flowing pressure below the bubble point?
Use a constant productivity index only when pressure stays above the bubble point and oil remains single-phase. Use the Vogel relationship when flowing bottomhole pressure is below the bubble point and solution gas evolves in the reservoir.
The two models encode different physics. A constant PI assumes a straight-line IPR, valid for undersaturated oil where mobility is roughly constant. Vogel, derived from simulation of solution-gas-drive reservoirs, is a dimensionless curve: q/qmax = 1 - 0.2(pwf/pr) - 0.8(pwf/pr)^2, where pr is average reservoir pressure. The gas that comes out of solution below the bubble point reduces oil mobility, so the actual IPR bends below the straight line a constant PI would predict.
Worked example (illustrative numbers): reservoir pressure 2,500 psia, bubble point 1,800 psia, a single test at pwf = 2,200 psia gives 400 STB/d. The plausible mistake is PI = 400/300 = 1.33 STB/d/psi, then q at pwf = 1,000 psia as 1.33 x 1,500 = 2,000 STB/d. The better decision: PI is legitimate only above pb, giving q = 933 STB/d at pb; below it, apply the Vogel segment, which yields roughly 1,790 STB/d. The straight-line extrapolation overpredicts because it ignores gas evolution, and in sizing or forecasting contexts that error compounds.
- pwf and pr both above pb: constant PI is defensible.
- pwf below pb: Vogel, or a composite IPR (PI segment above pb, Vogel segment below).
- Given a single test above pb and asked for a rate at low pwf: expect a two-phase calculation.
- Water injection or undersaturated conditions: question whether the two-phase curve applies at all.
Material balance or decline curve: match the tool to the data you actually have
Material balance uses pressure and PVT data to estimate original hydrocarbons in place and drive mechanism; decline curve analysis extrapolates rate history. Choose based on whether trustworthy pressure measurements exist, not on preference.
Material balance treats the reservoir as a tank: it tracks pressure drop against cumulative production, with methods such as the Havlena-Odeh straight-line plot and drive indices for water, gas cap, and solution gas drives. Its inputs are static bottomhole pressures, fluid PVT properties, and production volumes. Its outputs include original oil or gas in place and the strength of the aquifer or gas cap, which decline curves cannot reveal.
Decline curve analysis needs no pressure data and is fast, but it assumes the trends that produced the history will continue. It breaks across operational changes: installing artificial lift, acidizing, or converting a well changes the decline, and an extrapolation across the change date is answering a question about a different well. A defensible habit: if the dataset includes periodic static pressure surveys, attempt material balance; if it contains only monthly rates, decline analysis is the tool, and you should state its assumption explicitly rather than treat the extrapolation as a measurement.
- Pressure plus PVT data available: material balance path (tank model, Havlena-Odeh, drive indices).
- Rates only: decline curve path, with assumptions stated.
- Operational change in the rate history: segment the data before fitting anything.
Arps exponents: why the decline type you pick changes the reserves answer
Exponential, harmonic, and hyperbolic declines can match the same early rate history yet produce very different reserve estimates, because they assume different behavior of the decline rate D over time.
In Arps notation, b ranges from 0 to 1. Exponential decline (b = 0) has a constant fractional decline rate, so a plot of log rate versus time is a straight line and reserves are finite and easy to integrate. Hyperbolic decline (0 < b < 1) has D itself declining, so the curve flattens; harmonic decline (b = 1) is the extreme case with the longest tail. Fitting b is therefore a physical assumption about why the well declines, not a curve-fitting free-for-all.
The practical consequence shows up in economics-limited reserves. Two fits can both honor the first year of production, but the harmonic fit projects production far into the future and can report much larger reserves. When you work rate-time and rate-cumulative problems, first test whether log(q) versus time is straight; if it is, exponential is supported and the rate-cumulative plot gives reserves directly. If it curves, you must justify b from the drive mechanism or limit the forecast to an economic cutoff, and say so in your solution.
| Decline type | b exponent | Decline rate D over time | Rate-time form | Practical caution |
|---|---|---|---|---|
| Exponential | 0 | Constant | q = qi e^(-Dt) | Straight line on log q vs t; reserves integrate cleanly |
| Hyperbolic | 0 < b < 1 | Declining | q = qi (1 + b Di t)^(-1/b) | b must be justified, not just fitted |
| Harmonic | 1 | Declining | q = qi (1 + Di t)^(-1) | Longest tail; check against an economic limit |
Reservoir barrels versus stock tank barrels: fixing the unit frame first
Well tests report stock tank barrels; Darcy's law, velocities, and in-situ volumes need reservoir barrels. Convert with the formation volume factor before substituting any rate into a reservoir equation.
Oil shrinks as gas evolves on its way to the surface, so one reservoir barrel of oil yields less than one stock tank barrel; the formation volume factor Bo (reservoir barrels per stock tank barrel) links them. The same framing applies to gas with Bg and to solution gas-oil ratio. Before any radial flow, velocity, or pore-volume calculation, decide which frame every quantity lives in and write the unit beside it.
Worked example (illustrative numbers): a well produces 500 STB/d with Bo = 1.4 RB/STB. The plausible mistake is carrying 500 directly into a Darcy-law or velocity calculation, underestimating the in-situ rate by roughly 29 percent, since the true downhole oil rate is 500 x 1.4 = 700 RB/d. The better decision is to convert rates and, where relevant, compressibility terms into reservoir conditions as the first written step. This habit also catches the reverse error in facility-side problems, where surface capacities are asked and reservoir barrels must be divided back down.
- Reservoir-side equations (Darcy flow, velocities, pore volumes): multiply STB/d by Bo.
- Surface-side quantities (tankage, sales volumes): work in stock tank barrels.
- Gas problems: convert scf with Bg before comparing to reservoir volumes.
Ethics and safety scenarios: what the standards actually ask you to weigh
Professional standards questions ask you to identify duties: public safety first, competence within your field, truthful and objective reporting, and documenting decisions. Frame answers around obligations and escalation, not personal consequences.
The engineering ethical canons place the safety, health, and welfare of the public first, require practicing only within your areas of competence, and require objective and truthful statements in reports. In a petroleum context these duties surface as questions about pressure test data that looks inconsistent, a production report that would mislead a partner, or a task outside your experience that a supervisor assigns.
The reliable reasoning pattern is duty, verification, escalation, documentation. If test data is ambiguous, do not sign off on the convenient interpretation; re-verify, state the uncertainty, and recommend the check that resolves it. If a request falls outside your competence, decline to certify it and identify who is qualified. If public safety is implicated, escalating through the proper channels comes before loyalty to schedule or employer. Rehearsing this pattern on paper scenarios builds the habit of reasoning through duties and escalation before committing to a decision.
A four-week practice sequence with a self-check rubric
Run four phases: build the decision map, drill timed worked scenarios, do mixed identification-only sets, then complete mixed full problems. Score each attempt on decisions, setup, units, and limiting-case checks rather than the final number.
Week one: build a one-page map from the sections above (IPR/TPR, PI/Vogel, material balance/decline, Arps b, STB/RB) and re-derive each distinction from first principles. Week two: work slowly through full scenarios, writing your model decision before any arithmetic, like the Vogel example in this guide. Week three: take a stack of mixed problems and answer only the identification step for each, timed. Week four: solve complete mixed sets under time pressure and grade with the rubric below.
Practical exercise: take ten mixed well-performance and reserves problems. For each, write three decisions before calculating: which side of the well, which named model, which unit frame. Expected observations: in early attempts your decision notes flip IPR and TPR or omit the Bo conversion; by the third week the identification step should take under a minute and agree with the method the solution actually requires. If a missed answer traces to arithmetic rather than a wrong decision, the decision map is working and only speed needs work.
- Rubric, 1 point each: correct model identified before calculation; units written beside every quantity; answer checked against a limiting case (pwf = pr must give q = 0); error traced to a decision, not arithmetic.
- Readiness check: state from memory when constant PI versus Vogel applies.
- Readiness check: sketch a composite IPR (PI above bubble point, Vogel below) without notes.
- Readiness check: convert a stock tank rate to reservoir barrels and classify a rate history as exponential versus curved decline by a log plot.
- Readiness check: explain in two sentences why harmonic decline reserves need an economic limit.
References and further reading
Use these references to explore the concepts and check the latest information from the relevant organizations.