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Well testing and pressure transient analysis

Well testing gives permeability, skin factor, reservoir pressure and the distance to boundaries — averaged over a large volume of the reservoir, not at a point as core or logs do.

The lessons start with the radial flow equation and build up the methods of interpretation from simple semilog analysis to type curves and bounded reservoirs.

33 / 33 topicsWhere to start: Well inflow: the well performance diagram

Inflow to a well

  1. 01Well inflow: the well performance diagramHow rate, bottomhole pressure and reservoir pressure are related: drawdown, productivity index, the path of fluid from the reservoir to the separator, the operating point on the well performance diagram and the number of wells needed for planned production. Basic
  2. 02Steady-state radial flowThe Dupuit equation in SI, metric and oilfield units, the pressure distribution around a well, the effects of drainage radius and skin, average reservoir pressure and steady-state gas inflow. Intermediate
  3. 03Pseudo-steady-state flow and the shape factorInflow to a well in a closed area: a uniform rate of pressure decline, derivation of the formula with the −1/2 and −3/4 terms, the productivity index in terms of average pressure, Dietz shape factors and shape pseudo-skin, the time to reach the regime, drainage volumes and the average pressure of a block with several wells. Intermediate
  4. 04Skin factorThe extra resistance to inflow, or improvement of it, in the near-wellbore zone: the Hawkins formula, the effective wellbore radius, the flow efficiency and the cost of skin in rate. Intermediate
  5. 05Partial penetration and well deviationPseudo-skins of partial penetration and of a deviated hole: convergence of flow to the interval and the role of vertical permeability, calculating the pseudo-skin with allowance for anisotropy and the position of the interval, separating damage skin from geometric skin, early radial, spherical and late radial flow on the pressure record, vertical permeability from the spherical flow period, the negative slant skin and how it masks damage. Advanced
  6. 06Water and gas coningWhy bottom water or gas-cap gas is drawn towards a well: the mechanism of a cone, the critical rate from hydrostatic equilibrium and from other methods, and the scatter between the estimates; the effects of the perforated interval and vertical permeability, breakthrough time and the rise in water cut after it, gas coning and oil rims, ways of delaying breakthrough. Intermediate
  7. 07Inflow at high rates: non-Darcy flowInertial losses at high flow velocities: the Forchheimer equation and number, the inertial resistance coefficient from core and from correlations, the rate-dependent skin of a gas well, the two-term inflow equation in pseudo-pressures, separating skin from the D coefficient with a multi-rate test, isochronal tests, absolute open flow and what increases inertial losses. Advanced

Transient testing: fundamentals

  1. 08Well testing: purposes and types of testWhat a change in pressure reveals about a reservoir: why a transient is needed, the types of test from pressure build-up to drill stem testing and interference testing, the periods of a pressure record and planning the duration. Basic
  2. 09Dimensionless well solutions: skin, radius of investigation and unitsThe dimensionless groups of well testing and their constants in SI, metric and oilfield units; a finite-radius well and the line source — where they diverge; skin as an added term and as an effective radius, the start of the straight line for a stimulated well, a skin zone of finite size; the radius of investigation by four criteria — the disturbance front, the share of volume drained, the gauge threshold, the boundary on the derivative; drainage radius and transient productivity. Advanced
  3. 10Pressure drawdown analysisThe record of bottomhole pressure after a well is started at a constant rate: why a semilog straight line appears, where it starts and ends, how to find flow capacity and permeability from its slope and skin from its position; the constants in metric and oilfield units, the late-time portion and the volume of the drainage area. Intermediate
  4. 11Pressure build-up analysisThe Horner plot and the MDH method: flow capacity and permeability of the formation, skin factor and reservoir pressure from the pressure recovery after a well is shut in. Intermediate

Wellbore storage and type curves

  1. 12Wellbore storageWhy in the first minutes and hours after start-up or shut-in the pressure is governed by the wellbore, not the reservoir: the wellbore storage coefficient and its dimensionless form, the straight line on Cartesian axes and the unit slope on the log–log plot, the transition period, estimating the start of the semilog straight line in metric and oilfield units, ways of reducing wellbore storage and the limits of the model. Intermediate
  2. 13Type-curve matchingHow a pressure record is matched to the type curves of a well with wellbore storage and skin: why the record is a shifted copy of the dimensionless curve, a family of curves with one parameter, matching in pressure and in time, calculating permeability, the wellbore storage coefficient and skin in metric and oilfield units, checking against the Horner line and the non-uniqueness of a short record. Advanced
  3. 14Diagnosis with the pressure derivativeThe logarithmic pressure derivative and the diagnostic plot: the signatures of wellbore storage, the transition hump, radial flow, linear and spherical flow and boundaries; flow capacity from the level of the plateau and skin from the ratio of pressure to plateau, in metric and oilfield units; calculating the derivative from measurements, noise and smoothing, false signatures. Advanced
  4. 15Effect of producing time on build-up analysisWhy after a short producing period a build-up falls behind the drawdown curve and its derivative drops without any boundaries: superposition and the limit of recovery, the local slope and the error of the MDH method, the Agarwal equivalent time for the semilog plot, type curves and the skin formula, the derivative against equivalent time, planning the flow and the shut-in, when the time transformation does not help, and desuperposition. Advanced
  5. 16Nonideal wellbore storage, well clean-up and changing skinWhen the wellbore storage coefficient changes during the record: shut-in tubing containing gas (the gas and the weight of the liquid column in series), redistribution of gas and liquid and the hump on a build-up — estimating its size and timing from the wellbore profile, the empirical Fair and Hegeman models with redistribution pressure, the instantaneous coefficient from a flowmeter, rising and falling liquid level, water under the gauge, downhole shut-in and the test programme; well clean-up and changing skin — why a drawdown test overestimates permeability and how to obtain skin as a function of time; the signature of each phenomenon on the derivative. Advanced

Boundaries and late-time behaviour

  1. 17A sealing fault near the well: the method of imagesA straight sealing fault and the image well: doubling of the semilog slope and the step in the derivative, distance to the fault from the intersection time of the lines and from the point of the step, a fault right next to the well (hemiradial flow), a build-up near a fault and the maximum detection distance, limits of the method. Advanced
  2. 18Several boundaries: parallel faults and wedge-shaped blocksA well near several sealing boundaries: reflections of reflections and a derivative that “counts” them; a channel between parallel faults — linear flow, the ½ slope, channel width from the Δp–√t line and the position of the well from the geometric skin; a wedge between intersecting faults — the late-time level 360°/θ, the angle from it and from a derivative that is still rising; how boundaries combine, the duration of the test and what the record cannot distinguish. Advanced
  3. 19Semi-infinite systems: theory and test analysisReservoirs that are not closed by boundaries on all sides: the solution with reflections and a single characteristic length, the product solution for rectangular fault systems, a channel closed at one end — doubling of linear flow, channel width and distance to the closed end from the derivative point and from the Δp–√t lines, a well right at a boundary as a well with double the rate, recovery of pressure to the initial value and the trace of the closed end on a build-up after a short producing period, a worked record from an extended well test. Advanced
  4. 20Partially communicating faultsA fault of finite conductivity — a thin semipermeable zone: the dimensionless fault transmissibility α, reflection with “leakage”, a derivative rise to below the doubled level and a return to the plateau, the apparent skin of the fault; estimating α from the derivative maximum and the transmissibility of the fault zone, flow across the fault and the transmissibility multiplier of the model; the resolution window of the test and models with a similar signature. Advanced

Bounded drainage area

  1. 21Reservoir limit testA long producing period until pseudo-steady state is reached: the linear pressure decline and the unit slope of the derivative, pore volume, drainage area and hydrocarbons in place from the slope of the line, the shape factor from its intercept, the transition period and the duration of the test, variable rate and material balance time, sources of error. Advanced
  2. 22Build-up in a bounded reservoir and average reservoir pressureWhy a build-up in a closed area levels off at the average pressure and not the initial pressure, and how it differs from p*: the MBH method and its functions for different shapes of area, the Dietz and Ramey–Cobb formulas, choosing the producing time in the Horner function, late build-up points, repeat tests and material balance from average pressures. Advanced
  3. 23Equivalent producing time and synthetic flowing timeWhich producing time to put into the Horner function when the rate changed before shut-in or the well produced for a long time in a bounded area: the superposition function for build-ups and the derivative with respect to it, the equivalent Horner time Np/q and when it is wrong (a comparison on an example, a false “fault” after a rate reduction), the synthetic time at which p* becomes the pressure at the boundary of the drainage area, and a long build-up among producing neighbours. Advanced
  4. 24Testing in a developed reservoir: Slider's methodA build-up of a well among producing neighbours in a depleting block: why the pressure after shut-in passes a maximum and then falls, and the derivative imitates recharge; the build-up as the sum of a trend and the response to shut-in, Slider's method — correction for a linear trend and processing of the reconstructed drawdown (permeability, skin, boundaries); the rate of pressure decline of the block and where to get it, the size of the correction as a fraction of the plateau, an example of a block with four wells; when a linear trend does not work — changes in the rates of neighbours, injection, recharge. Advanced

Distributed pressure measurements

  1. 25Pressure measurement with the wireline formation testerThe wireline formation tester: probe, packer, pretest chamber and gauges; the pretest record, drawdown mobility under spherical flow, classes of measurement (valid, tight formation, supercharged, lost seal), accuracy of pressure and depth, the gradient from a set of pretests and what the measurements provide. Intermediate
  2. 26Supercharging and permeability from formation-tester pretestsWhy filtrate escaping through the mudcake raises the pressure at the borehole wall in tight streaks: the pressure divider and the model of filtrate injection, how supercharging distorts gradients and contacts, how to recognise it and allow for it. Permeability from a pretest: drawdown and spherical build-up, anisotropy, the observation probe and the dual-packer module, tool storage and the limits of the method. Advanced
  3. 27Comparing formation-tester, core and well-test dataWhy permeability from core, from formation-tester pretests and from a well test differs: the volume measured, the fluid and the end-point relative permeabilities, anisotropy, heterogeneity, damage. Bringing them to a common basis — core at reservoir conditions, the averaging window, corrections to drawdown mobility — comparison on logarithmic values and comparison of the interval's flow capacity kh with the build-up. Advanced
  4. 28Pressure gradients, fluid contacts and capillary equilibriumThe free water level and the gas–oil contact from the intersection of pressure lines: what pressure the tester sees at a contact, the uncertainty of the contact and how many pretests are needed, the capillary offset of the oil–water contact from the free water level, paleo-contacts and immobile oil, the water line from regional data, separate fluid systems and isolated blocks. Intermediate
  5. 29Forced-gradient technique and multi-well analysisA pressure line with a gradient from the fluid density of a sample, when points are few or supercharged: the level from reliable points, the left envelope and residual supercharging, contact uncertainty. Surveys of several wells: the accuracy of comparison, the plot of deviations from the field lines and the signatures of gauge errors, depth errors, supercharging and separate systems, the diagram of free-water-level estimates, the weighted mean contact and checking an outlying well. Advanced
  6. 30Perched and tilted contacts, trapped waterWhy water levels in wells differ although the oil line is common: perched water held behind a fault window or a saddle and its excess pressure, trapped water in lenses and closed blocks, the tilt of a contact in a flow of formation waters from the datum-corrected water pressures in three wells, with the uncertainty, signatures on pressure and logs, consequences for accumulation volume, well placement and edge-water support. Advanced
  7. 31Pressure measurements in producing reservoirs: barriers and accuracyA new well as an observation well: potential through the section, vertical flow and the viscous component of the gradient, its significance and vertical permeability. A barrier as a jump in potential, uneven depletion of two units and the time constant of the barrier, the parabolic profile of a tight unit, accuracy and supercharging without straight lines, repeat surveys and faults between blocks, pulse testing against a neighbouring well. Advanced
  8. 32Two-phase flow and reservoir description from formation-tester dataPressure profiles when two phases move in the reservoir: the mobility-weighted gradient, countercurrent flow in the gas-evolution zone and cocurrent flow in displacement from below with the viscous part, which phase's pressure the tool sees and the capillary correction, current contacts and the flushed zone, vertical interference tests in brief, water influx from the rise of the contact and calibration of the reservoir model. Advanced
  9. 33Lumped multi-tank material balance modelA reservoir as several tanks connected through the transmissibilities of faults and partitions: the balance of each tank and the sum of balances, when a block can be treated as a tank, a well in a small block and the rate limit set by a fault, the first well in an adjacent block, fitting transmissibilities and capacities to block pressures with uncertainties, choice of injection point, the time constants of a chain of tanks, comparison with a single tank and with a grid model. Advanced

This section is growing: new topics are published after a technical review.