Well testing: purposes and types of test

Quick refresher

Well testing is an inverse problem. We measure the pressure response to a change in rate, and we choose the parameters of a reservoir model to match it. The answer depends on the model we choose, so we check the interpretation against geology, logs and core.
A single stabilised measurement of rate and pressure gives the productivity index (the rate per unit of pressure drop), but it cannot separate permeability from skin. The way the pressure changes with time does separate them. The slope of the semilog straight line (the straight line on a plot of pressure against the logarithm of time) is set by the flow capacity $kh$ , and the skin only shifts the line.
The longer a test lasts, the farther it “sees”: the radius of investigation (how far the pressure disturbance has travelled) grows as the square root of $kt/(\phi\mu c_t)$ . In low-permeability reservoirs a test needs days or weeks.
The early part of the record reflects the wellbore and the near-wellbore zone. The middle part reflects radial flow in the reservoir (flow towards the well from all sides), which gives $kh$ and the skin. The late part reflects the boundaries and the volume of the drainage area.
Build-up tests are more common than drawdown tests, because after shut-in the rate is known exactly: it is zero. A drawdown test, however, does not need production to be stopped.
The test of an exploration well usually includes a short flow period, a first build-up, a main flow period and a final build-up. Safety matters more than any aim of the test.

Key relationships

r_i = 0.119\sqrt{\dfrac{k\,t}{\phi\,\mu\,c_t}}

radius of investigation, m ( $k$ in mD, $t$ in h, $\mu$ in mPa·s, $c_t$ in 1/MPa)

V_p = \dfrac{qB}{c_t\,|\dd p/\dd t|}

pore volume of a closed area from the rate of pressure decline

kh = 2.149\,\dfrac{qB\mu}{m}

flow capacity from the slope $m$ per decimal cycle, that is, per tenfold change in time (m³/d, mPa·s, MPa)

Common pitfalls

Believing that the permeability of the reservoir can be found from a single stabilised measurement.
Drawing the semilog straight line through early points that are distorted by wellbore storage (the well itself acts as a small tank and delays the response).
Planning a test of a low-permeability reservoir that lasts as long as a test of a high-permeability one.
Forgetting that an error in the rate measurement passes directly into the error in permeability.
Mixing up the drawdown curve in a producing well (the pressure decline after start-up) with the one in an injection well (the decline after injection is shut in).

After this lesson you can

explain why the change of pressure with time tells us about the reservoir, and why we need a transient process (pressure that is still changing) rather than a single stabilised measurement
list the main types of test (drawdown, build-up, fluid-level recovery, injection well tests, interference tests, drill stem tests and flow-after-flow tests) and say what each gives
describe the sequence of a test of an exploration well (a well drilled to find or appraise a deposit) and the purpose of each stage
tell the early, middle and late parts of a pressure record apart, and say what we find from each
estimate how long a test must last from the radius of investigation, and the pore volume of a closed area from the rate of pressure decline

Why wells are tested

The reservoir lies several kilometres deep, and we see it only through widely spaced wells. We judge it from several sources: seismic surveys and geological interpretation, cuttings (rock chips brought up by the drilling fluid) and core, logs, pressure measurements with a wireline formation tester (a tool lowered on a cable that measures the pressure in the rock), well tests and, finally, the production history. Each source “sees” its own volume of rock. We can build a reliable model of the reservoir only by combining them.

Well tests have a special place among them. They are the only direct way to measure how the reservoir works, that is, how it delivers fluid within hundreds of metres around the well. Core and logs describe the centimetres and metres near the wellbore. A well test averages the permeability over a very large volume, including fractures and heterogeneities (variations in the rock) that do not get into the core.

In essence, a test is an inverse problem (parameter estimation). In modelling, we know the properties of the reservoir and calculate the pressure from them. In interpreting a test, we have measured the pressure, and we choose the properties of the reservoir so that the calculated response matches the measured one. The diffusivity equation describes how the pressure responds to a change in rate. Its parameters — the flow capacity of the reservoir, the hydraulic diffusivity (how fast pressure spreads through the rock), the skin and the boundaries — are the result of the test.

What can be learned from well tests

What is determined: Reservoir pressure — initial or average
From which part of the record: pressure build-up after shut-in
Remarks: in a field under development, we need corrections for the limited size of the area (Build-up in a bounded reservoir and average reservoir pressure)

What is determined: Flow capacity $kh$ and permeability
From which part of the record: the middle part — radial flow
Remarks: permeability to the mobile fluid, averaged over a large volume

What is determined: Skin factor and the pressure drop across the skin
From which part of the record: the middle part and the bottomhole pressure before a rate change
Remarks: shows whether the near-wellbore zone needs treatment (Skin factor)

What is determined: Wellbore storage coefficient
From which part of the record: the early part
Remarks: volume and compressibility of the fluid in the wellbore (Wellbore storage)

What is determined: Boundaries: faults, pinch-outs, contours
From which part of the record: the late part
Remarks: the type of boundaries and the distance to them (A sealing fault near the well: the method of images)

What is determined: Volume of the drainage area
From which part of the record: the pseudo-steady-state part of a long flow period
Remarks: reservoir limit test (Reservoir limit test)

What is determined: Communication between wells
From which part of the record: interference test
Remarks: flow capacity and storativity (the capacity of the rock to store fluid) of the reservoir between the wells

What is determined: Fluid, samples, temperature, productivity
From which part of the record: test of an exploration well
Remarks: input for the estimate of hydrocarbons in place and for the field development plan

What is determined	From which part of the record	Remarks
Reservoir pressure — initial or average	pressure build-up after shut-in	in a field under development, we need corrections for the limited size of the area (Build-up in a bounded reservoir and average reservoir pressure)
Flow capacity $kh$ and permeability	the middle part — radial flow	permeability to the mobile fluid, averaged over a large volume
Skin factor and the pressure drop across the skin	the middle part and the bottomhole pressure before a rate change	shows whether the near-wellbore zone needs treatment (Skin factor)
Wellbore storage coefficient	the early part	volume and compressibility of the fluid in the wellbore (Wellbore storage)
Boundaries: faults, pinch-outs, contours	the late part	the type of boundaries and the distance to them (A sealing fault near the well: the method of images)
Volume of the drainage area	the pseudo-steady-state part of a long flow period	reservoir limit test (Reservoir limit test)
Communication between wells	interference test	flow capacity and storativity (the capacity of the rock to store fluid) of the reservoir between the wells
Fluid, samples, temperature, productivity	test of an exploration well	input for the estimate of hydrocarbons in place and for the field development plan

Why a transient process is needed

The simplest way to test a well is at steady state (nothing changes with time). We measure the rate $q$ and the bottomhole pressure $p_{wf}$ , and, if we know the reservoir pressure $\bar p$ , we get the productivity index $J = q/(\bar p - p_{wf})$ . That is enough to draw the inflow line (Well inflow: the well performance diagram). But it does not show why the productivity is what it is. $J$ is proportional to the flow capacity of the reservoir $kh$ , and inversely proportional to the sum of the logarithmic term and the skin factor. So a low $J$ can mean a tight reservoir (one with low permeability), or a good reservoir with a damaged near-wellbore zone.

What separates these causes is the way the pressure changes after a rate change. As long as the disturbance has not reached the boundaries, the bottomhole pressure follows a straight line against the logarithm of time. For a known rate and viscosity, the slope of this line is set only by the flow capacity $kh$ of the reservoir. The skin shifts the whole line without changing the slope. In the late, pseudo-steady-state part (the regime after the disturbance has reached all the boundaries), the pressure in two wells with the same productivity changes in the same way, if the rate and the volume of the area are the same. Neither this part nor a stabilised measurement can tell them apart.

CalculatedCalculated fall in bottomhole pressure after the start-up of two wells with the same productivity index (the data of the example are in the advanced section). Well A is in a 20 mD reservoir without skin. Well B is in a 40 mD reservoir with a skin of +7.3. The time scale is logarithmic. For the first tens of hours the curves have different slopes, which are set by the flow capacity of the reservoir. After pseudo-steady state is reached, they coincide.

Well-testing methods were developed largely to make this separation. Here is an example. An exploration well is often drilled with water-based mud at a large overbalance (the pressure in the well is much higher than in the reservoir), and its near-wellbore zone is damaged. Suppose the test has given the permeability and the skin separately. Then we can predict the productivity of future production wells. We put into the inflow equation the same permeability and the skin that we can reach with less damaging penetration and good perforation. That skin is about zero, and with underbalanced perforating (perforating with the well pressure below the reservoir pressure) it can even be negative (Skin factor).

Types of test

Tests differ in how they change the regime of the well and where they record the pressure. In Russian-language practice they are divided into two groups. In steady-state tests, we draw an inflow performance diagram from several stabilised rates. In transient tests, we record how the pressure changes with time after a rate change.

The main types of well test

Test: Drawdown test
What is done: the well is started at a constant rate and the fall in bottomhole pressure is recorded
What is obtained: $kh$ , skin; with a long record, the boundaries and the volume of the area
Special features: production is not interrupted, but a constant rate is hard to maintain (Pressure drawdown analysis)

Test: Build-up test
What is done: the well is shut in after flowing at a constant rate
What is obtained: $kh$ , skin, reservoir pressure
Special features: the rate is known exactly (it is zero), but the well does not produce (Pressure build-up analysis)

Test: Fluid-level recovery test
What is done: the pump is stopped and the rise of the liquid level in the well is followed
What is obtained: $kh$ , skin, reservoir pressure
Special features: for wells that do not flow naturally; after shut-in the fluid keeps flowing in at a changing rate (afterflow), so special processing methods are needed

Test: Test of an injection well
What is done: injection is stopped and the pressure decline is recorded (falloff test), or the injection rate is raised in steps
What is obtained: $kh$ , skin, reservoir pressure; from the rate steps, the fracture opening pressure (the pressure at which the rock cracks)
Special features: the injected water around the wellbore has a different viscosity and temperature

Test: Interference test
What is done: the rate of one well is changed and the pressure in a neighbouring well is recorded
What is obtained: communication between wells, $kh/\mu$ and the storativity of the reservoir $\phi c_t h$
Special features: the signal is small and arrives with a delay: accurate gauges and time are needed

Test: Drill stem test (DST)
What is done: the formation is isolated with a packer (a seal that closes off the tested interval) and a valve near the bottom is opened
What is obtained: fluid, samples, initial pressure, $kh$ , skin, productivity
Special features: the first test of a new well; more in the next section

Test: Flow-after-flow test
What is done: the well is brought to several stabilised rates
What is obtained: the inflow performance curve, the productivity index
Special features: each rate is held until it stabilises (Inflow performance relationship (IPR))

Test	What is done	What is obtained	Special features
Drawdown test	the well is started at a constant rate and the fall in bottomhole pressure is recorded	$kh$ , skin; with a long record, the boundaries and the volume of the area	production is not interrupted, but a constant rate is hard to maintain (Pressure drawdown analysis)
Build-up test	the well is shut in after flowing at a constant rate	$kh$ , skin, reservoir pressure	the rate is known exactly (it is zero), but the well does not produce (Pressure build-up analysis)
Fluid-level recovery test	the pump is stopped and the rise of the liquid level in the well is followed	$kh$ , skin, reservoir pressure	for wells that do not flow naturally; after shut-in the fluid keeps flowing in at a changing rate (afterflow), so special processing methods are needed
Test of an injection well	injection is stopped and the pressure decline is recorded (falloff test), or the injection rate is raised in steps	$kh$ , skin, reservoir pressure; from the rate steps, the fracture opening pressure (the pressure at which the rock cracks)	the injected water around the wellbore has a different viscosity and temperature
Interference test	the rate of one well is changed and the pressure in a neighbouring well is recorded	communication between wells, $kh/\mu$ and the storativity of the reservoir $\phi c_t h$	the signal is small and arrives with a delay: accurate gauges and time are needed
Drill stem test (DST)	the formation is isolated with a packer (a seal that closes off the tested interval) and a valve near the bottom is opened	fluid, samples, initial pressure, $kh$ , skin, productivity	the first test of a new well; more in the next section
Flow-after-flow test	the well is brought to several stabilised rates	the inflow performance curve, the productivity index	each rate is held until it stabilises (Inflow performance relationship (IPR))

The names follow Russian-language practice. For gas wells, isochronal tests are also used: tests at several rates of equal length.

Other measurements add to well tests. The wireline formation tester (WFT) measures the pressure at tens of points along the depth, taking only a few minutes per point, and it takes fluid samples (Pressure measurement with the wireline formation tester). Production logging (PLT) of producing wells, with flowmeters and thermometers, shows which intervals work and how much they deliver. In wells with submersible pumps, sensors at the pump intake — downhole pressure and temperature monitoring systems — record the pressure all the time, and every pump stop gives a build-up record. We can process this record if the rate history is known.

Testing an exploration well

The first test of a new well is the drill stem test (DST). We run an assembly into the well on pipe. It includes a packer (a seal that isolates the interval being tested from the column of drilling fluid), a test valve near the bottom (opened and closed from the surface, for example by changing the pressure in the annulus, the space between the pipe and the wall of the well), and downhole gauges (they record the pressure in memory or send it to the surface). At the surface the flow passes through a choke (a narrow opening that limits the flow) into a separator, which measures the rates of oil, gas and water separately. The gas is burned off in a flare.

The name goes back to the days when the assembly was run on drill pipe (the drill stem) straight into an uncased hole. Today the formation is more often tested after the casing is run and perforated, on special tubing. For interpretation, something else matters more. The valve shuts the well in right at the formation, so only a small volume remains below it, and the effect of the wellbore on the pressure record is short. The reservoir pressure at the start of the test is usually already known from wireline tester measurements.

SchematicBottomhole pressure record in a drill stem test (schematic, not to scale): 1 — running in the assembly (the gauge sees the pressure of the mud column); 2 — a short first flow period; 3 — the first build-up to the initial reservoir pressure; 4 — the main flow period; 5 — the final build-up; 6 — releasing the packer and pulling out. Below: the surface rate.

Sequence of a typical test

1
Short first flow period
It lasts a few minutes. Its purpose is to relieve the supercharging of the formation at the wellbore (the excess pressure caused by mud filtrate that has invaded the rock; it is noticeable in low-permeability formations) and to make sure that the formation communicates with the well. The withdrawal is so small that there is no depletion even in a small block.
2
First build-up
It lasts long enough for the pressure to almost stabilise. This is how we find the initial reservoir pressure $p_i$ . After a short clean-up of the wellbore, this record can be unreliable, and then we refine $p_i$ from the final build-up.
3
Main flow period
The rate is kept as constant as possible. Sometimes the rate is raised in steps to check whether sand is being produced. Fluid samples are taken. The bottomhole pressure and the time at the moment of shut-in are recorded exactly, because without them the skin cannot be found.
4
Final build-up
It usually lasts about one and a half times as long as the main flow period. We use it to find $kh$ , the skin and the pressure $p^*$ (the extrapolated reservoir pressure; Pressure build-up analysis). If the pressure recovers to a level clearly below the initial pressure, the drainage area is small and closed. This is an important conclusion about the size of the accumulation.

A test of an exploration well has these aims: to find out what fluid the reservoir yields; to measure productivity, reservoir pressure and temperature; to take samples for PVT studies (laboratory studies of how the fluid behaves at different pressures and temperatures); to get information about the reservoir (permeability, heterogeneity, boundaries); and to assess the condition of the near-wellbore zone. If the reservoir energy is not enough to lift the fluid to the wellhead (the top of the well at the surface), the record is limited to an inflow with the liquid level rising in the tubing, and a build-up. Special processing methods are used for such tests.

What a pressure record shows

We read a pressure record after a rate change in parts. The early-time region reflects what happens in the wellbore and right at the well. While the fluid in the wellbore is being compressed or is expanding, the rate at the sandface (the rock face at the well) differs from the rate at the surface. This is wellbore storage. The middle-time region is radial flow in the reservoir that does not yet “know” about its boundaries. On a semilog plot it is a straight line, and we find $kh$ and the skin from this line. The late-time region reflects the boundaries: faults, the pinch-out of the reservoir (where it thins to nothing), neighbouring wells, and a contour with constant pressure.

Suppose a well flows at a constant rate for long enough in a closed block. The disturbance then reaches all the boundaries, and pseudo-steady-state flow sets in. The pressure throughout the block declines at the same rate, as in a closed tank. The rate of decline depends only on the withdrawal, the compressibility (how much the fluid and rock expand when the pressure falls) and the pore volume of the block. The reservoir limit test is based on this. We find the pore volume of the drainage area from the slope of the line of pressure against time, plotted in ordinary coordinates, not logarithmic ones.

Rate of pressure decline in a closed area

\frac{\dd p}{\dd t} = -\frac{qB}{c_t V_p}

where:

$\dd p/\dd t$ rate of pressure decline — the same throughout the area and in the well, MPa/d
$q$ flow rate at standard conditions, m³/d
$B$ formation volume factor of the fluid (its volume in the reservoir per unit volume at standard conditions), m³/m³
$c_t$ total compressibility of rock and fluids, 1/MPa
$V_p$ pore volume of the drainage area, m³

Units: any consistent units (for example, m³/d, MPa/d, 1/MPa, m³)

Holds when

The area is closed (nothing flows in across the boundaries), and the rate is constant.
Pseudo-steady state has already been reached: the disturbance has reached all the boundaries.
The fluid is single-phase and slightly compressible, with constant compressibility.

This is the material balance of a closed tank: what is taken out must equal what the fluid and rock expand by. The withdrawal at reservoir conditions, $qB$ per unit of time, equals the expansion of the fluids and rock, $c_t V_p$ per unit fall in pressure. The smaller the block, the faster the pressure falls. The rate of decline does not depend on permeability or skin. They set only how far the bottomhole pressure lies below the average.

Worked examplePore volume of a block from a reservoir limit test

Given (assumed data)

Oil rate $q$ (constant): 90 m³/d
Formation volume factor $B$: 1.30 m³/m³
Total compressibility $c_t$: $1.4\cdot10^{-3}$ MPa⁻¹
Slope of the line of bottomhole pressure against time in the late part: −0.0045 MPa/h
Porosity $\phi$ ; net thickness $h$ ; water saturation $S_w$: 0.20; 12 m; 0.25

Solution

The rate of decline per day: $0.0045\cdot 24 = 0.108$ MPa/d.
The pore volume: $V_p = \dfrac{90\cdot 1.30}{1.4\cdot10^{-3}\cdot 0.108} = 774$ thousand m³.
The area of the block is $A = V_p/(\phi h) = 0.32$ km². The radius of a circle of the same area is $\sqrt{A/\pi} \approx 320$ m.
The oil in the block at standard conditions is $V_p(1 - S_w)/B = 446$ thousand m³, or about 379 thousand t at a density of 850 kg/m³.

Answer: The well drains a block with a pore volume of about 774 thousand m³. This is a circle with a radius of about 320 m, with oil in place of about 379 thousand t.

What it means. If the geological model promised a large accumulation, this result is a warning. The well stands in a small isolated block, so we cannot drill new wells nearby and count on the same oil in place. The result depends directly on the compressibility $c_t$ and on our confidence that pseudo-steady state has really been reached. We check this on the diagnostic plot. The data in this example are assumed for illustration.

The diagnostic plot shows most reliably which part of the record we have in front of us. It shows the pressure change and its logarithmic derivative (the slope of the pressure curve on a semilog plot) on a log–log scale (Diagnosis with the pressure derivative). Today, software does the interpretation. We choose a model of the reservoir whose calculated response matches the record, and we refine its parameters. For simple cases the model of a homogeneous reservoir with skin is enough. For complex cases we use models with faults, layering, anisotropy (different permeability in different directions), dual porosity (rock made of fractures and blocks of porous matrix) or zones of different permeability around the well. Different models sometimes describe the same record equally well, so we check the choice of model against geology and data from neighbouring wells.

How a test is planned

The main question in planning is how long the flow period and the shut-in should last. A pressure disturbance spreads from the well gradually. In time $t$ it noticeably covers an area with a radius of about the radius of investigation. The more permeable the reservoir and the less viscous the fluid, the faster this radius grows.

Radius of investigation

r_i = \sqrt{\frac{4kt}{\phi\mu c_t}}

where:

$r_i$ radius to which a noticeable pressure disturbance has travelled in time $t$ , m
$k$ permeability of the reservoir, m²
$t$ time since the rate change, s
$\phi$ porosity, fraction
$\mu$ fluid viscosity, Pa·s
$c_t$ total compressibility of rock and fluids, 1/Pa

Units: SI

Holds when

The reservoir is homogeneous, and the disturbance has not yet reached the boundaries.
The criterion $kt/(\phi\mu c_t r_i^2) = 1/4$ is a convention. If we choose a different level for what counts as a “noticeable” disturbance, the constant changes by tens of per cent.
In practice, whether we can detect a disturbance also depends on the resolution of the gauge (the smallest change it can show).

The radius grows as the square root of time. To “look” twice as far, the test must last four times as long. Porosity and compressibility vary little from one reservoir to another, so the speed at which the disturbance spreads is set mainly by the mobility $k/\mu$ . This is what the test measures.

In other unit systems (2)

Metric oilfield units

r_i\,[\text{m}] = 0.119\sqrt{\frac{k\,[\text{mD}]\;t\,[\text{h}]}{\phi\;\mu\,[\text{mPa·s}]\;c_t\,[\text{MPa}^{-1}]}}

$k$ in mD, $t$ in hours, $\mu$ in mPa·s, $c_t$ in 1/MPa.

$0.119 = \sqrt{4\cdot 3.553\cdot10^{-3}}$ , where $3.553\cdot10^{-3}$ is the multiplier of dimensionless time in these units. It converts mD to m², hours to seconds, mPa·s to Pa·s and 1/MPa to 1/Pa.

Oilfield units

r_i\,[\text{ft}] = 0.0325\sqrt{\frac{k\,[\text{mD}]\;t\,[\text{h}]}{\phi\;\mu\,[\text{cP}]\;c_t\,[\text{psi}^{-1}]}}

$k$ in mD, $t$ in hours, $\mu$ in cP, $c_t$ in 1/psi, $r_i$ in feet.

$0.0325 = \sqrt{4\cdot 2.637\cdot10^{-4}} = 1/\sqrt{948}$ , where $2.637\cdot10^{-4}$ is the multiplier of dimensionless time in oilfield units.

Worked exampleHow long the flow period must last to cover 300 m of the reservoir

Given (assumed data)

Required radius of investigation $r_i$: 300 m
Porosity $\phi$ ; oil viscosity $\mu$: 0.18; 1.1 mPa·s
Total compressibility $c_t$: $1.6\cdot10^{-3}$ MPa⁻¹
Permeability: 150 mD (reservoir A) or 5 mD (reservoir B)

Solution

From the metric form of the formula, $t = (r_i/0.119)^2\,\phi\mu c_t/k$ .
The numerator is the same for both reservoirs: $(300/0.119)^2\cdot 0.18\cdot 1.1\cdot 1.6\cdot10^{-3} = 2013$ mD·h.
Reservoir A: $t = 2013/150 = 13.4$ h.
Reservoir B: $t = 2013/5 = 403$ h, that is, about 16.8 d.
If we add the final build-up, which by the usual rule is one and a half times as long as the flow period, the test of reservoir B would take about 42 d.

Answer: A high-permeability reservoir needs only about 13.4 h of flow, but a low-permeability one needs about 16.8 d.

What it means. The time grows in proportion to the square of the radius, and in inverse proportion to the mobility $k/\mu$ . Keeping a drilling rig on location for weeks for a single test is expensive. So in low-permeability reservoirs we either accept a smaller radius of investigation, or we run long tests later, during an extended well test (a long trial production period). The same estimate shows how long to wait for each rate to stabilise in a flow-after-flow test: until the radius of investigation reaches the boundaries of the drainage area. The data in this example are assumed for illustration.

What is decided in planning

1
Objective
Decide what we need to find out: permeability and skin, reservoir pressure, boundaries, block volume, communication with neighbouring wells. The type of test and its duration depend on this aim.
2
Rate
The rate is limited by the capacity of the separator and the flare, sand production, the danger of drawing in water or gas, and the temperature limits of the equipment. It is best to keep the bottomhole pressure above the bubble point pressure (the pressure at which gas starts to come out of the oil), so that gas does not come out of solution at the wellbore. In tight reservoirs a stable rate may not be possible at all.
3
Duration
Choose the flow period from the radius of investigation. Make the build-up long enough to record at least one logarithmic cycle of radial flow (a tenfold range of time) after wellbore storage has ended. In the test of an exploration well, make it about one and a half times as long as the flow period.
4
Equipment
Use gauges with enough resolution, as close to the interval as possible. Shut the well in downhole where possible. Measure the rate accurately and record the rate history.
5
Design calculation
Using the expected reservoir properties, calculate in advance the performance of the “reservoir – tubing – choke” system with a nodal analysis program (Nodal analysis of the production system), together with the expected pressure record. If this record would not let us tell, for example, a fault from a deterioration of the reservoir, change the plan.
6
Cost of information
The costs are drilling rig standby, oil that is not produced, and gas burned in the flare. The duration of a test is always a compromise between its cost and the value of the additional information.

Terms and symbols

Well testing: Records of pressure and flow rate made during a deliberate change of the operating regime of a well.
Drawdown and build-up curves: The fall in pressure after a well is started, and the rise in pressure after it is shut in.
Fluid-level recovery test: A record of the rise of the liquid level in a well after the pump has been stopped.
Interference test: A test of communication between wells. The rate is changed in one well, and the pressure is recorded in another.
Drill stem test (DST): A test of a new well with an assembly that has a packer, a valve near the bottom and gauges.
Radius of investigation $r_i$: The distance to which a noticeable pressure disturbance has travelled during the test.
Reservoir limit test: A long flow period, carried on until pseudo-steady state is reached. The pore volume of the area is found from the rate of pressure decline.
Inverse problem: Choosing the parameters of a reservoir model so that it matches the measured pressure response.

Common mistakes and misconceptions

Wrong

“The permeability can be found from a stabilised measurement of rate and pressure.”

In fact

Such a measurement gives only the productivity index, in which permeability and skin cannot be told apart. We separate them with the pressure record in transient flow.

Wrong

“If the pressure at the end of the final build-up is lower than the initial pressure, the gauge is faulty.”

In fact

First check the main explanation: a small closed block that was noticeably depleted during the flow period. This is an important result of the test. We confirm it by comparing with the first build-up and by excluding gauge drift (a slow error in the gauge reading).

Wrong

“The longer the test, the more accurate the permeability.”

In fact

The accuracy is limited first of all by the rate measurement. The duration sets something else: how far the test “sees”. We choose it to suit the aim of the test.

Wrong

“An interference test characterises the reservoir around the responding well.”

In fact

The response carries information about the reservoir between the wells (its flow capacity and storativity along the path of the disturbance) and about whether there is a barrier between them.

Wrong

“The drawdown curve in an injection well is the same as in a producing well.”

In fact

In a producing well it is the pressure decline after start-up. In an injection well it is the decline after injection is shut in. In meaning, the second is the analogue of the build-up curve.

In depth: advanced detail

Model of the graph: the same productivity — different reservoirs

The graph in the section on the transient process is calculated for a well at the centre of a circular closed area, using two approximate solutions. While the disturbance has not reached the boundary, the logarithmic approximation holds:

Pressure drawdown in an infinite reservoir (logarithmic approximation)

p_i - p_{wf} = \frac{qB\mu}{4\pi kh}\left[\ln\frac{kt}{\phi\mu c_t r_w^2} + 0.809 + 2S\right]

where:

$p_i$ initial reservoir pressure, Pa
$p_{wf}$ bottomhole flowing pressure at time $t$ after start-up, Pa
$q,\ B,\ \mu$ flow rate at standard conditions, formation volume factor, viscosity, m³/s, m³/m³, Pa·s
$k,\ h$ permeability and thickness of the reservoir, m², m
$\phi,\ c_t,\ r_w$ porosity, total compressibility, well radius, —, 1/Pa, m
$S$ skin factor, —

Units: SI; the logarithm is natural

Holds when

The rate is constant from start-up, and wellbore storage is ignored.
The disturbance has not reached the boundaries, and the dimensionless time $kt/(\phi\mu c_t r_w^2)$ is greater than about 25.
The reservoir is homogeneous, and the fluid is single-phase and slightly compressible.

The slope per unit of the natural logarithm of time, $qB\mu/(4\pi kh)$ , depends only on the flow capacity. The skin adds a constant term. Per decimal cycle of time (a tenfold change in time) the pressure changes by $m = 2.149\,qB\mu/(kh)$ (m³/d, mPa·s, mD, m, MPa; $2.149 = \ln 10/(4\pi\cdot 0.0853)$ ). We find the same quantity from the slope of the Horner line (the straight line of the Horner plot, used to analyse build-up tests; Pressure build-up analysis). The constant is $0.809 = \ln(4/\gamma)$ , where $\gamma = 1.781$ .

When the disturbance reaches the boundary, pseudo-steady-state flow sets in. For a well at the centre of a circle, this happens when $kt/(\phi\mu c_t r_e^2)$ is about 0.25–0.3. The pressure falls everywhere at the same rate. The fall in bottomhole pressure is the sum of two parts: the depletion of the area and the drawdown:

Bottomhole pressure in pseudo-steady-state flow

p_i - p_{wf} = \frac{qB\,t}{c_t V_p} + \frac{q}{J},\qquad J = \frac{2\pi kh}{B\mu\left(\ln\dfrac{r_e}{r_w} - \dfrac34 + S\right)}

where:

$V_p$ pore volume of the area, $\pi r_e^2 h\phi$ , m³
$J$ productivity index with respect to the average pressure of the area, m³/(s·Pa)
$r_e$ radius of the circular drainage area, m
$t$ time after start-up, s

Units: SI

Holds when

The area is circular and closed, with the well at the centre.
The time is longer than the time needed to reach pseudo-steady state.

The first term is the depletion: the fall in the average pressure, found by material balance. The second term is the drawdown between the average pressure and the bottomhole pressure. Permeability and skin do not enter either term separately. For wells with the same $J$ , rate and area volume, the curves coincide (Pseudo-steady-state flow and the shape factor).

Worked exampleTwo wells with the same productivity

Given (assumed data)

Common data: $q$ = 50 m³/d; $B$ = 1.2; $\mu$ = 1.5 mPa·s; $h$ = 10 m
Reservoir: $\phi$ = 0.20; $c_t = 1.5\cdot10^{-3}$ MPa⁻¹; $r_e$ = 300 m; $r_w$ = 0.1 m
Well A: $k$ = 20 mD, $S$ = 0
Well B: $k$ = 40 mD, the skin is chosen so that the productivity is the same

Solution

The logarithmic term is $X = \ln(300/0.1) - 0.75 = 7.256$ .
Equal productivity means $20/X = 40/(X + S_{\text{B}})$ , so $S_{\text{B}} = X = 7.26$ .
The productivity index of both wells is $J = \dfrac{0.536\cdot 20\cdot 10}{1.5\cdot 1.2\cdot 7.256} = 8.2$ m³/(d·MPa), and the drawdown is $q/J = 6.09$ MPa. Here $0.536 = 2\pi\cdot 0.0853$ is the constant of the inflow equation in metric units (Steady-state radial flow).
The slope per decimal cycle of time is $m_{\text{A}} = 2.149\cdot\dfrac{50\cdot 1.2\cdot 1.5}{20\cdot 10} = 0.97$ MPa for well A and $m_{\text{B}} = 0.48$ MPa for well B, which is half as large.
The pressure drop across the skin of well B (Skin factor) is $\Delta p_s = 1.866\cdot\dfrac{50\cdot 1.2\cdot 1.5}{40\cdot 10}\cdot 7.26 = 3.05$ MPa. This is 50% of the drawdown ( $1.866 = 1/0.536$ ).

Answer: The stabilised measurements of the two wells are the same:

J \approx 8.2

m³/(d·MPa). But the semilog slope of B is half as large: its reservoir has twice the flow capacity, and half of the drawdown is lost in the near-wellbore zone.

What it means. A treatment of the near-wellbore zone of well A would give almost nothing, because its productivity is limited by the reservoir. In well B, removing the skin could roughly double the rate. Without a pressure record in transient flow, we cannot tell these wells apart. The data in this example are assumed for illustration.

Connections to other topics

Pressure build-up analysis — how flow capacity, skin and reservoir pressure are found from a build-up test.
Pressure drawdown analysis — the same analysis for a record after the start-up of a well.
Skin factor — what skin is and how much rate it “costs”.
Well inflow: the well performance diagram — the productivity index and the well performance diagram.
Wellbore storage — why early data describe the wellbore and not the reservoir.
Diagnosis with the pressure derivative — how the pressure derivative helps us recognise the parts of a record.
Reservoir limit test — the volume of the drainage area from a long flow period.
Pressure measurement with the wireline formation tester — pressure measurements and sampling with a wireline formation tester.
Dimensionless well solutions: skin, radius of investigation and units — the radius of investigation and the radius of drainage in more detail.

Check yourself

1
Which test will show whether two wells communicate across a suspected fault?
1. A.A build-up test in each well separately
2. B.A flow-after-flow test
3. C.An interference test: change the rate of one well and record the pressure in the other
4. D.A resistivity log
Show the answer
Correct answer: C. An interference test: change the rate of one well and record the pressure in the other
Only an interference test checks communication directly. If the fault is sealing, the disturbance from the active well will not reach the responding well, or it will arrive weakened and late. A build-up test in each well may show a boundary, but it will not say whether it is that boundary or how permeable it is.
2
Two wells give the same rate at the same drawdown. In their build-up tests the slope of the semilog straight line of the first is twice that of the second. Which conclusion is correct?
1. A.The reservoirs are the same, only the gauges differ
2. B.The second well is already in pseudo-steady state
3. C.The flow capacity $kh$ of the first is half that of the second, and the second has the larger skin
4. D.The first has twice the skin
Show the answer
Correct answer: C. The flow capacity $kh$ of the first is half that of the second, and the second has the larger skin
The slope is inversely proportional to the flow capacity $kh$ . With the same productivity, the lower flow capacity of the first well is balanced by the larger skin of the second.
3
How many hours must the flow period last for the radius of investigation to reach 200 m, if $k$ = 30 mD, $\phi$ = 0.20, $\mu$ = 2 mPa·s, $c_t = 1.5\cdot10^{-3}$ MPa⁻¹?
Show the answer
Use the metric form, $t = (r_i/0.119)^2\,\phi\mu c_t/k$ . Here $(200/0.119)^2 \approx 2.82\cdot10^{6}$ and $\phi\mu c_t/k = 2\cdot10^{-5}$ , so $t \approx 56$ h, which is more than two days. For a 300 mD reservoir, about 6 h would be enough.
4
Why is the final pressure build-up in the test of an exploration well made about one and a half times as long as the main flow period?
1. A.Because the formula for the radius of investigation needs it
2. B.So that the gauge warms up to reservoir temperature
3. C.To follow the record with confidence towards the reservoir pressure, and to notice the depletion of a small block
4. D.To collect more samples
Show the answer
Correct answer: C. To follow the record with confidence towards the reservoir pressure, and to notice the depletion of a small block
A long build-up lets us extrapolate the pressure (extend the curve beyond the recorded data) reliably and compare it with the initial pressure. If the pressure recovers to a level clearly below the initial pressure, the block is small and closed. This is one of the main questions of the test of an exploration well.
5
Why are build-up tests more common than drawdown tests, although the well does not produce during a build-up test?
Show the answer
After shut-in the rate is known exactly: it is zero. After start-up it is hard to hold a strictly constant rate, and its fluctuations distort the record. The price of a build-up test is the oil that is not produced during the recording. That is why, in production wells, engineers also try to use forced shut-ins (stops that happen anyway), for example records from submersible pump sensors.
6
From which part of the record is the pore volume of a closed drainage area found?
1. A.From the late part: the slope of the line of pressure against time, plotted in ordinary coordinates, in pseudo-steady state
2. B.From the first build-up in a drill stem test
3. C.From the middle part: the slope of the semilog straight line
4. D.From the early part: the section with a slope of 1 on the log–log plot
Show the answer
Correct answer: A. From the late part: the slope of the line of pressure against time, plotted in ordinary coordinates, in pseudo-steady state
In pseudo-steady state the pressure falls linearly with time, at the rate $qB/(c_t V_p)$ . If we know the rate, the formation volume factor and the compressibility, we can find $V_p$ .

Updated: 30 September 2026