Pressure measurement with the wireline formation tester

Quick refresher

A pretest draws a few cubic centimetres of fluid with the piston of the tool, and then the pressure recovers. The stabilised recovery pressure is the formation pressure at the test depth. The pressure in the borehole before and after the test is the pressure of the mud column (the drilling mud standing in the hole).
Almost all of the pressure drop during the draw is used up in the first few centimetres of rock next to the probe. The steady drawdown gives the mobility $k/\mu$ of the mud filtrate in the invaded zone. The filtrate is the liquid that has soaked into the rock from the drilling mud, and the invaded zone is the rock that it has entered and flushed. This is a local figure. It is not the permeability of the formation to oil.
A valid measurement: the pressure has stabilised, a repeat test has confirmed it, and the mud pressure before and after the test is the same. Tight formation: the pressure is still rising when the time at the test point (the depth where the tool is set) runs out, so the last value is only a lower limit. Supercharging (the mud filtrate has pushed the pressure up near the wall): the pressure has stabilised, but it is higher than the true value, and the mobility is low. Lost seal: the tool shows the mud pressure.
For the gradient, what matters is how well the gauge repeats its readings and how accurate the depths are, not the absolute accuracy of the tool. One metre of vertical depth changes the pressure by 7 kPa in oil and 10 kPa in water, and a quartz gauge can show a change of a hundredth of a kilopascal.
We find the gradient from all the valid points by the least-squares method (a best-fit straight line). Its error is the scatter of the points divided by the square root of the sum of the squared deviations of the depths from their mean. So the depth interval matters as much as the number of points.
The measurements give the initial pressure of the formations, the density and type of the fluid, the contacts, the pressure regime, information on whether formations are connected to each other, and places where samples can be taken.

Key relationships

\left(\dfrac{k}{\mu}\right)_d = \dfrac{C\,q}{2\pi\,r_{pe}\,\Delta p_d}

mobility from the drawdown at steady flow to the probe, SI; $C = 0.5$ for a sphere, $C = 1$ for a hemisphere

\left(\dfrac{k}{\mu}\right)_d = 39.02\,\dfrac{q}{\Delta p_d}

the same for the classic standard probe: $k/\mu$ in mD/(mPa·s), $q$ in cm³/s, $\Delta p_d$ in MPa (the constant is 5660 when $\Delta p_d$ is in psi)

\Delta p_{\text{over}} = p_{\text{m}} - p_{\text{res}}

overbalance (the excess of the mud pressure over the formation pressure) at the test depth

\rho = G/g

density of the fluid in the formation from the pressure gradient $G$ of the valid points

Common pitfalls

Using a pressure that is still rising: it is too low.
Taking a point to the right of the line of valid measurements (that is, at a higher pressure) for a layer with abnormal pressure, without checking its mobility. In a tight layer it is usually supercharging.
Taking the mobility from a pretest for the permeability of the formation to oil. It is the mobility of the filtrate in a few centimetres of flushed rock at the wall.
Calculating the gradient from depths along the hole in a deviated well (a well that is not vertical). We need true vertical depths.
Not comparing the mud pressure before and after the test. A difference shows that the tool has moved, the gauge has drifted, or the mud level in the well has changed.

After this lesson you can

describe how the formation tester is built (probe, packer, pretest chamber and pressure gauges) and the steps of a pretest
read the mud pressure, the formation pressure, the drawdown and the stabilisation time from a pressure record, and calculate the overbalance
calculate the fluid mobility from the drawdown for spherical flow to the probe, and explain which fluid and what volume of rock it refers to
assign a pretest to a class (valid, tight formation, supercharging or lost seal) and decide whether to use it in the interpretation
estimate the effect of gauge and depth errors, and build a pressure–depth plot from a set of pretests, with the gradient, the fluid density and their uncertainty
list the tasks that use the pressure measurements of the formation tester

How the formation tester is built

The formation tester is lowered on a cable into an open hole. This is usually done after the main set of logs (Open-hole logging: why, how and when), when the permeable layers have already been picked from the log curves. The tool is stopped opposite each chosen layer. Hydraulic back-up shoes press it against the borehole wall. On the opposite side, a probe presses against the wall. The probe is a tube about a centimetre across, surrounded by a rubber packer. The packer seals a patch of the wall off from the drilling mud in the hole. The probe passes through the mudcake (the layer of mud solids on the wall) to the rock.

Inside the tool, the probe is connected to a flowline. Three parts connect to this line. One is the pretest chamber, with a piston that draws a set volume of fluid at a set rate. Another is the set of pressure gauges. The third is an equalising valve, which links the line to the borehole. Modular tools (built from separate units) connect more to the same line. These are a pump for long pumping, a fluid analyser, sample chambers, and a module with two packers that seals off a stretch of the wall about a metre long. In Russian-language practice, pressure measurements with the formation tester are also called hydrodynamic logging (GDK in the Russian abbreviation). The name GDK-OPK also occurs (OPK is the Russian abbreviation for the wireline formation tester). Reports may also use the trade names of the service companies' tools (RFT, MDT and others).

SchematicThe formation tester at a test point (schematic, not to scale): the shoe and the packer press the tool against the wall, the probe passes through the mudcake, and fluid flows to it from all sides. The pretest chamber, the gauges and the equalising valve are connected to the flowline.

Probe and packer: They seal off a patch of the wall and connect the tool to the pore space of the rock. The size of the probe sets the flow area and the constant in the mobility formula. For tight rocks, and rocks that vary from place to place, there are probes of larger diameter and a dual-packer module (two packers that seal off a section of the wall).
Pretest chamber: Its piston draws a few cubic centimetres of fluid. In modern tools the volume and the rate are set from the surface for each test point. In early tools they were fixed.
Gauges: A quartz gauge is accurate and stable, but it responds more slowly and is sensitive to temperature. A strain gauge (it senses pressure through the tiny deformation of a metal element) is faster but less accurate. The formation pressure is taken from the quartz gauge.
Equalising valve: It equalises the pressure between the line and the borehole when the tool is set and when it is released. After the test, the pressure returns to the mud pressure through it.

The pretest and its record

Each pretest is a small hydrodynamic test (a test of how the formation reacts to a pressure change). It lasts from tens of seconds to a few minutes. The sequence is similar for all tools:

Sequence of a pretest

1
Stopping and depth correction
The tool is stopped at the planned depth. The depth is corrected using the tool's own gamma ray record (it shows the natural radioactivity of the rock). The pressure in the borehole is recorded. This is the pressure of the mud column, $p_{\text{m}}$ .
2
Setting
The shoes and the packer press against the wall. The pressure rises a little, because the packer squeezes the mudcake and the liquid in the line.
3
Drawdown
The piston of the chamber draws a set volume at a constant rate $q$ . The pressure falls below the formation pressure. If the mobility is high enough, it levels off at a constant value: the steady drawdown $\Delta p_d$ .
4
Build-up
After the piston stops, fluid flows in from the formation and compresses the liquid in the line. The pressure rises and stabilises. The stabilised value is the formation pressure $p_{\text{res}}$ at the test depth.
5
Repeat test
Often a second pretest is made at once, with a different rate or volume. The stabilised pressures must agree within a few tenths of a kilopascal, and the mobilities within the measurement error.
6
Release
The equalising valve is opened and the tool is pulled back from the wall. The pressure returns to the mud pressure, and it must agree with the measurement made before setting.

CalculatedCalculated record of the pretest at 2520.0 m from the example below: mobility 2.1 mD/(mPa·s), a draw of 5 cm³ at a rate of 0.2 cm³/s. The model is steady flow to the probe plus the compressibility of the liquid in the tool (advanced section).

What we read from a pretest record

Quantity: $p_{\text{m}}$ before and after the test
How we get it: the pressure in the borehole before setting and after release
What it is for: checks of the depth and the gauge, and that the tool did not move; the overbalance

Quantity: $p_{\text{res}}$
How we get it: the stabilised build-up pressure
What it is for: the formation pressure at the test depth

Quantity: $q$
How we get it: the volume drawn, divided by the piston travel time
What it is for: mobility

Quantity: $\Delta p_d$
How we get it: $p_{\text{res}}$ minus the pressure at the end of the draw
What it is for: mobility

Quantity: Stabilisation time
How we get it: from the moment the piston stops to a constant pressure
What it is for: a rough sign of the mobility; the class of the measurement

Quantity	How we get it	What it is for
$p_{\text{m}}$ before and after the test	the pressure in the borehole before setting and after release	checks of the depth and the gauge, and that the tool did not move; the overbalance
$p_{\text{res}}$	the stabilised build-up pressure	the formation pressure at the test depth
$q$	the volume drawn, divided by the piston travel time	mobility
$\Delta p_d$	$p_{\text{res}}$ minus the pressure at the end of the draw	mobility
Stabilisation time	from the moment the piston stops to a constant pressure	a rough sign of the mobility; the class of the measurement

The difference $p_{\text{m}} - p_{\text{res}}$ is the overbalance. On the record it shows as a step between the mud pressure and the formation pressure. Overbalance pushes filtrate into the formation and presses the stationary tool against the wall. Both the supercharging of tight layers (explained below) and the risk of the tool sticking depend on it.

A tool at a test point is under overbalance

While the tool stands still opposite a permeable formation, the mud pressure presses it against the wall. The longer it stays, the higher the risk of differential sticking (the tool gets stuck because of the pressure difference between the mud and the formation). So the time at each test point is limited, and in tight layers the measurement is stopped before the pressure stabilises.
A formation pressure close to the mud pressure is a reason to check not only the packer, but also whether the mud density is high enough. This is a teaching explanation, not an instruction. The order of work is set by approved test programmes and well control procedures, and it is carried out by staff with up-to-date training (Well control: primary barrier and kick indicators).

Mobility from the drawdown

Fluid flows to the probe from all sides, almost as to a point sink (a tiny point that draws fluid in). The area of the surface that the fluid crosses grows as the square of the distance. So the filtration velocity (the flow rate per unit area) and the pressure gradient fall in inverse proportion to the square of the distance. For flow to a hemisphere, the pressure in the rock at a distance $r$ differs from the formation pressure by $\Delta p_d\,r_{pe}/r$ . At ten effective probe radii, only 10% of the drawdown is left. With an effective radius of a few millimetres, this is the first few centimetres of rock. So the drawdown quickly levels off at a constant value. From it we find the drawdown mobility: the ratio of the permeability to the viscosity of the fluid (mobility of a phase).

Drawdown mobility at steady flow to the probe

\left(\frac{k}{\mu}\right)_d = \frac{C\,q}{2\pi\,r_{pe}\,\Delta p_d}

where:

$k$ permeability of the rock at the probe for the fluid that flows in, m²
$\mu$ viscosity of the fluid that flows in, usually the mud filtrate, Pa·s
$q$ volumetric rate of the draw by the piston, m³/s
$\Delta p_d$ steady drawdown: the formation pressure minus the pressure at the end of the draw, Pa
$r_{pe}$ effective radius of the probe: the radius of a spherical sink surface that gives the same flow as the round opening of the probe, m
$C$ flow shape factor: 0.5 for flow to a sphere surrounded by rock on all sides, 1 for flow to a hemisphere at an impermeable plane; for a probe on the wall of a borehole of usual diameter, about 0.67, —

Units: SI (any consistent system)

Holds when

The flow is steady: the piston works for longer than the pressure needs to level off at a constant value (advanced section).
One phase (one fluid) of known viscosity flows, usually the filtrate in the invaded zone.
The rock at the probe is uniform, and the flow follows Darcy's law. In an anisotropic rock (one with different permeabilities in different directions), the result reflects a mix of horizontal and vertical permeability. It usually lies between the spherical and the horizontal permeability.
There is no extra resistance at the opening of the probe from leftover mudcake, damaged rock or fine particles. If there is, the mobility comes out too low.

Twice the rate of draw gives twice the drawdown, and the mobility is the same. The size of the probe and the shape of the flow are combined in one constant, which the service company states for each type of probe. Below are its values for the classic standard probe.

In other unit systems (2)

Oilfield units, classic standard probe

\left(\frac{k}{\mu}\right)_d\,[\text{mD/cP}] = 5660\,\frac{q\,[\text{cm}^3/\text{s}]}{\Delta p_d\,[\text{psi}]}

$k/\mu$ in millidarcies per centipoise, $q$ in cm³/s, $\Delta p_d$ in psi.

5660 combines $C/(2\pi r_{pe})$ of this probe and the conversion of units. Probes of other sizes have their own constants.

Metric units, same probe

\left(\frac{k}{\mu}\right)_d\,[\text{mD/(mPa·s)}] = 39.02\,\frac{q\,[\text{cm}^3/\text{s}]}{\Delta p_d\,[\text{MPa}]}

$k/\mu$ in mD/(mPa·s) (the same as mD/cP), $q$ in cm³/s, $\Delta p_d$ in MPa.

$39.02 = 5660\cdot 0.0068948$ (1 psi = 0.0068948 MPa).

Worked exampleFormation pressure, overbalance and mobility from two pretests

Given (assumed data)

Test depth (vertical): 2503.5 m; water-based mud of density 1.20 g/cm³
Pressure in the borehole before setting and after release: 29.572 and 29.573 MPa
First pretest: 12 cm³ in 8.0 s; at the end of the draw 27.300 MPa; stabilised at 27.6964 MPa
Repeat pretest: 12 cm³ in 4.0 s; at the end of the draw 26.905 MPa; stabilised at 27.6966 MPa
Filtrate viscosity at formation temperature: 0.40 mPa·s; the probe is the classic standard one

Solution

The mud pressure before and after differs by 1 kPa, so the tool did not move and the gauge is stable. A check by hydrostatics (the pressure of a liquid column; 0.101 MPa is atmospheric pressure): $0.101 + 0.00981\cdot 1.20\cdot 2503.5 = 29.572$ MPa.
The stabilised pressures of the two pretests differ by 0.2 kPa, so the measurement is confirmed: $p_{\text{res}} = 27.6964$ MPa. Overbalance: $29.572 - 27.6964 = 1.876$ MPa.
First pretest: $q_1 = 12/8.0 = 1.50$ cm³/s; $\Delta p_{d1} = 27.6964 - 27.300 = 0.3964$ MPa; mobility $39.02\cdot 1.50/0.3964 = 148$ mD/(mPa·s).
Repeat test: $q_2 = 3.00$ cm³/s, $\Delta p_{d2} = 27.6966 - 26.905 = 0.7916$ MPa, mobility 148 mD/(mPa·s). Twice the rate gave twice the drawdown, as it should under Darcy's law.
Permeability to the filtrate: $k \approx 148\cdot 0.40 = 59$ mD. In oilfield units: $\Delta p_{d1} = 57.5$ psi and $5660\cdot 1.50/57.5 = 148$ mD/cP, the same number.

Answer: The formation pressure at 2503.5 m is 27.6964 MPa, the overbalance is 1.876 MPa, and the drawdown mobility is about 148 mD/(mPa·s). The rock at the wall passes the filtrate about as a rock of 59 mD would.

What it means. A high mobility and agreement between the two tests point to a valid measurement. At this mobility the pressure stabilises in seconds, and supercharging is negligible. The permeability of 59 mD refers to a few centimetres of rock flushed by filtrate, with residual oil (the oil that is left behind in the pores). It is not the permeability of the formation to oil. We use it as a relative indicator: to compare layers and to choose a point for a sample. The data in this example are assumed for illustration.

The mobility of the filtrate is not the same as the mobility of the oil in the reservoir. The viscosity of the filtrate of a water-based mud at formation temperature is 0.3–0.6 mPa·s, while that of oil ranges from less than 1 to tens of mPa·s. The permeability of the flushed zone to the filtrate is also reduced by the residual oil. In wells drilled with oil-based mud, a hydrocarbon filtrate flows to the probe, with a viscosity of about 1–2 mPa·s. So we convert the mobility from a pretest into permeability using the viscosity of the filtrate, not that of the formation fluid.

Mobility also sets how long we wait for the pressure to stabilise. As a rough guide: at a mobility above 10 mD/(mPa·s), the pressure recovers in seconds. At 1–10, it takes tens of seconds to minutes. At 0.1–1, it takes minutes to tens of minutes, and noticeable supercharging is already possible in such layers. At a mobility below about 0.1 mD/(mPa·s), the measurement often does not manage to stabilise in the permitted time. These limits are only approximate. They depend on the tool, the volume drawn and the mud.

Quality of the measurements: classes of pretests

Before we draw lines and calculate gradients, we assign each pretest to one of four classes. We use the shape of the record, the mobility, the repeat tests and the position of the point among its neighbours. Companies name the classes differently, but the idea is the same.

SchematicTypical records of pretests of the four classes (schematic): the dashed lines are the mud pressure and the true formation pressure.

Classes of pretests

Class: Valid
Signs: a clear drawdown and stabilisation; the repeat test agrees; the mud pressure before and after is the same
Cause: enough mobility, and the packer seals
What we do: use it in the interpretation

Class: Tight formation
Signs: a large drawdown and a slow rise; the pressure is still rising when the time at the test point runs out. A “dry” test: almost no inflow
Cause: very low mobility
What we do: the last pressure is a lower limit; do not use it for the gradient

Class: Supercharging
Signs: the pressure has stabilised, but the point is to the right of the line of the neighbouring valid points; the mobility is low; repeat tests may disagree
Cause: filtrate passing through the cake raises the pressure at the wall faster than the formation can carry it away
What we do: do not use it for the gradient; if needed, estimate a correction

Class: Lost seal
Signs: the pressure in the line equals the mud pressure or follows it
Cause: the packer did not seal off the wall: a cavity, an uneven wall, a weak cake
What we do: reject it; set the tool again nearby

Class	Signs	Cause	What we do
Valid	a clear drawdown and stabilisation; the repeat test agrees; the mud pressure before and after is the same	enough mobility, and the packer seals	use it in the interpretation
Tight formation	a large drawdown and a slow rise; the pressure is still rising when the time at the test point runs out. A “dry” test: almost no inflow	very low mobility	the last pressure is a lower limit; do not use it for the gradient
Supercharging	the pressure has stabilised, but the point is to the right of the line of the neighbouring valid points; the mobility is low; repeat tests may disagree	filtrate passing through the cake raises the pressure at the wall faster than the formation can carry it away	do not use it for the gradient; if needed, estimate a correction
Lost seal	the pressure in the line equals the mud pressure or follows it	the packer did not seal off the wall: a cavity, an uneven wall, a weak cake	reject it; set the tool again nearby

Other faults happen too. The probe or its filter may be blocked: when the piston moves, the pressure falls sharply and hardly recovers, and the record looks like a “dry” test. There may be gas in the line, which distorts the build-up. The tool may also move during the test.

Supercharging needs separate treatment: of the four classes, only this one looks like a good measurement. While the well is open, overbalance pushes mud filtrate through the cake into the formation (Borehole environment: invaded zone and mudcake). In a permeable layer, the filtrate spreads easily, and the pressure at the wall is almost the same as the formation pressure. In a tight layer, the rock cannot carry the filtrate away fast enough, and an excess pressure stays at the wall. The excess is greater when the permeability is lower and when the cake holds the mud back less well. The probe measures the pressure exactly at the wall. So it shows the formation pressure plus this excess. The signs are a low mobility and a point shifted to the right of the line of valid measurements. The topic Supercharging and permeability from formation-tester pretests explains how to estimate supercharging in numbers and how to allow for it.

Accuracy of pressure and depth

The error of a point on the pressure–depth plot is made up of the gauge error and the error of the depth to which the measurement is tied. We describe a gauge by these characteristics:

Resolution: The smallest pressure change that the gauge can tell apart. For quartz gauges it is thousandths and hundredths of a psi, that is, from thousandths to hundredths of a kilopascal.
Accuracy: How far the reading is from the true absolute pressure. For quartz gauges it is about 0.01–0.02% of the upper limit: about ±7–15 kPa at a limit of 70 MPa (10,000 psi). For strain gauges it is several times worse.
Repeatability and drift: How closely the gauge gives the same reading for the same pressure at different times. Drift is a slow change of the readings with time. Repeatability and drift are what matter for a gradient in one well: a constant error in the readings shifts the line but does not tilt it.
Temperature sensitivity: The readings of a quartz sensor depend on temperature. After the tool stops, it needs time to settle at the temperature around it (thermal equilibrium). Otherwise the pressure “drifts”. Modern sensors measure the temperature in the same crystal and correct for it.

Depth often adds more error than the gauge. The depth of the tool is matched to the open-hole logs using its gamma ray record (Gamma ray log and natural gamma ray spectrometry). The measurement must refer to the same depth as the curves from which the layer was chosen. Then the depth along the hole is converted to true vertical depth using the directional survey (the measured inclination and direction of the hole, Directional survey calculations). Gradients and contacts are calculated only from vertical depths. For a gradient inside one formation, the relative depths of the points matter: a constant shift of all the depths does not tilt the line. To compare wells, to place contacts and to convert pressures to the datum depth, we need absolute depths. The datum depth is the reference depth to which pressures are converted so that they can be compared. An absolute depth must be right in itself, not only in its spacing from the other points. In deviated wells, survey errors can make these depths wrong by metres.

Random error of a point on the pressure–depth plot

\sigma_p^2 = \sigma_{\text{gauge}}^2 + (G\,\sigma_z)^2

where:

$\sigma_p$ random error of the formation pressure, tied to its depth, Pa
$\sigma_{\text{gauge}}$ repeatability of the gauge at a test point (together with thermal effects), Pa
$G$ pressure gradient of the fluid in the formation, Pa/m
$\sigma_z$ random error of the true vertical depth, m

Units: SI (in practice kPa, kPa/m and m)

Holds when

The errors of pressure and depth are random and independent.
Systematic errors (errors that always push the same way, unlike random ones) are not included: a common shift of the depths, or a constant error of the gauge. They shift the line but do not change its slope. An error that grows with depth (cable stretch, survey error) changes the slope too.

The depth error enters multiplied by the gradient. In water it weighs one and a half times as much as in oil, and about five times as much as in gas. An error of 0.3 m of vertical depth in oil is about 2 kPa, which is tens to hundreds of times the resolution of a quartz gauge.

The pressure–depth plot from a set of pretests

The result of a survey (the whole series of pretests in a well) is a table of pretests by depth. We process it in order. First we classify each measurement. Then we draw lines through the valid points. Only after that do we draw conclusions about fluids and contacts. We draw a line through many points by the least-squares method:

Pressure gradient from the points by the least-squares method

G = \frac{\sum_i (z_i - \bar z)\,p_i}{\sum_i (z_i - \bar z)^2},\qquad s_G = \frac{s}{\sqrt{\sum_i (z_i - \bar z)^2}}

where:

$G$ pressure gradient: the slope of the line, Pa/m
$z_i,\ p_i$ true vertical depth and formation pressure of the $i$ -th valid measurement, m, Pa
$\bar z$ mean depth of the valid points, m
$s$ root-mean-square deviation of the points from the line, $\sqrt{\sum e_i^2/(n - 2)}$ , where $e_i$ is the deviation of a point from the line and $n$ is the number of points (two parameters of the line have already been fitted), Pa
$s_G$ standard error of the gradient, Pa/m

Units: any consistent system (in practice MPa and m; the gradient in kPa/m)

Holds when

All the points belong to one continuous phase (for example, one column of oil) in hydrostatic equilibrium: the fluid is at rest, so the pressure changes only with depth. They also belong to one hydraulically connected system, in which fluid can flow between all the parts.
The errors of the points are random and of equal size. Points that we know are shifted in one direction, such as a supercharged point or an unfinished build-up, have been excluded beforehand.
The density of the fluid in the interval is constant. For tall gas columns this is not so (pressure in a gas column).

The line passes through the point of mean depth and mean pressure. The error of the slope is smaller when the scatter of the points is smaller and the depth interval is wider: the extreme points weigh more than the middle ones. The fluid density is $\rho = G/g$ , and its standard error is $s_G/g$ (about the standard error).

Pretests of a new well in the oil rim (the thin oil layer between the gas and the water) of the accumulation from the topic on reservoir pressure

Depth, m: 2470.5
Mud, MPa: 29.184
Final pressure, MPa: 27.4635
Mobility, mD/(mPa·s): 85
Record: stabilised

Depth, m: 2476.0
Mud, MPa: 29.248
Final pressure, MPa: 27.4307
Mobility, mD/(mPa·s): < 0.1
Record: pressure still rising

Depth, m: 2481.5
Mud, MPa: 29.313
Final pressure, MPa: 27.5397
Mobility, mD/(mPa·s): 240
Record: stabilised

Depth, m: 2487.0
Mud, MPa: 29.378
Final pressure, MPa: 27.5807
Mobility, mD/(mPa·s): 36
Record: stabilised

Depth, m: 2492.5
Mud, MPa: 29.443
Final pressure, MPa: 27.6179
Mobility, mD/(mPa·s): 120
Record: stabilised

Depth, m: 2498.0
Mud, MPa: 29.507
Final pressure, MPa: 29.504
Mobility, mD/(mPa·s): —
Record: equals mud pressure

Depth, m: 2503.5
Mud, MPa: 29.572
Final pressure, MPa: 27.6964
Mobility, mD/(mPa·s): 148
Record: stabilised

Depth, m: 2509.0
Mud, MPa: 29.637
Final pressure, MPa: 27.7338
Mobility, mD/(mPa·s): 15
Record: stabilised

Depth, m: 2514.5
Mud, MPa: 29.702
Final pressure, MPa: 27.7746
Mobility, mD/(mPa·s): 64
Record: stabilised

Depth, m: 2520.0
Mud, MPa: 29.766
Final pressure, MPa: 27.8141
Mobility, mD/(mPa·s): 2.1
Record: stabilised

Depth, m: 2526.5
Mud, MPa: 29.843
Final pressure, MPa: 27.9046
Mobility, mD/(mPa·s): 0.35
Record: stabilised

Depth, m: 2531.0
Mud, MPa: 29.896
Final pressure, MPa: 27.8897
Mobility, mD/(mPa·s): 9.5
Record: stabilised

Depth, m	Mud, MPa	Final pressure, MPa	Mobility, mD/(mPa·s)	Record
2470.5	29.184	27.4635	85	stabilised
2476.0	29.248	27.4307	< 0.1	pressure still rising
2481.5	29.313	27.5397	240	stabilised
2487.0	29.378	27.5807	36	stabilised
2492.5	29.443	27.6179	120	stabilised
2498.0	29.507	29.504	—	equals mud pressure
2503.5	29.572	27.6964	148	stabilised
2509.0	29.637	27.7338	15	stabilised
2514.5	29.702	27.7746	64	stabilised
2520.0	29.766	27.8141	2.1	stabilised
2526.5	29.843	27.9046	0.35	stabilised
2531.0	29.896	27.8897	9.5	stabilised

The pressures are absolute (measured from zero pressure, not from the atmosphere), and the depths are vertical. “Mud” is the pressure in the borehole before the tool is set. The mud is water-based, with a density of 1.20 g/cm³. The data are assumed for illustration.

Worked exampleOil gradient and oil density in the formation from a set of pretests

Given (assumed data)

Pretests: the table above: 12 points from 2470.5 to 2531.0 m
Rule of thumb for supercharging: a mobility below about 1 mD/(mPa·s) and a point to the right of the line of valid measurements
Acceleration of gravity: 9.81 m/s²

Solution

Classification. At 2498.0 m the final pressure differs from the mud pressure by only 3 kPa: a lost seal. At 2476.0 m the pressure was still rising when the time at the test point ran out: a tight formation, and the measurement is only a lower limit. At 2526.5 m the pressure stabilised, but the mobility is 0.35 mD/(mPa·s): a candidate for supercharging. The other 9 points are valid.
Least squares through the 9 points: the mean depth is $\bar z = 2501.1$ m, the mean pressure is 27.6789 MPa, $\sum (z_i - \bar z)^2 = 3092$ m²; the gradient is $G = 7.065$ kPa/m.
The deviations of the points from the line are from −1.26 to +1.33 kPa; $s = 1.02$ kPa, $s_G = 1.02/\sqrt{3092} = 0.018$ kPa/m.
Oil density in the formation: $\rho = G/g = 7.065/9.81 = 0.720$ g/cm³, with a standard error of 0.002 g/cm³.
Checking the suspect points. At 2526.5 m the line gives 27.8587 MPa. The measurement is higher by 46 kPa, which is 45 times the scatter $s$ : this is supercharging. The point at 2476.0 m is below the line by 71 kPa: the build-up was not finished.
If the supercharged point is left in the interpretation by mistake, the gradient becomes 7.35 kPa/m (density 0.749 g/cm³). With the unfinished measurement as well, it becomes 7.74 kPa/m (0.789 g/cm³).
Checking the depths against the mud: the pressure in the borehole rises from 29.184 to 29.896 MPa over 60.5 m, that is, by 11.77 kPa/m. This is a density of 1.20 g/cm³, as the mud has. The overbalance at the valid points is from 1.72 to 2.01 MPa.

Answer: The oil gradient is 7.065 ± 0.018 kPa/m, and the oil density in the formation is 0.720 ± 0.002 g/cm³. Of the 12 pretests, 9 were used in the interpretation.

What it means. The gradient agrees with the oil line found for this accumulation in the topic Reservoir pressure and temperature (7.07 kPa/m). The new well has penetrated the same hydrodynamic system (the same connected set of layers), and a line through nine points is more reliable than a line through two. A scatter of about 1 kPa is tens to hundreds of times larger than the resolution of a quartz gauge. It comes from the depths (0.15 m of vertical depth in oil already gives 1 kPa) and from small effects at each test point. The two “bad” points, if left in, would overstate the density by 10%. The oil would be taken for noticeably heavier, and the contact drawn from such a line would shift. The data in this example are assumed for illustration.

CalculatedPretests from the example. Left: pressure against depth, with the points of formation pressure, the line through the valid points and the pressure of the mud column. The lost-seal point lies on the mud line. Right: deviations from the line in kilopascals. The valid points are within ±1.5 kPa, while the supercharged point and the point with the unfinished build-up lie far to the side.

What the pressure measurements are for

What we get from a survey with the formation tester

Task: Initial formation pressure of each formation
What we take from the measurements: the pressure of the valid points, converted to the datum depth
More detail: Reservoir pressure and temperature, General material balance equation for oil reservoirs

Task: Type and density of the fluid in the formation
What we take from the measurements: gradients from the valid points
More detail: this lesson

Task: Contacts and the free water level (the level where the oil pressure and the water pressure are equal)
What we take from the measurements: intersections of the lines of different fluids
More detail: basics, Pressure gradients, fluid contacts and capillary equilibrium

Task: Pressure regime and well design
What we take from the measurements: the pressure against the normal hydrostatic pressure; overbalance
More detail: Abnormal formation pressures: origin, prediction and recognition, Casing design

Task: Connection between formations, and barriers
What we take from the measurements: common or separate lines; pressure steps
More detail: Pressure measurements in producing reservoirs: barriers and accuracy

Task: Choice of intervals for samples and perforation (shooting holes through the casing)
What we take from the measurements: mobility from the pretests
More detail: Reservoir fluid sampling

Task	What we take from the measurements	More detail
Initial formation pressure of each formation	the pressure of the valid points, converted to the datum depth	Reservoir pressure and temperature, General material balance equation for oil reservoirs
Type and density of the fluid in the formation	gradients from the valid points	this lesson
Contacts and the free water level (the level where the oil pressure and the water pressure are equal)	intersections of the lines of different fluids	basics, Pressure gradients, fluid contacts and capillary equilibrium
Pressure regime and well design	the pressure against the normal hydrostatic pressure; overbalance	Abnormal formation pressures: origin, prediction and recognition, Casing design
Connection between formations, and barriers	common or separate lines; pressure steps	Pressure measurements in producing reservoirs: barriers and accuracy
Choice of intervals for samples and perforation (shooting holes through the casing)	mobility from the pretests	Reservoir fluid sampling

In an accumulation that is not yet in production, the layers of one hydrodynamic system (a connected set of layers) fall on common pressure lines. If formations are separated by thin impermeable layers or by faults, their points may lie on different lines, shifted from each other. This is a sign of different systems. They have to be developed, and accounted for in the material balance, separately. In wells drilled when production has already started, the profile shows which layers are depleted and which are supported by injection (water or gas pumped into the formation): topic Pressure measurements in producing reservoirs: barriers and accuracy.

The basics of finding contacts from the intersection of pressure lines are in the topic on reservoir pressure. Capillary equilibrium, the transition zone and the pitfalls of interpretation are in the topic Pressure gradients, fluid contacts and capillary equilibrium. The drill stem test (DST) complements the formation tester: it tests the formation farther from the well and brings the inflow to the surface through the drill pipe (Well testing: purposes and types of test).

Terms and symbols

Wireline formation tester (WFT): A tool on a logging cable for measuring formation pressure, estimating mobility and taking samples in an open hole. The method is also called hydrodynamic logging in Russian-language practice.
Pretest: Drawing a few cubic centimetres of fluid with the piston of the tool, with a record of the drawdown and the pressure build-up.
$p_{\text{m}}$ and $p_{\text{res}}$: The pressure of the mud column in the borehole, and the formation pressure at the test depth (the stabilised build-up pressure).
Drawdown mobility $(k/\mu)_d$: The ratio of permeability to viscosity from the steady drawdown of a pretest. It characterises the filtrate in a few centimetres of rock at the probe.
Valid measurement: A stabilised measurement, confirmed by a repeat test, with no signs of supercharging or lost seal.
Supercharging: An excess of the pressure at the wall over the formation pressure, caused by mud filtrate. It shows in tight layers.
Tool storage $S$: The volume of liquid in the flowline and the pretest chamber, multiplied by its compressibility. It sets the stabilisation time.

Common mistakes and misconceptions

Wrong

“The last pressure on the record is the formation pressure.”

In fact

Only if the pressure has stabilised. If it is still rising, the last value is a lower limit. In a tight layer, it may fall tens of kilopascals short of the formation pressure.

Wrong

“A point to the right of the line means a layer with a different, abnormal pressure.”

In fact

First check the mobility and the repeat tests. In a tight layer this is most often supercharging. A separate pressure system is confirmed by several valid points on their own line.

Wrong

“The mobility from a pretest is the permeability of the formation to oil divided by the viscosity of the oil.”

In fact

It is the mobility of the filtrate in a few centimetres of flushed rock at the probe. To get permeability we use the viscosity of the filtrate, and we use the result as a relative indicator.

Wrong

“The gauge shows changes of hundredths of a kilopascal, so the gradient is just as accurate.”

In fact

The scatter of the points is set by the depths and by the conditions at each test point: 0.1 m of vertical depth in oil is already 0.7 kPa. The accuracy of the gradient is set by the number of valid points, their scatter and the depth interval.

In depth: advanced detail

Tool storage and the stabilisation time

Between the probe and the gauge are the flowline and the pretest chamber, filled with a compressible liquid (its volume shrinks a little when the pressure rises). For the pressure in them to rise by 1 MPa, a volume $S$ must come in from the formation. This is the tool storage: the volume of the liquid multiplied by its compressibility. For hundreds of cubic centimetres of liquid, it is tenths of a cubic centimetre per megapascal. The flow to the probe is proportional to the difference between the formation pressure and the pressure at the probe. This gives the same equation as for wellbore storage (the effect of the fluid stored in the wellbore) in well testing, but with a volume of hundreds of cubic centimetres:

Pressure at the probe with tool storage

S\,\frac{\dd p}{\dd t} = -q_{\text{pist}} + \frac{k/\mu}{K}\,(p_{\text{res}} - p),\qquad \tau = \frac{S\,K}{k/\mu}

where:

$S$ tool storage: the volume of liquid in the line and the chamber multiplied by its compressibility, cm³/MPa
$p$ pressure at the gauge, MPa
$q_{\text{pist}}$ rate of the draw by the piston; zero during the build-up, cm³/s
$K$ probe constant from the mobility formula (39.02 for the classic standard probe), mD·MPa·s/(mPa·s·cm³)
$k/\mu$ mobility, mD/(mPa·s)
$\tau$ time constant: it sets how fast the pressure approaches its steady value, s

Units: cm³, MPa, s; mobility in mD/(mPa·s)

Holds when

The flow to the probe is quasi-steady: in the rock at the probe the pressure adjusts much faster than in the tool.
Tool storage is constant. The transient spherical flow in the formation (flow that has not yet become steady) is not included. It gives a slow “tail” to the build-up: the pressure gains the last few kilopascals not exponentially but noticeably more slowly. So the stabilisation time from this estimate is a lower limit. With a strict criterion (tenths of a kilopascal), the real time is several times longer.

The pressure approaches its steady value exponentially: the remaining gap shrinks by the same factor in each equal step of time. The time constant $\tau$ is inversely proportional to the mobility. The time for the gap to shrink from the drawdown $\Delta p_d$ to the resolution $\delta p$ is about $\tau\ln(\Delta p_d/\delta p)$ . At the same rate of draw, in a tight layer both $\tau$ and the drawdown are larger. So the stabilisation time grows even faster than the mobility falls.

Worked exampleHow long to wait for stabilisation

Given (assumed data)

Pretest at 2520.0 m: mobility 2.1 mD/(mPa·s); a draw of 5 cm³ at a rate of 0.2 cm³/s
Tool storage: $S = 0.25$ cm³/MPa (assumed)
Stabilisation is taken as reached: when 0.1 kPa remains to the formation pressure

Solution

Time constant: $\tau = 0.25\cdot 39.02/2.1 = 4.65$ s. The piston works for $5/0.2 = 25$ s, which is more than five $\tau$ , so the drawdown has time to become steady.
Steady drawdown: $39.02\cdot 0.2/2.1 = 3.72$ MPa. By the end of the draw 99% of it is reached, $\Delta p_d = 3.690$ MPa, and the mobility from this drawdown is overstated by only 0.7%.
Build-up time to 0.1 kPa: $4.65\cdot\ln(3.690/0.0001) = 49$ s.
A layer with a mobility of 0.1 mD/(mPa·s) at the same tool storage: $\tau = 98$ s. Even if we reduce the rate of the draw to 0.0095 cm³/s so that the drawdown stays the same, a draw of 5 cm³ takes 9 min, and the stabilisation takes another 17 min.

Answer: By the storage model, the pressure comes to within 0.1 kPa of the formation pressure about 49 s after the piston stops. In a layer with a mobility twenty times lower, it takes 17 min. These are lower limits.

What it means. The estimate allows only for the tool storage. The transient spherical flow in the formation adds a slow “tail” to the build-up, and the pressure takes several times longer to gain the last tenths of a kilopascal. In a layer with a mobility of about 2 mD/(mPa·s), this is minutes, not tens of seconds. The time at a test point is limited by the risk of sticking and by the cost of the work. So in tight layers we reduce the volume and the rate of the draw. If this does not help, we accept a measurement that has not stabilised and mark it as a “tight formation”. The tool storage in the example is assumed. Tool designers reduce it by making the volume of the line between the probe and the gauge smaller. The data in this example are assumed for illustration.

What permeability the probe sees

The drawdown mobility is measured correctly, but it is not what we usually want to know. Four things affect the result. Anisotropy. The fluid flows to the probe both along the layers and across them. So in a layered rock the mobility reflects a mix of horizontal and vertical permeability. It usually lies between the spherical permeability $(k_h^2 k_v)^{1/3}$ and the horizontal permeability. Flushed zone. The filtrate flows through rock that still holds residual oil, so the permeability is an effective one (for one fluid, with another present), not the absolute one (that of the rock alone). Resistance at the opening. Leftover mudcake, fine particles and damaged rock at the probe add a pressure drop and make the mobility too low. This is like the skin of a well (the extra pressure drop in the damaged zone around it, Skin factor). Small volume. A few centimetres of rock at the wall do not represent a formation whose properties vary from place to place.

So we use the mobility from pretests to compare the permeability of one layer with another through the section (a relative profile), and as a sign of the quality of the pressure measurement. The topic Supercharging and permeability from formation-tester pretests covers the numerical estimates of permeability. They come from the pressure build-up after a pretest, from multi-probe tools with an observation probe at some vertical distance, and from dual-packer tests of an interval.

Connections to other topics

Reservoir pressure and temperature — fluid gradients, normal and abnormal pressure, contacts from two points per zone.
Reservoir fluid sampling — how the same tool takes samples of formation fluids and how contamination is monitored.
Borehole environment: invaded zone and mudcake — the invaded zone and the mudcake, where supercharging comes from.
Well testing: purposes and types of test — the drill stem test and other tests that complement the formation tester.
Flow regimes — spherical flow among other flow geometries.
Wellbore storage — the same storage mechanism as in the tool, but at the scale of the well.
Supercharging and permeability from formation-tester pretests — how to estimate supercharging and permeability from the build-up after a pretest.
Pressure gradients, fluid contacts and capillary equilibrium — contacts, the free water level and capillary equilibrium from gradients.
Pressure measurements in producing reservoirs: barriers and accuracy — pressure profiles in producing formations: depletion, barriers, accuracy.

Check yourself

1
A pretest with the classic standard probe: 8 cm³ drawn in 5.0 s, a steady drawdown of 0.52 MPa, a filtrate viscosity of 0.50 mPa·s. Find the drawdown mobility and the permeability to the filtrate.
Show the answer
$q = 8/5.0 = 1.6$ cm³/s; $(k/\mu)_d = 39.02\cdot 1.6/0.52 \approx 120$ mD/(mPa·s); $k \approx 120\cdot 0.50 = 60$ mD. This is the permeability of the rock flushed by filtrate, a few centimetres from the wall. It is not the permeability of the formation to oil.
2
After the piston stroke the pressure in the line rose to 31.25 MPa and does not change. The mud pressure before setting was 31.25 MPa, and the neighbouring valid points are at about 28.9 MPa. Which class does the measurement belong to?
1. A.Lost packer seal
2. B.Valid
3. C.Tight formation
4. D.Supercharging
Show the answer
Correct answer: A. Lost packer seal
The pressure in the line equals the mud pressure and is 2.3 MPa higher than at the neighbouring points. The packer did not seal off the patch of wall, and the tool measured the pressure in the borehole. The measurement is rejected, and the tool is set again nearby. With supercharging the excess is tens of kilopascals, not megapascals, and the pressure does not equal the mud pressure.
3
A stabilised point lies 25 kPa to the right of the line of the neighbouring valid measurements. Its mobility is 0.4 mD/(mPa·s), and for the neighbours it is 20–200. What is the most likely explanation?
1. A.A separate formation with abnormally high pressure
2. B.A gauge error: the tool must be recalibrated
3. C.A lost packer seal
4. D.Supercharging of a tight layer: the point is excluded from the gradient
Show the answer
Correct answer: D. Supercharging of a tight layer: the point is excluded from the gradient
A low mobility and a shift to the right on a stabilised record are typical signs of supercharging: filtrate raises the pressure at the wall of a tight layer. A separate pressure system would be confirmed by several valid points with normal mobility on their own line. With a lost seal, the pressure would equal the mud pressure.
4
In a deviated well with a zenith angle of 35°, two valid measurements in a water-bearing formation are 40 m apart along the hole and differ by 0.346 MPa. Find the gradient and the density of the water. What do we get if we use the distance along the hole by mistake?
Show the answer
Vertically the distance is $40\cdot\cos 35^\circ = 32.77$ m. The gradient is $0.346/32.77 = 10.56$ kPa/m, and the density is $10.56/9.81 = 1.08$ g/cm³: saline water. Along the hole we would get $0.346/40 = 8.65$ kPa/m and 0.88 g/cm³. The water would “turn into” oil.
5
What affects the gradient in a water-bearing formation (about 10.4 kPa/m) more: a random error of the vertical depth of 0.3 m, or the resolution of a quartz gauge of 0.01 kPa?
Show the answer
The depth error gives $0.3\cdot 10.4 \approx 3$ kPa per point, which is hundreds of times the resolution of the gauge. So the accuracy of the gradient is set by how well the depths are matched to the logs and by the directional survey. It also depends on the number of points and the interval between the extreme ones.
6
The rate of the draw is the same, and the mobility of the layer is 10 times lower. How does the stabilisation time of the pressure after the pretest change?
1. A.It does not change
2. B.It grows 10 times
3. C.It falls 10 times
4. D.It grows more than 10 times
Show the answer
Correct answer: D. It grows more than 10 times
The time constant $\tau = SK/(k/\mu)$ grows 10 times, and the drawdown at the same rate also grows 10 times. So the time $\tau\ln(\Delta p_d/\delta p)$ grows by more than 10 times: the growth of the logarithm adds to the growth of $\tau$ .

Updated: 15 October 2026