Sand control methods

Quick refresher

A barrier does not have to be smaller than all the grains. Grains larger than about half the width of a slot settle into arches at it, and the fine particles must pass, or the screen will plug.
In sand control the sizes of sand are counted from the large grains: $D_{10}$ is the size above which lie 10% of the mass. The uniformity coefficient is $C = D_{40}/D_{90}$ . Up to 3 is a well-sorted sand, and more than 5 is a poorly sorted one.
The median size of the gravel is taken 5–6 times the median size of the reservoir sand. The pores of a dense pack of gravel let through only grains smaller than 0.155 of its size.
The slot of a screen in a gravel pack is made smaller than the smallest gravel grain, about 0.6–0.8 of its size. For 20/40 gravel (grains between the openings of sieves No. 20 and No. 40, that is, 0.84 and 0.42 mm) it is about 0.30 mm.
A pack in a cased hole is reliable, but the tunnels filled with gravel take away productivity. In an open hole the pack hardly hinders the inflow. In permeable reservoirs a frac-pack gives the best inflow.
We monitor the protection with sand sensors, pressures and well tests. A sudden production of sand means a damaged screen or a void in the pack, and a slow fall of productivity means plugging.

Key relationships

C = \dfrac{D_{40}}{D_{90}}

uniformity coefficient; $D_p$ is the size above which lie $p$ % of the mass

D_{50,g} = (5\text{–}6)\,D_{50,\text{s}}

choosing the gravel by the median sizes

d_{\max} = \left(\tfrac{2}{\sqrt3} - 1\right)D \approx 0.155\,D

the largest grain that passes through a pore of a dense packing of spheres of diameter $D$

M = \rho_g(1 - \phi_g)\,V

mass of gravel for a pack of volume $V$

Common pitfalls

Mixing up the counting of the percentiles. In soil mechanics $D_{10}$ is the fine part (10% is finer), and in sand control it is the coarse part (10% is coarser).
Choosing a screen “finer, to be safe”. It will hold back the fine particles as well, plug, and take away productivity.
Taking a gravel coarser than the recommended one, for the sake of permeability. The sand of the reservoir will enter the pores of the gravel, and the mixture will be less permeable than the sand itself.
Counting the pack as finished without comparing the mass of gravel placed with the calculated one. Voids in the pack are a path for sand and a cause of erosion of the screen.
Choosing the gravel from a sample of produced sand. The produced sand is enriched in fine grains. The basis of the choice is the core of the productive layers.

After this lesson you can

explain how sand is held back by arches at the slot of a screen and by the pores of a gravel pack, and why fine particles must pass
work out the sieve analysis of a sand (a test in which the sand is shaken through sieves with ever smaller openings): find the sizes $D_{10}$ , $D_{40}$ , $D_{50}$ , $D_{90}$ , the uniformity coefficient and the share of fines, and assess the sorting (how uniform the grain sizes are)
choose the gravel from the ratio of the median sizes of gravel and sand, and the width of the screen slot to suit the gravel
compare screens, gravel packs in open and cased holes, frac-pack and chemical consolidation, and choose a method for the given conditions
calculate the volume of gravel for a pack, estimate how complete the placement was, and name the signs of failure of the protection during production

How sand is held back

There are two ways to stop sand: to put a barrier in its path, or to bind the grains near the well. The barrier is a sand screen, sometimes together with a layer of gravel. Any barrier adds resistance to inflow. So the aim is to stop the load-carrying grains, which the flow would otherwise carry away, and to let the fine particles of clay and dust pass. They do not carry load, and if they are held back, the screen will plug (sand and fines).

The slot of a screen can be wider than many of the grains. When several grains come up to the slot at the same time, they lean against each other and against the edges of the slot, and settle into an arch. Fluid passes through the arch, but grains do not. As early as the 1930s, experiments showed that a uniform sand forms stable arches over a slot up to two grain diameters wide. The arches hold while the flow is constant, but they rearrange at starts and stops. So a screen on its own is reliable only with a well-sorted sand.

A gravel pack works differently: a layer of sorted gravel between the screen and the reservoir becomes a filter itself. The pores between the gravel grains are smaller than the sand grains, so the sand stops at the boundary with the gravel and does not mix with it. The screen holds the gravel, because its slots are smaller than the gravel grains. The size of the pores in a dense packing is easy to estimate by geometry:

The largest grain that passes through a pore of a packing of equal spheres

d_{\max} = \left(\frac{2}{\sqrt3} - 1\right)D \approx 0.155\,D\quad\text{(dense packing)},\qquad d_{\max} = \left(\sqrt2 - 1\right)D \approx 0.414\,D\quad\text{(cubic)}

where:

$d_{\max}$ diameter of the largest sphere that passes through a pore between neighbouring grains, mm
$D$ diameter of the gravel grains, mm

Units: any units of length

Holds when

The spheres are equal. In a dense packing three touching grains form a triangular constriction, and in a cubic packing a square one of four.
Real gravel is a mixture of grains between two sieves, and it is not perfectly round. The estimate shows the order of magnitude and not an exact limit.

A circle inscribed between three touching circles of diameter $D$ has the diameter $(2/\sqrt3 - 1)D$ : its centre is at a distance of $D/\sqrt3$ from the centres of the circles. In a dense packing the pores are almost three times smaller than in a loose cubic one. So the gravel must lie densely. In a loose packing the same gravel would let through grains 2.7 times larger.

SchematicThe main mechanical methods of protection (schematic, not to scale): a screen in an open hole, a gravel pack in an open hole and in a cased hole, and a frac-pack.

Methods of sand control

Method: Screen without gravel
What holds the sand back: arches of grains at the slots or meshes of the screen
Where it is most often used: a clean, well-sorted sand; long horizontal wellbores

Method: Gravel pack in an open hole
What holds the sand back: the pores of the gravel
Where it is most often used: a heterogeneous sand with fines; high productivity

Method: Gravel pack in a cased hole
What holds the sand back: the pores of the gravel in the ring and in the perforation tunnels
Where it is most often used: several layers that must be isolated from each other

Method: Frac-pack
What holds the sand back: the gravel in the ring and a fracture filled with proppant
Where it is most often used: permeable weak reservoirs, damage, layered sandstones

Method: Chemical consolidation
What holds the sand back: resin that has bound the grains of the reservoir
Where it is most often used: short intervals of clean sand, when no equipment may be left in the wellbore

Method	What holds the sand back	Where it is most often used
Screen without gravel	arches of grains at the slots or meshes of the screen	a clean, well-sorted sand; long horizontal wellbores
Gravel pack in an open hole	the pores of the gravel	a heterogeneous sand with fines; high productivity
Gravel pack in a cased hole	the pores of the gravel in the ring and in the perforation tunnels	several layers that must be isolated from each other
Frac-pack	the gravel in the ring and a fracture filled with proppant	permeable weak reservoirs, damage, layered sandstones
Chemical consolidation	resin that has bound the grains of the reservoir	short intervals of clean sand, when no equipment may be left in the wellbore

The alternative to protection is managing sand production with no mechanical barrier (lesson on sand production).

Sieve analysis and the description of a sand

We choose the protection by the sizes of the grains of the reservoir. A sample is taken from the core of the productive layers and separated into single grains without crushing them. It is then shaken through a set of sieves with smaller and smaller openings. This is a sieve analysis. We weigh what stays on each sieve and build the cumulative curve: what share of the mass is coarser than a given size. The size of a sieve is given by a number, the count of wires per inch: the larger the number, the finer the mesh. Laser particle analysis is used more and more. Its results differ from the sieve ones, so we apply the selection criteria to the kind of data from which they were obtained.

Uniformity coefficient of a sand

C = \frac{D_{40}}{D_{90}}

where:

$C$ uniformity coefficient, —
$D_{40},\ D_{90}$ sizes above which lie 40% and 90% of the mass of the sand, mm

Units: dimensionless

Holds when

The sizes are found from the cumulative curve by interpolation between the sieves in the logarithms of the size.
The sample represents the productive interval. If there are several samples, we choose the protection by the finest of the productive layers.

The closer $C$ is to one, the more uniform the sand. A sand is usually taken as well sorted at $C$ up to 3, moderately sorted from 3 to 5, and poorly sorted above 5. We also look at the ratio $D_{10}/D_{95}$ and at the share of particles finer than 44 µm (those that passed sieve No. 325). The more fines and the wider the distribution, the worse a screen without gravel works.

Sieve analysis of a sandstone sample (100 g, assumed data)

Sieve No.: 30
Mesh opening, mm: 0.595
Retained on the sieve, g: 0.3
Cumulative coarser, %: 0.3

Sieve No.: 40
Mesh opening, mm: 0.420
Retained on the sieve, g: 1.5
Cumulative coarser, %: 1.8

Sieve No.: 50
Mesh opening, mm: 0.297
Retained on the sieve, g: 4.2
Cumulative coarser, %: 6.0

Sieve No.: 60
Mesh opening, mm: 0.250
Retained on the sieve, g: 5.0
Cumulative coarser, %: 11.0

Sieve No.: 70
Mesh opening, mm: 0.210
Retained on the sieve, g: 7.0
Cumulative coarser, %: 18.0

Sieve No.: 80
Mesh opening, mm: 0.177
Retained on the sieve, g: 10.0
Cumulative coarser, %: 28.0

Sieve No.: 100
Mesh opening, mm: 0.149
Retained on the sieve, g: 13.0
Cumulative coarser, %: 41.0

Sieve No.: 120
Mesh opening, mm: 0.125
Retained on the sieve, g: 14.0
Cumulative coarser, %: 55.0

Sieve No.: 140
Mesh opening, mm: 0.105
Retained on the sieve, g: 13.0
Cumulative coarser, %: 68.0

Sieve No.: 170
Mesh opening, mm: 0.088
Retained on the sieve, g: 10.0
Cumulative coarser, %: 78.0

Sieve No.: 200
Mesh opening, mm: 0.074
Retained on the sieve, g: 8.0
Cumulative coarser, %: 86.0

Sieve No.: 270
Mesh opening, mm: 0.053
Retained on the sieve, g: 7.0
Cumulative coarser, %: 93.0

Sieve No.: 325
Mesh opening, mm: 0.044
Retained on the sieve, g: 3.0
Cumulative coarser, %: 96.0

Sieve No.: pan
Mesh opening, mm: —
Retained on the sieve, g: 4.0
Cumulative coarser, %: 100.0

Sieve No.	Mesh opening, mm	Retained on the sieve, g	Cumulative coarser, %
30	0.595	0.3	0.3
40	0.420	1.5	1.8
50	0.297	4.2	6.0
60	0.250	5.0	11.0
70	0.210	7.0	18.0
80	0.177	10.0	28.0
100	0.149	13.0	41.0
120	0.125	14.0	55.0
140	0.105	13.0	68.0
170	0.088	10.0	78.0
200	0.074	8.0	86.0
270	0.053	7.0	93.0
325	0.044	3.0	96.0
pan	—	4.0	100.0

4 g passed through sieve No. 325 (44 µm) into the pan below the sieves: these are the particles finer than 44 µm.

Worked exampleGrain sizes and sorting from a sieve analysis

Given (assumed data)

Sample: 100 g of sandstone from the core of a productive layer, separated into grains; the sieving is in the table above

Solution

The median $D_{50}$ lies between sieves No. 100 (0.149 mm, 41.0%) and No. 120 (0.125 mm, 55.0%). The fraction of the way is $(50 - 41)/(55 - 41) = 0.643$ .
Interpolation in the logarithms of the size: $D_{50} = 0.149\cdot(0.125/0.149)^{0.643} = 0.133$ mm.
In the same way: $D_{10} = 0.259$ mm, $D_{40} = 0.151$ mm, $D_{90} = 0.061$ mm, $D_{95} = 0.047$ mm.
The uniformity coefficient is $C = 0.151/0.061 = 2.5$ . The ratio is $D_{10}/D_{95} = 0.259/0.047 = 5.5$ . Particles finer than 44 µm: 4%.

Answer: The sand is fine-grained (

D_{50}

= 0.133 mm) and well sorted (

C

≈ 2.5), but it has a noticeable share of fines: 4%.

What it means. By sorting, the sand suits even a screen without gravel, but the share of fines is at the limit of what such screens carry without plugging. The decision needs sand retention tests (next section). The sample came from core: sand produced by the well is not good for the choice, because it is enriched in fine grains and fragments. If there are thin shale layers in the interval that will not produce, we leave their samples out when choosing the gravel, or the gravel will come out too fine. The data in this example are assumed for illustration.

CalculatedCumulative sieve curve of the sample from the example (the points are sieves) and the same curve for the 20/40 gravel chosen below. The dashed verticals are the Saucier window for the median size of the gravel: from 5 to 6 median sizes of the sand.

Choosing the gravel and the screen slot

The gravel must be fine enough that the sand does not enter its pores, and coarse enough that the pack does not take away productivity. In the 1970s R. Saucier pumped fluid through the reservoir sand into gravel of different sizes, and compared the permeability of the pack before and after the test. While the median size of the gravel was no more than about six median sizes of the sand, the sand stopped at the boundary, and the permeability of the gravel was kept. At a larger ratio the sand entered the pores of the gravel, and the mixture became less permeable than the reservoir sand itself. Only at a ratio of more than about 15 did the sand pass right through the gravel. This gives the Saucier criterion:

Choosing the gravel by the median sizes

D_{50,g} = (5\text{–}6)\,D_{50,\text{s}}

where:

$D_{50,g}$ median size of the gravel, mm
$D_{50,\text{s}}$ median size of the reservoir sand, mm

Units: any units of length, the same for both sizes

Holds when

The sand is well or moderately sorted. The gravel is of a narrow size: almost all the mass is between two neighbouring sieves.
For poorly sorted sands the criterion by the median is not reliable. We then use the Schwartz criterion: the size of the gravel $D_p$ is taken as six times the same size $D_p$ of the sand, and the point of the curve is chosen by the sorting: $D_{10}$ for $C$ up to 5, $D_{40}$ for $C$ from 5 to 10, and $D_{70}$ for $C$ above 10 (the worse the sorting, the finer the point of choice). And we run sand retention tests.

The window of 5–6 times is a compromise. A smaller gravel also holds the sand back, but its permeability, which is proportional to the square of the grain size, is lower. A larger one lets sand into the pores. Gravel is made in standard sizes, so from the window we choose the nearest standard size, and when in doubt we go to the finer one.

Standard gravel sizes and the sands they suit

Gravel: 40/60
Sieve openings, mm: 0.420–0.250
Midpoint, mm: 0.335
$D_{50}$ of the sand by Saucier, mm: 0.056–0.067
Screen slot, mm: 0.15–0.20

Gravel: 30/50
Sieve openings, mm: 0.595–0.297
Midpoint, mm: 0.446
$D_{50}$ of the sand by Saucier, mm: 0.074–0.089
Screen slot, mm: 0.18–0.24

Gravel: 20/40
Sieve openings, mm: 0.841–0.420
Midpoint, mm: 0.630
$D_{50}$ of the sand by Saucier, mm: 0.105–0.126
Screen slot, mm: 0.25–0.34

Gravel: 16/30
Sieve openings, mm: 1.190–0.595
Midpoint, mm: 0.892
$D_{50}$ of the sand by Saucier, mm: 0.149–0.178
Screen slot, mm: 0.36–0.48

Gravel: 12/20
Sieve openings, mm: 1.680–0.841
Midpoint, mm: 1.260
$D_{50}$ of the sand by Saucier, mm: 0.210–0.252
Screen slot, mm: 0.50–0.67

Gravel	Sieve openings, mm	Midpoint, mm	$D_{50}$ of the sand by Saucier, mm	Screen slot, mm
40/60	0.420–0.250	0.335	0.056–0.067	0.15–0.20
30/50	0.595–0.297	0.446	0.074–0.089	0.18–0.24
20/40	0.841–0.420	0.630	0.105–0.126	0.25–0.34
16/30	1.190–0.595	0.892	0.149–0.178	0.36–0.48
12/20	1.680–0.841	1.260	0.210–0.252	0.50–0.67

The midpoint is the average of the openings of the two sieves. The screen slot is 0.6–0.8 of the smallest gravel grain. The permeability of gravel grows as the square of the grain size: going to the next larger size roughly doubles it.

There are requirements for the gravel besides its size. Almost all the mass must lie between two sieves. The grains must be rounded and spherical, strong, with low solubility in acid, and free of clay. There is also artificial gravel, ceramic granules. They are stronger and rounder, and at the same size they give a more permeable pack. Lighter grades settle less during placement in horizontal wellbores. Gravel with a resin coating sets in the reservoir after placement into a permeable, strong layer.

The slot or mesh of a screen is chosen for what it has to hold. In a gravel pack the screen holds the gravel, so the slot is smaller than the smallest gravel grain. Without gravel the screen holds the reservoir sand. By the classical experiments the slot can be up to two $D_{10}$ , since the arches are made up of the coarse part of the sand. But in practice it is chosen more cautiously and checked by sand retention tests: fluid with the reservoir sand is pumped through a sample of the screen, and we measure how much sand has passed and how the pressure drop grows.

Worked exampleWhich gravel and which slot for the sand of the example

Given (assumed data)

Reservoir sand: $D_{50}$ = 0.133 mm, $D_{90}$ = 0.061 mm, $C$ ≈ 2.5 (previous example)
Standard gravel sizes: the table above

Solution

The Saucier window: from $5\cdot0.133 = 0.67$ to $6\cdot0.133 = 0.80$ mm.
The nearest sizes: 20/40 has a midpoint of 0.63 mm, and the ratio is $0.63/0.133 = 4.7$ . 16/30 has 0.89 mm, and the ratio is 6.7. The first is a little finer than the window, and the second is coarser.
A check by the pores: in a dense packing of the finest grains of 20/40 (0.42 mm) a pore lets through only grains smaller than $0.155\cdot0.42 = 0.065$ mm. This is about a tenth of the sand, the finest ( $D_{90}$ = 0.061 mm). The other nine tenths stop at the boundary with the gravel.
The screen slot for 20/40: from $0.6\cdot0.42 = 0.25$ to $0.8\cdot0.42 = 0.34$ mm. We take the standard 0.30 mm (0.012 in).
Gravel 16/30 would be more permeable by a factor of $(0.89/0.63)^2 = 2.0$ , but at a ratio of 6.7 the sand starts to enter its pores.

Answer: Gravel 20/40 with a screen slot of 0.30 mm.

What it means. We chose the finer of the two neighbouring sizes. The loss of gravel permeability compared with 16/30 hardly shows in the inflow in an open hole, while sand in the pores of the gravel would make the pack worse than the reservoir itself. In a cased hole, where all the inflow goes through tunnels with gravel, the permeability of the gravel matters more (losses in a gravel pack), but there too an invasion of sand costs more. The data in this example are assumed for illustration.

More detail:Why exactly 5–6 times

A pore of a dense packing lets through grains smaller than 0.155 of the size of the gravel. At a ratio of the median sizes of 6, this is 0.93 of the median sand grain. Half the sand, the coarser half, cannot enter at all. The finer grains come to the pores of the gravel in a crowd and settle into arches, as at the slot of a screen. Only the finest particles pass through the gravel, and this is as it should be. At a ratio of 10 the pore is already 1.55 times larger than the median grain, and a large part of the sand enters the gravel. The arches inside the gravel are unstable, and the mixture of sand and gravel plugs the pores.

This also gives the requirement on the density of the packing. In a loose cubic packing the pore is 2.7 times larger than in a dense one. Gravel placed loosely, for example with voids from settling or incomplete placement, lets through sand that a dense pack of the same gravel would hold back. So the gravel is placed so that the flow compacts it, and after placement the pack is checked for voids.

Sand screens

A sand screen is a pipe with a permeable wall that lets fluid through and holds back gravel or sand. Screens differ in how this wall is made, and on this depend the accuracy of the slot size, the share of open area, the resistance to plugging and erosion, and the strength.

Slotted liner: A pipe with slots cut in it. It is the cheapest and strongest, but the slots cannot be very narrow, and the open area is small, a few per cent or less. It is good for a coarse uniform sand, or simply for holding up the wall of the hole.
Wire-wrapped screen: Wedge-shaped wire wound with a constant gap onto longitudinal rods over a perforated pipe. The gap is held accurately, and the wedge profile widens the slot inwards, so a grain that has passed the narrow place does not get stuck. The open area is about ten per cent. It is the main screen of gravel packs.
Pre-packed screen: Two concentric screens with a layer of gravel bonded with resin between them: a pack made at a factory. It holds the sand without placing gravel in the well, but it plugs more easily with fine particles.
Premium mesh screen: Several layers of metal mesh with a drainage layer under a protective shroud. It has a large open area and resists plugging. It is used without gravel more often than the others, in long horizontal wellbores.
Expandable sand screen: A screen that, after it is run in, is expanded inside the hole until it touches the wall, so there is no annular gap along which sand could move. Its collapse resistance is lower than that of ordinary screens, and it is used only to a limited extent.

The main causes of screen failure are erosion and plugging. If the wall of the hole has collapsed unevenly, or the pack is incomplete, the inflow concentrates on a small part of the screen, and the sand wears the screen through at a high velocity. Fine particles, remains of drilling fluid and products of corrosion plug a screen. So screens without gravel are run in a well-sorted sand with few fines, and the interval is drilled with a special reservoir drill-in fluid. Its filter cake must come off the wall at start-up and pass through the screen or dissolve in the produced fluid, and not stick to the screen (Drilling fluids: functions and properties). In long horizontal wellbores screens are supplemented with isolating packers (seals that close off parts of the annulus), including swelling ones, and with inflow control devices (valves that even out the inflow along the well) (Horizontal wells).

Gravel packing: design, placement and checking

In an open hole (one with no casing across the reservoir) the screen is set across the reservoir, the hole is often enlarged, and the space between the screen and the wall is filled with gravel. The flow passes through the layer of gravel radially, over the whole wall, so such a pack hardly lowers the productivity. In a cased hole the gravel fills the ring between the screen and the casing and the perforation tunnels. All the inflow goes through narrow tunnels with gravel, and the losses in them are noticeable. Their calculation is in the lesson on the effect of completion on inflow. But the casing with cement isolates the layers and lets us shut off a watered-out interval later. For a pack in casing we perforate densely, with large holes, and before placement the tunnels are often filled with gravel under pressure.

The gravel is placed through a crossover tool, which changes the direction of the flow. The mixture of gravel and fluid goes down the pipes, and through the crossover tool it comes out into the ring between the screen and the casing or the wall. The gravel settles, and the fluid passes through the screen, rises up the wash pipe (a pipe inside the screen), and through the same crossover tool goes up the annulus (the space between the pipes and the casing) to the surface. Part of the fluid goes into the reservoir. When the gravel has covered the screen, the pressure rises sharply, and the pack is finished. We pull out the crossover tool, and the excess gravel is washed out of the pipes to the surface by reverse circulation (pumping the fluid down the annulus and up the pipes).

Placing gravel with a low-viscosity and a viscous fluid

Feature: Gravel concentration
Brine (water pack): low: about 100–250 kg per m³ of fluid
Viscous fluid: high: up to 1000–1800 kg/m³

Feature: Rate
Brine (water pack): high
Viscous fluid: low

Feature: How the pack grows
Brine (water pack): the gravel settles and the pack grows from the bottom up. In a horizontal wellbore it is a wave along the bottom of the wellbore, and then a return wave along the top
Viscous fluid: the fluid holds the gravel, and the pack compacts as the fluid goes into the reservoir and through the screen

Feature: Risks
Brine (water pack): a long time and large volumes of fluid, mixing of the gravel with the reservoir sand
Viscous fluid: a premature plug in a long deviated interval; polymer residue

Feature	Brine (water pack)	Viscous fluid
Gravel concentration	low: about 100–250 kg per m³ of fluid	high: up to 1000–1800 kg/m³
Rate	high	low
How the pack grows	the gravel settles and the pack grows from the bottom up. In a horizontal wellbore it is a wave along the bottom of the wellbore, and then a return wave along the top	the fluid holds the gravel, and the pack compacts as the fluid goes into the reservoir and through the screen
Risks	a long time and large volumes of fluid, mixing of the gravel with the reservoir sand	a premature plug in a long deviated interval; polymer residue

In long and deviated intervals, where a plug of gravel can block the ring too early, we use shunt tubes on the screen: the mixture bypasses the plug and fills the voids below.

The placement fluids are filtered brines compatible with the reservoir (usually with potassium chloride against swelling of clays). Their density is chosen to hold the reservoir pressure. After placement, while there is no equipment in the well, we limit the loss of fluid into the reservoir with viscous pills (small volumes of thick fluid) that have a breakable filler, or with mechanical valves. We must not kill the well (stop it flowing by filling it with a heavy fluid) with drilling fluid that has solids: it would plug the pack.

Calculated mass of gravel for a pack in casing

M = \rho_g(1 - \phi_g)\left[\frac{\pi}{4}\left(D_c^2 - d_s^2\right)(L_s + L_r) + n\,\frac{\pi}{4}d_p^2\,l_p\right]

where:

$M$ mass of gravel, kg
$\rho_g,\ \phi_g$ density of the gravel grains and porosity of the pack, kg/m³, —
$D_c,\ d_s$ inside diameter of the casing and outside diameter of the screen, m
$L_s,\ L_r$ length of the screen and the reserve of gravel above it, m
$n,\ d_p,\ l_p$ number of perforation tunnels, their diameter and their length behind the casing, —, m, m

Units: SI

Holds when

The reserve above the screen makes up for settling and compaction of the pack as the well works.
Tunnels and voids behind the casing usually take more gravel than their dimensions give, especially if the reservoir has already produced sand. So a placed mass larger than calculated is a good sign, and a smaller one is a reason to check.

We compare the calculated mass with the placed one: the pumped mass minus the mass washed out by reverse circulation.

Worked exampleIs the pack completely filled

Given (assumed data)

Design: casing 168 mm (inside diameter 150.5 mm), a screen of 114 mm outside diameter and 15 m long, a reserve of gravel above the screen of 9 m
Perforations: 15 m at 40 holes per metre, tunnels of 20 mm and 0.25 m long behind the casing
Gravel: 2650 kg/m³, pack porosity 0.38
Placement: 1100 kg of gravel pumped, 800 kg washed out by reverse circulation

Solution

The area of the ring: $\dfrac{\pi}{4}(0.1505^2 - 0.114^2) = 0.00758$ m². For $15 + 9 = 24$ m this is 0.182 m³.
The tunnels: $600\cdot\dfrac{\pi}{4}\cdot0.02^2\cdot0.25 = 0.047$ m³ ( $40\cdot15 = 600$ tunnels).
In all 0.229 m³. The density of the pack is $2650\cdot(1 - 0.38) = 1643$ kg/m³, and the calculated mass is $0.229\cdot1643 = 376$ kg.
The mass placed is $1100 - 800 = 300$ kg, which is 80% of the calculated one. 76 kg is missing, or $76/1643 = 0.046$ m³, which is what 6.1 m of the ring holds.

Answer: The pack is filled to about 80%: somewhere in it is a void equal to about 6.1 m of the ring.

What it means. If the gravel is missing only at the top, its top is 6 m lower than calculated, but still 3 m above the screen. This is what the reserve is left for. If the void is inside the interval of the screen (the gravel has got stuck as a plug and not gone down, or has not filled the tunnels), the sand will go straight to the screen and wear it through quickly. The two cases can only be told apart by a log run through the screen. Tools that measure the density of the medium behind the pipe show a lower density against voids. The decision, to repeat the placement or to start the well, is made from the log and the cost of repeated work. The data in this example are assumed for illustration.

Frac-pack: hydraulic fracturing with a gravel pack

A frac-pack (hydraulic fracturing with a gravel pack) is a short, wide fracture made in a weak permeable reservoir and filled with proppant of gravel size, together with a gravel pack in the ring around the screen, made in one operation. The fracture bypasses the damaged zone near the wellbore, and it connects to the well thin layers that the perforations may have missed. Above all it changes the geometry of the inflow: the fluid comes to the fracture over a large area at a low velocity, and the load on the grains near the well is smaller. In the 1990s, on the shelf of the Gulf of Mexico, such jobs became one of the main ways of completing high-rate wells in weak sandstones.

The dimensions of the fracture follow the same rules as in ordinary hydraulic fracturing (Fracture design: size and conductivity). In a permeable reservoir the proppant number is small, and the optimal fracture is short, a few metres or the first tens of metres, and very wide. Its conductivity must be comparable with that of the reservoir. Ordinary injection cannot create such a width. We get it by deliberately stopping the growth of the fracture in length with proppant at its end, and continuing to pump to widen the fracture (Fracturing fluids and tip-screenout fracturing). A soft, weak rock opens wide and helps with this.

CalculatedThe dimensionless productivity index of the well against the permeability of the reservoir: a frac-pack (15 t of proppant, width not more than 15 mm), a pack in casing with clean and with plugged gravel (the lower curves), and an ideal open hole without skin (a square area of 400 × 400 m, a reservoir of 10 m). For the packs only the viscous skin of the tunnels with gravel is counted. Inertial losses, perforation skin and damage would lower their curves further.

Worked exampleFrac-pack against a pack in casing

Given (assumed data)

Reservoir and well: $k$ = 500 mD, $h$ = 10 m; a square area of 400 × 400 m, $r_w$ = 0.108 m; the well of the example on the gravel pack in the lesson on the effect of completion
Pack in casing: the skin of the tunnels with gravel is 0.333 (clean gravel) and 3.33 (plugged), from the same example
Frac-pack: 15 t of ceramic proppant 20/40 (2700 kg/m³, pack porosity 0.38), fracture height 14 m, pack permeability in the reservoir 200 D, the largest width that can be reached 15 mm

Solution

Pack in casing: $\ln(400/0.108) - 1.311 = 6.906$ , and $J_D = 1/(6.906 + S)$ , which is 0.138 with clean gravel and 0.098 with plugged gravel. The ideal open hole ( $S$ = 0) gives 0.145.
Proppant in the reservoir: $V_{prop} = \dfrac{15{,}000\cdot10/14}{2700\cdot0.62} = 6.40$ m³. The proppant number is $N_{prop} = \dfrac{2\cdot200{,}000\cdot6.40}{500\cdot400^2\cdot10} = 0.0032$ .
The optimum ( $F_{CD} \approx 1.7$ ) would need a fracture of half-length 8.7 m and width 37 mm, and such a width cannot be made. At a width of 15 mm: $x_f = \dfrac{6.40}{2\cdot10\cdot0.015} = 21.3$ m, $F_{CD} = \dfrac{200{,}000\cdot0.015}{500\cdot21.3} = 0.28$ .
By the model of a fracture in a closed area ( $I_x = 2\cdot21.3/400 = 0.11$ ): $J_D = 0.2346$ . The equivalent skin is $S = 1/J_D - 6.906 = -2.64$ .
The productivity of the frac-pack is higher than that of the pack in casing by a factor of 1.7 (clean gravel) and 2.4 (plugged), and higher than that of the ideal open hole by a factor of 1.6.

Answer: A frac-pack gives the well an equivalent skin of about −2.64 instead of +0.3…+3.3 for the pack in casing, and a productivity 1.7–2.4 times higher.

What it means. Even a width of 15 mm is 2.5 times less than the optimal one, and the fracture works with an $F_{CD}$ of 0.28. This is why in permeable reservoirs we try hard to build up the width. The real skins of such wells are usually higher than the calculated ones. The fracture can be choked at the wellbore, its walls can be damaged by the fluid, and at high rates inertial losses grow in the pack (choking of the fracture and skin of its faces). But the skins of packs in casing are also larger in practice than counted here: perforation skin, damage behind the tunnels and inertial losses are added to the tunnels with gravel. The data in this example are assumed for illustration.

An intermediate option is to pack the tunnels and the ring with brine at a high rate, at a pressure above the fracture pressure. A short, small fracture filled with gravel forms in every tunnel, and the tunnels are packed better than with ordinary placement. But a fracture as long as in a frac-pack is not made.

Chemical consolidation of the near-wellbore zone

In chemical consolidation a resin (epoxy, furan or phenolic) is pumped into the reservoir near the well. The resin coats the grains. Then an overflush (a fluid pumped behind the resin) pushes its excess out of the pores, and the resin remains only at the contacts of the grains. After curing (hardening) it binds them together, and the pores stay open. The wellbore is then free: there is no screen and no gravel in it. The treatment can be done through the tubing, or with coiled tubing (a long flexible pipe run into the well on a reel), without pulling the equipment and without a workover rig.

The order of the treatment

1
Preparation
Flushing and, if needed, an acid treatment, so that the reservoir takes the fluid evenly.
2
Preflush
It pushes the water and oil out of the pores and prepares the surface of the grains, so that the resin sticks to them.
3
Resin
The calculated volume per metre of interval, behind a spacer that separates it from the other fluids.
4
Overflush
It pushes the excess resin deeper into the reservoir and restores permeability. The resin stays at the contacts of the grains.
5
Curing
The time of curing at reservoir temperature, and then a careful start.

Short intervals. The resin must get into every perforation tunnel, and an untreated tunnel becomes a source of sand. So a few metres are consolidated in one treatment, and long intervals are done in parts.
Clean sands. Clay takes up the resin and prevents it from bonding with the grains. With as little as ten per cent of clay the strength of the consolidated rock falls sharply. The main field of use is clean permeable sandstones.
Loss of permeability. Part of the pores remains filled with resin. If the overflush is incomplete, the permeability falls noticeably.
Limitations. The temperature of the reservoir, the curing time, the difficulty of pumping several fluids one after another, and the uncertainty of how they are distributed along the interval.

The same resins are used in another way. Gravel and proppant with a resin coating set in the reservoir and are not produced into the well. This is how proppant is held in fractures after hydraulic fracturing. Chemical consolidation is more often chosen for repairs, when a well without protection has started to produce sand, and we need to manage without a workover.

Choosing a method and monitoring

Where to start the choice

Conditions: The strength is almost enough, and sand production can be held within allowable limits
The usual choice: sand management without mechanical protection

Conditions: A well-sorted sand with few fines, a long horizontal wellbore
The usual choice: a screen without gravel, chosen by sand retention tests

Conditions: A heterogeneous sand, many fine particles, a high rate
The usual choice: a gravel pack in an open hole

Conditions: Several layers that must be isolated, a vertical well
The usual choice: a gravel pack in casing or a frac-pack

Conditions: High permeability, damage, a thinly layered reservoir
The usual choice: a frac-pack

Conditions: A short interval of clean sand, a repair without pulling equipment
The usual choice: chemical consolidation

Conditions	The usual choice
The strength is almost enough, and sand production can be held within allowable limits	sand management without mechanical protection
A well-sorted sand with few fines, a long horizontal wellbore	a screen without gravel, chosen by sand retention tests
A heterogeneous sand, many fine particles, a high rate	a gravel pack in an open hole
Several layers that must be isolated, a vertical well	a gravel pack in casing or a frac-pack
High permeability, damage, a thinly layered reservoir	a frac-pack
A short interval of clean sand, a repair without pulling equipment	chemical consolidation

This is a starting point. The final choice is made by comparing productivity, reliability and cost over the life of the well.

Besides productivity and price, we compare reliability (the share of failures in similar wells) and what will happen with workovers. It is hard to run logs through a screen in a producing well, or to isolate a watered-out interval. Pulling a screen with gravel is a long and risky job. We choose the protection for the whole life of the well: later depletion and water cut will weaken the rock (Sand production: types, prediction and cost of the problem), and redoing the protection in a producing well costs more than building it with a margin at the start.

Start-up. We raise production in steps, watching the sand and the pressures. A screen and a pack can also be destroyed by a sharp start, especially if the pack has voids.
Sand. Acoustic sensors and erosion probes on the flowlines, sampling, and measuring the sand in the separators. A sudden appearance of sand after a period of clean work is a sign of a failed screen or a void in the pack.
Productivity. Well tests regularly give the skin. Its slow growth means plugging of the pack or the screen by fine particles, salts and products of corrosion. If the inertial part grows faster than the viscous one, part of the tunnels with gravel is blocked (Effect of completion on inflow).
Regime. Even behind protection we limit the drawdown and the velocity at the screen: a large velocity speeds up erosion and the production of fines, and the pressure drop across the pack grows with the rate faster than linearly.

Terms and symbols

Sieve analysis: Shaking a sample of sand through sieves with smaller and smaller openings, and building the cumulative curve of grain sizes.
$D_{10}$ , $D_{50}$ , $D_{90}$: The sizes above which lie 10%, 50% and 90% of the mass of the sand (counted from the large grains).
Uniformity coefficient $C$: It equals $D_{40}/D_{90}$ . Up to 3 the sand is well sorted, and above 5 it is poorly sorted.
Saucier criterion: The median size of the gravel is 5–6 times the median size of the reservoir sand.
Sand screen: A pipe with a permeable wall: slotted, wire-wrapped, mesh, pre-packed or expandable.
Gravel pack: A layer of sorted gravel between the screen and the reservoir, in an open or a cased hole.
Frac-pack: A short, wide fracture with proppant and a pack in the ring around the screen, made in one operation.
Chemical consolidation: Binding the grains of the reservoir near the well with resin, with no equipment in the wellbore.
Sand retention test: Pumping fluid with the reservoir sand through a sample of a screen: how much sand has passed, and how the pressure drop grows.

Common mistakes and misconceptions

Wrong

“The finer the slot of the screen, the more reliable the protection.”

In fact

A slot that is too fine holds back the fine particles too, and they must pass. The screen plugs, the productivity falls, and the pressure drop across the screen grows and may crush it. We choose the slot for the gravel, or, without gravel, for the coarse part of the sand, with a check by tests.

Wrong

“A coarser gravel will give the same protection with a higher permeability.”

In fact

At a ratio of the median sizes above about 6 the sand enters the pores of the gravel, and the mixture becomes less permeable than the reservoir itself. In the lesson's example, the coarser 16/30 gravel would have been twice as permeable, but the ratio of 6.7 is already outside the window.

Wrong

“The sand produced by the well is good for choosing the gravel.”

In fact

Produced sand is enriched in fine grains and fragments, and it does not represent the reservoir. We choose from the core of the productive layers, and if there are several samples, from the finest of the working layers.

Wrong

“The pack is finished, since the pressure has risen, which means that the gravel has covered the screen.”

In fact

A rise of pressure shows only that a plug has formed somewhere, and below it a void may remain. We compare the placed mass with the calculated one (in the lesson's example, 80%), and if it falls short we check the pack with a log through the screen.

Wrong

“In a permeable reservoir hydraulic fracturing is not needed: the inflow is good anyway.”

In fact

It is precisely in a permeable reservoir that a pack in casing takes away the most: its skin is proportional to $kh$ . A short, wide fracture with a pack bypasses both the tunnels with gravel and the damage. In the lesson's example the productivity grew 1.7–2.4 times against a pack in casing.

In depth: advanced detail

What the experiments with sand and gravel showed

In Saucier's experiments, fluid was pumped through a layer of reservoir sand into a layer of gravel, and the permeability of the gravel was measured at the start and after a long pumping. The result is conveniently described by the ratio of these permeabilities as a function of the ratio of the median sizes of the gravel and the sand. Up to a ratio of about 6 it stays close to one: the sand is held at the boundary. Between 6 and 15 it falls. The sand enters the gravel, and the worst mixtures are less permeable than the reservoir sand itself. At ratios of more than about 15 the permeability of the gravel again hardly changes, but only because the sand passes right through it and is produced into the well.

Two conclusions for practice follow. The gravel must not be coarser than the window: the harm from the invasion of sand is greater than the gain from a coarse grain. And the gravel should not be taken much finer than the window either. At a ratio of 3–4 the sand is also held, but the permeability of the pack, which is proportional to the square of the gravel size, is 2–4 times lower, and a fine gravel plugs more easily with remains of the placement fluid. For heterogeneous sands with a large share of fines we shift the window by tests, and not by the table.

Connections to other topics

Sand production: types, prediction and cost of the problem — why the reservoir produces sand, the critical drawdown, and managing production without protection.
Effect of completion on inflow — how much productivity the tunnels with gravel take away in a cased hole.
Fracture design: size and conductivity — fracture dimensions from the proppant number, the basis of designing a frac-pack.
Fracturing fluids and tip-screenout fracturing — how short, wide fractures are made by stopping their growth in length.
Well completion: opening the reservoir and the tubing string — designs of the bottom of the well: open hole, screen liner, cased hole.
Horizontal wells — completion of horizontal wellbores with screens and inflow control devices.
Drilling fluids: functions and properties — reservoir drill-in fluids whose cake does not plug the screen.
Formation damage and damage skin — damage to the reservoir during gravel placement and when killing the well.

Check yourself

1
A sieve analysis gives $D_{40}$ = 0.22 mm and $D_{90}$ = 0.048 mm. How well is the sand sorted, and what does it mean for the choice of protection?
1. A.Well sorted: a screen without gravel will do
2. B.Moderately sorted: a gravel pack is more likely to be needed
3. C.We cannot judge from these data
4. D.Poorly sorted: no protection is needed
Show the answer
Correct answer: B. Moderately sorted: a gravel pack is more likely to be needed
$C = 0.22/0.048 \approx 4.6$ , between 3 and 5, so the sand is moderately sorted. A screen without gravel in such a sand risks plugging with fine grains or letting sand through until arches form. A gravel pack is more reliable, and if we still use a screen, it should be chosen by sand retention tests.
2
The median size of the reservoir sand is 0.085 mm. Which standard gravel suits it by the Saucier criterion, and which screen slot should we take for it?
Show the answer
The window is from $5\cdot0.085 = 0.43$ to $6\cdot0.085 = 0.51$ mm. The nearest is gravel 30/50 with a midpoint of 0.446 mm (the ratio is 5.2). The smallest grain of 30/50 is 0.297 mm, and the slot is 0.6–0.8 of it, that is, 0.18–0.24 mm. We take the nearest standard size in this range.
3
Why must the gravel in a pack lie densely? How many times larger a grain will the pore of a loose cubic packing let through than that of a dense one?
Show the answer
Through a pore of a dense packing a sphere not larger than $0.155D$ passes, and through a pore of a cubic one $0.414D$ , which is 2.7 times larger. A loose pack, or one with voids, will let through sand that a dense pack of the same gravel would hold back. So the gravel is compacted during placement, and the pack is checked for voids.
4
During placement of a pack in casing, 450 kg of gravel was placed against a calculated 380 kg. How should we understand this?
1. A.The screen is destroyed
2. B.The gravel went into the pipes, and the pack must be repeated
3. C.A calculation error: more than the calculated mass cannot be placed
4. D.A good sign: the gravel has filled the tunnels and the voids behind the casing
Show the answer
Correct answer: D. A good sign: the gravel has filled the tunnels and the voids behind the casing
The tunnels and the voids behind the casing, especially in a reservoir that has already produced sand, hold more than their dimensions give. An excess over the calculation says that the gravel has got to where it is needed most. The alarming sign is a shortfall.
5
Why in a highly permeable weak reservoir does a frac-pack usually give more than a pack in casing, although the fracture is short?
Show the answer
The skin of the tunnels with gravel is proportional to the $kh$ of the reservoir, so in a permeable reservoir a pack in casing loses the most. The fracture bypasses both the tunnels and the damaged zone, and the inflow to its plane goes at low velocities. In the lesson's example, at 500 mD, the equivalent skin is about −2.6 against +0.3…+3.3 for a pack in casing.
6
When is chemical consolidation preferable to mechanical protection?
Show the answer
When the interval is short (a few metres), the sandstone is clean, with little clay, and it is important to leave the wellbore free. An example is the repair of a well that has started to produce sand, without pulling the equipment and without a workover rig. In long, shaly or heterogeneous intervals mechanical protection is more reliable.

Updated: 10 October 2026