Reservoir architecture and performance

Quick refresher

Architecture is described by three questions: what are the bodies (shape and size), how are they stacked (order and overlap), and how are they joined (connectivity, barriers, baffles)? The answers depend on the depositional environment (the setting where the sand was laid down, such as a river, a delta or a shore) and on the scale.
By the ratio of body size to well spacing, we tell apart “layer-cake” (bodies larger than the spacing), “jigsaw” (comparable) and “labyrinth” (much smaller). In Russian-language practice, macro-heterogeneity is described by the coefficients of sandiness (the share of reservoir rock), dissection (the average number of reservoir layers per well), lithological connectivity (how much neighbouring layers merge) and lithological continuity (how widely a layer is present).
The connectivity of randomly placed bodies does not grow smoothly with the net-to-gross ratio (the share of reservoir rock in the total thickness). It jumps near the percolation threshold, the point where separate bodies suddenly join into one network. The threshold is about 0.3 in a 3D volume and about 0.67 in a 2D section (a flat slice). So a correlation diagram, which is a section drawn between wells, shows bodies as disconnected where in the volume they are already joined.
The share of the reservoir that wells penetrate grows with the density of the well grid. Pressure support also depends on whether the rows of injectors and producers run across or along the elongated bodies.
A barrier stops flow for the life of the development, and a baffle only slows it. Over geological time a baffle equalises pressures and contacts. So equal initial pressures do not prove that blocks will communicate during production.
The architecture shows in how wells behave: early water through connected permeable bodies, wells that do not respond to injection, fast pressure decline in isolated compartments, and oil in bodies that no well has penetrated.

Key relationships

C = \dfrac{V_{\max}}{V_{\text{res}}},\qquad C_w = \dfrac{V_w}{V_{\text{res}}}

connectivity: the share of the reservoir in the largest body, and the share connected to wells

K_{\text{sand}} = \dfrac{h_{\text{eff}}}{h_{\text{t}}},\qquad K_{\text{dis}} = \dfrac{1}{N}\sum_{i=1}^{N} n_i

sandiness (net-to-gross) and dissection of a horizon

\tau = \dfrac{V_p\,c_t}{T},\qquad T = \dfrac{k_b A}{\mu\,b}

pressure equalisation time of a block through a baffle

Common pitfalls

Calling bodies disconnected only because they are not connected on a correlation diagram. In the volume, bodies connect at a lower net-to-gross ratio.
Thinking that equal initial pressures and contacts prove that blocks communicate during development.
Carrying connectivity from one well grid to another. The share of the reservoir that wells penetrate depends on their density.
Taking a tight thin layer in the core of one well for a continuous barrier.
Laying out rows of injectors without knowing which way the sand bodies run.

After this lesson you can

describe the shapes and sizes of sand bodies in different depositional environments and the hierarchy of scales of structure, from a lamina (a thin layer a few millimetres thick) to an accumulation, and say which scale matters for which decision
explain what reservoir connectivity is, why it changes abruptly with the net-to-gross ratio (percolation), and why a cross-section between wells understates connectivity
use a model to estimate how much of the reservoir the wells penetrate at a given well spacing, and how the direction of the rows of injectors and producers relative to elongated bodies changes pressure support
tell barriers from baffles, recognise compartments, and use the pressure equalisation time to judge whether compartments communicate during production and whether they communicated over geological time
link signs in well performance (early water, no response to injection, fast pressure decline, unswept zones) to the reservoir architecture, and choose measures

Bodies, their stacking and their links

A reservoir is not one continuous “layer” with one set of properties. It is a structure built of sand bodies of different shapes and sizes, stacked on one another, partly eroded and separated by shales. To describe it, we answer three questions. What are the bodies? We ask about their shape, width, length, thickness and internal layers. How are they stacked? Do they lie apart, or do they overlap and cut into one another? How are they joined? Where do they touch with sand, and where are they separated by shales, tight thin layers or faults?

The answers depend on the scale. What is heterogeneity inside a body at one scale is a boundary between bodies at another. It helps to think of a hierarchy in which each level is built of the elements of the previous one (scales of heterogeneity).

Levels of structure of a clastic reservoir

Level: Laminae and cross-bed sets
Size: mm to dm
What separates: a change of grain size, mica-rich and clay-rich laminae
What it decides: $k_v/k_h$ , residual oil

Level: Element: a channel bar, a mouth bar or a lobe
Size: metres in thickness, tens to hundreds of metres in area
What separates: shale drapes, erosion surfaces
What it decides: vertical sweep, water and gas coning

Level: Sand body, channel belt, shoreline bar
Size: metres to tens of metres; hundreds of metres to kilometres
What separates: floodplain and inter-channel shales
What it decides: connectivity, well spacing

Level: Horizon, member
Size: tens of metres; kilometres to tens of kilometres
What separates: continuous shales of flooding surfaces
What it decides: development units, crossflow

Level: Accumulation and its blocks
Size: kilometres
What separates: faults, pinch-outs, changes of facies
What it decides: separate compartments, hydrocarbons in place

Level	Size	What separates	What it decides
Laminae and cross-bed sets	mm to dm	a change of grain size, mica-rich and clay-rich laminae	$k_v/k_h$ , residual oil
Element: a channel bar, a mouth bar or a lobe	metres in thickness, tens to hundreds of metres in area	shale drapes, erosion surfaces	vertical sweep, water and gas coning
Sand body, channel belt, shoreline bar	metres to tens of metres; hundreds of metres to kilometres	floodplain and inter-channel shales	connectivity, well spacing
Horizon, member	tens of metres; kilometres to tens of kilometres	continuous shales of flooding surfaces	development units, crossflow
Accumulation and its blocks	kilometres	faults, pinch-outs, changes of facies	separate compartments, hydrocarbons in place

These are orders of magnitude. A clastic reservoir is one made of grains of older rocks, such as sandstone. The elements are the genetic units (units defined by how they were deposited) of the lesson on facies (Facies, facies successions and sedimentary logs). How properties change inside the elements is covered in the lesson Reservoir quality: geological controls on porosity and permeability.

For development, a layer is often divided into flow units. These are members (groups of layers) that can be followed between wells and that have similar properties and a common behaviour when fluid flows. They include both reservoir rock and non-reservoir interlayers. This idea is most useful where members are continuous, as in a “layer-cake”. Do not mix them up with hydraulic units, which are rock types set by the flow zone indicator (a number that groups rocks by how easily fluid flows through their pores; rock types). A rock type describes the pores and can occur anywhere in the section. A flow unit is a place in the section.

The shape and size of sand bodies

By their shape in plan (seen from above) and in section, sand bodies are divided into several kinds. Sheets are wide and extend in all directions. Belts (and strips) are elongated along the flow or the shore. Ribbons (shoestrings) are narrow channel bodies. Lobes are fan-shaped bodies at river mouths and on submarine fans. Pods (lenses) are small isolated bodies. For channel bodies, the ratio of width to thickness matters. For ribbons it is less than about 15. For sheets it is larger, often many times larger.

Sand bodies of the main depositional environments

Environment: Aeolian dunes and ergs (sand seas)
Bodies: sheets and wedges of dune complexes
Body thickness: metres to tens of metres
Extent: kilometres to tens of kilometres

Environment: Braided rivers
Bodies: stacked channels and bars that merge into sheets
Body thickness: metres; belts, tens of metres
Extent: hundreds of metres to kilometres

Environment: Meandering rivers
Bodies: channel bars and meander belts among floodplain shales
Body thickness: a few metres
Extent: channel, tens to hundreds of metres; belt, up to kilometres

Environment: Deltas
Bodies: distributary channels (ribbons) and mouth bars (lobes)
Body thickness: metres
Extent: channels, tens to hundreds of metres; bars, hundreds of metres to kilometres

Environment: Shoreface, beaches, bars
Bodies: sheets elongated along the shore
Body thickness: metres to tens of metres
Extent: kilometres across the shore, tens of kilometres along it

Environment: Tidal channels and shoals
Bodies: ribbons and pods
Body thickness: metres
Extent: tens to hundreds of metres

Environment: Submarine fans
Bodies: channels (ribbons) and lobes (sheets)
Body thickness: metres to tens of metres
Extent: channels, hundreds of metres to kilometres; lobes, kilometres to tens of kilometres

Environment	Bodies	Body thickness	Extent
Aeolian dunes and ergs (sand seas)	sheets and wedges of dune complexes	metres to tens of metres	kilometres to tens of kilometres
Braided rivers	stacked channels and bars that merge into sheets	metres; belts, tens of metres	hundreds of metres to kilometres
Meandering rivers	channel bars and meander belts among floodplain shales	a few metres	channel, tens to hundreds of metres; belt, up to kilometres
Deltas	distributary channels (ribbons) and mouth bars (lobes)	metres	channels, tens to hundreds of metres; bars, hundreds of metres to kilometres
Shoreface, beaches, bars	sheets elongated along the shore	metres to tens of metres	kilometres across the shore, tens of kilometres along it
Tidal channels and shoals	ribbons and pods	metres	tens to hundreds of metres
Submarine fans	channels (ribbons) and lobes (sheets)	metres to tens of metres	channels, hundreds of metres to kilometres; lobes, kilometres to tens of kilometres

These are approximate orders of magnitude, for a first judgement. We take the dimensions of a specific layer from analogues in the same basin, from outcrops, from seismic data and from correlation. The environments themselves are covered in the topics Continental environments: aeolian and fluvial and Coastal, shallow-marine and deep-marine environments.

We measure the thickness of a body from core and logs. But a thick sandstone is often made of several stacked bodies, so the thickness of one body is less than the thickness of the member (Facies, facies successions and sedimentary logs). We can hardly measure the width and length in wells. We estimate them in several ways. One is from analogues, such as outcrops (places where the rock shows at the surface) and modern rivers and coasts, where the link between the width of a channel and its depth is known. Another is from seismic data, when the bodies are thicker than its resolution or show on maps of seismic attributes. A third is from well tests (pressure tests), where a narrow body shows up as a channel with parallel boundaries (Several boundaries: parallel faults and wedge-shaped blocks). The last is from how wells behave during development. We estimate the probability that a body penetrated by one well reaches the next well from the width of the body and the distance between wells (choice of a correlation model).

“Layer-cake”, “jigsaw” and “labyrinth”

When we correlate sections, we tell apart “layer-cake” and “jigsaw” (correlation models). For development, a third case is added: the “labyrinth”. Here the bodies are much smaller than the distance between wells. They are joined rarely, and often only through thin poor-quality sands. We cannot match them between wells by a deterministic method (one that gives a single answer). We describe the structure statistically, with models that have many equally likely versions. And whether the bodies are connected to wells becomes the main uncertainty.

CalculatedThree types of structure in the lesson's model: sections across the bodies, through a row of wells spaced 500 m apart. The colours show the reservoir that is connected to at least one well of the grid (anywhere in the volume of the block) and the reservoir that is connected to no well. The vertical scale is exaggerated 15 times.

Three types of structure

Type: “Layer-cake”
Bodies and links: continuous layers, the thickness changes smoothly
Correlation: reliable from logs
Model and development: a layered model; even a sparse grid penetrates almost all the reservoir

Type: “Jigsaw”
Bodies and links: bodies are comparable with the well spacing and lie against one another; in places the contacts are tight
Correlation: facies analysis is needed; several versions
Model and development: a model with bodies and baffles; a denser grid pays off only in places

Type: “Labyrinth”
Bodies and links: small bodies and lenses, joined rarely and through poor sands
Correlation: unreliable even at a spacing of hundreds of metres
Model and development: a stochastic model with many variants; a dense grid

Type	Bodies and links	Correlation	Model and development
“Layer-cake”	continuous layers, the thickness changes smoothly	reliable from logs	a layered model; even a sparse grid penetrates almost all the reservoir
“Jigsaw”	bodies are comparable with the well spacing and lie against one another; in places the contacts are tight	facies analysis is needed; several versions	a model with bodies and baffles; a denser grid pays off only in places
“Labyrinth”	small bodies and lenses, joined rarely and through poor sands	unreliable even at a spacing of hundreds of metres	a stochastic model with many variants; a dense grid

These are parts of a continuous series, not strict classes: one layer can change type through the section and across the area.

In Russian development projects, the macro-heterogeneity of a horizon is described by numbers that are calculated from all the wells and maps:

Macro-heterogeneity coefficients

K_{\text{sand}} = \frac{\sum h_{\text{eff}}}{\sum h_{\text{t}}},\qquad K_{\text{dis}} = \frac{1}{N}\sum_{i=1}^{N} n_i,\qquad K_{\text{mer}} = \frac{S_{\text{mer}}}{S},\qquad K_{\text{cont}} = \frac{S_{\text{res}}}{S}

where:

$K_{\text{sand}}$ sandiness coefficient, the share of reservoir rock in the section (net-to-gross ratio), —
$h_{\text{eff}},\ h_{\text{t}}$ effective thickness (the sum of the reservoir layers) and total thickness of the horizon in a well, m
$K_{\text{dis}}$ dissection coefficient, the average number of reservoir layers per well, —
$n_i,\ N$ number of reservoir layers in the $i$ -th well; number of wells, —
$K_{\text{mer}}$ lithological connectivity (merging) coefficient: the share of the area where neighbouring layers merge, with no non-reservoir rock between them, —
$K_{\text{cont}}$ lithological continuity coefficient: the share of the area where the layer is present as reservoir, —
$S_{\text{mer}},\ S_{\text{res}},\ S$ area of the merging zones, area where the reservoir is present, area of the accumulation, km²

Units: dimensionless; thicknesses and areas in the same units

Holds when

The coefficients are calculated for a layer or horizon that was picked by correlation.
$K_{\text{sand}}$ depends on the cut-offs by which the reservoir is picked (cut-offs are the limit values of porosity and similar properties below which rock does not count as reservoir). Here it is weighted by thickness.
$K_{\text{mer}}$ and $K_{\text{cont}}$ are taken from maps that were built from wells, so their accuracy is limited by the density of the grid.
In some methods the merging area is related not to the whole area of the accumulation but to the area where the reservoirs of the layer are present. When comparing objects, check how $K_{\text{mer}}$ was calculated.

The lower the sandiness and continuity, and the higher the dissection, the more complex the structure. $K_{\text{dis}} = 1$ means a horizon of a single layer. Larger values mean many thin layers. The merging coefficient shows where neighbouring layers communicate vertically through “merging windows”. These numbers are handy for comparing objects. But they do not say how the bodies are joined in the volume. For that we need connectivity models (next section).

Worked exampleMacro-heterogeneity of a horizon from five wells

Given (assumed data)

Total thickness of the horizon, m: 42; 45; 40; 44; 39
Effective thickness, m: 18; 23; 14; 21; 16
Number of reservoir layers: 4; 3; 6; 4; 5

Solution

Sandiness: $K_{\text{sand}} = (18 + 23 + 14 + 21 + 16)/(42 + 45 + 40 + 44 + 39) = 92/210 = 0.44$ .
Dissection: $K_{\text{dis}} = (4 + 3 + 6 + 4 + 5)/5 = 22/5 = 4.4$ .
Average thickness of one reservoir layer: $92/22 = 4.2$ m. In well No. 3 it is $14/6 = 2.3$ m.

Answer: Sandiness is about 0.44 and dissection is 4.4. The horizon is made of four or five reservoir layers with an average thickness of about 4.2 m.

What it means. This is an interbedded section (sand and shale in alternating layers): the reservoir takes less than half of the thickness and is split into several layers. These numbers do not say whether the layers communicate between wells. That depends on the size of the bodies and on whether the layers merge. But a net-to-gross ratio of about 0.4 lies in just the range where connectivity in the volume changes most sharply with it (next section). So for such a horizon a connectivity model and a check with pressures are especially important. The data in this example are assumed for illustration.

Connectivity and net-to-gross ratio: percolation

The connectivity of a reservoir is the share of its volume that is joined into one whole. We tell apart static connectivity, which comes from the geometry of the bodies, and dynamic connectivity. Dynamic connectivity also takes into account how well the bodies pass fluid to each other. Here we talk about static connectivity.

Measures of connectivity

C = \frac{V_{\max}}{V_{\text{res}}},\qquad C_w = \frac{V_w}{V_{\text{res}}}

where:

$C$ share of the reservoir in the largest connected body, fraction
$V_{\max}$ volume of the largest connected body, m³
$V_{\text{res}}$ volume of all the reservoir, m³
$C_w$ share of the reservoir that is connected to at least one well, fraction
$V_w$ volume of the bodies that wells penetrate or that are connected to them, m³

Units: fractions

Holds when

Bodies are connected if they touch with sand across a surface. Touching along an edge or at a point does not count.
Static connectivity takes into account the geometry of the bodies, but not the permeability of contacts or the baffles inside bodies.

$C$ shows whether the layer has one large body. This is a property of the geology. $C_w$ shows how much of the reservoir is available to a given grid of wells. This is a property of the geology and the grid together.

While sand bodies are few, each lies by itself. As the net-to-gross ratio grows, bodies start to touch and merge into groups. At some value, one group first stretches across the whole layer. This is the percolation threshold. (In Russian-language physics literature it is called the “flow threshold”.) Connectivity changes sharply around it. A little below the threshold, the largest body holds only a small part of the reservoir. A little above it, the largest body holds most of the reservoir. For identical bodies that are placed at random and may overlap freely, theory gives a threshold of about 0.28–0.29 of the volume in space and about 0.67–0.68 of the area on a plane.

The difference between space and a plane explains a common mistake. A correlation diagram is a flat section, and bodies on it can join only in its plane. In a volume they join by going around, through neighbouring sections. So the threshold is more than twice as low. Let us test this on a model.

The lesson's model

1
Block
3 × 3 km in area and 40 m in thickness, with cells of 50 × 50 × 1 m.
2
Bodies
Channel belts 300 m wide, 1200 m long and 4 m thick, all stretched in one direction. They are dropped into the block at random places until the net-to-gross ratio reaches the set value. Overlapping bodies merge.
3
Links
Bodies are connected if their cells touch along a face. For each realisation (one random version of the model), we find the connected groups of cells in the volume and in a vertical section across the bodies through the middle of the block.
4
Statistics
For each net-to-gross ratio there are 40 realisations with reproducible random numbers. The examples use means over them (details are in the advanced section).

Worked exampleConnectivity in the volume and in a section

Given (assumed data)

Model: described above; 40 realisations for each net-to-gross ratio
Net-to-gross ratio: 0.2; 0.3; 0.4; 0.5; 0.7

Solution

At a net-to-gross ratio of 0.2, the largest body of the block holds 0.20 of all the reservoir, and in the section 0.17. The bodies are disconnected in both.
At 0.3, it is 0.40 in the volume and 0.21 in the section. At 0.4, it is 0.81 and 0.24. At 0.5, it is 0.97 and 0.35.
At 0.7 the section is connected too: 0.88 (in the volume, 1.00).
Spread: at 0.3, the standard deviation of $C$ between realisations is 0.14, and the standard error of the mean is about 0.02. The means are known to about this accuracy, while single realisations differ a lot.

Answer: In the volume, connectivity grows sharply between net-to-gross ratios of 0.25 and 0.45. At 0.4, 0.81 of the reservoir is already in one body, while in a section through the same block it is only 0.24. The section catches up with the volume only at a ratio of about 0.7.

What it means. A correlation diagram is a flat section. In a “jigsaw” with a net-to-gross ratio of 0.4–0.5, it will show disconnected bodies, although in the volume most of the reservoir is already joined by going around the plane of the diagram. The conclusion “the bodies are not connected”, taken from one diagram, understates connectivity and overstates the number of wells that are needed. The model, on the other hand, counts any contact of sands as communication. In reality, bodies may be separated by a shale drape (a thin shale layer laid over a body) or by mud clasts (pebbles of shale) on an erosion surface. In this direction the model overstates connectivity. The threshold in the model is blurred, because the block is only 2.5 times longer than a body. In an infinite block the transition would be sharper. The spread between realisations is a reminder that the connectivity of a particular layer is known only as a probability. The data of the model are assumed for illustration.

CalculatedShare of the reservoir in the largest connected body against the net-to-gross ratio: in the volume of the model block and in a vertical section through it (means over 16 realisations). The dashed verticals are the percolation thresholds for identical randomly placed bodies in unbounded space and on a plane. At a small net-to-gross ratio, both curves reflect only the size of the largest of the few bodies.

Real bodies are not identical, and they are not placed at random. Channels gather into belts and cut into one another. Bodies are elongated in one direction. Large and small bodies are mixed. All this shifts the threshold and makes it less sharp. So we estimate the connectivity of a particular layer with models that use its own body sizes and net-to-gross ratio, and we check it against pressures and the behaviour of wells.

How much of the reservoir the wells see

Not all connected bodies give production. Only those that wells penetrate, or that are connected to wells, do. The share of the reservoir connected to wells, $C_w$ , grows with the density of the well grid. In a waterflood, pressure support also matters. A body works with pressure support only if it is connected to both an injector and a producer. Bodies connected only to producers give up their oil by depletion (the pressure falls as fluid is taken out, with no water to replace it). Bodies connected only to injectors take in water, which does not help production.

Worked exampleWell grid and pressure support in a “jigsaw”

Given (assumed data)

Model: the same, net-to-gross ratio 0.3; 40 realisations
Wells: vertical, on a square grid with spacings of 1000, 500 and 250 m, which is 1, 4 and 16 wells per km²
Waterflood: line drive: rows of injectors and producers alternate. The rows run either across the bodies (the water moves along them) or along the bodies (the water moves across them)

Solution

Share of the reservoir connected to wells: at 1000 m, 0.86; at 500 m, 0.95; at 250 m, 0.99.
Rows across the bodies: the share of the reservoir connected to both an injector and a producer is 0.68 at 1000 m and 0.92 at 500 m.
Rows along the bodies: 0.48 and 0.74.
At 500 m with rows along the bodies, 0.11 of the reservoir is connected only to producers (these bodies will work by depletion) and 0.11 only to injectors.

Answer: The density of the grid decides how much of the reservoir is penetrated: from 0.86 with one well per km² to 0.99 with sixteen. The orientation of the rows decides how much of the penetrated part gets support: at 500 m, 0.92 with rows across the bodies and 0.74 with rows along them.

What it means. Going from one well per km² to four adds about 0.10 of penetrated reservoir. Going from four to sixteen adds only about 0.04 more. Infill drilling (adding wells between the existing ones) pays off while it penetrates unconnected bodies. We learn the direction in which bodies are elongated from the facies model, from palaeocurrents (directions of ancient flows) in core and on borehole image logs (Primary sedimentary structures), from seismic data and from interference tests. In an interference test we change the rate of one well and watch the pressure in its neighbours. Rows across the bodies give better support, but water also goes faster along the same bodies to the producers. Connectivity and sweep (the share of the reservoir that the water really pushes oil out of) are different questions, and we calculate sweep separately (Displacement in heterogeneous reservoirs). The model counts any contact of bodies as a link and ignores their permeability, so real support will be worse than the calculated one. The data of the model are assumed for illustration.

Barriers and baffles

A barrier is an obstacle that no flow can cross during the life of the development: a continuous shale, a tight continuous thin layer, a sealing fault. A baffle is an obstacle that slows the flow or makes it go around, but does not stop it. Examples are discontinuous shale layers, shale drapes on the boundaries of stacked bodies, tight concretions (hard lumps of cemented rock) and partly communicating faults (Partially communicating faults). The same rock can be a barrier or a baffle. Its extent and continuity decide which.

Barriers and baffles in clastic reservoirs

What: Shales of flooding surfaces
Where: marine and delta sequences
Extent: kilometres to tens of kilometres
How it acts: separate layers vertically; more often barriers

What: Floodplain and inter-channel shales
Where: river sequences
Extent: hundreds of metres to kilometres
How it acts: baffles between channel belts; the flow goes around them

What: Shale drapes and mud clasts on erosion surfaces
Where: stacked channels
Extent: tens to hundreds of metres
How it acts: baffles between the tiers of one body

What: Thin shale layers (laminae) on the slopes of channel bars
Where: meandering rivers
Extent: metres to tens of metres
How it acts: inclined baffles inside a body

What: Carbonate concretions and cemented thin layers
Where: early cement (burial)
Extent: metres to hundreds of metres
How it acts: baffles, sometimes barriers

What: Faults
Where: any sequence
Extent: hundreds of metres to kilometres
How it acts: barriers or baffles (Faults)

What	Where	Extent	How it acts
Shales of flooding surfaces	marine and delta sequences	kilometres to tens of kilometres	separate layers vertically; more often barriers
Floodplain and inter-channel shales	river sequences	hundreds of metres to kilometres	baffles between channel belts; the flow goes around them
Shale drapes and mud clasts on erosion surfaces	stacked channels	tens to hundreds of metres	baffles between the tiers of one body
Thin shale layers (laminae) on the slopes of channel bars	meandering rivers	metres to tens of metres	inclined baffles inside a body
Carbonate concretions and cemented thin layers	early cement (burial)	metres to hundreds of metres	baffles, sometimes barriers
Faults	any sequence	hundreds of metres to kilometres	barriers or baffles (Faults)

Extent is given as an order of magnitude. For a barrier, continuity matters most: a continuous shale tens of centimetres thick separates layers more reliably than a metre-thick layer with gaps cut through it.

Baffles inside a member lower its vertical permeability. The longer they are compared with the gaps between them, the stronger the effect. They also decide whether layers have time to exchange fluid over the distance between wells (effective length-to-thickness ratio). Barriers let us develop layers separately and hold back water and gas coning (the cone-shaped rise of water or gas towards a well; Water and gas coning), but they also cut parts of the layer off from injection.

We recognise barriers from pressure measurements through the section in a layer that is already producing. If the pressure above and below a thin layer differs, that layer separates the layers (Pressure measurement with the wireline formation tester; for more, see the topic Pressure measurements in producing reservoirs: barriers and accuracy). Production and injection profiles (logs that show how much each interval gives or takes), vertical interference tests between intervals, and the history of water and gas breakthrough also help. A tight thin layer in the core of one well says nothing about its extent.

Reservoir compartments

A reservoir compartment is a part of an accumulation that does not communicate with the rest during development. Compartments can be stratigraphic (disconnected bodies, pinch-outs, barriers in the section) or structural (sealing faults, Faults). Often both causes act.

Before development, compartments show different contacts (the depths where oil gives way to water) and free water levels, different pressure gradients from the formation tester (a tool that measures pressure at chosen points in the well; Pressure gradients, fluid contacts and capillary equilibrium), differences in the composition of oil and gas, and faults on seismic data.
During development, we see pressure that falls faster than the volume on the map implies. The connected pore volume from tests and material balance is smaller than the mapped one (Reservoir limit test). A reservoir limit test is a well test that shows how much pore volume the well really drains. Neighbouring wells do not respond in an interference test (interference test).

Communication depends on time. Over millions of years even a tight baffle has time to equalise the pressures and contacts on both sides. So equal initial pressures do not prove that compartments will communicate during production. The estimate is given by the pressure equalisation time: the time constant of a compartment that is joined to a neighbouring layer through a baffle.

Time constant of a compartment behind a baffle

\tau = \frac{V_p\,c_t}{T},\qquad T = \frac{k_b\,A}{\mu\,b}

where:

$\tau$ time constant: in this time the pressure difference between the compartment and the neighbouring layer falls by a factor of $e \approx 2.72$ , s
$V_p$ pore volume of the compartment, m³
$c_t$ total compressibility of the rocks and fluids of the compartment, 1/Pa
$T$ transmissibility of the baffle: the flow rate through it per unit of pressure difference, m³/(s·Pa)
$k_b$ permeability of the baffle, m²
$A$ area of the baffle across the flow: the length of the boundary times its height, m²
$\mu$ viscosity of the fluid that flows through the baffle, Pa·s
$b$ width (thickness) of the baffle in the direction of flow, m

Units: SI

Holds when

The pressure inside the compartment is the same everywhere, because the compartment is much more permeable than the baffle.
The pressure on the other side is constant: the neighbouring layer is much larger than the compartment, or is supported by injection. If the compartments are comparable in size, replace $V_p$ with $V_1V_2/(V_1 + V_2)$ .
Flow through the baffle is single-phase (only one fluid flows) and nearly steady. We ignore the compressibility of the baffle itself.

The pressure difference between the compartment and its neighbour dies away as $e^{-t/\tau}$ (the derivation is in the advanced section). If $\tau$ is much longer than the period of development, the compartment works on its own. If it is much shorter, the compartment works as part of the common layer. Over geological time, which is hundreds of thousands to millions of years, almost any baffle has time to equalise the pressure.

In other unit systems (1)

Metric oilfield units

T\,[\text{m}^3/(\text{d}\cdot\text{MPa})] = 0.0853\,\frac{k_b\,[\text{mD}]\;A\,[\text{m}^2]}{\mu\,[\text{mPa·s}]\;b\,[\text{m}]},\qquad \tau\,[\text{d}] = \frac{V_p\,[\text{m}^3]\;c_t\,[\text{MPa}^{-1}]}{T}

$k_b$ in mD, $A$ in m², $\mu$ in mPa·s, $b$ in m, $V_p$ in m³, $c_t$ in 1/MPa.

$0.0853$ is the same constant as in Darcy's law in metric oilfield units (Darcy's law).

Worked exampleDo the compartments communicate: during production and over geological time

Given (assumed data)

Compartment: 1500 × 800 m, thickness 20 m, porosity 0.20; total compressibility $1.5\cdot10^{-3}$ MPa⁻¹
Baffle: a strip of shaly sandstone 50 m wide along the long side of the compartment (1500 m, over the whole thickness of 20 m), permeability 0.002 mD
Fluid: oil, 1.5 mPa·s
Neighbouring layer: large, with its pressure supported by injection
Production from the compartment: 80 m³/d; the pressure difference across the baffle after a few years is about 10 MPa

Solution

Pore volume: $V_p = 1500\cdot 800\cdot 20\cdot 0.20 = 4{,}800{,}000$ m³. Then $V_p c_t = 7200$ m³/MPa.
Area of the baffle: $A = 1500\cdot 20 = 30{,}000$ m². Transmissibility: $T = 0.0853\cdot 0.002\cdot 30{,}000/(1.5\cdot 50) = 0.0682$ m³/(d·MPa).
Time constant: $\tau = 7200/0.0682 = 105{,}572$ d, or about 289 years.
Over 20 years of development, the difference between the compartment and the neighbouring layer dies away only to $e^{-20/289} = 0.93$ of the initial one. The inflow through the baffle at a difference of 10 MPa is $0.0682\cdot 10 = 0.68$ m³/d, against production of 80 m³/d.
A million years is about 3460 time constants. By the time the field was discovered, the pressures and contacts on both sides of the baffle had long been equalised.

Answer: The time constant is about 289 years. During production, the compartment behaves almost as a closed one: the inflow is 0.68 m³/d, less than 1% of production. Yet before production started, the pressures and contacts in it and in the neighbouring layer were the same.

What it means. From the initial data, such a compartment cannot be told from a communicating one: there is a common contact and one pressure line from the formation tester. Only the response to production gives it away. The pressure falls faster than expected for the whole area, and wells of the neighbouring layer do not react. The calculation is simplified: the pressure in the compartment is taken as the same everywhere, and the baffle as uniform. If the baffle has sand “windows”, the link will be orders of magnitude better. This is the main uncertainty, and we test it with an interference test before injection starts. Multi-tank material balance models are covered in the topic Lumped multi-tank material balance model. The data in this example are assumed for illustration.

How the structure shows in well performance

Signs in well performance and their possible causes in the structure of the layer

What is seen: Early water breakthrough in some wells, fast growth of water cut
Probable cause: connected high-permeability bodies between the injector and the producer
What to check and do: tracers (markers added to the injected water), injection profiles; limit injection, level the profile (Displacement in heterogeneous reservoirs)

What is seen: A producer does not respond to injection
Probable cause: its bodies are not connected to the injectors
What to check and do: an interference test; move the injection, or add an injector

What is seen: Pressure falls faster than calculated
Probable cause: a compartment, a small connected volume
What to check and do: reservoir limit tests, material balance (Reservoir limit test)

What is seen: A new well between old ones met the layer at the initial pressure
Probable cause: a body that is not connected to the old wells
What to check and do: infill drilling guided by the connectivity model

What is seen: Some intervals in the section do not work
Probable cause: barriers and baffles in the vertical direction
What to check and do: production profiles; additional perforation, separate production of layers

What is seen	Probable cause	What to check and do
Early water breakthrough in some wells, fast growth of water cut	connected high-permeability bodies between the injector and the producer	tracers (markers added to the injected water), injection profiles; limit injection, level the profile (Displacement in heterogeneous reservoirs)
A producer does not respond to injection	its bodies are not connected to the injectors	an interference test; move the injection, or add an injector
Pressure falls faster than calculated	a compartment, a small connected volume	reservoir limit tests, material balance (Reservoir limit test)
A new well between old ones met the layer at the initial pressure	a body that is not connected to the old wells	infill drilling guided by the connectivity model
Some intervals in the section do not work	barriers and baffles in the vertical direction	production profiles; additional perforation, separate production of layers

Each sign has other causes too: the state of the near-wellbore zone, leaking cement behind the casing, the work of the equipment. We rule these out before we look for the cause in the geology.

Summaries of field data show the same pattern. Other things being equal, recovery is higher in continuous layers of shallow-marine origin, and lower in river and other “labyrinth” sequences. In these, part of the oil stays in bodies that no well has penetrated and behind baffles. For such layers the main tool is not the force of injection but the placement of wells by a model of the structure. We drill infill wells where the model predicts unpenetrated bodies. We use inclined and horizontal wells through several bodies (Horizontal wells). We move injection to bodies that are connected to producers (Why water is injected: pressure maintenance and oil displacement).

Terms and symbols

Reservoir architecture: The shape, size, structure and arrangement of the reservoir bodies and of the rocks that separate them. In Russian-language practice it is called macro-heterogeneity.
Sheet, belt, ribbon, lobe, pod: The shapes of sand bodies: wide in all directions, elongated, narrow, fan-shaped, and small and isolated.
“Layer-cake”, “jigsaw”, “labyrinth”: Bodies larger than the distance between wells, comparable with it, and much smaller than it.
$K_{\text{sand}}$ , $K_{\text{dis}}$ , $K_{\text{mer}}$ , $K_{\text{cont}}$: The coefficients of sandiness, dissection, lithological connectivity and lithological continuity.
Connectivity $C$ and $C_w$: The share of the reservoir in the largest connected body, and the share connected to wells.
Percolation threshold: The net-to-gross ratio at which a connected group of bodies first stretches across the whole layer.
Barrier and baffle: A barrier is an obstacle that nothing crosses during development. A baffle is an obstacle that only slows the flow.
Reservoir compartment: A part of an accumulation that does not communicate with the others during development.
Flow unit: A member that can be followed between wells and has a common behaviour when fluid flows.
Time constant of a compartment $\tau$: $V_p c_t/T$ is the time in which the pressure difference across the baffle falls by a factor of $e$ .

Common mistakes and misconceptions

Wrong

“The sandstones are not connected on the correlation diagram, so the bodies are disconnected.”

In fact

The diagram is a flat section, and in the volume bodies connect by going around its plane. In the lesson's model, at a net-to-gross ratio of 0.4, about a quarter of the reservoir is connected in the section, and more than 80% in the volume.

Wrong

“The initial pressures and the contact in two compartments are the same, so the compartments communicate.”

In fact

Over millions of years even a tight baffle equalises the pressure. Whether compartments communicate during development is decided by the time constant. In the lesson's example it is about 290 years, and during production the compartment works almost as a closed one.

Wrong

“There is a tight thin layer in the core, so the layers are separated.”

In fact

Core shows one point, and a thin layer may pinch out within a hundred metres. We check separation by pressures through the section in a producing layer, by production profiles and by interference tests.

Wrong

“Each new well adds reserves in proportion to the number of wells.”

In fact

In a “layer-cake”, new wells only speed up the withdrawal of the same reserves. They give new reserves when they penetrate unconnected bodies. In the lesson's model, at a net-to-gross ratio of 0.3, going from one well to four per km² adds about 10% of penetrated reservoir, and going from four to sixteen adds about 4%.

Wrong

“Rows of injectors can be oriented however is convenient.”

In fact

In a layer made of elongated bodies, rows across the bodies give a clearly larger share of reservoir with pressure support: in the lesson's model, at 500 m, about 0.92 against 0.74. But the water also goes faster along the same bodies.

In depth: advanced detail

A little percolation theory

Percolation theory studies when randomly placed elements form a connected network. In the simplest lattice problem (a lattice is a regular grid of cells), each cell is sand with probability $p$ , and otherwise shale. Neighbouring sand cells are connected. The threshold for a square lattice on a plane is about 0.593, and for a cubic lattice in space about 0.312. For overlapping bodies that are placed freely, the thresholds as fractions of the volume are as follows: spheres, about 0.290, and identically oriented cubes, 0.277. On a plane, circles give about 0.676, and identically oriented squares about 0.667.

Space against plane. In space each body has more neighbours and more ways to go around, so the threshold is more than twice as low.
Elongated bodies with one orientation. Stretching all the bodies and the layer itself in one direction does not change the links. So the threshold as a fraction of volume for identical elongated oriented bodies is the same as for cubes. What changes is only the direction along which a link appears first in a layer of finite size.
Different orientations. Long bodies with different directions cross each other more often, and their threshold is lower, down to fractions of a per cent for very elongated ones, as for fractures.
A finite layer. If the bodies are not much smaller than the layer, the transition is blurred. In a layer a few bodies in size, one body can already connect wells.
Connectivity and conductivity. A little above the threshold, the connected network rests on narrow necks, and its conductivity is low although the link exists. So near the threshold, connectivity does not yet guarantee good pressure support.

How the lesson's model is built

The block is divided into cells. At first all the cells are non-reservoir.
A body is a rectangular block of cells of a given size, with its long side along the $y$ axis. Its corner is chosen uniformly at random in an extended area, so a body may partly stick out of the block. Then the density of bodies is the same at the edges too.
Bodies are added one at a time until the share of reservoir cells reaches the set value (the last body may exceed it by fractions of a per cent). Overlapping bodies merge.
Connected groups are found by joining neighbouring reservoir cells that touch along a face (the union–find algorithm). In a section it is the same, but only in its plane.
A well is vertical and penetrates all the groups that its column of cells passes through. A group is connected to an injector or a producer if at least one such well penetrates it.
The random numbers come from the same reproducible generator as in the lesson Probabilistic volumetrics by Monte Carlo simulation, with its own starting number for each net-to-gross ratio. The results are means over realisations.

The limits of the model are these. All contacts of bodies are counted as conducting. There are no baffles inside bodies. The bodies are identical and do not attract each other as real stacked channels do. And the block is finite. The first two assumptions overstate connectivity. The last two can shift it either way. The model is good for understanding how connectivity behaves. For a particular layer, the body sizes, their distribution and the conductivity of contacts are taken from geology and checked against well behaviour.

Where the time constant of a compartment comes from

Let the pressure $p$ in the compartment be the same over its volume, and on the other side of the baffle let the pressure $p_n$ be held. The flow rate through the baffle by Darcy's law is $q = T\,(p_n - p)$ , where $T = k_b A/(\mu b)$ . This inflow raises the pressure in the compartment: $V_p c_t\,\dd p/\dd t = T\,(p_n - p)$ .

Let the difference be $\Delta = p_n - p$ . Then $\dd\Delta/\dd t = -\Delta/\tau$ with $\tau = V_p c_t/T$ , and $\Delta(t) = \Delta_0\,e^{-t/\tau}$ . If a well drains the compartment at the same time, a withdrawal term is added to the right-hand side. But the time in which the baffle can equalise the pressure stays the same, $\tau$ . The baffle itself has volume and compressibility, so a disturbance passes through it not instantly but in a time of the order of $\phi\mu c_t b^2/k_b$ . For a narrow baffle this is much less than $\tau$ .

Connections to other topics

Well correlation — “layer-cake” and “jigsaw” in correlation, and the probability that a body reaches the next well.
Facies, facies successions and sedimentary logs — facies, genetic units and the vertical sequences that the bodies are built from.
Reservoir quality: geological controls on porosity and permeability — what sets the quality of the reservoir inside bodies, and rock types.
Reservoir heterogeneity and permeability averaging — scales of heterogeneity, $k_v/k_h$ , the number $R_L$ and the correlation length.
Displacement in heterogeneous reservoirs — calculation of waterflooding of layered reservoirs: sweep through the section, and water cut.
Faults — faults as barriers and baffles, and sealing of accumulations.
Pressure gradients, fluid contacts and capillary equilibrium — contacts and pressure lines, by which separate hydrodynamic systems are recognised.
Reservoir limit test — the connected pore volume of a well from a reservoir limit test.
Horizontal wells — wells that penetrate several sand bodies at once.

Check yourself

1
A layer is made of randomly placed sand bodies, with a net-to-gross ratio of 0.4. On a correlation diagram through the wells the bodies look disconnected. What is most likely in the volume?
1. A.The bodies are connected only through the wellbores
2. B.Connectivity cannot be estimated without seismic data
3. C.The bodies are just as disconnected
4. D.Most of the reservoir is connected into one whole, by going around the plane of the diagram
Show the answer
Correct answer: D. Most of the reservoir is connected into one whole, by going around the plane of the diagram
The percolation threshold is about 0.3 in space and about 0.67 on a plane. At a ratio of 0.4, bodies in the volume already merge into large groups (in the lesson's model, more than 80% of the reservoir is in one body), but in a flat section they do not yet (about a quarter). A correlation diagram understates connectivity.
2
In four wells of a horizon, 3, 5, 4 and 6 reservoir layers are picked. The total effective thickness over the wells is 58 m, out of a total of 160 m. Find the dissection and sandiness coefficients and say what they tell about the structure.
Show the answer
$K_{\text{dis}} = (3 + 5 + 4 + 6)/4 = 4.5$ . $K_{\text{sand}} = 58/160 \approx 0.36$ . The reservoir takes about a third of the section and is split on average into four or five layers about $58/18 \approx 3.2$ m thick. The net-to-gross ratio is close to the percolation threshold in the volume. So the connectivity of the layers will depend strongly on the size of the bodies and on where they merge. It must be estimated with a model and checked with pressures.
3
Why do equal initial pressures in two neighbouring compartments not prove that they will communicate during development?
1. A.Over geological time the baffle equalises the pressure, and over the years of development it passes too little fluid
2. B.Pressures in compartments are never equal
3. C.The formation tester measures pressure inaccurately
4. D.During development the pressure in the compartments rises
Show the answer
Correct answer: A. Over geological time the baffle equalises the pressure, and over the years of development it passes too little fluid
The time constant of a compartment behind a tight baffle can be hundreds of years. This is an instant by geological standards, so by the time of discovery the pressures and contacts have equalised. But over 20–30 years of development, only a small part of the production passes through such a baffle, and the compartment works almost as a closed one.
4
The transmissibility of a baffle is 0.5 m³/(d·MPa), the pore volume of the compartment is $3\cdot10^6$ m³, the total compressibility is $1\cdot10^{-3}$ MPa⁻¹, and the pressure on the other side is held. In what time does the pressure difference across the baffle fall by half?
Show the answer
$V_p c_t = 3\cdot10^6\cdot 10^{-3} = 3000$ m³/MPa. $\tau = 3000/0.5 = 6000$ d, which is about 16.4 years. The difference halves in $\tau\ln 2 \approx 4160$ d, which is about 11.4 years. Over the life of the development, the compartment is noticeably replenished, but far from at once.
5
A layer is made of channel belts about 300 m wide, elongated from north to south. How should we lay out the rows of injectors and producers so that more of the reservoir gets pressure support?
1. A.Only an areal pattern; a row pattern is impossible
2. B.Rows from west to east, the water moves from north to south
3. C.Rows from north to south, the water moves from west to east
4. D.The orientation of the rows does not matter
Show the answer
Correct answer: B. Rows from west to east, the water moves from north to south
Rows across the bodies (west to east) cross each belt with several wells of both types, and the water goes along the belts to the producers. In the lesson's model, at a spacing of 500 m, about 0.92 of the reservoir gets support this way, against 0.74 with rows along the bodies. The price is an earlier water breakthrough along the same belts.
6
A new well, drilled between two old ones that already produce a lot of water, met the layer at the initial pressure. What does this say, and what should we do next?
Show the answer
The well penetrated a body that is not connected to the old wells. This is bypassed oil (oil that the waterflood has not reached). We must estimate the size of this body (reservoir limit test, correlation, seismic data), and refine the connectivity model, since there may be more such bodies. Then we decide how to develop it: by depletion, or with an injector of its own.

Updated: 16 October 2026