Continental environments: aeolian and fluvial

Quick refresher

Sandy deserts lie where far less rain falls than can evaporate: in the belts of subtropical anticyclones (high-pressure zones with dry, sinking air), in the rain shadow of mountains, and in the interiors of continents. An erg is a “sand sea” of dunes and megadunes (draa) with interdune depressions between them.
Wind sorts and rounds sand well and carries off clay, so aeolian sandstones are among the best reservoirs. The most permeable laminae in them are the grain-flow laminae of the lee slope (the steep, sheltered side of a dune), and the tightest are the thin wind-ripple laminae. A cross-set is anisotropic. Across the wind, along the strike of the laminae, permeability is higher than downwind. Vertically it is lowest of all.
Only the lower parts of dunes are preserved. When dunes of spacing $\lambda$ (the distance between crests) climb at angle $\zeta$ , the thickness of a set is $\lambda\tan\zeta$ . The bounding surfaces of the sets and interdune and fluvial interbeds divide an aeolian unit into parts that communicate poorly in the vertical direction.
We distinguish rivers by the number of channels and by sinuosity (how winding they are). Braided rivers have many mobile channels and little clay, and leave wide stacked sheets. Meandering rivers have one sinuous channel, and leave belts of point bars among floodplain clays. Anastomosing rivers have stable channels between vegetated islands, and leave narrow thick ribbons.
In a meander belt, permeability falls upwards. The inclined clay drapes of lateral accretion and the clay plugs of oxbow lakes (cut-off river bends) divide the body into parts. Water moves along the base of the point bars, and oil remains in their upper part.
We estimate channel width from depth as $w = 6.8\,h^{1.54}$ . By two published formulas, the meander belt is roughly 6–10 times wider than the channel. These are estimates from modern rivers, with a scatter of several times. We use them as model scenarios, not as an answer.

Key relationships

t = \lambda\tan\zeta

thickness of a cross-set when dunes of spacing $\lambda$ climb at angle $\zeta$

k_x = \dfrac{k_\parallel k_\perp}{k_\parallel\sin^2\delta + k_\perp\cos^2\delta}

downwind permeability of a cross-set when the laminae dip at $\delta$

w = 6.8\,h^{1.54}

channel width from bankfull depth, m; meandering rivers with sinuosity above 1.7

W_\text{mb} = 7.44\,w^{1.01}

meander-belt width from channel width, m

Common pitfalls

Taking the thickness of a whole channel sandstone for the depth of a single channel: thick fluvial sandstones are made up of stacked channels.
Putting the thickness of braided-river or deltaic-distributary deposits into the formulas for meandering rivers.
Treating an aeolian unit as uniform: the bounding surfaces of the sets and interdune interbeds sharply reduce vertical permeability.
Sampling aeolian sandstone core in one direction and not knowing where the wind blew from: permeability downwind and across the wind differs by several times.
Treating a belt width calculated from a formula as known more accurately than to within a factor of a few.

After this lesson you can

describe deserts, ergs and dunes, distinguish dune deposits from interdune ones and explain what the thickness of the cross-sets of aeolian sandstones depends on
explain how grain-flow, grainfall and wind-ripple laminae differ, and calculate the permeability of a cross-set across the wind, downwind and vertically
distinguish braided, meandering, anastomosing and straight rivers by the shape of the channel, the sediment load and the sand bodies
recognise in the deposits of a meandering river point bars with lateral-accretion surfaces, oxbow clay plugs, levees, crevasse splays and the floodplain, and explain how each element affects waterflooding
estimate the width of the channel and of the channel belt from the thickness of a channel cycle, using published empirical formulas and keeping their limits in mind, and estimate the probability that the belt reaches a neighbouring well

Land as a depositional environment

On land, wind, rivers and ephemeral streams carry sediment, and it accumulates in deserts, river valleys and plains, at the foot of mountains and in lakes. For deposits to be preserved, there must be room for them. The crust must subside, or the base level (the level of a lake or the sea, below which rivers cannot cut their beds) must rise (accommodation). Where there is no room, wind and rivers merely pass the sediment through.

Continental deposits share some features. They contain no marine fauna. In a humid climate they have root traces and plant debris. In a dry climate they have red and brown colours, which iron oxides give, and salts that precipitated as water evaporated. Colour and salts hint at the climate, but we find the environment from the combination of facies and their order (Facies, facies successions and sedimentary logs). The climate also sets the range of environments: in a dry belt, dunes, salt flats, ephemeral streams and alluvial fans; in a humid one, perennial rivers (rivers that flow all year), swampy floodplains and coals.

Continental environments and their sand bodies

Environment: Erg (sandy desert)
What carries the sediment: wind
Sand bodies: units of cross-sets tens to hundreds of metres thick, separated by interdune interbeds
Reservoir properties: high porosity and permeability, anisotropy along the laminae

Environment: Braided river
What carries the sediment: floods, a large bedload
Sand bodies: wide stacked sheets of channels and bars
Reservoir properties: good; flat clay interbeds

Environment: Meandering river
What carries the sediment: steady flow, a large suspended load
Sand bodies: belts of point bars among floodplain clays
Reservoir properties: better at the base, worse upwards; inclined interbeds

Environment: Anastomosing river
What carries the sediment: quiet flow between vegetated islands
Sand bodies: narrow thick ribbons
Reservoir properties: good within the ribbons, connectivity low

Environment: Alluvial fan
What carries the sediment: debris flows and sheet floods
Sand bodies: wedges of gravels and sands at the foot of mountains
Reservoir properties: poor sorting, properties change sharply

Environment	What carries the sediment	Sand bodies	Reservoir properties
Erg (sandy desert)	wind	units of cross-sets tens to hundreds of metres thick, separated by interdune interbeds	high porosity and permeability, anisotropy along the laminae
Braided river	floods, a large bedload	wide stacked sheets of channels and bars	good; flat clay interbeds
Meandering river	steady flow, a large suspended load	belts of point bars among floodplain clays	better at the base, worse upwards; inclined interbeds
Anastomosing river	quiet flow between vegetated islands	narrow thick ribbons	good within the ribbons, connectivity low
Alluvial fan	debris flows and sheet floods	wedges of gravels and sands at the foot of mountains	poor sorting, properties change sharply

These are typical features, for a first judgement. Lake deltas and beaches are built like marine ones (Coastal, shallow-marine and deep-marine environments). Carbonate environments are covered separately (Carbonate sediments, environments and carbonate porosity).

Deserts, ergs and dunes

A desert is an area where far less rain falls than could evaporate. Such conditions arise in the belts of subtropical anticyclones (high-pressure zones), where descending air is dry; in the rain shadow of mountain ranges (the dry side, away from the rain-bearing wind); in the interiors of continents far from the oceans; and on coasts washed by cold currents. Sand covers only part of the deserts. The rest is stony and gravelly plains, dry watercourses and salt flats. Large sand masses are called ergs (sand seas), and separate sand fields without tall dunes are called sand sheets.

Wind carries sand mainly in leaps (saltation). A grain is thrown up, flies along a shallow arc and, striking the surface, knocks out other grains. Larger grains creep along in jerks. Wind lifts dust high and carries it far beyond the erg. So aeolian sand is well sorted, usually fine- and medium-grained. Frequent impacts round the grains well, their surface is often frosted (matt), and there is almost no clay or mica flakes in the sand (sorting, roundness).

Wind ripples: very low elongated ridges a few centimetres high; they move over any slopes of dunes and across the interdune depressions (wind structures).
Dunes: ridges with a spacing from metres to several hundred metres and a height from tens of centimetres to a hundred metres.
Draa, or megadunes: ridges with a spacing from hundreds of metres to several kilometres and a height from twenty to hundreds of metres; their slopes are covered with dunes of a smaller order.

The shape of dunes depends on how much sand there is and how constant the wind is. Where there is little sand and the wind blows in one direction, barchans grow. These are crescents whose horns point downwind. With plenty of sand they merge into transverse dunes with crests across the wind. Two winds that alternate and meet at an angle build longitudinal (linear) dunes, elongated along the direction of their combined push (their resultant). Winds from many directions build star dunes with several crests radiating from the summit.

Between dunes and draa lie interdune (inter-barchan) depressions. In the core of an aeolian unit, their deposits are thin interbeds among the cross-bedded sands of the dunes. For development, the main question is how tight these interbeds are. The depth of the water table beneath the floor of the depression sets the answer. Over a deep water table, the depression is dry. The wind sweeps out the fine sand, leaving a lag of coarse grains, and drives ripples across the floor. Such an interbed is close in properties to dune sand. When the capillary fringe (the wet zone just above the water table) rises to the surface, the depression becomes damp. Damp sand traps the flying grains, and instead of ripples, irregular laminae and adhesion warts (small bumps where wind-blown sand sticks to damp ground) grow. When the water reaches the surface, the depression becomes wet. Mud settles in puddles and small ponds and cracks as it dries, salts precipitate, and plants and animals settle. The higher the water table stood, the tighter and more clayey the interbed, and the more strongly it divides the sandstones vertically.

Dune laminae, cross-sets and bounding surfaces

A dune grows and moves in the same way as a ridge under water, called a subaqueous ridge (bedforms). The wind drives sand up the gentle windward (stoss) slope, and beyond the crest the sand settles on the steep leeward slope. But three different processes work on the lee slope of a dune, and each one leaves its own laminae.

Laminae of an aeolian dune

Type of laminae: Grain-flow
How they form: avalanches of sand sliding down when the slope is steeper than the angle of repose
Where on the dune: middle of the lee slope
Structure and properties: tongues up to a few centimetres thick, coarser and looser: the best reservoir

Type of laminae: Grainfall
How they form: grains that have flown over the crest settle out of the air
Where on the dune: upper part of the lee slope
Structure and properties: thin laminae draping the slope

Type of laminae: Wind-ripple
How they form: ripples migrate over the slope and build up the bed
Where on the dune: windward slope, toe, interdune depressions
Structure and properties: millimetre-scale laminae, fine at the bottom and coarse at the top; tight

Type of laminae	How they form	Where on the dune	Structure and properties
Grain-flow	avalanches of sand sliding down when the slope is steeper than the angle of repose	middle of the lee slope	tongues up to a few centimetres thick, coarser and looser: the best reservoir
Grainfall	grains that have flown over the crest settle out of the air	upper part of the lee slope	thin laminae draping the slope
Wind-ripple	ripples migrate over the slope and build up the bed	windward slope, toe, interdune depressions	millimetre-scale laminae, fine at the bottom and coarse at the top; tight

The share of each type depends on the size of the dune and on the wind: large dunes with a high lee slope have more grain-flow laminae.

The dip of grain-flow laminae is close to the angle of repose of dry sand (the steepest slope at which it stays in place), about 30–34°. So aeolian cross-laminae are steeper than many subaqueous ones. The group of laminae of one dune, called a cross-set, is cut off above and below by bounding surfaces. We divide them by scale. Reactivation surfaces within a set are the trace of a change of wind, when the slope was partly eroded and then built up again. Superposition surfaces are the traces of small dunes running over the slope of a draa. Interdune surfaces are the paths of the interdune depressions, along which each following dune cuts off the previous one. If accumulation in an erg stops for a long time, the wind blows the sand out down to the water table, and a levelled surface of non-deposition forms, which can be traced over a large area.

For dune sand to remain in the section, the floor of the erg must build up. The dunes then not only migrate but also rise: they climb at a small angle $\zeta$ . As with climbing ripples, $\tan\zeta$ is the ratio of the rate of bed build-up to the rate of dune migration (angle of climb). Build-up is usually much slower than migration, so the angle is small, and less than the dip of the windward slope. The windward slope of each dune is eroded, and only the lower part of its leeward laminae is preserved. The paths of the interdune depressions are parallel lines rising downwind at angle $\zeta$ . Adjacent paths are offset by the dune spacing $\lambda$ , so the vertical distance between them is $\lambda\tan\zeta$ .

Thickness of a cross-set when dunes climb

t = \lambda\tan\zeta,\qquad \tan\zeta = \frac{V_{agg}}{V_{mig}}

where:

$t$ thickness of one cross-set, measured vertically, m
$\lambda$ dune spacing — the distance between adjacent crests (or troughs), m
$\zeta$ angle of climb — the inclination of the path of an interdune depression to the horizontal, °
$V_{agg},\ V_{mig}$ rate of build-up of the bed and rate of dune migration, m/yr

Units: any identical units of length

Holds when

Two-dimensional dunes of the same size and spacing that migrate and climb at constant rates.
The angle of climb is less than the dip of the windward slope (the windward slope is eroded). If it is greater, the windward laminae are preserved too, and the sets pass into one another.
The thickness measured at right angles to the bounding surfaces is $\lambda\sin\zeta$ . At small angles it is the same.
In ergs with a high water table, the sand is preserved even without climbing: the wind cuts the dunes down to the damp layer, and the rise of the water table sets the thickness of the sets.

The thickness of the sets depends not only on the size of the dunes but also on how fast the bed built up. A small angle gives thin sets from large dunes. Sets as thick as the dunes are high mean very rapid accumulation.

Worked exampleHow much is left of the dunes

Given (assumed data)

Dunes: transverse, spacing $\lambda$ = 300 m, height 15 m
Angle of climb: two cases: 0.4° and 1.5°
Thickness of the aeolian unit: 60 m

Solution

At $\zeta = 0.4°$ : $t = 300\cdot\tan 0.4° = 300\cdot 0.006981 = 2.09$ m, that is $2.09/15 = 0.14$ of the dune height.
While the bed rises by 1 m, the dune travels $1/0.006981 = 143$ m.
At $\zeta = 1.5°$ : $t = 300\cdot 0.026186 = 7.86$ m, that is $7.86/15 = 0.52$ of the height; the dune travels $1/0.026186 = 38$ m per metre of build-up.
Number of sets in 60 m of the unit: $60/2.09 \approx 28.7$ at 0.4° and $60/7.86 \approx 7.6$ at 1.5°.
The set would equal the dune height at $\tan\zeta = 15/300$ , that is, at $\zeta = 2.9°$ . This is already almost the dip of the windward slope, at which the windward laminae begin to be preserved too.

Answer: At an angle of climb of 0.4°, the sets are about 2.09 m thick, only 0.14 of the dune height, and there are about 29 of them in 60 m of the unit. At 1.5°, they are 7.86 m thick, and there are about 8 sets.

What it means. The same dunes leave sets whose thickness differs almost fourfold. What decides is the rate of build-up of the bed. So we cannot use the thickness of the sets directly to judge the height of the dunes. But thick sets point either to large dunes or to rapid accumulation. For development, something else matters. A surface lined with tight ripple laminae bounds each set. The thinner the sets, the more such surfaces there are per metre of section, and the lower the vertical permeability (next section). The data in this example are assumed for illustration.

CalculatedThe dunes of the example, climbing at 1.5°. Beneath the active dunes lie cross-sets bounded by the paths of the interdune depressions. Each set is the lower part of the leeward laminae of one dune. The vertical scale is exaggerated 8 times.

Aeolian sandstones as reservoirs

Well-sorted clean sand gives high initial porosity and permeability. On a porosity–permeability plot, aeolian sandstones usually lie above the fluvial ones of the same succession (deposition and burial). Two things spoil them: early cement of the dry climate (carbonate, gypsum and anhydrite), and authigenic clay minerals, especially fibrous illite, which blocks the pore channels (clay minerals). The heterogeneity of an aeolian unit builds up at three scales.

Laminae. Grain-flow laminae are several times more permeable than thin ripple laminae. In the sandstones of the Tensleep Formation (Pennsylvanian–Permian) at one of the fields in Wyoming (USA), according to published measurements, the grain-flow sandstones have a mean porosity of 24.4% and a horizontal permeability of 1580 mD. The wind-ripple sandstones have 18.3% and 293 mD.
Sets. The lower bounding surfaces of the sets are lined with ripple laminae, so they are tighter than the main part of a set. The thinner the sets, the more of them there are per metre of section (the previous example).
Unit. Interdune, salt-flat and fluvial interbeds act as baffles and barriers (partial and complete stops to flow) in the vertical direction (baffles). In the Nugget aeolian sandstone (southwest Wyoming, USA), the permeability of interdune deposits is, according to published data, four to five orders of magnitude lower than that of dune deposits.

The permeability of a cross-set itself depends on direction. The laminae of a transverse dune strike across the wind and dip downwind at angle $\delta$ . Flow across the wind runs along the laminae. For it, the arithmetic mean over the thicknesses of the laminae, $k_\parallel$ , applies. Flow across the laminae is governed by the harmonic mean, $k_\perp$ (averaging over layers). Flow downwind has to go now along the laminae and now across them. Suppose that on average it is horizontal, because less permeable surfaces bound the set above and below. Then the equivalent permeability (the permeability of a uniform rock that would pass the same flow) turns out to be:

Permeability of a cross-set downwind, across the wind and vertically

k_x = \frac{k_\parallel k_\perp}{k_\parallel\sin^2\delta + k_\perp\cos^2\delta},\qquad k_y = k_\parallel,\qquad k_z = \frac{k_\parallel k_\perp}{k_\parallel\cos^2\delta + k_\perp\sin^2\delta}

where:

$k_x$ horizontal permeability downwind — in the direction of dip of the laminae, mD
$k_y$ horizontal permeability across the wind — along the strike of the laminae, mD
$k_z$ vertical permeability, mD
$k_\parallel,\ k_\perp$ permeability of a package of laminae along the laminae (arithmetic mean) and across them (harmonic mean), mD
$\delta$ dip angle of the laminae, °

Units: any identical units of permeability

Holds when

The laminae are flat and parallel, and each one is homogeneous. The set is much longer than the distance over which a lamina crosses it from base to top.
$k_x$ is for a flow that is horizontal on average (no net vertical crossflow). If vertical crossflow is free, $k_\parallel\cos^2\delta + k_\perp\sin^2\delta$ applies instead of $k_x$ , and this is an upper bound.
$k_z$ is for a flow that is vertical on average. The derivation is in the advanced section.

At $\delta = 0$ , all three formulas give the usual averaging of horizontal layers. At $\delta = 90°$ , the harmonic mean applies downwind. The steeper the laminae and the more their permeabilities differ, the more the permeability across the wind exceeds the permeability downwind.

Worked examplePermeability of a cross-set downwind, across the wind and vertically

Given (assumed data)

Grain-flow laminae: fraction 0.6, 1500 mD
Ripple and grainfall laminae: fraction 0.4, 60 mD
Dip of the laminae $\delta$: 28°
The set and its base: set 2.7 m; the base is lined with a ripple layer 0.3 m thick with a permeability of 30 mD

Solution

Along the laminae: $k_\parallel = 0.6\cdot1500 + 0.4\cdot60 = 924$ mD; across: $k_\perp = 1/(0.6/1500 + 0.4/60) = 141.5$ mD.
$\sin^2 28° = 0.2204$ , $\cos^2 28° = 0.7796$ .
Downwind: $k_x = \dfrac{924\cdot141.5}{203.65 + 110.31} = \dfrac{130{,}746}{313.96} = 416$ mD, where $203.65 = 924\cdot0.2204$ , $110.31 = 141.5\cdot0.7796$ .
Across the wind: $k_y = k_\parallel = 924$ mD; vertically: $k_z = 130{,}746/(720.35 + 31.19) = 174$ mD, where $720.35 = 924\cdot0.7796$ , $31.19 = 141.5\cdot0.2204$ .
Anisotropy of the set: $k_y/k_x = 924/416 = 2.22$ , $k_z/k_y = 174/924 = 0.19$ .
Together with the lining of the base (3.0 m): across the wind $(2.7\cdot924 + 0.3\cdot30)/3.0 = 835$ mD; downwind $(2.7\cdot416 + 0.3\cdot30)/3.0 = 377$ mD; vertically $3.0/(2.7/174 + 0.3/30) = 118$ mD.

Answer: The set transmits 924 mD across the wind, 416 mD downwind and 174 mD vertically. With the tight lining of its base, the values are 835, 377 and 118 mD.

What it means. Because of the dip of the laminae alone, the horizontal permeability across the wind is 2.22 times higher than downwind. A lining a tenth of the set thick lowers the horizontal values by only a tenth. It lowers the vertical permeability by as much as about a third, because it acts in series with the whole set. According to published data, in most aeolian reservoirs the ratio of the horizontal permeabilities in the two directions, along the wind and across it, is from 4 : 1 to 25 : 1, and in places up to 200 : 1. Lamina contrasts in nature can be stronger than in the example, and the sets are curved. So we take core plugs in two horizontal directions, along and across the wind, and we reconstruct the wind direction from the dip azimuths of the laminae on image logs (palaeocurrents). The data in this example are assumed for illustration.

CalculatedPermeability of the cross-set of the example against the dip of the laminae. Across the wind it does not depend on the angle. Downwind it falls as the angle grows, and vertically it rises a little. The points mark the 28° of the example.

Three rules for development follow from this. First, we orient rows of injection and production wells and horizontal wells with the wind in mind, using the wind direction reconstructed from the laminae. This is the same as taking palaeocurrents into account in fluvial units. Second, inflow to a horizontal well takes place in the plane perpendicular to the well. So a well drilled along the wind collects oil from the more permeable direction, across the wind (Horizontal wells). According to the published description of one of the aeolian fields of the North Sea, the horizontal well there was planned in the dip direction of the laminae, to connect more grain-flow laminae. Third, tight linings of the sets and interdune interbeds restrain water and gas cones (the cone-shaped rise of water or gas towards a well), but they also cut off parts of the reservoir from injection (anisotropy of a package).

River types: number of channels and sinuosity

We describe a river by two features: how many channels are active at the same time, and how sinuous (winding) each of them is. Sinuosity is the ratio of the channel length to the valley length over the same reach (stretch of river).

Channel sinuosity

P = \frac{L_\text{ch}}{L_\text{v}}

where:

$P$ sinuosity, —
$L_\text{ch}$ channel length along its axis (the line of greatest depths) over the reach, m, km
$L_\text{v}$ length of the same reach along the valley axis, m, km

Units: any identical units of length

Holds when

The reach is several bends long. For a single bend, the value is random.
For a multichannel river, sinuosity is calculated for the main channel or separately for each channel.

A straight channel has $P = 1$ . Single-channel rivers with $P$ of 1.5 and more are usually called meandering. In strongly sinuous rivers, $P$ reaches 2–3.

CalculatedThree channels over the same valley length with different sinuosity. The model assumes that the angle between the channel and the valley axis varies as a sine of the distance travelled. This describes the shape of bends well.

River types

Type: Braided
Channels: many shallow mobile channels, low sinuosity
Sediment load and banks: a large bedload, steeper gradient, erodible banks
Sand bodies: wide stacked sheets, little clay

Type: Meandering
Channels: one, sinuosity 1.5 and more
Sediment load and banks: a large suspended load, clayey vegetated banks
Sand bodies: belts of point bars among floodplain clays

Type: Anastomosing
Channels: several stable ones with vegetated islands between them
Sediment load and banks: low gradient, aggrading bed, cohesive banks
Sand bodies: narrow thick ribbons in clays and peat

Type: Straight
Channels: one, almost straight
Sediment load and banks: occurs rarely and over short reaches
Sand bodies: isolated ribbons of channel fill

Type	Channels	Sediment load and banks	Sand bodies
Braided	many shallow mobile channels, low sinuosity	a large bedload, steeper gradient, erodible banks	wide stacked sheets, little clay
Meandering	one, sinuosity 1.5 and more	a large suspended load, clayey vegetated banks	belts of point bars among floodplain clays
Anastomosing	several stable ones with vegetated islands between them	low gradient, aggrading bed, cohesive banks	narrow thick ribbons in clays and peat
Straight	one, almost straight	occurs rarely and over short reaches	isolated ribbons of channel fill

The types are parts of a continuous series: one river may change downstream from braided to meandering, and may behave differently in flood and at low water.

A well cuts through the deposits of braided rivers as a thick, almost continuous unit of sands and gravelstones (cemented gravel), with only occasional thin flat clay interbeds. On the log it is a cylinder with serrations at the interbeds (GR curve shapes). This structure is a consequence of the river's regime. Its discharge falls to low water at times and rises sharply in a flood at others. It carries a lot of sand and gravel, its gradient is greater than that of a meandering river, and its banks are made of the same loose material. Each flood rearranges the shallow, wide channels. The bars between them grow downstream and sideways, and over the years dozens of channels pass through one point of the bed, cutting off each other's deposits. The body is multistorey (channels lie on top of one another) and multilateral (channels lie side by side). Its size is set by the belt over which the channels wandered, not by a single channel. Clay manages to settle only at low water, in abandoned channels, and remains as thin flat interbeds.

In anastomosing rivers, clay, peat and roots bind the banks, the gradient is low, and the valley floor builds up quickly. It is hard for the river to erode its banks, so it does not wander. Instead it divides the valley into several stable channels between vegetated islands, and each channel grows upwards together with the valley. In section these are narrow ribbons of sand, with a width-to-thickness ratio usually less than 15, surrounded by floodplain clays and peat. The connectivity of such ribbons is low. Even with a noticeable share of sand in the section, neighbouring wells often cut different bodies.

Where a mountain stream emerges from a gorge onto a plain, it loses gradient and confinement, and drops its debris in a fan. This happens especially along active faults at the foot of ranges. This is how an alluvial fan grows. Debris flows build it, leaving a poorly sorted mass of fragments in clay. Sheet floods, spreading in a wide layer, build it too (gravity flows). The properties of such a reservoir change over distances of metres. Washed gravels and sands of flood channels lie beside the clayey deposits of debris flows, and the size of the fragments decreases quickly from the apex to the edge of the fan. So we correlate the sand bodies of alluvial fans with caution, and we estimate the hydrocarbons in place in them with a large scatter.

Example: the Jurassic of South Mangyshlak

According to published geological descriptions (data as of 2001), the Lower and Middle Jurassic productive succession of South Mangyshlak, where Uzen and Zhetybai are located, is made up, up to and including the Bajocian, of coal-bearing continental clastic rocks (rocks made of fragments). Higher up, in the Bathonian, marine interbeds are more common. The best reservoir properties are those of the channel sandstones of braided rivers, which are present in several productive layers. The lithology of Jurassic units that accumulated in fluvial and coastal environments changes sharply from place to place. So the potential of stratigraphic traps (traps formed by changes in the rock itself, not by folds or faults) was probably considered high. By that time only one small accumulation was known in a Middle Jurassic fluvial channel sandstone, at the Burmasha field, and no exploration aimed specifically at such traps had been carried out.

Meandering rivers: point bars, oxbow lakes and the floodplain

In a bend, water near the surface is pressed towards the outer bank, and water near the bed flows towards the inner one. The flow spirals like a screw. The outer (concave) bank is eroded, and a point bar grows at the inner one. The bend shifts towards the concave bank, and the bar builds sideways behind it. This is lateral accretion. Each former position of the bar slope is preserved as a gentle inclined surface dipping towards the channel. Where floods alternate with low water, clay drapes settle on these surfaces. The bar deposits then consist of inclined sand packages separated by clay films, called inclined heterolithic stratification (IHS).

The point-bar deposits become finer upwards. At the base of the channel lies a lag of pebbles and fragments of eroded clays. Above it are sands with large-scale and then small-scale cross-bedding, and at the top are silts and clays of the floodplain (fining upward in a channel). The thickness of a complete succession is close to the depth of the channel.

Oxbow lake and clay plug: in a flood, the river breaks through the narrow neck of a bend or cuts across a bar along a swale (a shallow hollow). The abandoned loop becomes an oxbow lake and fills with clay. A clay plug tens to hundreds of metres wide cuts the sand belt from top to bottom.
Levees: in a flood, the water leaving the channel immediately loses speed and drops sand and silt at the bank. This is how levees grow, sloping gently towards the floodplain. Their deposits are thin interbedding, a poor reservoir.
Crevasse splays: the flow breaks through a levee and spreads over the floodplain as a tongue of sand. The tongue is usually from tens of centimetres to a couple of metres thick and tens to hundreds of metres wide, and it becomes finer away from the breach.
Floodplain: clays and silts settling from flood water, with plant roots and soils and, in a humid climate, with coal interbeds.
Avulsion: an abrupt shift of the river. It breaks through a levee, moves to a lower part of the floodplain and builds a new belt, while the old one is left buried in clays.

The sand body of a meandering river is not the channel but the meander belt. This is the strip over which the river wandered until it left after an avulsion. It contains point bars of different years, separated by oxbow clay plugs. The belts lie in floodplain clays. The share of belts in the section and the frequency of avulsions decide how often they touch (connectivity and percolation).

SchematicSection across a meander belt (schematic, vertical scale greatly exaggerated). It shows point bars with inclined clay drapes of lateral accretion, an oxbow clay plug, a levee and a crevasse splay among floodplain clays. The arrows show the path of the injected water along the base of the bars. The upper part of the bars remains unswept.

Permeability falls upwards: the coarsest and most permeable sands lie at the base of the bar. Water is heavier than oil, so in waterflooding it moves along the bottom of the belt and breaks through early to the producing wells (succession and reservoir behaviour, gravity in waterflooding).
Inclined clay drapes of lateral accretion stop the water from rising into the upper part of the bar, so oil remains there.
Oxbow clay plugs separate neighbouring bars; wells on opposite sides of a plug may not communicate.
Levees and crevasse splays are thin, poor sands that connect the belt only weakly with neighbouring bodies.

Example: Kumkol, South Turgay Basin

The South Turgay Basin arose as a continental rift (a long zone where the crust stretched and sank) in the Jurassic. The Jurassic deposits associated with the rift are mostly lacustrine (lake deposits) and partly alluvial. At the Kumkol field, the productive horizons are the Lower Cretaceous M-I (deposits of a meandering river) and M-II (deposits of a braided river), both in the Aryskum horizon of the Neocomian, and also the Upper Jurassic horizons of the Kumkol Formation (delta-front deposits). The point bars of horizon M-I are 6–7 m thick. Inside them lie clay drapes of lateral accretion 0.2–0.6 m thick, dipping, by calculation, at 5–6°. Abandoned channels separate bars of different ages from one another. The mean permeability of the point bars is 746 mD, and of the floodplain sands 319 mD. According to the interpretation of water cut (the share of water in the produced fluid) in 367 wells and to reservoir simulation (the state at the beginning of the 2010s), the base of the bars is strongly swept. Their top and most of the floodplain sands are weakly swept or not swept at all. Such intervals make up 40% of the thickness of the bars. Residual oil in the upper part of the bars is regarded as the main target for further recovery. At the neighbouring South Kumkol field (the state in the mid-2010s), braided-river sandstones form an extensive connected body with horizontal clay interbeds. Waterflooding sweeps it evenly, and the interbeds themselves hold back the residual oil. In the sandstones of meandering rivers, water passes through the middle and lower parts of the bars.

Dimensions of channels and channel belts

Wells show the thickness of channel bodies, but they can hardly measure the width. We take the width from seismic data, if the bodies are thick enough; from outcrop analogues (similar rocks exposed at the surface); and from relationships between dimensions found on modern rivers. For a first estimate, compilations of the dimensions of ancient channel bodies from many basins are useful. By the width-to-thickness ratio (W/T), the bodies are divided into ribbons (narrow: W/T less than 5; wide: 5–15) and sheets (narrow: 15–100; wide: 100–1000; very wide: more than 1000).

Dimensions of channel sand bodies from a published compilation of ancient deposits

Bodies: Meandering rivers
Thickness: 1–38 m, more often 4–20 m
Width: 30 m–15 km, more often 0.3–3 km
W/T: 7–940, more often 30–250

Bodies: Braided and low-sinuosity rivers
Thickness: 1–1200 m (composite units), more often 5–60 m
Width: from 50 m to 1300 km and more, more often 0.5–10 km
W/T: from 15 to 15,000 and more, more often 50–1000

Bodies: Incised-valley fills
Thickness: 2–210 m, more often up to 60 m
Width: 0.1–105 km, more often 0.2–25 km
W/T: 4.6–3640, more often 10–1000

Bodies	Thickness	Width	W/T
Meandering rivers	1–38 m, more often 4–20 m	30 m–15 km, more often 0.3–3 km	7–940, more often 30–250
Braided and low-sinuosity rivers	1–1200 m (composite units), more often 5–60 m	from 50 m to 1300 km and more, more often 0.5–10 km	from 15 to 15,000 and more, more often 50–1000
Incised-valley fills	2–210 m, more often up to 60 m	0.1–105 km, more often 0.2–25 km	4.6–3640, more often 10–1000

The compilation covers more than 1500 channel bodies and valley fills from ancient and Quaternary deposits. The dimensions refer to sand bodies, not to individual channels. The thick “bodies” of braided rivers are units of many stacked channels. Incised valleys (valleys cut by rivers when base level fell) are filled with more than river sediments (Coastal, shallow-marine and deep-marine environments).

If core shows a complete cycle of one channel, from the erosional base with gravel to the floodplain clays, its thickness is close to the bankfull depth of the channel. This is the depth when the water fills the channel up to its banks. For modern meandering rivers, relationships are known between channel width and this depth, and between meander-belt width and channel width.

Width of a meandering-river channel from its depth

w = 6.8\,h^{1.54}

where:

$w$ channel width at bankfull level, m
$h$ channel depth at bankfull level; in an ancient section, the thickness of a complete channel cycle, m

Units: metres only: the formula is empirical, with a dimensional coefficient

Holds when

It comes from modern meandering rivers with sinuosity above 1.7. It does not apply to braided rivers or deltaic distributaries.
The width-to-depth ratio grows with the size of the river, so empirical formulas that relate it to other properties of the channel are more reliable for small rivers.
The thickness of a cycle is less than the channel depth if its top has been cut off by the next channel or if the sediment has compacted. In that case the width is underestimated. The thickness of a whole unit of stacked channels overestimates the depth.

Width grows faster than depth: a channel twice as deep is about $2^{1.54} \approx 2.9$ times wider. We use the formula to estimate limits, not an exact value.

Width of a meander belt from channel width

W_\text{mb} = 7.44\,w^{1.01}\qquad\text{or}\qquad W_\text{mb} = 4.3\,w^{1.12}

where:

$W_\text{mb}$ width of the meander belt — the strip between the outer edges of the bends, m
$w$ channel width at bankfull level, m

Units: metres only

Holds when

Both formulas come from published data on modern rivers. The second one comes from almost two hundred river reaches in different countries, for channels from 1.5 m to 4 km wide.
The belt width of a modern river is the span of its bends now. An ancient belt over which the river wandered for a long time may be wider, and belts narrow downstream.
The two formulas are two variants of an estimate. Their disagreement reminds us how rough the estimate is. It is not a call to choose the “right” one.

The belt is several times wider than the channel: for rivers from tens of metres to a kilometre wide, about 6–10 times. It is the width of the belt, not of the channel, that sets the width of the sand body of a meandering river.

Worked exampleChannel and belt width from core and what follows for a neighbouring well

Given (assumed data)

Lower channel cycle: 4.6 m (the core from the lesson on facies: from the base of the channels at 2427.2 m to the erosion surface at 2422.6 m, by which the upper channel truncated the top of the cycle)
River depth from the thickness of cross-sets: 2.8–4.6 m (the estimate of the same lesson)
River type: meandering with sinuosity above 1.7 (an assumption of the example, based on inclined lateral-accretion surfaces in the core and on image logs)
Neighbouring well: 400 m across the belt axis

Solution

Channel depth from the thickness of the cycle: $h = 4.6$ m; the lower estimate from the sets is 2.8 m.
Channel width: $w = 6.8\cdot 4.6^{1.54} = 6.8\cdot 10.487 = 71.3$ m; at $h = 2.8$ m, $6.8\cdot 2.8^{1.54} = 33.2$ m.
Belt width: $7.44\cdot 71.3^{1.01} = 554$ m or $4.3\cdot 71.3^{1.12} = 512$ m — 7.8 and 7.2 times wider than the channel; at $h = 2.8$ m, 256 and 217 m.
Ratio of belt width to thickness: $554/4.6 = 120$ — a wide sheet in the classification, a usual value for meandering rivers.
Take a belt that one well has penetrated. The probability that a neighbouring well 400 m away across its axis also penetrates it (the formula of the lesson on correlation) is $1 - 400/554 = 0.28$ . By the second formula it is $1 - 400/512 = 0.22$ . For a narrow belt of 256 m, it is zero. For a well 200 m away, it is $1 - 200/554 = 0.64$ .

Answer: The channel is about 71.3 m wide and the belt about 512–554 m (at the smaller depth estimate, 217–256 m). A neighbouring well 400 m away will hit the same belt only with a probability of 0.22–0.28, and in the narrow case it will not.

What it means. A 1.6-fold difference in the depth estimate gives a two-fold scatter in belt width. This is larger than the difference between the two formulas. The truncated top of the cycle and compaction of the sediment reduce the thickness, so the true width is more likely to be closer to the larger estimate. A model includes several width scenarios, and we check them against seismic attributes, pressures and the response of wells to injection. The conclusion for development does not depend on the scenario. At a 400 m spacing, we cannot correlate such belts deterministically (well to well, with certainty). The reservoir is a “mosaic” or a “labyrinth” (architecture types). Horizontal wells drilled across the elongation of the belts help to penetrate several belts with one well. The data in this example are assumed for illustration.

In the same way, in the mid-2010s, the dimensions of the bodies of the Lower Cretaceous horizon M-I of the Kumkol field were estimated. From the point-bar thickness of 6–7 m, a channel width of 100–140 m was estimated, and a meander-belt width of 800–1100 m by the first of the two formulas for the belt. Let us check this: $6.8\cdot 6^{1.54} \approx 107$ m and $6.8\cdot 7^{1.54} \approx 136$ m, belt $7.44\cdot 107^{1.01} \approx 834$ m and $7.44\cdot 136^{1.01} \approx 1063$ m. At the usual well spacings of several hundred metres, such belts too are penetrated only selectively (some wells hit them and some miss).

CalculatedChannel width and meander-belt width against channel depth, by the two formulas for the belt (logarithmic scales). The points show the example at a depth of 4.6 m.

Fluvial reservoirs in development

The river type decides almost everything that matters for development: the share of reservoir in the section, the size and shape of the bodies, their connectivity, the distribution of permeability through the thickness, and which interbeds obstruct the water. We recognise the environment from core and the succession of facies. Between wells, we recognise it from the shape of the log curves and from seismic data, always checking one against the other (GR curve shapes).

Continental reservoirs in development

Body: Aeolian unit
GR curve: cylinder, low readings
Net-to-gross ratio and connectivity: high, bodies laterally continuous
Main heterogeneity: laminae and linings of sets, interdune interbeds

Body: Braided river
GR curve: cylinder with serrations
Net-to-gross ratio and connectivity: high, bodies merge
Main heterogeneity: flat clay interbeds

Body: Meander belt
GR curve: bells, often stacked on one another
Net-to-gross ratio and connectivity: medium and low, belts in clays
Main heterogeneity: permeability falls upwards, inclined drapes, plugs

Body: Anastomosing river
GR curve: bell or cylinder, narrow
Net-to-gross ratio and connectivity: low, ribbons isolated
Main heterogeneity: ribbon boundaries

Body: Crevasse splay, levee
GR curve: funnel or serrations, thin
Net-to-gross ratio and connectivity: low
Main heterogeneity: thin poor sands

Body	GR curve	Net-to-gross ratio and connectivity	Main heterogeneity
Aeolian unit	cylinder, low readings	high, bodies laterally continuous	laminae and linings of sets, interdune interbeds
Braided river	cylinder with serrations	high, bodies merge	flat clay interbeds
Meander belt	bells, often stacked on one another	medium and low, belts in clays	permeability falls upwards, inclined drapes, plugs
Anastomosing river	bell or cylinder, narrow	low, ribbons isolated	ribbon boundaries
Crevasse splay, levee	funnel or serrations, thin	low	thin poor sands

Curve shapes suggest the environment but do not prove it. GR sees radioactivity, not grain size, and it smooths thin beds.

Connectivity. At a low net-to-gross ratio, the meander belts lie separately in clays. At a high one, they merge. The lesson on reservoir architecture covers the jump in connectivity near the percolation threshold (the point where isolated bodies suddenly link up into one connected body). The width of the belts relative to the well spacing decides how many of them the wells penetrate (wells and connectivity).
Orientation. The belts are elongated along the palaeocurrent, which we reconstruct from cross-bedding in core and on image logs (palaeocurrents). Waterflood rows across the belts put more of the reservoir under pressure support, but water moves faster along the belts to the production wells.
Inflow profile. In meander belts, the base is watered out, and oil remains in the upper parts of the bars and behind the clay plugs. We can recover more with infill wells (extra wells between existing ones) and horizontal wells in the upper part of the reservoir, by shutting off the swept base, and by redistributing injection (Displacement in heterogeneous reservoirs).
Barriers. The flat interbeds of braided rivers and the floodplain clays between belts divide the unit vertically. A tight interbed in one well does not yet mean a continuous barrier (barriers and baffles).

The uneven surface of an erg, the hollows between dunes and channel belts buried in floodplain clays create stratigraphic traps. In such a trap, a sand body pinches out up the dip or is surrounded on all sides by non-reservoir rock (stratigraphic traps). Facies maps and seismic attributes help to find these traps, and models of body dimensions, such as those given above, help to evaluate them.

Terms and symbols

Erg: A sandy desert — a mass of dunes and megadunes (draa) with interdune depressions.
Interdune deposits: Deposits of the depressions between dunes — dry, damp and wet; in the damp and wet ones, tight interbeds that divide the aeolian unit.
Grain-flow, grainfall and wind-ripple laminae: Three types of laminae of the lee slope of a dune; the first are the best reservoir, the last the tightest.
Bounding surfaces: Surfaces that bound cross-sets: reactivation, superposition and interdune surfaces.
Angle of climb $\zeta$: The inclination of the path of the ridges to the horizontal; set thickness $\lambda\tan\zeta$ .
Sinuosity $P$: The ratio of channel length to valley length.
Braided river: A river with many shallow mobile channels and bars; its deposits are wide stacked sheets.
Meandering river: A river with one sinuous channel; its deposits are belts of point bars among floodplain clays.
Point bar and lateral accretion: A bar at the inner bank of a bend that grows sideways as the bend shifts; its inclined layers are lateral-accretion surfaces.
Clay plug: The clay fill of an abandoned bend (oxbow lake), which cuts the sand belt.
Levee, crevasse splay, avulsion: A ridge of flood deposits beside the channel, a tongue of sand beyond a breach of the levee, an abrupt shift of the river to a new place.
Channel belt (meander belt): The strip over which the river wandered before an avulsion; the sand body of a meandering river.

Common mistakes and misconceptions

Wrong

“A cross-set several metres thick is a deposit of a river dune.”

In fact

Then the river would have been tens of metres deep. Sets of metres and tens of metres are usual for aeolian dunes. Sorting and roundness, grain-flow and ripple laminae, and the absence of marine fossils confirm the conclusion.

Wrong

“An aeolian sandstone is uniform: one plug characterises the reservoir.”

In fact

Permeability across the wind and downwind differs by several times, and vertically it is lower still. The linings of the sets and interdune interbeds add heterogeneity. We take plugs in two horizontal directions and vertically.

Wrong

“The belt width can be calculated exactly from the thickness of the sandstone.”

In fact

The relationships come from modern rivers with a large scatter, the depth is known only roughly, and ancient belts narrow downstream. The result is a range, and we put it into the model as several scenarios.

Wrong

“If the reservoir is fluvial, it consists of narrow ribbons.”

In fact

Braided rivers leave wide merging sheets with a high share of sand. Anastomosing rivers leave narrow isolated ribbons. We find the type of river from core and the succession of facies.

Wrong

“In waterflooding of a meander belt the oil is displaced evenly through the thickness.”

In fact

Point-bar permeability falls upwards, water is heavier than oil, and the inclined clay drapes do not let it up. The base is swept, and the top stays oil-saturated. This is the main resource for further recovery.

In depth: advanced detail

Where the formulas for tilted laminae come from

In axes tied to the laminae, the permeability tensor (the set of numbers that describes permeability in each direction) is diagonal: $k_\parallel$ along the laminae and $k_\perp$ across. We rotate the axes by the dip angle $\delta$ , so that the $x$ axis is horizontal and points downwind, and $z$ is vertical. The components of the tensor are: $k_{xx} = k_\parallel\cos^2\delta + k_\perp\sin^2\delta$ , $k_{zz} = k_\parallel\sin^2\delta + k_\perp\cos^2\delta$ , $k_{xz} = (k_\parallel - k_\perp)\sin\delta\cos\delta$ . The $y$ axis lies in the plane of the laminae, and $k_{yy} = k_\parallel$ .

Darcy's law in two dimensions: $q_x = -(k_{xx}\,\partial_x p + k_{xz}\,\partial_z p)/\mu$ , $q_z = -(k_{xz}\,\partial_x p + k_{zz}\,\partial_z p)/\mu$ . If the flow is horizontal on average, $q_z = 0$ , so $\partial_z p = -(k_{xz}/k_{zz})\,\partial_x p$ . We substitute this and get $q_x =-\dfrac{k_{xx}k_{zz} - k_{xz}^2}{k_{zz}}\,\dfrac{\partial_x p}{\mu}$ . The determinant of the tensor does not depend on rotation: $k_{xx}k_{zz} - k_{xz}^2 = k_\parallel k_\perp$ . So $k_x = k_\parallel k_\perp/k_{zz}$ , which is the formula of the main text.

In the same way, for a flow that is vertical on average ( $q_x = 0$ ), we get $k_z =k_\parallel k_\perp/k_{xx}$ . If the pressure varies only horizontally, however ( $\partial_z p = 0$ ; vertical crossflow is free), the permeability along $x$ equals $k_{xx}$ . This is greater than $k_x$ , and it is an upper bound. In a reservoir, the sets are bounded above and below, so $k_x$ applies at distances much greater than the length of a lamina. In a reservoir model with a diagonal permeability tensor, we specify this anisotropy by the values of $k_x$ , $k_y$ and $k_z$ of the cells.

For a horizontal well, what matters is the permeability in the plane perpendicular to it. Along an infinitely long well the pressure does not change, and the geometric mean of the principal permeabilities in that plane sets the planar inflow. For a well drilled downwind (along $x$ ), this is $\sqrt{k_{yy}k_{zz}} = \sqrt{k_\parallel(k_\parallel\sin^2\delta + k_\perp\cos^2\delta)}$ . For a well drilled across the wind (along $y$ ), it is $\sqrt{k_{xx}k_{zz} - k_{xz}^2} = \sqrt{k_\parallel k_\perp}$ , at any dip angle. For the set of the example, these are about 539 and 362 mD, so the well drilled downwind is about one and a half times more favourable.

Why width estimates give only an order of magnitude

Which depth. The thickness of a channel cycle is closer to the greatest depth at the concave bank, while some empirical relationships use the mean depth of the cross-section, which is noticeably smaller. If we put the thickness in place of the mean depth into such a relationship, we overestimate the width. So we use a formula together with the definition of depth for which it was found.
What has survived. The next channel may have cut off the top of a cycle, and the sediment has compacted on burial. Both causes reduce the thickness and so underestimate the width. The thickness of a unit of stacked channels, on the contrary, overestimates the depth of one channel (stacked channels).
Which river. The relationship between width and depth was found for sinuous rivers; in braided rivers the channels are much wider at the same depth, and their bodies are units of many channels.
Where along the river. According to observations in the Holocene Rhine–Meuse delta and in the lower Mississippi valley, channel belts surrounded by cohesive floodplain deposits narrow downstream by a factor of 4–6.5, and the width-to-thickness ratio decreases by a factor of 2.5–5. A single formula for the whole belt does not take this into account.
Scatter of the relationships themselves. The points of modern rivers fall around the lines of the relationships with a scatter of tens of per cent. On the advice of specialists in fluvial deposits, we use such relationships only as guides for a set of scenarios, not as a prediction.

Connections to other topics

Facies, facies successions and sedimentary logs — facies, fining-upward successions and GR curve shapes.
Primary sedimentary structures — cross-bedding, climbing of bedforms, palaeocurrents and river palaeodepth from sets.
Sediment texture: grain size, sorting and shape — sorting and roundness of aeolian and fluvial sands.
Reservoir architecture and performance — body shape, connectivity and percolation, barriers and baffles.
Reservoir quality: geological controls on porosity and permeability — how the environment and diagenesis set porosity and permeability.
Well correlation — correlation of fluvial sandstones and the probability that a body reaches a neighbouring well.
Reservoir heterogeneity and permeability averaging — anisotropy and measures of permeability heterogeneity.
Displacement in heterogeneous reservoirs — waterflooding of layered reservoirs: sweep and gravity.
Horizontal wells — productivity of horizontal wells in an anisotropic reservoir.
Coastal, shallow-marine and deep-marine environments — deltas, beaches, the shelf and deep-water fans.
Diagenesis: compaction, cementation and dissolution — compaction, cementation and dissolution after burial.

Check yourself

1
The mean thickness of cross-sets in a clean, well-rounded sandstone without clay is 3 m. Could river dunes have left them?
Show the answer
Dune height is on average about 2.9 times the thickness of the sets: $2.9\cdot 3 \approx 8.7$ m. River depth is 6 to 10 dune heights, that is, about 52–87 m. There are almost no such rivers, but the wind builds dunes tens of metres high. So an aeolian origin is more likely. Grain-flow and wind-ripple laminae with inverse grading, and the absence of marine fossils, confirm it.
2
In an aeolian reservoir the laminae dip to the east — the wind blew from the west. A horizontal well can be drilled from west to east or from north to south. In which case will the inflow be higher, other things being equal, and why?
1. A.The direction does not matter: only vertical permeability matters
2. B.West to east, because permeability is higher along the well
3. C.West to east: inflow takes place in the plane perpendicular to the well, that is from the north and south — across the wind, where permeability is higher
4. D.North to south: the well runs along the strike of the laminae, in the most permeable direction
Show the answer
Correct answer: C. West to east: inflow takes place in the plane perpendicular to the well, that is from the north and south — across the wind, where permeability is higher
Fluid converges on a horizontal well in the plane perpendicular to it. A west-to-east well receives inflow from the north and south — across the wind, along the strike of the laminae, where permeability is greatest. A north-to-south well is fed from the west and east — downwind, where the flow has to cross the tight ripple laminae. For the set in the example of the lesson, the equivalent permeability in the plane of inflow is about one and a half times higher for the first well. Fluid hardly flows along the well, so the permeability along the well has almost no effect on inflow.
3
A river: one channel, sinuosity 2.1, clayey vegetated banks, in flood the water spills over a wide floodplain. What sand bodies will it leave?
1. A.Belts of point bars with inclined clay drapes and oxbow clay plugs among floodplain clays
2. B.Narrow thick ribbons that hardly shifted sideways
3. C.Tongues of sand becoming finer from the apex of a fan to its edge
4. D.Wide stacked sheets with rare flat clay interbeds
Show the answer
Correct answer: A. Belts of point bars with inclined clay drapes and oxbow clay plugs among floodplain clays
One channel with sinuosity above 1.5 and stable banks is a meandering river. Its sand body is a meander belt: point bars building sideways, with inclined clay drapes, cut by oxbow clay plugs and surrounded by floodplain clays. Sheets are a sign of braided rivers, narrow ribbons of anastomosing ones, and tongues becoming finer from the apex of alluvial fans.
4
The thickness of a complete channel cycle of a meandering river is 6.0 m. Estimate the width of the channel and of the meander belt and the probability of meeting the same belt in a well 600 m away across its axis.
Show the answer
$w = 6.8\cdot 6.0^{1.54} \approx 6.8\cdot 15.79 \approx 107.4$ m; belt $7.44\cdot 107.4^{1.01} \approx 837$ m (by the second formula $4.3\cdot 107.4^{1.12} \approx 809$ m). The probability of meeting the same belt is $1 - 600/837 \approx 0.28$ , so the wells more likely meet different bodies. The estimate is rough. A truncated top of the cycle underestimates the width, stacked channels overestimate the depth, and the belt may narrow downstream by several times.
5
After ten years of waterflooding a reservoir made of a meander belt, the production wells give 90% water. Where is the oil most likely to remain, and what can be done about it?
Show the answer
The water has passed along the permeable base of the point bars. Their upper part, which the inclined clay drapes of lateral accretion separate off, is weakly swept. So are the bars behind oxbow clay plugs. We locate residual oil with cased-hole logging and inflow profiles. We recover more by perforating additional intervals, by drilling horizontal wells in the upper part of the reservoir, by shutting off the swept base, and by moving injection to unswept bars.

Updated: 17 October 2026