Bulk-Volume Water

Chapter 7, Archie's Equation and Water Saturation

Learning objectives

  • Compute bulk-volume water from the logs as porosity times water saturation, and compare it with a bed's Buckles line
  • Explain why bulk-volume water is nearly constant in one rock type at irreducible water, and draw the Buckles line as a hyperbola of porosity against water saturation
  • Sort a half foot as at its line, in the transition zone or in the water leg, and say what the sources conclude about its water
  • Say why a line belongs to one rock type, and why where the transition zone starts depends on how close to irreducible is taken to count

Water in the Whole Rock

Section 1.3 defined the bulk-volume water, BVW=ϕSwBVW = \phi S_w, the share of the whole rock that is water, and Section 1.5 followed Ogbon-1's water saturation up from 100 % at the oil-water contact toward the irreducible 18 % of its drainage model. This section asks what the product does in rock at irreducible water, and what it tells a petrophysicist who has only logs.

Figure 7.3 reads Ogbon-1's net reservoir half foot by half foot, the way Section 1.1 reads it: porosity from the density log, water saturation from Archie's equation, and net reservoir by the book's cutoffs, set out in Section 13.1. Plate (a) is the plot Buckles used, porosity against water saturation, with every net-reservoir half foot of the well as a dot; plate (b) follows the bulk-volume water down the well. The figure starts at 5890 ft in the upper oil sand, where the rock is 23.2 % pore space and 19 % of that space is water, so 4.4 % of the whole rock is water.

At 5890 ft, in the upper oil sand, the rock is 23.2 % pore space and 19 % of thatspace is water, so 4.4 % of the whole rock is water. The bed's Buckles line, thewater its irreducible 18 % holds at its mean porosity of 23.0 %, is 4.1 %: this halffoot holds 1.06 times its line. Its saturation is 0.9 units over irreducible, withinthe 5 saturation units counted as at the line, so the water counts as irreducible.(a) Porosity against water saturation0204060801000102030Water saturation (% of the pore space)Porosity (%)irreduciblebed's line(b) Bulk-volume water01020305800590060006100620063006400Fraction of the rock (%)Depth (ft)φ 23.2 %BVW 4.4 %line 4.1 %Key: in (a) a dot is one net-reservoir half foot, orange at its line (within 5 saturation units ofirreducible), green in the transition zone, blue in the water leg; the grey dashed vertical is theirreducible water saturation, the dashed hyperbola the bed's Buckles line and the solid one the linethrough the half foot read. In (b) porosity is black, bulk-volume water blue, hydrocarbon shaded orange,the water above each bed's dashed line shaded blue, and the dotted line is the depth read.Where it sits: irreducible (within 5 saturation units of irreducible). The bed's line: 4.1 % (18 % ofthe bed's 23.0 % mean porosity). Water above the line: 0.2 % of the rock. Times its line: 1.06.Bulk-volume water: 4.4 % (φ Sw of the whole rock; 18.8 % is hydrocarbon).

Why the Product Goes Constant

Buckles (1965) analysed a large set of reservoir measurements and found that a hyperbola, the porosity times the water saturation equal to a constant, was a good first-order description of the field data (Kansas Geological Survey, PfEFFER Concepts). The irreducible saturation, the Survey says, generally marks the point at which hydrocarbons have permeated the entire macropore system, and it is controlled by surface tension at the internal surfaces and by capillary pressure. What is left is held by the rock's pores, so for rock of one kind the bulk-volume water at irreducible saturation is a constant of that rock, whatever its height in the column. The Survey calls it the irreducible bulk-volume water, says it will be effectively constant "provided that there is a limited range in pore size", and calls its value for a field or reservoir the Buckles number.

The AAPG Wiki states the same in terms of the column: in zones of the same pore type and geometry the bulk-volume water depends on the height above the free-water level, roughly constant above the transition zone and variable below it. With the constant written ϕ Swi=C\phi\,S_{wi} = C, a line of that constant on a plot of porosity against water saturation is the hyperbola

ϕ=CSw,\phi = \frac{C}{S_w},

a Buckles line: it passes through every porosity and saturation that make the same bulk-volume water. A rock at its line holds only the water its pores keep. A rock above its line holds more.

Reading Ogbon-1's Beds

Each reservoir bed of Ogbon-1 has a line of its own: the well's irreducible saturation, 18 %, times the bed's mean porosity. That is the figure's own reading; an analyst without core would take the line from the lower edge of the cloud on plate (a). The upper oil sand's line is 4.1 %, the shaly oil sand's 3.1 %, the tight limestone's 1.6 % and the main sand's 4.7 %. Over its 72 ft the upper oil sand's porosity runs from 22.0 % to 24.0 %, a spread of 9 % of its value, and its water saturation from 18.7 % to 19.1 %, a spread of 2 %. Its bulk-volume water runs from 4.1 % to 4.6 %, between 1.00 and 1.10 times the bed's line: the spread of its porosity, since its saturation hardly moves. On plate (a) the bed is a short, nearly upright cluster close to its hyperbola, and on plate (b) its bulk-volume water runs close to its dashed line.

The main sand shows what leaving the line looks like. At 6140 ft, near its top, the porosity is 26.3 % and the water saturation 27 %, so the bulk-volume water is 7.2 %, 1.53 times the line of 4.7 %. At 6190 ft the saturation is 49 % and the bulk-volume water 12.3 %, 2.6 times the line: 7.6 % of the rock is water above it, against 12.8 % hydrocarbon. By the 50 % water-saturation cutoff of Section 13.1 that half foot is still pay; by its line it is well into the transition zone. At 6200 ft the bulk-volume water is 16.2 %, 3.5 times the line. Below the oil-water contact, 6213.1 ft, the pores are full of water and the bulk-volume water is the porosity itself: 25.7 % at 6230 ft.

What the Line Says About the Water

This is what the line is used for. Franklin and Olson (1996) give it as a rule of experience: "Experience shows that bulk volume water (BVW) is constant for a homogeneous formation above the transition zone, where hydrocarbon is produced water-free." And: "Conversely, BVW is not constant in homogeneous formations within or below the transition zone, where water is producible." The AAPG Wiki reads the Buckles plot the same way: points from a reservoir of consistent pore type and geometry fall on a hyperbolic line where the water is near immobile, and scatter where the formation lies below the top of the transition zone.

Figure 7.3 sorts every half foot of Ogbon-1 by that rule: at its line, in the transition zone, or in the water leg. It does not model how much water a well would make; it shows where the bulk-volume water leaves its line, which is where the sources' rule says the water becomes producible. With the figure's tolerance of 5 saturation units, 205.0 ft of Ogbon-1's 386 ft of net reservoir are at their lines: the whole of the upper and shaly oil sands, 61.0 ft of the tight limestone and none of the main sand. 94.5 ft are in the transition zone, the main sand's 77.5 ft above the contact and the limestone's lowest 17.0 ft, and 86.5 ft are in the water leg.

How Close Is at the Line?

Ogbon-1's water saturation only approaches its irreducible 18 % from above, so no half foot is ever exactly at it, and where the transition zone starts depends on how close to irreducible is taken to count. The figure takes within 5 saturation units, the convention of Section 1.5, and its second slider changes it. At 1 saturation unit only 60.0 ft are at their lines and 239.5 ft are in the transition zone, the whole of the shaly oil sand and the tight limestone among them; at 15 units 250.0 ft are at their lines, 28.0 ft of them in the main sand. The 86.5 ft of water leg is the same at every tolerance. "Irreducible" in a log analysis is a distance the analyst chooses.

A Line Belongs to a Rock Type

Four beds, four lines. Ogbon-1 was built with one irreducible saturation, 18 %, for every rock, so each bed's irreducible bulk-volume water follows its porosity, and the half feet at irreducible water stand in a vertical column at 18 % on plate (a), not along one hyperbola. Buckles's rule is for rock of one kind, and the well's four reservoir beds are four kinds. A line drawn in one does not carry to another. At 6080 ft the tight limestone has 8.5 % porosity; lend it the upper oil sand's line of 4.1 % and the rock is said to hold 49 % irreducible water, where the well holds 18 %. Its bulk-volume water, 1.9 %, is under that borrowed line, but so would be any saturation up to 49 %. Its own line is 1.6 %, and its water holds 1.14 times that.

A reservoir of several rock types needs a line for each, and the Survey's condition, a limited range in pore size, says when one line will do.

Where the Number Comes From

Every bulk-volume water here is a porosity times an Archie saturation, and Archie's saturation rests on a formation-water resistivity and three constants, which Ogbon-1 was built with: Rw=0.040R_w = 0.040 ohm.m, a=1a = 1, m=2m = 2 and n=2n = 2. Sections 7.4 and 7.5 ask what a wrong exponent or a wrong water resistivity does to the saturation, and so to the bulk-volume water and to the line it is compared with.

References

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