--> ABSTRACT: Assessing the Relative Importance of Compaction Processes and Cementation to Reduction of Porosity in Sandstones, by Colin R. Pate; #91023 (1989)

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Assessing the Relative Importance of Compaction Processes and Cementation to Reduction of Porosity in Sandstones

Colin R. Pate

Houseknecht (1987) has made a major contribution toward the examination of the respective roles of compaction and cementation in determining ultimate sandstone porosity. He has combined detailed petrographic analyses of numerous sandstone samples with a simple graph to quantify the relative roles of compaction and cementation in the destruction and occlusion of original porosity. Unfortunately, his graph and numerical estimates are in error due to a flaw in the equation he used to calculate the fractions of original porosity destroyed by compaction. In this discussion, I point out the problem and derive simple equations that can be used to correct Houseknecht's (1987) graph and to reinterpret his results. These corrections do not completely invalidate Houseknecht's study; the simply show that mechanical compaction was even more important in the reduction of sandstone porosity than he initially indicated.

Perrier and Quiblier (1974) pointed out that in problems relating to compaction it is useful to refer to the amounts of solids and pore fluids as fractions of the total thickness of a given layer. This means that in a sedimentary layer with an initial average porosity PHIO, the total initial thickness (HT) is the sum of the thicknesses of detrital grains (HSO) and initial pore thickness (HWO), so that HWO/HT = PHIO and HSO/HT = (1 - PHIO). This is shown graphically in Figure 1. (A listing of all the variables used in this discussion is given in Appendix 1.)

After compaction and cementation of this layer, the pore space thickness is reduced to HW, the pore space thickness lost due to compaction is HL, and the cement thickness is HC. The total solid thickness is now HS (= HSO + HC). Assuming, as Houseknecht (1987) did, that there is no grain dissolution or only local dissolution and reprecipitation, we can say that at burial the thickness is

EQUATION (1)

Houseknecht (1987) used petrographic techniques to measure the amounts of cements and intergranular volume (also known as minus-cement porosity), and expressed the quantities of both as percentages of the whole rock in its present compacted and cemented state. This can be formulated mathematically as follows:

EQUATION (2)

and

EQUATION (3)

Houseknecht (1987) plotted these values on his intergranular volume vs. cement diagram (modified in Figure 2). Two special cases should be noted on this diagram. Along the vertical axis, HC is zero and

EQUATION (4)

and along the horizontal axis HL is zero and

EQUATION (5)

In Houseknecht's (1987) equation 3, he stated that the intergranular porosity of a sandstone is given by the difference between its intergranular volume and its cement content. This is correct and can be expressed as

EQUATION (6)

In Houseknecht's (1987) equation 2, he stated that along the horizontal axis of his diagram (Figure 2) the fraction of original porosity filled by cement is given by the amount of cement (expressed as a fraction of the initial total thickness) divided by the initial porosity. This can be expressed as

EQUATION (7)

In Houseknecht's (1987) equation 1, he stated that he calculated the amount of original porosity destroyed during compaction by taking the difference between the initial porosity (HWO/HT) and the present intergranular volume (HW/[HT - HL]) and dividing by the initial porosity (HWO/HT), so that

EQUATION (8)

However, note (following equation 7) that along the vertical axis of Figure 2

EQUATION (9)

Houseknecht's (1987) equation is wrong because his expression (equation 8) does not reduce to equation 9. As a result, his intergranular volume-cement diagram, which he used to estimate the amount of original porosity destroyed by cementation and mechanical compaction, is also wrong.

Equations 1-9 can be expanded to determine the relative importance of compactional processes and cementation during porosity elimination and occlusion. (These equations are expressed graphically in Figure 3 and 4.) We know that

HS = HC + HSO,

and we can let HL = HC. Since

PHIO × HT = HL + HC + HW

and

(1 - PHIO) × HT = HS - HC,

then

EQUATION (10)

This equation can be expanded to cover cases where HL = N × HC:

EQUATION (11)

Since HW/(HT - HL) = IGP (intergranular porosity), then for any value of HS

EQUATION (12)

HW and HS are then used in equation 11 to get a value for HC and, depending on the value of N, a value for HL. The value of HS is arbitrary; it makes no difference to the final result, as long as the value is used consistently in

Fig. 1. Diagram depicting burial history of sandstone layer. Area within each of two rectangles is same and is product of thickness of layer and maximum reading on fractional volume (porosity) scale (1.0). Because porosity is dimensionless ratio, area of each rectangle has dimension of length, or thickness. As layer is buried, original pore space thickness (HWO) is reduced both by mechanical compaction (HL) and cementation (HC). HL is lost as layer compacts, so actual thickness at any depth is HT - HL. See also Appendix 1.

Fig. 2. Modified version of diagram Houseknecht (1987) used to assess relative roles of compaction and cementation in reducing sandstone porosity. Scales giving amount of original porosity destroyed by cementation and mechanical compaction are in error. Therefore, dashed, diagonal line (where cementation supposedly equals compaction) is also wrong. (See text.) A and B are Houseknecht's (1987) mean values for intergranular volume and cement of his Nugget Sandstone and Bromide sandstone samples, respectively.

equations 11 and 12. Now, since HT = HL + HW + HS, the points HC/(HT - HL) and (HW + HC)/(HT - HL) can be generated, for given values of N, and plotted on the corrected intergranular volume-cement diagram (Figure 3).

Houseknecht (1987, p. 639) stated that the dashed line on Figure 2 (modified from Houseknecht's [1987] Figure 4) "...separates samples in which compaction has been more important than cementation (lower left) from samples in which cementation has been more important than compaction in determining intergranular porosity (upper right)." In fact, as can be seen on Figure 3, the line where HL = HC is actually closer to the cement axis than the compaction axis. With respect to his Ordovician Bromide sandstone samples, Houseknecht (1987) stated (p. 640) "...that 70% of the samples plot in the lower left portion of the diagram, indicating that a larger percentage of their original porosity has been destroyed by compactional processes than by cementation." If he were to replot these samples o the corrected intergranular volume-cement diagram, he would see that over 90% of the samples had their original porosity destroyed mainly by compaction. Likewise, for his Jurassic Nugget Sandstone samples the figure would be 100%, not 90%.

Figure 3 cannot be used directly to estimate the amount of original porosity destroyed by cementation and compaction. To do this, another diagram, a graph of cement and intergranular volume expressed as fractions of the original thickness (HT), must be generated.

Figure 4 is a plot of HC/HT vs. (HW + HC)/HT, and the corresponding values of HL/HWO and HC/HWO. Notice that, unlike Houseknecht's (1987) diagram (Figure 2), the intergranular porosity lines are not parallel. (Intergranular porosity is still expressed as HW/[HT - HL].) This placement occurs because, as indicated previously, along the horizontal axis HT remains constant, and along the vertical axis HT decreases. The decrease in HT down the vertical axis also causes the slight kinking of the HL vs. HC lines on Figure 3, as well as the displacement of these lines toward the cement axis. Figures 3 and 4 must be used together to estimate the relative importance of compaction and cementation in reducing porosity, as the next example will show.

Houseknecht (1987, p. 641) stated that for his Bromide sandstone samples (point B on Figure 2), "The mean value for all data...are 20.6% intergranular volume and 15.2% cement (which includes all cements). Assuming that the original porosity of the Bromide was 40%, then 48% of the original porosity has been destroyed by compactional processes, whereas only 38% has been destroyed by cementation." In fact, if his mean values are plotted on Figure 3, they lie fairly close to the grid node at the intersection of the 5% intergranular porosity line and the HL = 2 × HC line. By locating this point of the grid on Figure 4, one can see that 60% of the original porosity was destroyed by compaction and only 29% was filled with cement. Further calculations have shown that an original porosity of 50% would be reduced 74% by compaction and only 19% by cementation. Assuming an initial porosity of 30%, these values change to 37% and 43% for compaction and cementation, respectively.

Fig. 3. Corrected and expanded version of figure 2. Lines radiating outward from upper left corner join points at which HL and HC are related by some value (N). For example, where N = 1, HL = HC; pore thickness lost to compaction is equal to pore thickness lost by filling with cement. A and B are mean values for the Nugget and Bromide samples, respectively. Note that for Bromide samples, effects of compaction are about twice as great as effects of cementation. For Nugget sample, overall, compaction was almost four times greater than cementation.

Fig. 4. Plot of cement and pore volume expressed as ratios of initial total thickness. Notice that radiating HL/HC lines are now straight, and the HL = HC line is parallel to diagonal line bisecting diagram. Points A and B have been transferred to this grid from Figure 3 so that amount of original porosity destroyed by compaction and cementation can be estimated (see text for details).

In the case of the Nugget sandstone samples (point A on Figure 2), Houseknecht (1987, p. 640) states, "The mean values for all data...are 15.3% intergranular volume and 10.8% cement (which includes all cements). Assuming that the average original porosity of the Nugget was 40%, then 62% of the original porosity has been destroyed by compactional processes, whereas only 27% has been destroyed by cementation." However, plotting the mean values on Figures 3 and 4 actually show that 73% of the original porosity was destroyed by compaction and 20% of the original porosity was filled with cement. For an initial porosity of 60%, 83% of the original porosity was destroyed by compaction and 13% was filled with cement; for an initial porosity of 30%, 58% of the original porosity was destroyed b compaction and 31% was filled with cement.

Note that all of the equations presented here assume no grain dissolution occurred, i.e., that HSO remained constant. If considerable pressure solution did occur, then these equations will be invalid unless mass was conserved through completely local reprecipitation. Houseknecht (1987) also mentions that errors in the initial porosity assumption will result in errors in the estimates of compaction and cementation. Thus, uncertainty in the initial porosity figure will probably overshadow errors caused by assuming constant HSO.

APPENDIX 1

Nomenclature

HC = Total thickness of cement
HL = Thickness of pore space lost due to mechanical compaction
HS = Total solid thickness (cement plus detrital grains)
HSO = Initial total thickness of detrital grains
HT = Total initial thickness of a sedimentary layer
HW = Pore space thickness after mechanical compaction and cementation
HWO = Initial pore space thickness
IGP = Intergranular porosity
PHIO = Initial average porosity of the layer

AAPG Search and Discovery Article #91023©1989 AAPG Eastern Section, Sept. 10-13, 1989, Bloomington, Indiana.