SPE Society of Petroleun Engineers of "'ME

SPE 11970

Porosity Reduction in Sandstone by W.E. Dibble Jr., Petrophysical Services Inc., Amos Nur, * Standford u.; and J.M. Potter, Petrophysical Services, Inc . Member SPE-AIME

Copyright 1983 Society of Petroleum Engineers of AIME

This paper was presented at the 58th Annual Technical Conference and Exhibition held in San Francisco, CA, October 5-8,1983. The material is subject to correction by the author. Permission to copy is restricted to an abstract of not more than 300 words. Write SPE, 6200 North Central Expressway, Drawer 64706, Dallas, Texas 75206 USA. Telex 730989 SPEDAL.

ABSTRACT

Porosity reduction in siliceous sedimentary rocks is worthy of detailed study because the processes involved control the final porosity and permeability observed in all oil and gas reservoirs_ In addition, porosity reduction and petroleum generation and migration may also be related.

The effects on porosity reduction of the major porosity-controlling variables are virtually unknown and have been the subject of new experimental studies. Cores of St. Peter Sandstone have been subjected to high effective stress at room temperature and with fluid flow occurring at various rates. Relatively rapid pressure solution occurs even at room temperature in a flowing system.

INTRODUCTION

Porosity is one of the most important aspects of fluid-bearing rocks. However, at the present state of knowledge, it is impossible to predict the porosity or porosity distribution ~ prior in rocks in situ. The porosity of sedimentary rocks, for example, actually represents only the end state of a long and probably complicated series of processes causing mostly porosity reduction. Several processes are involved in porosity reduction including solution and pressure solution, transport through the fluid of components contained in solids, cementation, and additional dissolution and recrystallization processes. Major questions about these porosity reduction processes and their interrelationships exist.

The relationship between silica cementation and pressure solution in siliceous sedimentary rocks is unclear. It is generally not known if the silica cement in a quartz sandstone is locally or regionally derived or if the sedimentary system is open or closed with respect to fluid flow during porosity reduction. The quantitative significance

References at end of paper.

of local pressure solution in supplying silica for quartz overgrowths has been questioned by Hayes 1 Blatt2 even suggests that the bulk of the quartz cement in orthoquartzites is precipitated at very shallow depths from vertically circulating surface waters. One possibility is that quartz overgrowths formed at shallow depth and low effective stress may have resulted from pressure solution at greater depth at higher effective stress. Including fluid flow as a transport mechanism, and consequently, considering open systems is critical to any general diagenetic model.

The rate of porosity reduction is another significant problem of sandstone diagenesis with implications for both reservoir quality and production. If porosity reduction in sediments were rapid relative to sedimentation rate, high porosity in sedimentary basins would be limited to only the most shallow rocks. In fact, original porosity in oil reservoirs can persist to great depths suggesting that porosity reduction rates under some conditions are sluggish even over geologic time spans. However, if porosity reduction rates could be enhanced, perhaps by reducing pore pressures during production or by changing fluid flow rates or fluid chemistry, permanent formation damage could result.

Quantitative understanding of the effects of mechanical stress and fluid flow on porosity and permeability at constant pore pressure and confining stress are essential for our understanding the diagenetic processes in sandstones. In this paper the pertinent theory relating the critical porosity reduction variables is reviewed; the relevance of porosity reduction processes to oil and gas generation, migration and trapping is discussed; and results and implications of previous and on-going experimental work are presented.

POROSITY REDUCTION PROCESSES

The most fundamental fluid/rock interactions in the earth's crust involve porosity reduction processes. Porosity reduction processes involving

2 POROSITY REDUCTION IN SANDSTONE SPE 11970

pressure solution and cementation can produce a variety of porosity types and distributions within an oil and gas reservoir (e.g., Wescott 3): Under-standing the mechanisms for porosity changes in sandstones is important for prediction of the type and magnitude of porosity, for well completion, for understanding reservoir response, and for determining the fluid migration history of a sedimentary formation.

Furthermore, the relation between porosity and permeability which control oil and gas production are of great importance, and complex, as each reservoir is unique simply because of the many variables that 'influence porosity reduction. These variables include temperature, pore fluid pressure, lithostatic stress, fluid chemical composition, mineralogic composition, and fluid flow rate. Important differences in porosity and in permeability between reservoirs or even within a single reservoir may be caused by small changes in the porosity-reducing controlling variables. Despite the economic and scientific significance of porosity and permeability relationships in porous media such as sandstones, the effects of each controlling variable on the magnitude and rate of porosity reduction are virtually unknown.

Porosity reduction in sandstones is produced by two fundamental coupled reactions. Pressure solution is a coupled chemical-mechanical process involving dissolution at grain contacts. Directed stresses in rocks can produce high strain at grain contacts, a solid with a greater solubility than unstressed solid, and dissolution if fluid is present. The chemical dissolution process con-tributes to the transfer of components to other parts of the system.

The second fundamental part of the porosity reduction process in siliceous rocks involves the growth of unstrained or low strain solid. The thermodynamic driving force for the coupled pressure solution/crystal growth process in fluid-saturated quartz sandstones may be easily defined in principle. The total reaction free energy for dissolution of stressed quartz and growth of unstressed quartz is simply related to the difference between the solubilities of stressed and unstressed quartz at constant temperature and pressure.

For chemical equilibrium to be attained, the solubility of quartz must be the same throughout the system. Such uniformity of quartz solubility can occur only after all stressed quartz has dissolved. The elimination of strain in the system can be complete when chemical-mechanical equilibrium is attained, i.e. when the pore fluid pressure, Pf' equals the confining or lithostatic pressure, PL:

(1)

Whereas, for pressure solution and crystal growth to occur, non-equilibrium conditions apply, and

(2 )

The driving force for both pressure solution and crystal growth processes is related to the effective stress or PL - Pf . The total porosity reduction reaction affinity is simply the difference between the chemical potentials of Si02 in stressed and unstressed quartz. If the fluid or pore pressure is hydrostatic, the porosity reduction reaction affinity increase with depth. Thus, if hydrostatic fluid pressures predominate at significant depths, a large driving force can be generated to drive porosity reduction and lead eventually to the attainment of chemical-mechanical equilibrium (eqn. 1).

Any departure from equilibrium defined by eqn. (1) implies neither chemical nor mechanical equilibrium rigorously holds. Chemical-mechanical equilibrium will be attained in any open system if either porosity or permeability are reduced to zero by the general porosity reduction process. The porosity need not approach zero, however, as long as eqn. (1) holds, i.e. the fluid supports part of the lithostatic load. This latter constraint implies that for a non-zero porosity to exist at chemical-mechanical equilibrium, very low permeabilities must be produced somewhere by the porosity reduction process.

The relationship between effective stress (PL - Pf) and porosity reduction rate and magnitude has yet to be determined. On-going experimental studies hopefully will provide a useful empirical relationship between these variables. The relationship between porosity, volumetric strain, and chemical mass transfer can be more readily defined, however.

The pore volume, Vp , is defined as follows:

where VT is the total volume and Vs is the solid volume. Since Vs = ms/ps, then

(3)

(4)

where ms is the mass and Ps' the density, of the solid. By differentiating Eqn (4) at constant Ps:

dV dVT - ~ dm p = Ps s (5)

d, and dVT/V~ dE, we have:

(6) 1 d = dE - 0 dms VTPs

where is the porosity VT - Vs)/VT), E represents the volumetric strain, and V~ an initial total volume.

Eqn (6) indicates that changes in porosity are functions of both mechanical and chemical factors. The simple compaction of sediments without crystal growth, dE, is the combined chemical/mechanical

SPE 11970 W.E. Dibble, Jr., A. Nur, and J.M. Potter 3

part of the absolute porosity reduction process. An additional chemical part of the process is related to dissolution and growth of solids in an open system, dms. If ms increases per unit volume of rock via overgrowth cementation processes, the porosity decreases. If ms decreases via any kind of dissolution process in an open system, the porosity increases.

From Eqn (6) the relation for the rate of porosity change can be obtained:

d dt (7)

where S is the volumetric strain rate. For an open system involving only quartz sandstones, dms/dt = -dm~~8 /dt where the latter quantity represents 1 z the net mass flux of SiOz out of the rock and is related to dissolution and growth rates of quartz and the flow rate. Thus, if there is a net positive mass flux of SiOz out of a quartz sandstone in an open system, the mass of the solid per unit volume will decrease and the porosity will increase at constant volumetric strain:

d (l/psV~) net dmSi02 (8)

On the other hand, in a closed system, dmnet 0, and SiOz

d = ds (9)

In an open quartz sandstone system undergoing compaction, the rate of porosity change is, therefore,

d = s dt

dmnet 1 Si02

+-----psV~ dt

RATE-LIMITING POROSITY-REDUCING PROCESS

(10)

Porosity reduction is a chemically limited process, and the rates of porosity reduction are determined by chemical reaction rates. In a closed quartz sandstone system undergoing porosity changes, the steady-state condition is simply:

dissolution mass flux = growth mass flux. (11)

The rate of the overall porosity reduction process will then be determined by the slowest part of the overall process, either dissolution or growth.

The rate-limiting porosity-reducing process can be deduced from the experimental work per-formed by Sprunt and Nur 4 Hollow cores of St. Peter sandstone were subjected to various combinations of pore and confining pressures at about 275C. The rate of porosity reduction was initially large but declined significantly after 2 weeks. The porosity reduction in 2 weeks was approximately 55% and occurred solely by pressure

solution and not grain crushing.

At constant effective stress (Pc - Pf = 500 bars), the rate of porosity reduction increased with pore pressure 4 , i.e. after two weeks of reaction, the porosity reduction was greater at the larger pore pressures. However, since the solubility of quartz increases with pore pressure, rates of both dissolution and growth will increase also.

The influence of effective stress on porosity reduction rates as determined by Sprunt and Nur 4 is much more revealing. The rate of growth of unstressed quartz will not depend directly on effective stress, PL - Pf' but the rate of dissolution of stressed quartz at grain contacts should be strongly dependent on PL - Pf . In experiments in which pore pressure was fixed and confining pressure was increased, it was found that the rate of porosity reduction was independent of effective stress 4 This result indicates that the rate-controlling porosity-reducing process is the growth of unstressed quartz.

The mass flux terms may be most simply derived from expressions given by Dibble and Tillers so that eqn. (11) can be written:

dissolution growth (12) flux (stressed qtz) flux (unstressed qtz)

a where Vd and Vg represent the dissolution velocity of stressed quartz and growth velocity of unstressed quartz, respectively, and Sand p refer to surface area and density. If the growth of quartz is rate-controlling and the surface area of quartz dissolving at grain contacts is less than the 0 surface area of growing quartz (SO < S), then Vd may be much larger than Vg .

The steady-state condition for an open system is as follows:

V~ Sapo - Vg S P (13)

where dm~i6z/dt is the net Si02 mass flux from the rock and is a constant at steady-state and constant flow rate. If the rate-controlling process in an open system is the growth of quartz, dm~i6 /dt can be a large positive quantity. 2

The hypothesis that quartz growth is rate controlling during porosity reduction is supported by observations of pressure solution textures in quartz sandstones. For example, grain indentations have been found in the absence of local quartz overgrowths. One example is the Devonian Oriskany Sandstone shown on page 165 of Scholle's6 AAPG Memoir. Another excellent example is that of Dyer 7 who showed that no growth of quartz occurred during pressure solution in Moab Sandstone. Pressure solution grain indentations are ubiquitous in the

4 POROSITY REDUCTION IN SANDSTONE SPE 11970

Moab, but no quartz cement or overgrowths can be found. In both cases, all the silica dissolved at grain contacts had to be removed from the rock by fluid flow producing a significant net mass flux of silica from the rock.

POROSITY REDUCTION EXPERIMENTS

No experiments had previously been performed that conclusively demonstrated that pressure solution can even occur in quartz sandstones at room temperatures. An initial experiment of an on-going series was performed to test the following hypotheses:

1) pressure solution strain could occur in a quartz sandstone at room conditions,

2) outlet aqueous silica concentrations at high effective stress could be greater than those produced by dissolution of unstressed quartz, and

3) silica mass fluxes could be significant in a sandstone subjected to flow at high effective stress.

In this experiment, a core of St. Peter Sandstone jacketed with teflon was subjected to a constant confining pressure of just over one kilobar. The pore pressure was maintained at one bar for the duration of the flow-through. Previous to generating such high effective pressure, distilled water was flowed through the core at rates comparable to those used at the higher effective stress. Outlet silica concentrations were below quartz saturation under low effective stress conditions. The temperature was maintained at 23 2 C. St. Peter Sandstone is a nearly pure quartz sandstone which had already experienced pressure solution at grain contacts and extensive overgrowth cementation processes. Permeabilities generally range from 500 md to over one Darcy in the st. Peter.

Initial measured porosity was 18%. Flow rates were controlled accurately using a flow controllers.

Just after the effective stress had been increased slowly to one kilobar, flow of distilled water was initiated at a rate of 20 ml/day. Samples of outlet fluid were taken at intervals ranging from ~ to one day and analyzed colorimetrically for silica by the methods outlined in Marshal1 9 At a constant flow rate, net silica mass fluxes were observed to decrease rapidly and the flow rate was decreased after 1.5 days to 10 ml/day. A maximum net silica mass flux of 180 ~g/day was measured at a flow rate of 20 ml/day. The aqueous silica concentration was initially 50% greater that the quartz solubility value, but declined to less than quartz saturation in 3 days. The flow rate was decreased further in steps to 1 ml/day, and a steady-state silica flux of 3 ~g/day was attained. Decreasing the flow rate to less than 1 ml/day was impractical considering the small quantities of sample obtained.

Discussion

The rate of quartz dissolution even at elevated temperature has been shown to be linear (dc/dt = constant) in distilled waterlOo If quartz dissolution and growth kinetics are linear and reaction velocities constant, net silica mass fluxes will be independent of flow rate. The observed decrease in net silica mass fluxes strongly suggests quartz dissolution velocities decrease with time in our experiments. These results are consistent with stress relaxation occurring relatively rapidly via pressure solution at room temperature in a flowing system.

As quartz with higher strain and solubility is dissolved at grain contacts, dissolution rates may decline leading to lower net silica fluxes. The high initial fluxes and concentrations greater than quartz solubility values suggest dissolution rates are greater than quartz growth rates. However, after silica concentration levels dropped to below quartz saturation, only quartz dissolution could occur. Experiments under way at higher temperatures should allow a better assessment of pressure solution rate processes and mechanisms to be made.

Application to Oil Migration

Porosity reduction and oil generation often occur simultaneously. It has even been suggested recentlyll that porosity reduction in the Monterey Formation may lead directly to expulsion of hydro-carbons and migration up dip to more porous reservoir rocks. The timing of oil generation relative to porosity reduction is critical if such diagenetic changes can contribute to oil flow. Thus, the rate controls on porosity reduction in siliceous rocks such as the Monterey need to be understood.

Results of our preliminary experiments suggest the rate of porosity reducing processes may be influenced by flow rate. As noted by Sprunt and Nur 4 , porosity reduction rates increased as a result of slow fluid flow in one of their otherwise closed system experiments. More experimental work needs to be performed to determine the quantitative effect of such parameters as flow rate and temperature on porosity reduction rates.

NOMENCLATURE

ms Mass of solid (g)

Pc Experimental confining pressure (bar or 100 kPa)

Pf Pore fluid pressure (bar or 100 kPa)

PL Lithostatic pressure (analogous to Pc' bar)

S Surface area of unstressed solid (cm 2 )

V~ Dissolution velocity of stressed solid (cm/s) Vg Growth velocity of unstressed solid (cm/s)

SPE 11970 W.E. Dibble, Jr., A. Nur, and J.M. Potter

Vp Pore volume (cm 3)

Vs Solid volume (cm 3)

VT Total volume (cm 3)

E Volumetric strain (%)

E Volumetric strain rate

Porosity (%)

Ps Solid density (g / cm 3)

ACKNOWLEDGEMENT

Manuscript preparation services rendered by Kathy King are gratefully acknowledged.

REFERENCES

1. Hayes, J.B., 1979, "Sandstone diagenesis The hole truth": SEPM Spec. Pub. No. 26, 127-139.

2. Blatt, H., 1979, "Diagenetic processes in Sandstones": SEPM Spec. Pub. No. 26, 141-157.

3. Wescott, W.A., 1982, "Nature of porosity in Tuscarora Sandstone in the Appalachian basin": Oil and Gas Jour., Aug. 23, 1982, 159-173.

4. Sprunt, E.S. and Nur, A., 1977, "Destruction of porosity through pressure solution": Geophysics, ~, 726-741.

5. Dibble, W.E. and Tiller, W.A., 1981, "Non-equilibrium water/rock interactions - I. Model for interface-controlled reactions": Geochim. Cosmochim. Acta., 45, 79-92.

6. Scholle, P.A., 1929, "Constituents, textures, cements, and porosities of sandstones and associated rocks": Am. Assoc. Pet. Geologists, Memoir ~, 201 pp.

7. Dyer, J.R., 1982, "Jointing in sandstones, Arches National Park, Utah": PhD. Thesis, Stanford University.

8. Dibble, W.E. and Potter, J.M., 1982, "Effect of fluid flow rates on geochemical processes": SPE 10994, presented at the 57th Annual Fall Meeting, Soc. Pet. Eng., New Orleans, LA, Sept.

9. Marshall, W.L., 1980, "Amorphous silica solubilities - I. Behavior in aqueous sodium nitrate solutions: 23-300C, 0-6 Molal": Geochim. Cosmochim. Acta, 44, 907-913.

10. Van Lier, J.A., de Bruyn, P.L., and Overbeek, J. Th. G., 1960, "The solubility of quartz": J. Phys. Chern., ~, 1675-1682.

11. McGuire, M.D., Bowersox, J.R., and Earnest, L.J., 1983, "Diagenetically enhanced entrapment of hydrocarbons - Southeastern

Lost Hills fractured shale pool, Kern County, California": in Petroleum Generation and Occurrence in the Miocene Monterey Formation, California, Pacific Section SEPM, C.M. Isaacs & R.E. Garrison eds., p. 171-183.

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