Chapter 4 Possible impact of subsidence on gas leakage to the surface from subsurface oil and gas reservoirs

Subsidence due to Fluid Withdrawal. Developments in Petroleum Science, 41

edited by G.V. Chilingarian, E.C. Donaldson and T.E Yen 9 1995 Elsevier Science B.V. All rights reserved

193

Chapter 4

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE TO THE SURFACE FROM SUBSURFACE OIL AND GAS RESERVOIRS A L E X A N D E R E. G U R E V I C H and G E O R G E V. C H I L I N G A R I A N

INTRODUCTION

Fractures in rocks in producing oil and gas fields are due to: (1) previous tectonic and diagenetic history, (2) current tectonic and seismo-tectonic movements, and (3) deformations caused by compaction of reservoir rocks and subsidence of overlying formations. The new deformations, both natural and man-induced, enhance previously formed fractures and form new ones. Fracturing modifies production, gives rise to upward gas migration, and damages surface and subsurface structures. In most cases, water or gas are injected to maintain formation fluid pressure in producing oil and gas reservoirs. This eliminates almost completely major subsidence above oil and gas producing fields, which have high permeability, simple structure, and high hydraulic connectivity of their reservoirs. However, in compartmentalized reservoirs, especially those that are divided into blocks by faults, stresses in the boundary zones of adjacent blocks can be high enough to cause fracturing. A free gas phase exists in natural gas reservoirs, oil reservoirs with a gas cap, and in underground gas storages. In oil reservoirs, reduction of formation pressure below the bubble pressure produces gas caps. If there are paths for escape from a pool, free gas migrates to the surface, which may be a cause of explosions and fires. In areas subjected to earthquakes, the upward gas migration can be a major hazard. If the oil or gas pool is intersected by an active fault, during an earthquake there will be an upsurge of gas that can cause fires well beyond the ability of Fire Departments to control them. Then a real possibility exists, especially in the presence of winds, of major disastrous fires. The basis to more effective solutions to this problem may be provided by a more thorough and rigorous analysis of the nature of the processes involved.

C U R R E N T T H E O R I E S OF F L U I D - S O L I D F O R C E I N T E R A C T I O N : A C R I T I C A L R E V I E W

There is no consensus of opinion in the literature on whether the total formation fluid pressure or just a part of it imparts stresses in a fluid-filled rock. This diversity of opinions reflects the fact that there is no consensus in understanding of the physics of fluid-solid interactions and that neither opinion can be considered as final and complete. A short analysis of the problem is, therefore, necessary.

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A.E. G U R E V I C H

A N D G.V. C H I L I N G A R I A N

Correct understanding of the fluid-solid force interaction is a must for the analysis of deformations of fluid-saturated rocks. The outcome of such an analysis has many areas of application: earthquake mechanism, hydraulic fracturing, compaction of rocks in the course of geological history and owing to reservoir pressure decline, and deformation of rocks in subsiding formations above compacting depleted reservoirs. The same theoretical basis is used in solving deformational problems in earthquake prediction and hydraulic methods of dissipating tectonic stresses by means of small earthquakes, deformations associated with oil, gas, and water production (including sand production), and environmental consequences of this production. Although this basis is very important, it is not completely clarified. Studies of fluid-solid interaction should, therefore, be continued. It is obvious that fluid-solid force interaction takes place only at the fluid-solid contacts on the surfaces of mineral and rock grains. The force acting against this surface is pore pressure. As Jaeger (1979) notes, "Pore pressures produce two separate effects: they compress the solid matter, thus reducing the volume of the solid matrix; and create body forces proportional to the variations of the pressure dp." The term "body force" is rather confusing in this application. It is correct physically to define the latter forces not as body forces (like gravity, acting on every particle of a body), but as resultants of nonuniform surface forces (pore pressures) acting against the surfaces of solid grains. There are two different approaches to the role of pore pressure in deformations of the fluid-filled rocks. One is a poro-elasticity approach (Biot, 1941; Geertsma, 1957, 1973; Jaeger and Cook, 1969; Jaeger, 1979; Fjaer et al., 1992). This approach can be illustrated by the formula for a component of the stress tensor (Geertsma, 1973):

O'ij = 2 G [eij -[-

V eSij] -(l-fl)pSij

1 -- 2 V

where cri.i = stress component related to the bulk stress system; eij = strain component; e ~-,eij dilatation or relative volume change of the bulk material; G = bulk shear or rigidity modulus; v = Poisson's bulk ratio; p = pore-fluid pressure; 13 = ratio between rock matrix and rock bulk compressibility; and ~ij ---- Kronecker's delta. This approach is based on the rigorous and definite physical concept, but it is correct for and can be applied to purely elastic, reversible deformations only. The majority of deformations due to natural and engineering processes, however, contain irreversible components that often prevail. The other approach, introduced by Terzaghi in 1923 (see Terzaghi, 1943; Terzaghi and Peck, 1967), is a concept of effective stress. It is assumed that the load, applied to a fluid-filled soil or rock, is supported by the sum of effective stress (grain-to-grain stress) of the solid frame and of pore fluid pressure. This concept was formulated purely phenomenologically. It has no clear and definite physical basis, which causes certain confusion. To some extent, an analysis of physical aspects of this concept was presented by Gurevich (1980). The effective-stress concept was first formulated on the basis of laboratory experiments. It was assumed that the applied load, L, is supported by the sum of the pore =

=

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE

195

pressure increase Ap, caused by the load application, and the stress in a solid flame, ere. The support provided by solids, within this scheme, was called effective stress. Effective stress is just a computed value and not a measured one, and is determined as follows: ere = L -

Ap

(4-1)

It is necessary to emphasize that Ap, although called the pore pressure, actually was the pressure increase, the elastic response of the pore water to deformation of a sample, caused by the applied load, and not the total pore pressure itself. The height of a laboratory specimen is, usually, about 1 inch. Thus, the hydrostatic pore pressure, before load application, is negligible in such a specimen and the excess pressure above the hydrostatic one was taken for the whole pressure value. Numerically, mathematically this was correct, but physically it was not and led to unavoidable confusion. Thus, in fact the load was supported by the excess pore pressure and additional stress in solid frame. In this model, physical meanings of measured values are quite definite: L is a new, additional load applied to a physical body in mechanical equilibrium, Ap is elastic response of the pore fluid to the total (elastic, reversible, and plastic, irreversible) deformation of the specimen. The physical meaning of the value ere, however, is not defined clearly. It is assumed that effective stress is the stress in the solid frame under these conditions, whereas actually it is the stress in the model medium, being an average stress on a horizontal plane. Later this concept was extended to the relation between the total load, including the weight of rock column, and the total pore fluid pressure acting through a buoyancy mechanism. Whereas in the previous model fluid pore pressure existed only dynamically, in the course of the deformation process, in this extended case pore fluid pressure exists even at equilibrium. At equilibrium, pore fluid pressure due to its gradient provides buoyancy of grains which results in the reduction of their weight. But owing to the fact that grain contacts are not point contacts, relation O'e = L - p

(4-2)

where total value of pressure acts, is doubtful for the majority of cemented rocks (Laubscher, 1960; Jaeger, 1979; Gurevich, 1980). It is easy to see that Eqs. 4-1 and 4-2 are physically different. In dynamic situation, hydrostatic uplift and elastic response act together. Thus, physical meaning of the effective stress concept being applied to deformations of rocks in situ is rather obscure physically and often leads to confusion. This is especially so because the effective-stress concept completely ignores both the nature of deformations and mechanical properties of rocks that are deformed. It does not take into account that not just a small piece but a large mass of rocks is being deformed as a single whole. Thus, when deformation can not be reduced to a one-dimensional model, some additional problems arise. For example, generation of vertical tension and strain of rocks in the course of subsidence of formations above a compacting reservoir is not compatible with the effective-stress concept:

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the overburden weight is not fully transmitted to the reservoir but, nevertheless, compaction continues. Substantial additional problems arise from heterogeneity of the rock mechanical properties and fractures. Owing to heterogeneity, some scale effects arise and should be somehow taken into account (Enever et al., 1990: Ito et al., 1990; Li, 1990; Ratigan, 1990; Bell and Dusseault, 1991). One more source of confusion is a tendency to believe that compaction in the laboratory tests and compaction in situ do not differ. At the same time, dependence of compressibility on loading history is a well known fact and actually measured compaction in situ is also lower than predicted from laboratory tests. For example, radioactive bullet surveys in the Groningen gas field showed that the actual compaction values were three times lower than the amount predicted (Mess, 1979). Actually, compaction in the natural environment is accompanied by many more processes and occurs at a much slower rate (Gurevich, 1969, 1980). Compaction in nature depends both on acting overburden or tectonic load and on rock strength. The rock strength is influenced by the continual tectonic movements. However slow and weak, these movements break one grain contact here, one there and, thus, provide rearrangement of grain packing and compaction without additional load. The same impact on compaction is provided by periodic changes of temperature, by seismic waves, and other factors. These mechanisms of compaction are missing in laboratory tests. In situ loading and compaction are sometimes more than six to eight orders of magnitude slower than in the laboratory tests. This means that molecular processes of slippage along grain crystal boundaries also play an incomparably more significant role in nature than in the laboratory. In addition, Gurevich et al. (1987) believe that a similarity between three-dimensional laboratory tests and natural three-dimensional deformations is at least doubtful. Any piece of rock in situ compressed by vertical force cannot change its form horizontally because it is surrounded by adjacent "pieces" that tend to have the same horizontal deformation but in opposite direction. Thus a layer of rock subjected to a vertical compression deforms only vertically. If a specimen in a laboratory test, coated on its sides with elastic material (copper foil, rubber, or other), is hydraulically compressed horizontally and by a plunger vertically, vertical compression turns an initially cylindrical specimen into a barrel; this cannot happen in situ. Naturally, stress and strain distributions in a laboratory specimen and in situ are also different. This is a very serious problem, because 3-D tests of cylindrical specimens are widely used. The effective stress concept is attractive because of its simplicity. It is believed to work well in simple cases when deformation is just a one-dimensional compression. Rieke and Chilingarian (1974) relied heavily on uniaxial compaction apparatuses because they believed that "as the overburden load becomes large enough, the pressures are probably uniaxial." In more complex situations, when deformation is two- or three-dimensional and cannot be represented by a simple compression only, this concept may not be adequate to represent the actual phenomena. To overcome this problem, the physical basis of this concept should be analyzed in great detail.

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE

197

FRACTURING DUE TO SUBSIDENCE

Subsidence phenomena have not been studied well enough from the viewpoint of fracturing, increase in the vertical permeability of rocks, and, thus, in the upward migration of gas leaking from pools. Therefore, only indirect estimations are possible.

History and causes of subsidence Subsidence caused by withdrawal of groundwater, oil, and gas has been observed and studied for more than a hundred years (Poland and Davis, 1969; Strehle, 1989). Some of the earliest best known examples of subsidence due to groundwater withdrawal are Osaka, Japan (first noted in 1885), London, England (first noted in 1865), and Mexico City, Mexico (first noted in 1929). One of the earliest examples of subsidence caused by withdrawal of oil is Goose Creek oil field, Texas, USA (first noted in 1918), described by Pratt and Johnson (1926). Thus, the phenomenon of subsidence is well known and thoroughly studied by many investigators up to now. It is physically obvious and fully recognized that subsidence is caused by compaction of reservoir rocks due to the increase of stress due to reduction of fluid pore pressure. Pratt and Johnson (1926) also indicated one more factor, which is important in formations with loose sands and other unconsolidated granular sediments: extraction of sand.

Rates of subsidence Published information on total and annual rates of subsidence is relatively abundant but quite incomplete. It allows to get an idea of an approximate maximum amount of subsidence. It is impossible, however, to get some definite dependence of the subsidence rates on pressure decline rates and on thicknesses, depths, and characteristics of reservoir and overlying rocks. The authors would also recommend the following references: Carbognin et al., 1979; Deflache, 1979; Holzer and Thatcher, 1979; Kumar, 1979; Lofgren, 1979; Scott, 1979; Meyer and Powly, 1988; Strehle, 1989; Andronopoulos et al., 1991; Balestri and Villani, 1991; Bravo et al., 1991; Esaki et al., 1991; Holdahl et al., 1991; Gambolati et al., 1991; Morales et al., 1991; Murria, 1991; Pottgens and Brouwer, 1991; Prokopovich, 1991; Rivera et al., 1991. The total subsidence can reach as much as 10 m. The largest subsidence in the San Joaquin Valley, California, by the year 1970, reached 8.5 m (28 ft). In Wilmington oil field total subsidence was 8.8 m. Lesser values of subsidence of the order of 0.9-1.5 m (3-5 ft) are commonplace. The annual rate of subsidence depends on the rate of pore pressure decline and may be as high as 0.6 m (2 ft) per year. In the San Joaquin Valley average annual rate of subsidence was up to 2.4 m (8 ft) for 10 years (1959-1969), i.e., 24 cm (0.8 ft) per year. In the Wilmington field the annual rate was up to 70 cm (2.3 ft), the total for a period of 3 years (from 1951 to 1954) being 2.1 m (7 ft). Rates of about 0.3 m (1 ft) per year are encountered often: 25 cm (0.84 ft) per

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A.E. GUREVICH AND G.V. CHILINGARIAN

year in Taipei basin, Taiwan; and 32 cm (1.07 ft) per year (in 1960) in Tokyo, Japan. Rates of the order of several cm per year are quite common.

Stress and strain distribution in subsiding formations Distribution of stress and strain within the rock mass above the compacting reservoir is the most important feature of subsidence from a viewpoint of fracturing of rocks and increase in vertical permeability. Several points should be emphasized. Horizontal tension is the highest in the zone around the central core of the subsidence bowl where horizontal compression predominates (Fig. 4-1). Horizontal displacement in the Wilmington oil field reached a maximum of about 3.66 m (Allen, 1973; Kosloff et al., 1980). This extension can be presented, for example, as four new 0.5 mm-wide fractures per each meter in the zone of tension. Vertical tension is the highest in approximately the same zone. Figure 4-2, modified after Poland and Davis, 1969, shows measured elongations in five successive moments. This combination of horizontal shear stress with vertical tension caused several small earthquakes (Lee, 1979; Kosloff et al., 1980). As Kosloff et al. emphasize, "The hypocenters were at shallow depths between 450 and 550 rn in bedded shale formation. The fault planes were always close to horizontal (Richter, 1958; Mayuga, 1970; Kovach, 1974)." Locations of epicenters are shown in Fig. 4-3 modified after Kosloff et al. (1980). It is obvious that these deformations, that released tensile strain and caused earthquakes, also formed open fractures, both lateral and vertical.

z o

EXTENSI ON ZONE

" :

:~ .

COMPRESSI ON

9

ZONE

9

:

-~-~

: :

!

EXTENSION

ZONE

/-

I

:

E

M

(n r

9

ou [ E

~ .

9

SIDEN

Fig. 4-1. Scheme of compressive and tensile stress distribution in subsiding formations.

POSSIBLE IMPACTOF SUBSIDENCEON GAS LEAKAGE

199

Fig. 4-2. Scheme of casing count surveys of a typical well in the Wilmington oil field. (Modified after Poland and Davis, 1969.)

Fig. 4-3. Locations of epicenters and slip planes of subsidence earthquakes. (Simplified after Kosloff et al., 1980.)

It is necessary to e m p h a s i z e that the very fact of the existence of vertical tensile strains and elongations above the compacting reservoir is a direct evidence that the weight of the o v e r b u r d e n is not t r a n s m i t t e d fully to the c o m p a c t i n g rocks due to the

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A.E. GUREVICH AND G.V. CHILINGARIAN

Fig. 4-4. Deformation pattern of strata above longwall extraction with strong overburden (physical model). (Simplified after Whittaker and Reddish, 1989.)

bridge-effect of overlying formations. That means that the effective-stress concept and models based on it do not exactly fit this deformation. In a sense, the existence of vertical tensile strain means that the reservoir compacts faster than the overlying beds bend down. Thus, beds break apart vertically. It is worth noting that in the case of sand production, when extraction of sand forms a cavity around the borehole, this effect will be enhanced and deformation similar to those shown in Fig. 4-4, modified after Whittaker and Reddish (1989), may be possible. The role of the strength of formations above a compacting reservoir is also indicated by a time lag in subsidence. Meyer and Powly (1988) noted that "surface subsidence commonly lags behind cumulative production". This means that for some time compaction of the reservoir is compensated not by equal subsidence but by vertical extension of the formation above the reservoir, whereas the deformation zone slowly expands upwards. Thus, first fractures should form in the caprock of a depleting reservoir. This may impair the caprock's reliability and provide some paths for the leakage of gas from the pool.

Surface fissures caused by subsidence Tensile horizontal strain causes fissures on the Earth's surface (Guacci, 1979; Holzer, 1984; Lister and Secrest, 1985; Love et al., 1987; Pewe et al., 1987; Pampeyan et al., 1988; Beckwith et al., 1991; Contaldo and Mueller, 1991; Haneberg et al., 1991; Keaton and Shlemon, 1991). Mostly, large surface fissures are caused by withdrawal of water from shallow aquifers, as a rule, alluvial. Withdrawal of oil, with substantial formation pressure decline, also causes surface deformation, which mostly consists of horizontal displacements and fractures (Pratt and Johnson, 1926; Strehle, 1989). Cracking of surface due to oil and gas withdrawal is usually not

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE

201

Fig. 4-5. Trench logs of the Pixley fissure, San Joaquin Valley, California. (Simplified after Guacci, 1979.)

investigated. Thus, fissures due to water withdrawal give useful indirect information on phenomena above oil and gas fields. Holzer (1984) reviewed occurrences and origins of earth fissures associated with groundwater overdraft in Arizona, California, and Nevada. Mostly, these fissures are associated both in space and time with the dewatering of phreatic aquifers. The preferred mechanism of fissuring is localized differential compaction of unconsolidated aquifer material over bedrock irregularities. Jachens and Holzer (1979) believe that "The association of earth fissures with zones of variable aquifer thickness suggests that differential compaction is occurring near these fissures... This is the dominant source of horizontal tension causing earth fissures in Picacho Basin. This analysis indicates that tensile strains at fissures at times of their formation ranged from 0.1 to 0.4%." These observations of the relationship between fissures and heterogeneity of formations are very important. The deepest fissure reported ~ more than 16.8 m (55.1 ft) was located near Pixley in the San Joaquin Valley, California (Guacci, 1979). It was 0.8 km (0.5 mi) long and 2.4 m (8 ft) wide. The fissure was open to a depth of 1.8 m (6 ft) (Fig. 4-5). Beckwith et al. (1991) report that "Cracks that were clearly attributed to hydrocompaction extended up to 4.4 rn (14.5 ft) deep and were no more than 1 cm (0.4 in) wide."

202 WEST 0

l.iJ U z

,,,

A.E. GUREVICH AND G.V. CHILINGARIAN EAST

196• DATUM

0,5

1,0

t Fig. 4-6. Subsidence profiles across the Picacho fault, Arizona. (Simplified after Holzer and Thatcher, 1979.)

One of the most extensive investigations was carried out by Contaldo and Mueller (1991) who studied 13 discrete locations in the Mimbres Basin in southwestern New Mexico. They found out that "measurable fissure depths range from less than 0.3 to 12.8 m... and the width of fissures ranges from incipient hairline to 9.7 m." The issue of the full depth range of fissures, most important from the gas leakage viewpoint, stays unexplored. It may be suggested that actually cracks extend much deeper than measured, but the whole problem needs more extensive field exploration.

Impact of subsidence on faults Papers on faulting related to subsidence are not numerous (Kreitler, 1977; Gabrish and Holzer, 1978; Holzer and Thatcher, 1979; Van Sickle and Groat, 1981). Holzer and Thatcher (1979) investigated changes of surface altitudes on both sides of the Picacho fault (Fig. 4-6). They simulated the process of differential movements of fault sides and showed that the difference in changes of altitudes of sides depends on the angle of a fault. Physically, it is quite clear that existing faults will provide differential movements of their sides if a shear stress exists, relative to the fault plane. The most important question from the upward gas migration viewpoint is: what are the widths of old and new fractures, that such differential movements can provide? This issue is still to be explored.

MECHANISMS OF GAS SEEPAGE FROM POOLS

Gas may migrate upwards through the water-filled permeable rocks either actively, by molecular diffusion and/or by mechanical flow, and/or passively, being transported in solution by upward flow of water (Gurevich, 1969). These three mechanisms work both separately and in combination. As gas is transported by the upward water flow, there is a partial gas separation and subsequent free-phase gas flow along with water. But mostly only one mechanism prevails.

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE

203

Upward diffusion of gas Gas diffuses from a flee-gas accumulation in all directions. There is no need in sophisticated mathematical models, however, to make an approximate, especially maximized, estimate of possible upward diffusion of gas. Moreover, sophisticated estimation is meaningless due to many uncertainties in parameters of this diffusion flow. It is most reasonable to assume that this flow is strictly vertical and to evaluate its rate assuming a steady-state flow (Fig. 4-7). Then diffusion flow, I (cm3/sec), through a unit (1 cm 2) area of horizontal cross-section will be

I-

D(C/z)

(4-3)

where D is the diffusion coefficient, C is the concentration of gas in water just above the gas pool, and z is the depth of the top of the gas pool. It is most reasonable, for this kind of estimation, to assume a uniform value for the diffusion coefficient within the whole range of depths, z. In the case of a steady-state diffusion and complete saturation of water with gas on the boundary with the gas pool, the value of C/z may be obtained from a solubility coefficient. Indeed, gas concentration will be proportional to pressure, and in the case of hydrostatic pressure distribution the value of C/p = C/pgz is equal to the value of the solubility coefficient. Somewhat overestimating the real values, the solubility coefficient for a natural gas may be taken as 0.3 (m3/m3)/MPa, which corresponds to C/z = 0.003 (m3/m3)/m. The diffusion coefficient value may be assumed, also with an obvious overestimation, to be 10 -6 cm2/s. Using these values, the diffusion flow rate through a unit horizontal area will be 3 x 10 -11 cm3/s.

Fig. 4-7. Schematic diagram of steady-state diffusion from the gas pool to the surface.

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A.E. GUREVICH AND G.V. CHILINGARIAN

This diffusion flow encounters, at a shallower depth, a lateral flow of groundwater that absorbs the incoming gas. If the width (W) of a gas source and, therefore, of the assumed lateral extent of vertical diffusion flow, can be traversed by a certain particle of the lateral groundwater flow within time t, then the volume of gas (Q) absorbed by a unit column of flowing groundwater from the diffusion flow will be:

Q = I t = I W~ v

(4-4)

where v is the lateral velocity of groundwater flow. Assuming typical values of W = 10 km and v = 1 m/day, Q will be equal to 2.6x10 -2 cm 3. Taking the height of a groundwater column, i.e., thickness of a groundwater aquifer, as 10 m, which is smaller than usual, gives average gas concentration in water of 0.000026 cm3/cm 3. Thus, even with overestimation this lucid calculation gives a concentration of gas in water very far from the saturation value (approximately 0.03 m3/m 3 or more). This means that diffusion flow cannot form free gas phase near the surface.

Mechanical mechanisms of gas migration Gas migration mechanisms depend on whether gas displaces pore water or not, and on whether a gas globule is smaller than the conducting channels or vice versa. Thus, it is convenient to consider these cases separately.

Upward migration of separate gas globules Transport of globules through porous media. The term "porous media" is referring here to rocks with intergranular and microfracture porosity. It is assumed that every gas globule is sufficiently larger than the individual pore throat or microfracture channel and the gas moves through a water-filled rock. Floating-up of oil and gas globules have been thoroughly investigated in petroleum geology (Aschenbrenner and Achauer, 1960; Gurevich, 1969; Berg, 1975; and many others). To begin moving upwards, such a globule should overcome capillary pressure at the upper gas-water interface where gas displaces water. Such a globule moves very slowly and, thus, for small globules pressure losses to overcome friction are often negligible. Except for some very special cases of intensive underground water flows, it is the excess pressure of gas that overcomes the capillary pressure at the advancing interface. Whatever the globule's shape, this excess pressure, Ap, will be equal to the difference in pressure in gas and in the corresponding column of the surrounding water. It is equal to the difference between specific weights of gas and water (see Fig. 4-8): Ap = (Yw- yg)h

(4-5)

where Yw and yg are specific weights of water and gas, respectively, and h is the globule height. The value of Yw may be assumed to be 1 g/cm 3 and that of gg, 0.2 g/cm 3 at a depth of about 2000 m, i.e., at a pressure of about 200 kg/cm 2.

205

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE

PRESSURE

~aTE~-S~TURa~ED ROCKS GAS

--~

WATER

\

"i .

W~T~RrSa;URaTZD

ROCKS

DEPTH

Fig. 4-8. Schematic diagram of excess pressure formation.

Capillary pressure, Pc, at the gas-water interface that resists the upward progress of globule depends on the values of the surface tension, contact angle, and pore radius (Fig. 4-9): Pc = 2o cos 0 / r

(4-6)

where cr is the surface tension, 0 is the contact angle, and r is the radius of a pore throat. It is obvious that to enable a globule to move upwards, the excess pressure should exceed the capillary pressure: Ap > Pc

(4-7)

Equation 4-7 can be rewritten in the following form: h >

2o- cos 0 r ( y w - yg)

(4-8)

The surface tension value for the gas-water interface depends on temperature and pressure. It is about 40 dynes/cm at a pressure of 200 kg/cm 2 and a temperature of 60~ The angle 0 may be assumed to be 60 ~ Radii of pore throats in very coarse, medium, and very fine sands are about 0.02, 0.005, and 0.001 cm, respectively. The

206

A.E. GUREVICH AND G.V. CHILINGARIAN

Water

I

I I

Gas

Fig. 4-9. Schematic diagram of the gas-water interface in a water-wet pore throat. values of h, necessary for the gas globule to begin moving upwards, will be 2.5, 10.2, and 51.0 cm, respectively. Clays have smaller pore openings and, thus, the gas globule height necessary to overcome the capillary forces will be greater. Pore radii of 10/zm and lower are common for clays. Thus, initial heights of at least 5 m are necessary. In gas pools or gas caps, the height of a continuous gas body almost always exceeds 5 m and often is more than 20 or 30 m. In most cases, therefore, the upward migration of gas through a caprock is possible. In recent unconsolidated clays that did not lose their colloidal properties, pore channels are blocked with bound water, partly or completely, at depths with temperatures below 50~ Gas cannot penetrate such a clay mechanically, i.e., as a free phase. After gas enters the caprock, its migration rate depends on the rate of water displacement. At low permeabilities of caprocks, it is very slow and geological times are required for gas to reach the earth's surface. Buoyancy as such does not determine the upward movement of a gas globule through a porous medium. The excess pressure, that overcomes capillary-force resistance, depends only on the height of the globule and on the pressure losses, within the globule, in the upward flow. The value of the buoyant force acting on the globule is not important in this case.

Floating-up of gas globules in water If the gas globule size is smaller than that of a channel, a fracture for instance, the entire globule floats up. In this case buoyancy force Fb moves the globule upwards (Fig. 4-10). For a spherical globule, this force is equal to: Fb = ~R3(yw - yg) where R is the radius of the globule.

(4-9)

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE

207

Fig. 4-10. Gas bubble floating up through water in an open fracture.

The frictional resistance, according to the Stokes law, is:

Ff = 6zr lzRv

(4-10)

where/z is the dynamic viscosity of water and v is the velocity of the bubble floating up or of the water flowing down. This globule will stay still in the case of downward flow of water if the forces of buoyancy and friction are equal. On equating Eqs. 4-9 and 4-10, therefore, one will obtain a formula for the critical velocity v: V

2R2 [

1 ] ~Z(yw - yg)

(4-11)

At a temperature of 25~ and a pressure of 20 kg/cm 2, the specific weight of a hydrocarbon (methane) gas is about 0.015 g/cm 3. Water viscosity is n e a r 10 - 2 P. Then, for a bubble with the radius of 0.1 cm, critical velocity is 0.22 cm/s. Thus, a bubble of gas can float up in a rather strong, for a geological environment, downward stream of water. This conclusion is especially important in the case of a depleted reservoir with a pressure noticeably lower than the hydrostatic one. Open fractures often exist in normal fault systems.

Upward migration of the continuous gas phase The continuous gas phase can move from a gas pool to the surface or to another pool, lying at a shallower depth, through subvertical zones with higher permeability and/or through open fractures.

Upward flow of gas through porous media. If, owing to facies variation, lithological heterogeneity, or presence of a microfractured zone there is a vertical zone or

208

A.E. GUREVICH AND G.V. CHILINGARIAN

sequence of zones of higher permeability above a gas pool, gradually continuous gas flow will be established. In such a flow there is no need to overcome the capillary forces and to displace water. Owing to lower density, pressure at the top end of a static gas column will be always higher than that at the top of the water static column through which the gas has to move (Fig. 4-8). It is possible to make an order of magnitude estimation of the flow rate in the vertical column of gas saturating permeable rocks. At any depth, the vertical flow rate of gas will be: -

k

(4-12)

Vp -- ~ ( - - O p / O z -Jr-yg)

where k is the permeability coefficient. If bottom and top pressures in the gas column are equal to water pressures, then Op/Oz are equal to the specific weight of water (1 g/cm3), i.e., 10 .3 kg cm -2 cm -1. Assuming that permeability k is 10 .2 D and gas viscosity/z is 1.5 x 10 .2 cP, v will be 7 x 10 .4 cm/s or 60 cm per day. Actual rates of the upward gas migration depend on the permeability of such subvertical zones of rocks and mostly on the lowest permeability along this path.

Upward gas migration through open fractures. It is obvious that fluid motion through open fractures is incomparably easier than through porous media, because the latter provide much more resistance to flow (friction) than the open space of a fracture. Ignoring high gas compressibility, it is possible to make an order of magnitude estimation of such gas migration using Boussinesque's formula: U= ~

3Z

"[- yg

(4-13)

where b is the fracture width. Using the same gradient and assuming b to be 1 cm, gives v equal to 5 m/day.

Leakage of gas through open fractures Abandoned boreholes penetrating gas reservoirs become rapidly filled with gas (Fig. 4-11). Pressure distribution in the gas column in the borehole is described by a well-known formula: PH ---=Pb exp --

0.00341Hp) ZT

(4-14)

where PH and Pb are pressures at a distance H from the well bottom and at the bottom, respectively; p is the gas density relative to that of air (0.7 for methane); Z is the average gas supercompressibility (deviation from ideal gas behavior); and T is the average absolute temperature. Assuming that the depth of a gas reservoir is 3500 ft (1068 m), formation pressure (depleted) is 200 psi (14 kg/cm2), temperature is 307~ and supercompressibility is 0.98, the wellhead pressure will be 185 psi (13 kg/cm2). If pressure distribution

POSSIBLE IMPACT OF SUBSIDENCE ON GAS LEAKAGE

209

Fig. 4-11. Schematic diagram of the pressure distribution in a gas-filled wellbore and in surrounding water-saturated formations. Arrows show escape of gas through holes in the casing, formed as a result of corrosion.

in water-saturated formations surrounding the well is hydrostatic, then at a depth of 426 ft (130 m) pressure in the borehole will exceed outside pressure and gas can escape into these formations and then to the surface through damaged or poor cement sheath and holes in the casing. The latter are caused by chemically aggressive corrosive waters.

SUMMARY

To summarize, the writers would like to list the areas of necessary research in this field: (1) Theoretical analysis of the fluid-solid force interaction for the full scope of natural deformation patterns and development of a system of models for these patterns. (2) Special analysis of actual force interaction in laboratory experiments and of adequacy of laboratory tests to phenomena in situ. (3) Development of new, physically definite models for different patterns of fluid-filled rock deformation. (4) A most thorough investigation of the physics and mechanics of reservoir rocks compaction and deformation of overlying subsiding rocks. Role and parameters of creep (deformation in time under constant load and effective stress) should be investigated for the compaction process. The role of discontinuous deformations should be explored for processes in subsiding formations. The precise physical mechanism of the time lag should be analyzed and included in models. (5) Empirical correlations between subsidence rates and fracturing, on the one hand, and lithology, thicknesses, and tectonic history of deforming formations combined with rates and areas of pressure decline, on the other hand, should be developed.

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(6) Rates of subsidence corresponding to an economically acceptable level of damages should be defined for different combinations of geologic environments and parameters of production. (7) Analysis of the San Andreas fault zone complex to determine areas (faults) where oil and gas fields may produce upsurge of gas to the surface during earthquakes, with resulting fires, especially in urban environments. It is necessary to establish the most dangerous areas and develop recommendations on preventive measures. (8) The authors propose that continuous measurements of properly placed gas detectors possibly can serve as an earthquake predictive technique.

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