In-situ pore pressure determination by the evaluation of fractures induced during straddle-packer operations in the badurach geothermal reservoir Текст научной статьи по специальности «Науки о Земле и смежные экологические науки»

УДК 550.34

M. Albrecht, V. A. Mansurov

IN-SITU PORE PRESSURE DETERMINATION BY THE EVALUATION OF FRACTURES INDUCED DURING STRADDLE-PACKER OPERATIONS IN THE BAD URACH GEOTHERMAL RESERVOIR

During stress measurements by hydraulic fracturing, fractures are opened and induced in the near borehole stress field as a result of the inflation of a straddle-packer. Such very small events are surprisingly enough information along with televiewer measurements of the packer position to determine the in situ pore pressure. It is described the theory that goes along with the new procedure, the developed evaluation scheme leading to results for the geothermal reservoir in Bad Urach as well as the equipment designed for this unique field test.

Fracture analysis in the polyaxial, near borehole stress

field. Using the theory for stress measurements with hydraulic fracturing, the basic principles were developed by which it is possible to analyse fractures induced by effective gauge pressure in the polyaxial, near-borehole stress field.

Hubbert & Rubey [1] and Hiramatsu & Oka [2] describe the near borehole stress field with superposed effective gauge pressure:

(2 0) + й|- , (1)

Г, \ RY ан + ah 2 J R Y

1 "I" I 2 + 1 - 4 \ r, +< r 1

1 + 1*

a„ = a - 2

1 + 31*

r

\ У

(20)-p,\R I > (2)

1 + 2

r

V

- 3

I r

V У

t

Fig. 1. Description of stress in the near-borehole stress field with superposed effective gauge pressure

(aH + ah) cos (2 0), (3)

sin (2 0), (4)

where o„ - maximum effective or main stress; O, - minimum

H ’ h

effective or main stress; Ov - effective superposed pressure; p. - effective gauge pressure; v - Poisson number; R - borehole radius; r - radial distance from the borehole; 0 - strike direction towards direction of main stress; O0r - effective shear stress; Orr - effective radial stress; O00 - effective tangential stress.

Transforming their description of the stress field (see Fig. 1) into the fissure plane or any plane with the dip angle 6 leads to the maximum effective shear stress and the existing effective normal stress as given in Equation.

Where rn - the direction of maximum effective shear

* max

stress on the plane towards the dip of the plane.

oT = ° 8 sin (2 a )cos (cpmax )- a,r sin (a) sin (cp^ ), (5)

°n = °ee sin (a)2 + ^ cos (a)2, (6)

In stress measurements by hydraulic fracturing the normal stress acting on a fissure is equated with the rest or shut-in pressure after stopping the injection. Baumgartner [3] i. e. works with the far-field solution (r > 10*R) of Equation (6). The maximum effective shear stress according to Equation

(5) is evidently made up of two biaxial stress systems; on the one hand the minimum and maximum main stress lead to the shearing portion, which is described in strike direction by O0r. On the other hand a shearing portion going in the direction of the dip results from the vertical stress component Ozz dominated by the superposed pressure and the effective tangential stress O00. While in principle both shearing portions can exist independently of one another, consideration of the shear direction for the maximum effective shear stress is of major importance for interpreting fractures in the nearborehole stress field. The reason is that a fracture only occurs when the ratio of effective shear stress to normal stress first exceeds the coefficient of sliding friction p.. According to Talebi et al. [4] the cohesion (see [5]) is ignored for investigations in the granite. The fracture condition is consequently described by Equation

■> ц.

(7)

In the far field of a borehole the fracture analysis is conducted in Talebi et al. [4] by the graphic solution for biaxial systems, known as a Mohr diagram (see [5]). In the following the fracture analysis will, however, be conducted in the polyaxial, near-borehole stress field, and so the full dependences of the equations (1) to (4) on the borehole distance must be considered taking account of the fracture condition (Equation (7)). The graphic solution used for this shall therefore be called «generalized Mohr diagram».

Influence of pore pressure and effective gauge pressure on the fracture condition. Using a strike 101 < 25° relative to the maximum main pressure and a dip a >70° the stress can be determined by opening a fissure by means of hydraulic fracturing using the classic interpretation; the minimum main stress is determined here independently of the pore pressure by the shut-in pressure P . according to Equation

Sh. (8)

The maximum main stress is then calculated after determination of the refrac pressure P from Equation

SH =(3Sh - Pr)-P0. (9)

It seems reasonable to introduce a basic stress S°H which corresponds to the maximum main stress for dwindling pore pressure. The maximum main stress considering the pore pressure is then obtained according to Equation

SH=S°H-Po. (10)

With these parameter settings all physical quantities (SA, P., S°H) determined from the stress measurement are incorporated in the equations for the effective shear and normal stress, independent of the pore pressure. By separating the influence of the pore pressure it is then possible to determine the influence of the pore pressure on the fracture condition (Equation (7)).

The effective shear and normal stress and the shear direction can now be calculated in accordance with Equations, separated into a pressure, basic stress and pore pressure portion:

accommodate the acceleration sensors a dog piece was mounted on the end piece of the central bar (see Fig. 3, b).

Фшах = arctan

sin (a)

[ST -ВД(Г,0)]

sin (2 a)

so - S00 + p,\R I + P,n2(r,0, V)

1 ( R

- = +— p, | —

•(H)

sin (2 a) cos (t )P0T (r, 0, a, фшах, v), (12)

= SN+ASW = SN + p,

R

sin (a)" -P0N(?-, 0, a,v). (13)

Evaluation scheme to determine the in situ pore pressure.

When placing straddle-packers the shift in stress points leads to fractures, as with the use of straddle packer related injection pressure. The fractures occur at a distance from the borehole for which the fracture condition is satisfied. It is thus sensible to draw up an evaluation scheme for the determination of the in situ pore pressure as shown in Fig. 2.

Since the shear direction for the maximum shear stress always points in the direction of the dip of the fissure for fractures in the borehole wall (r = R), it is possible to establish a relation with fissure images made, for example, with a televiewer or FMS (formation micro scanner). If, when the packer is placed, the inflation pressure is recorded like the injection pressure, it is possible to determine from the pressure curve the effective gauge pressure p. for each event. Using the minimum main stress Sh and the basic stress SH it is now possible to present generalized Mohr diagrams without pore pressure fraction and with hydrostatic pore pressure fraction.

From this a pore pressure can be obtained graphically which just satisfies the fracture condition on the borehole wall. If the effective gauge pressure is set to zero, the fracture condition can no longer be satisfied. If the stress ratio between shear and normal stress is set equal to the sliding friction coefficient according to Equations (12) and (13) in accordance with the fracture condition, a pore pressure can be determined analytically. For fractures which can be reliably assigned to a number of fissures it is then possible to calculate a pore pressure adjusted to the ensemble of fissures using the least square method.

System extention Design of the straddle-packer to accommodate seismic sensors. Fig. 3 shows the extension made to the aluminium straddle-packer. The placing area of the packer has remained unchanged as shown in Fig. 3, a. To

Fig. 2. Evaluation scheme for the determination of the in situ pore pressure

Field data acquisition in the crystalline of Bad urach.

The aluminium straddle-packer equipped with seismic sensors was placed in the Urach 3 borehole at a depth of 3 355 m (see Fig. 4). Urach 3 is located in Bad Urach, southern Germany.

When the packer was inflated 12 events were registered. It was not possible to conduct a stress measurement subsequently because no pressure had built up in the packer interval.

The time curve of the packer pressure as shown in Fig. 5 is broken down into three phases. During the first phase the pressure in the packer rises from the hydrostatic pressure of the water column in the hydraulic line in a strictly monotonous fashion. This corresponds to the pressure buildup in the stable aluminium packer. If the aluminium yields to the packer pressure, the packer diameter increases and the pressure gradient becomes zero. In this phase the packer is placed on the borehole wall. When the aluminium is on the borehole wall in the third phase, the pressure differential to the 52,6 MPa plateau pressure of the placing phase acts on the near-borehole rock. The pressure differential corresponds to the effective gauge pressure p..

The two events in the first phase are not related to the interaction with the crystalline but must have been caused by the packer’s own dynamic.

All other events (see Table 1) are in the third phase. They occurred during the exertion of an effective gauge pressure on the near-borehole rock.

Figure 6, a shows a detailed view of event 7. As was observed with all other events, the wave onset located in the time window of the length Atpol is subject to interference from the onset of the natural vibrations of the packer at the time tR. The polarisation angle is consequently determined by a polarisation analysis of the polarisation window Atpol

[6]. This polarisation should be identical for all signal transformations, i.e. for the ground displacement, the velocity and the measured acceleration. Cassell et al. (1990), however, take as a basis a purely subjective evaluation of the transformation on which the polarisation is based. To avoid

this, an evaluation criterion was developed based on the rectilinearities of the first onsets without any transformation:

£ r -ф,

Ф = -Е1----------------

^ RG

(14)

Only transformations are considered with rectilinearities exceeding a specific threshold. In the case of the given signals a threshold value of 0.9 proved acceptable.

Table 1

Events during the exertion of an effective gauge pressure pt in phase 3

Event 1 2 3 4 5 6 7 8 9 10

pi MPa 0.2 0.9 1.2 1.5 2.4 3.0 3.2 5.2 9.0 12.1

Fig. 3. Extension of the aluminium straddle packer with seismic sensors: a - unmodified MESY packer element; b - dog piece to accommodate the acceleration sensors

Fig. 4. Tow-arm FMS caliber log (Schlumberger-Service) from the Urach 3 borehole

Fig. 5. Packer pressure curve when placing the packer and the time points (o) at which events were registered

i=1

The degree RG of rectilinearity gives the number of the transformations to be taken as a basis for the averaging. The results are recorded in Table 2.

The result obtained from Table 2 is shown in Fig. 7. The polarisation angles were mirrored with reference to the y axis in order to obtain a direct comparison with the fissure image obtained by the high-temperature televiewer (manufacturer: DMT).

To record the fissure geometries for the purpose of fracture analysis the depth interval of 3 352...3 357 m was analysed that has been recorded previously by the DMT

high-temperature televiewer. The depth interval had to be extended in each case by one metre beyond the packer limits to consider a realistic depth error of 1 m.

Fig. 8 shows the normed televiewer log including the identified fissures, which are shown in synthetic form next to the televiewer log.

The magnetically oriented results are shown in the combined presentation of rose diagram and polar projection in Fig. 9. According to Heinemann & Troschke [7] the main stress direction for the Urach 3 borehole is at N172°E ±7°. Consequently the strike ofthe fissures identified in the packer

Table 2

Degree of rectilinearity RG and polarisation angle of the events from phase 3

Event 1 2 3 4 5 6 7 8 9 10

RG 1 1 2 3 1 2 3 1 0 1

ф 12.2 87.9 -21.2 -8.8 27.9 11.5 12.3 10.6 - 19.4

10 f. з

n\

1 ' X

Fig. 7. Polarisations or dip angles of the events from phase 3

Fig. 6. Enlargement of the polarisation window AtPol to determine the polarisation angle of event 7 out of phase 3 (a) and the related hodograph (b). In addition the polarisation direction determined according to Montalbetti & Kanasewich [6] is plotted as well

Fig. 8. Televiewer log of the packer position in the Urach 3 borehole (DMT Service)

position (see Table 3) points in the direction of the maximum main stress and the borehole brake-outs, evident in the televiewer log, point in the direction of the minimum main stress (see Barton et al. [8]).

Application of generalized Mohr diagrams to determine the in situ pore pressure. Correlating dips of events that occurred on pre-existing fissures and dips of fissures identified through i. e. televiewer measurements allow to identify the corresponding effective gauge pressure that caused the events. Those results are entered into the evaluation scheme of Fig. 2 to determine the in situ pore pressure at the packer position. A comparison of Figure 7 and Fig. 9 produces the correlations as shown in Table 4.

A hydraulic fracturing test performed by the company MESY at a depth of 3 350 m resulted in a minimum main stress of S, = 42 MPa and a maximum main stress of SH = 88 MPa - corresponding to a superposition pressure Sv - according to Heinemann & Trotschke [7] with the assumption of a negligible pore pressure. According to Rummel et al. [9] a Poisson number of 0.25 and a sliding friction coefficient of 0.7 can be calculated for this depth. With the rock parameters and the main stresses given for the project depth it is now possible to calculate generalized Mohr diagrams.

Figure 10, a shows the generalized Mohr diagram for negligible pore pressure. Figure 10, b shows the shear direction assigned to the fissures for the maximum shear

S

Fig. 9. Dip (■) and dip direction (-) of the fissures identified in the packer position

stresses as a function of the relative borehole distance R / r. The curves shown in Fig. 10, a, for each fissure, correspond to the ratio of OT to ON that is changing with the distance from the borehole. The beginning of the curves (marked with points (•)) corresponds to the effective tangential or normal stresses present on the borehole wall. The other end of the curve corresponds to the infinite distance from the borehole (r > 10*R), as is referred to as a special case in the conventional Mohr diagram. The radial stress ratios do not satisfy the fracture condition (Equation (7)). As a result the Bad Urach crystalline would be stable for negligible pore pressure both in the vicinity of the borehole and at a greater distance from it.

Figures 11, a and b show the results for a pore pressure of 33 MPa, corresponding to the hydrostatic pressure. The maximum main stress was corrected according to Equation (10). It is evident that the stress ratios mainly satisfy the fracture condition. A stable state is only achieved when no sliding on the fissure planes is possible because of compaction of the crystalline. Only fissure 4 (see Table 4) is stable in the vicinity of the borehole.

Fig. 12 shows the extended Mohr diagram for a pore pressure of 26 MPa, which results in fulfilment of the fracture condition by shifting the stress ratios with negligible pore pressure (see Fig. 10). The effective gauge pressure from Table 4 has been included as well.

Fig. 13 shows the extended Mohr diagram for the pore pressure determined in Fig. 12 without effective gauge pressure (p= 0 MPa). It can be seen that there was a stable near-borehole system at the beginning of the packer measurement, which only became unstable when the effective gauge pressures of Table 4 were reached.

The result is a pore pressure of 78% of the hydrostatic pressure for a depth of 3 355 m in the Bad Urach crystalline.

A new scientific method has been developed to determine the in-situ pore pressure from within a borehole. The first field results are promising, to say the least. Applying the new method allowed to successfully determine the pore pressure for the Bad Urach crystalline. This now allows to calculate reliable stability assessments for Hot Dry Rock (HDR) reservoirs.

References

1. Hubbert, M. K. Role of fluid pressure in mechanics of overthrust faulting / M. K. Hubbert, W. W. Rubey // Bull. of the Geophys. Society of America, Vol. 70. 1959. P. 115.

Table 3

Strike relative to the maximum main stress direction N172°E ±7° and fracture dip identified in the packer position

Fissure 1 2 3 4 5 6 7 8

Strike,0 6 -19 4 36 75 7 -11 -27

Dip, o 76 49 75 61 66 81 73 73

Table 4

Fissure and event correlations

Fissure 1 2 3 4 5 6 7 8

Event 6 - 1, 7 3 - 8 5 -

Strike, o 6 4 36 7 -11

О £ Q 76 75 61 81 73

Pi, MPa 3.0 0.2, 3.2 1.2 5.2 2.4

a b

Fig. 10. Extended Mohr diagram for negligible pore, including the effective gauge pressures (a); shear directions of the maximum shear stresses as a function of the relative borehole distance R / r (b). The fissures are numbered according to Table 4

Fig. 11. Extended Mohr diagram for pore pressure corresponding to the hydrostatic pressure, including the effective gauge pressures (a); shear directions of the maximum shear stresses as a function of the relative borehole distance R / r (b). The fissures are numbered according to Table 4

Fig. 12. Extended Mohr diagram for a pore pressure of 26 MPa, including the effective gauge pressures (a); shear directions of the maximum shear stresses as a function of the relative borehole distance R / r (b). The fissures are numbered according to Table 4

o„ IMPal

R/r

b

Fig. 13. Extended Mohr diagram for negligible pore pressure, without the effective gauge pressure (p = 0 MPa) (a); shear directions of the maximum shear stresses as a function of the relative borehole distance R / r (b).

The fissures are numbered according to Table 4

2. Hiramatsu, Y. Determination of the stress in the rock unaffected by boreholes or drifts from measured strains or deformations / Y. Hiramatsu, Y. Oka // Intern. J. Rock Mech. Min. Sci. 1968. № 5. P. 337-353,

3. Baumgartner, J. Anwendung des Hydraulic-Fracturing-Verfahrens fuer Spannungsmessungen im gekluefteten Gebirge, dargestellt anhand von Messergebnissen aus Tiefbohrungen in der Bundesrepublik Deutschland, Frankreich und Zypern / J. Baumgartner // Ber.e des Inst. fu Geophysik der Ruhr-Univ. Bochum. Reiche A. Vol. 21. 1987.

4. Talebi, S. Seismoacoustic activity generated by fluid injections in a granitic rock mass, Proceedings fourth conference on Acoustic Emission/Microseismic activity in geologic structures and materials / S. Talebi, F. H. Cornet, L. Martel L // Ser. in rock and soil mechanics. Trans Tech Publ. 17. 1985. P. 491-509.

7. Heinemann, B. Zusammenfassung der in der Bohrung Urach-3 von 1978 bis 1990 durchgefuehrten HDR-relevanten

geowissenschaftlichen Untersuchungen / B. Heinemann,

B. Troschke / Geothermik-Consult/ Passau, 1991.

5. Price, N. J. Analysis of geological structures / N. J. Price, J. W. Cosgrove. Cambridge : University Press, 1990.

6. Montalbetti, J. F. Enhancement of teleseismic body phases with a polarization filter / J. F. Montalbetti, E. R. Kanasewich // Geophys. J. Rock Astr. Soc. Vol. 21. 1970. P. 119-129.

8. Barton, C. A. In-situ stress orientation and magnitude at the Fenton geothermal site, New Mexico, determined from wellbore breakouts / C. A. Barton, M. D. Zoback, K. L. Burus // Geophys. Research Letters. 1988. N° 11.

9. Ultrasonic veolocity and fracture properties of the rock core from the Urach borehole crystalline section / F. Rummel, H. J. Alheid, R. Winter, T. Woehrl ; The Urach geothermal project (Swabian Alb). Verl-Buchh. Schweizerbart, 1982. P. 135-146.

М. Альбрехт, В. А. Мансуров ОПРЕДЕЛЕНИЕ ПОРОВОГО ДАВЛЕНИЯ В ГЕОМЕТРИЧЕСКОМ РЕЗЕРВУАРЕ

В процессе измерений, проводимых методом гидравлического разрушения, в результате инфильтрации трещины, существующие вблизи скважины, открываются. Такие очень малые события дают достаточную информацию для определения порового давления. Описана теория и предложена новая процедура, а также оборудование разработанное для данных измерений.

УДК 538.955; 539.125.523.348

С. С. Аплеснин, Н. И. Пискунова, Н. С. Мирошниченко

ФОРМИРОВАНИЕ МАГНИТНОГО ПОРЯДКА И ЗАРЯДНОГО УПОРЯДОЧЕНИЯ В СА^^М^з ^ = LA, Р^ SM)

Методом Монте-Карло найдена область существования зарядового упорядочения в Са^ЯМпО3 (Я = La, Рг, Sm), возникающего вследствие дипольного взаимодействия положительно- и отрицательно заряженных частиц, образовавшихся при нестехиометричном замещении. В модели со случайным и упорядоченным распределением анизотропных ферромагнитных связей, возникших в результате заполнения d3z2J - и р- орбиталей марганца и кислорода, вычислена фазовая диаграмма существования О- и С-типов магнитных структур и область их сосуществования.

Окислы переходных металлов типа _К1-хАхМп03 = La, Рг, Ш, Sm и др.; А = Са, Sr, Ва, РЬ) в последнее время являются объектами интенсивных экспериментальных и теоретических исследований. При изменении концентрации двухвалентного иона наблюдается ряд фазовых переходов с разнообразными типами структурного, магнитного, зарядового и орбитального упорядочения. При этом особое внимание уделяется концентрациям х < 0,5 в связи с существованием эффекта колоссального магнитосопротивления в области высоких температур, механизм которого до конца не изучен. Одной из возможных причин этого эффекта, по мнению авторов, могут может быть изменения в магнитной структуре, вызванные зарядовым упорядочением. Авторами было проведено исследование влияния зарядового упорядочения на изменение магнитного порядка в перовскитоподоб-

ной структуре, существующего в области больших концентраций только для ионов Са, в то время как для ионов А = Sr, Ва, РЬ реализуется гексагональная структура.

Модель. Нестехиометричное замещение ионов кальция редкоземельными элементами вызывает локальное изменение потенциала электрического поля и образует избыточные электроны, которые располагаются на е^ уровнях ионов марганца. Эти электроны гибридизируются с электронами, расположенными на _р-орбиталях кислорода. Энергия гибридизации электронов, вычисленная с использованием двухцентровых интегралов (рду) и (рйр) на р- и ^2_г2-орбиталях превышает энергию гибридизации на рх- и ^х2_у2-орбиталях почти на 20 % и составляет Е, 3Дг2 / Ех, х2у2 = 2 /^3 [11]. Локальные искажения структуры, обусловленные замещенными редкоземельными элементами, индуцируют дополнительные виртуальные перехо-