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Oil and gas development from underground reservoirs disturbs original rock mass balance. The tending of the rock mass to achieve a new, even only temporary balance is manifested in the movements of the ground surface. Movements can affect ground infrastructure like offshore platforms, pipelines and buildings. For increasing the efficiency of the preventive actions a'priori precisely prediction of the subsidence is necessary. By the prediction of surface subsidence changes of pore pressure in time due to exploitation and geometry of the reservoir have to be taken into account. The prediction method based on the influence function of Knothe will be presented in the paper. Some applications according to the oil and natural gas developments will be discussed
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SUBSIDENCE PREDICTION CAUSED BY THE OIL AND GAS
DEVELOPMENT
Anton Sroka
Institute of Mining Surveying and Geodesy
Technische Universität Bergakademie Freiberg/ Germany
Email: anton.sroka@tu-freiberg.de
Ryszard Hejmanowski
Dept. of Mining Damage and Geoinformatics
Faculty of Mining Surveying and Environmental Engineering
AGH University of Science and Technology/Cracow/ Poland
Email: hejman@agh.edu.pl
Abstract: Oil and gas development from underground reservoirs disturbs original rock mass
balance. The tending of the rock mass to achieve a new, even only temporary balance is
manifested in the movements of the ground surface. Movements can affect ground
infrastructure like offshore platforms, pipelines and buildings. For increasing the efficiency of
the preventive actions a’priori precisely prediction of the subsidence is necessary. By the
prediction of surface subsidence changes of pore pressure in time due to exploitation and
geometry of the reservoir have to be taken into account. The prediction method based on the
influence function of Knothe will be presented in the paper. Some applications according to
the oil and natural gas developments will be discussed
1. Introduction
Surface subsidence of areas where oil, gas and water are exploited are a serious problem in
various parts of the World. In the coastal regions, vertical movements of the surface may
result in flooding or generate extra costs for securing the banks. Such problems were
encountered, e.g. in the area of Maracaibo Lake in Venezuela (ca. 3.5 m – maximum
subsidence), Mexican Gulf, in California (ca. 10 m – maximum subsidence) and in Japan. The
subsidence troughs may be huge in size and the damage to the objects standing on them is
comparable to those in the mining areas. Considerable deformations of surface usually can be
found in the places where thick fluid reservoirs occur and the host rocks have compaction
qualities.
Surface deformations in the areas of oil and gas exploitation can be efficiently predicted on
the basis of methods employing the influence functions. These methods make use of relatively
uncomplicated mathematical models and are simple in use. Regarding their high efficiency,
these methods are not frequently met in the World’s literature, therefore the Authors decided
to discuss the prediction model based on an influence function applicable to fluid mineral
reservoirs.
3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006
2. Rudiments of the proposed method
2.1. Discretization of reservoir
All the considerations made in this paper will refer to an elementary part of a reservoir. The
whole reservoir will be divided into elementary cubicoids having a square base of side L and
height M
0
, corresponding to the original thickness of the fluid reservoir [7](fig.1).
0
L
L
Fig.1. Element of reservoir
This approach enables a description of a varying thickness of a reservoir and simplification of
numerical operations. Once the whole gas reservoir field has been divided into elements, the
following situation is obtained, fig. 2.
X,Y,Z,M ,p ,p(t)
00
Fig. 2. Gas field divided into elements
3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006
2.2. The main cause-and-effect relation
Geometrical-integral influence exploitation model bases on the following cause-and-effect
relation (1). Accordingly, the result, i.e. surface subsidence can be determined as a loop of
two functions: influence function or transformation function
),,( tzr
ϕ
, and a function
describing the cause of rock movement, i.e. compaction
)(tK
.
),,()(),,( tzrtKtzrS
ϕ
= (1)
where:
- increase of compaction volume of reservoir element in time t. )(tK
φ
(H,t)
φ
(z ,t )
1
z= z
0
z= z
1
z= H
r = 0
cause
effect z
1
effect z
Η
M(t)
M
0
Fig.3. Causal nexus for exploitation of one reservoir element
It should be noted that both functions in eq. (1) are functions of time.
3. Calculation model
Being a cause of rock mass movements, in the case of oil and gas exploitation, compaction
depends on changes of pore pressure in the gas or oil field. This relation may be described
linearly to some extent:
[]
00
)()( MtppctM
m
=
(2)
where:
M(t) – change of thickness of fluid reservoir,
c
m
– compaction coefficient,
p
0
– original/primary? pore pressure,
p(t) – pore pressure in a moment t,
M
0
– original/primary? thickness of the analysed element of reservoir.
The compaction coefficient c
m
depends on the properties of reservoir rocks, depth of
reservoirion and original/primary? pressure p
0
[e.g., 15, 16]. The compaction volume for thus
defined element of reservoir (fig.1) is:
3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006
2
)()( LtMtK = (3)
where:
K(t) – bulk/volume compaction in a time t
The influence functions have been known to be used for predicting surface deformations since
Bals published his work in 1931 [1]. In other works employing influence functions written by
Litwiniszyn [12] and Knothe [9], the influence functions were justified in the form of a
validated Gauss function. The form of the function for predicting the surface may assume the
following form:
=
2
2
2
exp
1
),(
KK
R
r
R
Hr
πϕ
(4)
where: H – depth of exploitation,
r – horizontal distance of calculated point from the reservoir element,
R
K
– radius of scattering of exploitation influences after Knothe for a surface:
β
ctgHR
Hz
K
=
= )(
(5)
β
- angle of the main influence range, after Knothe.
Predicting the subsidence within a rock mass, the R
K
value should be calculated from the
following relation:
β
ctgzH
H
z
RzR
nnn
H
KK
==
1
)(
)()( (6)
where: n – coefficient of boundary surface [11, 2, 3, 4, 10, 13].
For calculating this coefficient, n = 0.5 can be assumed.
Basing on elasticity theory, in 1970s Geertsma proposed an influence function in the
following form [5, 6]:
3
1
)(
d
H
d
=
π
υ
ϕ
(7)
where: υ - Poisson coefficient,
d – distance of the calculated point from the reservoir element.
Other examples of influence functions to be potentially used for predicting deformations in
the exploitation conditions can be found in literature, e.g. Kochmański, Perz. The application
of the function in the form presented in (4) seems to enable a more precise validation of the
model. Owing to the fact the process of rock mass deformation over the oil or gas exploitation
area develops in time, it is crucial to introduce a function of time f(t). It describes the delaying
impact of the rock mass:
)(),(),,( tfzrtzr =
ϕ
ϕ
(8)
According to Knothe, the function has the form:
)exp(1)( tctf
= (9)
where: c – time coefficient, which gives a full description of the delaying influence of a
porous reservoir rock on the lowering pore pressure and the delayed influence of the onlying
rocks.
3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006
Predicting the surface subsidence, they can be calculated by superpositioning the elementary
subsidence’s. Elementary subsidence caused by exploitation of a fluid from one or any
element of reservoir will be written in compliance with (1) as:
),,()()(
,,,
tzrtKtS
ijijiij
ϕ
= (10)
where: j – number of calculation point,
i – number of reservoir element,
()()
22
, ijijij
yyxxr += ,
.
ijij
zzz =
,
Using the linear superpositioning, a subsidence of any point in a time t can be calculated
from:
=
=
=
Ni
i
ijj
tStS
1
,
)()( (11)
where: N – number of reservoir elements (
Ni
1
).
The subsidence distribution over a large fluid reservoir with the on-going exploitation can be
calculated on the basis of known reservoir pressure distributions. Having divided of the whole
reservoir into constituent elements it was possible to precisely describe the reservoir pressure
distribution, its changeability in time and space, and hence to precisely model the surface
subsidence in time. If the element of a reservoir were treated as an object initiating rock mass
movements, it can be described values of such attributes as, e.g. location (x, y, z), thickness
M
0
, primary pore pressure p
0
, pressure caused by exploitation in the successive moments of
time p
1
(t
1
), p
2
(t
2
), etc. Contemporary numerical techniques enable operation of attributes for
each reservoir element not only at the stage of calculation and prediction of subsidence’s.
Having had a description of attributes, spatial analyses can be made. Their objective can be,
e.g. determining efficiency of a given exploitation method or prevention against too big
deformations of the sea bed on shelves or on the surface.
4. Practical application
4.1. Prediction of surface subsidence
The Authors verified the presented model on some real-life examples. These were oil
reservoirs under the North Sea and gas reservoirs in one of European countries.
The modeling in the case of the gas field was made in stages. The results of calculations were
compared with the levelling measurement and presented in figure 5. Parameters of the
calculation model, i.e. R
K
, c, c
m
, were determined on the basis of data measured as subsidence
points on surface by a moment t and as compaction properties of the reservoir. The prediction
of subsidence for the successive period (t
i+1
) was calculated with the use of these parameters
and expected decreases of pore pressure value in time t
i+1
. Therefore, it was possible to obtain
an exceptionally high accuracy of predicted subsidence’s, which was not attainable with other
methods [7, 8]. In view of the cause-and-effect relation mentioned in section 2, the parameters
of the model can be also identified. This was indicated by, among others, results of analyses
carried out for a gas field, where the inverse analysis of measured surface subsidences enabled
3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006
determining the compaction coefficient value c
m
[14]. The obtained values were convergent
with the results of laboratory tests by Teeuw [15].
0 102030405060708090
Observed points [km]
observed predicted
Fig. 4. Prognosed surface subsidences against measured values
4.2. Geodesy surveying measurements of surface subsidence
While presenting the applicability of the model, attention was drawn to the fact that
knowledge of the actual course of surface deformation was extremely important.
Measurements of deformations are usually made with the use of such geodesy surveying
methods as levelling of measuring points. For the last 10 years GPS and remote sensing
methods (e.g., InSAR) have been more and more commonly applied. By determining the
increase of subsidence between individual moments of time, a whole description of changes
in the trough over the exploited reservoir is being made. Designing the parameters or
elaborating remote sensing data, the measurement points should be so densely distributed as
to make their maximum distance equal to:
K
Rl = 1,0 (12)
Taking into account (5), this can be written as:
)(1,0
β
ctgHl = (13)
It should be noticed that this distance in the average conditions of fluids exploitation is
considerable.
The time elapsed between measurements is also important for the specific fluid reservoirs. It
should be less than the time of occurrence of the assumed boundary difference of subsidence
S
G
. With such a criterion, it is possible to determine an average admissible time span
between the successive measurements of surface subsidence:
3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006
β
2
2
_
__
0
_
ctg
F
H
pMc
S
t
tm
G
=
(14)
where:
- low thickness of reservoir,
0
_
M
- average decrease of reservoir pressure in time t,
t
p
_
_
- average depth of deposition,
F – total surface of the reservoir.
As the decrease of pressure can be written as:
tpt
t
p
p
t
=
=
_
, (15)
where: - gradient of pore pressure, then eq. (14) will finally take the form:
p
β
ctgH
FpMc
S
t
m
G
_
_
0
_
=
(16)
It follows from eq. (14) that the time span between individual observations depends on a
parameter typical of mineral exploitation rate. In this case it is described by a gradient of pore
pressure decrease.
References:
[1] Bals R.: Beitrag zur Frage der Vorausberechnung bergbaulicher Senkungen. Mitt. Aus
dem Markscheidewesen, 1931/32.
[2] Bartosik-Sroka T., Sroka A.: Zmienność wartości parametrów teorii T.Kochmańskiego
i S.Knothego w górotworze. Rudy i Metale Nieżelazne, nr 7., 1974.
[3] Drzęźla B.: Badania teoretyczne i modelowe ruchów górotworu przy eksploatacji
górniczej. Politechnika Śląska, Gliwice, 1971 (niepublikowane).
[4] Drzęźla B.: Zmienność zasięgu wpływów eksploatacji w górotworze. Przegląd Górniczy,
nr 10. Katowice 1979.
[5] Geertsma J.: Land subsidence above compaction oil and gas reservoirs. SPE-European
Spring Meeting 1972; SPE AIME Nr 3730, pp 17.
[6] Geertsma J., Van Opstal, G.: A numerical technique for predicting subsidence above
compaction reservoirs, based on the nucleus of strain concept. Verhandlingen Koniklijk
Nederlands Geologisch Mijnbouwkundig Genootschap., Vol. 28, pp.63-78, 1973.
[7] Hejmanowski R.: Zur Vorausberechnung förderbedingten Bodensenkungen über Erdöl-
und Erdgaslagerstätten. PhD. Thesis. Technical University Clausthal, Germany, 1993.
[8] Hejmanowski.R., Sroka A.: Time-space ground subsidence prediction determined by
volume extraction from the rock mass: Land subsidence : proceedings of the sixth
international symposium on Land subsidence : Ravenna 24–29 September 2000. Vol. 2:
Measuring and monitoring theory and modeling, 2000. pp. 367–375.
[9] Knothe. S.: Równanie profilu ostatecznie wykształconej niecki osiadania. Archiwum
Górnictwa i Hutnictwa, t.1, z.1, 1953.
3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006
[10] Kowalski A.: Określenie zmienności parametru promienia zasięgu wpływów głównych
w górotworze teorii Budryka-Knothego na podstawie badań geodezyjnych
przemieszczeń pionowych górotworu. Praca doktorska. GIG, Katowice, 1984
(niepublikowane).
[11] Krzysztoń D.: Parametr zasięgu niecek osiadania w ośrodku sypkim. Archiwum
Górnictwa, t.10, z.1., 1965.
[12] Litwiniszyn J.: Przemieszczenia górotworu w świetle teorii prawdopodobieństwa.
Archiwum Górnictwa i Hutnictwa, t.2, z.4., 1954.
[13] Mikołajczak J.: Uwagi do równania promienia zasięgu wpływów głównych. Ochrona
Terenów Górniczych, nr 69/3. Katowice 1984.
[14] Sroka A., Schober F.: Studie zur Analyse und Vorhersage der Bodensenkungen und
Kompaktionsverhaltens eines Erdgasfeldes. Abschlussbericht, 1989.(niepublikowane)
[15] Teew.D.: Laboratory measurement of compaction properties of Groningen reservoir
rock, Verhandlingen Koniklijk Nederlands Geologisch Mijnbouwkundig Genootschap.,
Vol. 28, pp.19-32, 1973.
[16] Van Kesteren. J.: Estimate of compaction properties of Groningen reservoir rock.
Verhandlingen Koniklijk Nederlands Geologisch Mijnbouwkundig Genootschap., Vol.
28, pp.33-40, 1973
3rd IAG / 12th FIG Symposium, Baden, May 22-24, 2006
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L'objectif de cette thèse a été de concevoir et développer un simulateur de dommages permettant d'étudier la vulnérabilité d'un territoire soumis à des aléas de mouvements de terrains associés à la présence d'exploitations souterraines. Ce développement repose sur la combinaison d'une méthode de prévision des affaissements miniers, de fonctions de vulnérabilité pour l'évaluation des dommages et d'une base de données des bâtiments. L'enjeu scientifique est le développement de fonctions de vulnérabilité pour les bâtiments en zone d'affaissement minier. Ces fonctions sont comparables à celles utilisées vis-à-vis d'autres aléas comme les séismes et les tsunamis. On a développé et appliqué une méthodologie basée sur des simulations de type Monte-Carlo qui utilise les méthodes existantes d'évaluation des dommages dans les zones d'affaissement minier (méthodes empiriques ou analytiques). Elle permet de prendre en compte l'incertitude sur les paramètres géométriques et mécaniques du bâti. Afin de valider cette méthodologie, les dommages estimés par les fonctions vulnérabilité développées pour des bâtiments en maçonnerie du bassin ferrifère lorrain sont comparées aux dommages observés, consécutifs aux affaissements de 1996 à 1999 en Lorraine. Dans une étape suivante, la méthode des fonctions d'influence a été implémentée dans le simulateur avec certains développements permettant de tenir compte de la variabilité des angles d'influences et permettre le calcul des déformations horizontales du terrain. Les résultats de cette méthode sont validés sur un cas d'affaissement observé dans le bassin ferrifère de lorrain. Enfin, une approche probabiliste d'évaluation des dommages est implémentée pour tenir compte de différents scénarios d'affaissement possibles. L'application sur les bâtiments de la ville de Joeuf, permet d'illustrer les différents résultats obtenus
Conference Paper
Modelling of strains and deformations in salt mine areas encounters considerable difficulties because of the varying strength properties of salt, complex morphological formation of dome deposits and rheological properties of salt. Due to such properties the impact of salt extraction increases over hundreds of years and accurate determination of strains at a given moment and place is burdened with high uncertainty. Numerical modelling is useful when the model is reduced to one or several chambers. A broader range considerably lowers the accuracy and efficiency of calculations in such models. Stochastic models allow for 3D modelling of an entire mining complex, provided the model has been parametrized in detail. The process of strain and deformation modelling was presented on the example of one of the biggest salt mines in Europe, where the volume of over 21 million m³ of salt deposit was extracted. The stochastic model could be parametrized thanks to the documented measurements results of panel convergence and levelling on the surface. The use of land subsidence inversion in the least squares method allowed to estimate the optimum values of the model parameters. The correctness of the evaluation was qualitatively and quantitatively confirmed graphically by comparing modelled and measured values of subsidence. The presented model can be applied in the future extraction projects for predicting strains and deformations for an arbitrary moment
Article
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The modeling of strains and deformations in salt mine areas encounters considerable difficulties because of the varying strength properties of salt, the complex morphological build of dome deposits and the rheological properties of salt. These properties have impacted the development of salt extraction for hundreds of years and the fact that the accurate determining of strains in a given specified moment and place are burdened with high uncertainty. Numerical modeling is useful when the model is reduced to one or several salt chambers. A broader range of underground post mining void considerably lowers the accuracy and efficiency of the calculations of such models. Stochastic models allow for a 3D modeling of the entire mining complex deposit, provided the model has been parametrized in detail. The methods of strains and deformations modeling were presented on the example of one of the biggest salt mines in Europe, where a volume of over 21 million m3 of salt was extracted. The stochastic model could be parametrized thanks to the documented results of measurements of convergence of the underground mining panels and leveling on the surface. The use of land subsidence inversion in the least squares method allowed for estimating the optimum values of parameters of the model. Ground deformation modeling was performed using the two-parameter time function, which allows for a simulation to be carried out in time. In the simulation, the convergence of underground excavations and the transition in time the effects of convergence into ground subsidence was taken into account. The detailed analysis of the geological conditions lead to modeling deviation of the subsidence trough. The accuracy of the modeling results was qualitatively and quantitatively confirmed by a comparison of the modeled to measured values of the vertical ground movement. The scaled model can be applied in future mining extraction projects in order to predict the strains and deformations for an arbitrary moment in time.
Article
Notable subsidence above producing oil and gas fields is the exception rather than the rule. A simple procedure is outlined to single out the exceptional but real problem areas. This exercise in potential-problem analysis shows that the huge Groningen gas field in The Netherlands is a candidate for causing subsidence troubles in a lowland area. Introduction During the last 20 years, the Royal Dutch/Shell Group has conducted extensive investigations into the phenomenon of reservoir compaction and subsidence. These have included research projects to study subsidence above Bolivar Coast oil reservoirs in Venezuela and to examine the huge Groningen gas reservoir in The Netherlands. The latter investigation was conducted by a team of specialists from both the Koninklijke/Shell Exploratie en Produktie Laboratorium (KSEPL) and BV Nederlandse Aardolie Maatschappij (NAM), the latter being the producing company owned jointly by Shell and Esso. Details of the Groningen investigation are published elsewhere but as it may have consequences for other operating companies working in lowland and other subsidence-prone areas, we shall consider here the causes of subsidence above hydrocarbon-producing reservoirs in a more general way, and review the state of the art of its prediction. A simple method will be presented for estimating the order of magnitude of both compaction and the accompanying subsidence. Application of this method, which can be used to explore the need for an investigation in depth, requires hardly any specialist knowledge. The objective is twofold: to demonstrate that land subsidence due to hydrocarbon production seldom leads to serious subsidence, and production seldom leads to serious subsidence, and to pinpoint the few potential problem areas. Earlier Field Observations The literature on subsidence deals mainly with a few notable examples, such as the Goose Creek oil and gas field in Harris County, Tex., where dramatic subsidence occurred between 1918 and 1925, and the Wilmington field below Long Beach, Calif., where almost 10 m of subsidence was experienced in 1960. Further subsidence could be avoided in this latter case after unitization and pressure maintenance as a result of water injection. More recently, a search for additional, documented surface depressions over oil and gas fields in the U. S. was reported by Yerkes and Castle. This search revealed only a few other significant cases, mainly fields close to Wilmington, such as those at Buena Vista, Huntington Beach, and Inglewood. From this concentration of subsidence bowls, it may be inferred that such events are somehow related to a similarity in reservoir conditions. Shell has been confronted only once with a major land-subsidence problem. It is related to the production of oil and gas in Venezuela, where subsidence above a number of important oil reservoirs bordering Lake Maracaibo is a constant phenomenon, and huge dykes have been built to protect the coastal area from flooding. Its cause is discussed by Van der Knaap and Van der Vlis. Subsidence data for oil and gas fields outside the Americas are very scarce indeed. Okumara and Hirono describe a case from the Niigata district of Japan that results from the production of methane dissolved in water. In Italy, AGIP has been accused of contributing to subsidence in the Po Delta by producing from a number of gas fields. JPT P. 734
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