Peng S., Zhang J., Engineering Geology for Underground Rocks

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3.5 Pore pressure prediction 55

pressure. Non-hydrostatic abnormal pressure has many origins. The over-

burden stress is a major reason to induce an abnormal pressure. During

burial process, increasing overburden and no fluid expulsion from the

pores of the formation causes pore pressure increase, producing overpres-

sured pore pressure. The incidents due to inappropriate pore pressure pre-

diction have caused significant non-productive time in the drilling indus-

try. Therefore, various models have been proposed to predict formation

pore pressure (Standifird et al. 2004).

Assuming the normally pressured and overpressured formations with

identical elastic velocities/resistivities have identical effective stresses, the

overpressured pore pressure can be calculated by comparing it to the hy-

drostatic pressure.

Using well log data, Eaton (1975) established the following empirical

relationship between the pore pressure gradient and the formation resistiv-

ity:

2.1

)(



pOBGOBGPP

(3.27)

where PP is the formation pressure gradient; OBG is the overburden stress

gradient; p

is the hydrostatic pore pressure gradient (0.465 psi/ft or 1.03

MPa/km); R is the shale resistivity; R

is the shale resistivity at normal hy-

drostatic pressure (R

= 3.5 ohm·m).

Using sonic log data, overpressured pore pressure can be obtained by the

following equation (Eaton 1975):

)(



pOBGOBGPP

(3.28)

where DT is the interval transit time of shale; DT

is the interval transit

time of shale in normal hydrostatic pressure (DT

= 80 Psec/ft).

A case study involves an offshore Nigeria well for a prediction of in-situ

stress and pore pressure prior to drilling. Pore pressure analysis from resis-

tivity and sonic log data is shown in Fig. 3.4 using Drillworks software

(Zhang et al. 2006). It can be seen that the formations are overpressured at

the studied depths, because the pore pressure is far higher than the normal

hydraulic pressure gradient (1.03 sg).

The pore pressure purposed basin modeling is an advanced tool for pore

pressure prediction (Matthews and Standifird 2006, Williams and Madatov

2005). This model integrates the effects of pore pressure data in offset

wells and formation physical properties (such as pore specific surface area,

compaction constant) as well as formation geologic structures. The basin

56 3 In-situ stress and pore pressure

model can also be updated as new data is acquired. This can provide a

drilling look-ahead prediction that may be valid for several thousand feet

ahead of the bit (Standifird and Matthews 2005). Therefore, the pore pres-

sure prediction from the basin model gives more reasonable results.

Fig. 3.4. Well log data plots with depth for gamma ray (GR), resistivity (Res),

sonic slowness (DT), and pore pressure gradient (PP) predicted by these log data.

In the far right track the definitive pore pressure gradient (PP Def) is also plotted

according to the well log prediction from resistivity (PP Res), and from sonic (PP

DT) and real-time pore pressure measurements. Note that the unit of sg is the spe-

cific gravity, and the NCT is the normal compaction trend line (Zhang et al. 2006).

3.6 Numerical modeling of in-situ stress 57

3.6 Numerical modeling of in-situ stress

Research shows that tectonic stress or tectonic residual stress has a signifi-

cant effect on in-situ stress (Peng 1995). To estimate the distributions of

in-situ stress in sedimentary formations it needs to consider the influence

of rockmass structure, for instance, lithology and pre-existing geologic

structures (Peng 1999). Therefore, understanding sedimentary rockmass

geologic structures is important for predicting origin stress state and stress

redistributions due to mining and other perturbation

(Peng 1998). A case

study is examined in coal seam #13-1 and surrounding rock formations in

mining face #1221, Pansan colliery, Huainan Coalfield, eastern China

(Peng and Meng 2002). The finite element method is applied to model the

formation discontinuities and geological structures of sedimentary rocks.

Three models are analyzed to investigate the influence of sedimentary

rockmass structures on distributions of in-situ stress.

3.6.1 Geological models

Based on the three-dimensional seismic data, the buried depth of coal

seam #13-1 in face #1221 is 524 m. The average thickness of the seam is

3.85 m. The immediate roof of coal seam consists of mudstone and sandy

mudstone with a thin layer of coal, and the main roof consists of medium-

grained sandstone and fine-grained sandstone (Peng and Meng 1999). The

thicknesses of both roof varies. There are two high-angle normal faults in

the west side of mining panel, the offset of the faults varies from 3 to 8 m,

as shown in Fig. 3.5. In the finite element modeling three models are

adopted. The length of Model 1 is 208 m, which is located in the east of

the mining panel. The lithology and thickness of the coal roof keep basi-

cally constant in the lateral direction. Therefore, the rocks belong to con-

tinuous media (Fig. 3.6).

Model 2 has a length of 112 m, close to Model 1 as shown in Fig.3.5. In

this model both rock lithology and thickness vary in transverse direction,

as shown in Fig. 3.7. The length of Model 3 is 132 m, located in the west

of the mining panel. The surrounding strata of the coal seam is cut by high-

angle normal faults, thus the formations belong to fractured media (Fig.

3.8).

58 3 In-situ stress and pore pressure

Fig. 3.5. Geologic cross section used for numerical modeling in mining Face

#1221.

Fig. 3.6. Finite element model for Model 1.

3.6 Numerical modeling of in-situ stress 59

Fig. 3.7. Finite element model for Model 2.

Fig. 3.8. Finite element model for Model 3 with fault effects.

60 3 In-situ stress and pore pressure

3.6.2 Computational models

Finite element meshes and boundary conditions

According to the geological conditions shown in Fig. 3.5, the meshes pre-

sented in Figs 3.6-3.8 are used for finite element calculation. In the model-

ing the quadrangular elements are adopted. Model 1 has 520 elements and

512 nodes (Fig. 3.6), Model 2 has 284 elements and 286 nodes (Fig. 3.7),

and Model 3 has 333 elements and 318 nodes (Fig. 3.8).

In the horizontal direction the uniaxial strain boundary conditions are

applied, i.e. the horizontal displacements at left and right boundaries are

zero, and only vertical movements at boundaries are allowed.

The bottom of the model is fixed, namely both the horizontal and verti-

cal displacements at bottom boundary are zero.

The vertical stress, calculated from the buried depth of model is 10.35

MPa. This stress is applied on the top boundary.

Mechanical model and properties of the rocks

Elastoplastic model is adopted to describe the mechanical behavior of sedi-

mentary rockmass. The Drucker-Prager failure criterion is applied, and it

can be expressed as follows (see Chap. 4 for more details):

 kJIf

(3.29)

where D and k are rock strength parameters and can be calculated from co-

hesive strength (c) and internal friction angle (

), as follows:

2/12

)sin39(

sin



(3.30)

2/12

)sin39(

cos3





(3.31)

Rock physical and mechanical parameters are obtained from lab tests

and are listed in Table 3.1.

3.6 Numerical modeling of in-situ stress 61

Table 3.1. Rock physical and mechanical parameters in the models

lithology Density

(g/cm

)

UCS

(MPa)

Tensile

strength

(MPa)

Friction

angle

(q)

Cohesion

(MPa)

Young’s

modulus

(MPa)

Poisson's

ratio

Medium-

grained

sandstone

2.63 116.68 2.2 36.0 12.11 36104 0.178

Sandy

mudstone

2.30 71.40 1.0 35.0 10.2 19566 0.216

mudstone 2.63 66.11 0.80 42.0 1.43 18261 0.268

coal 1.52 22.30 0.88 38.4 3.50 18480 0.303

Sandstone

with

mudstone

1.52 11.50 0.88 38.4 3.50 18480 0.268

Fine-grained

sandstone

2.61 104.12 3.2 40.0 11.6 36410 0.143

Siltstone 2.50 94.54 1.2 37.0 11.0 20871 0.164

Faulted zone 1.32 3.31 0.040 30 0.072 913.10 0.268

Numerical results

In Model 1, where the rocks belong to continuous media, the in-situ stress

field is mainly induced by overburden gravitational load. The vertical

stress increases as the buried depth increases (Fig. 3.9). However, in

Model 2 the thickness of sandstone of the roof become gradually thinner,

consequently, the initial stress field is obviously disturbed in the location

where sandstone disappeared. The in-situ vertical stress concentration oc-

curs in the layer where the lithology changes, as shown in Fig. 3.10. In

Model 3 the in-situ stress field is obviously different from Model 1 be-

cause of existence of the fault, as shown in Fig. 3.11. A low vertical stress

distribution area appears within the faulted zone. However, high stress

zone exists between the normal rocks and the fault. The high stress is 1.5

times higher than the normal in-situ vertical stress. The additional high

stress is mainly caused by the discontinuity of formations, which disturbs

initial stress field. This will affect stability of underground structures, such

as tunnels.

62 3 In-situ stress and pore pressure

Fig. 3.9. In-situ vertical stress distribution in Model 1. The coordinates are dis-

tances in m, and contours are in-situ vertical stress in MPa. Negative value in this

calculation means compressive stress.

Fig. 3.10. In-situ vertical stress distribution with variable thickness of the roof in

Model 2. The coordinates are distances in m, and contours are in-situ vertical

stress in MPa. Negative value in this calculation means compressive stress.

3.6 Numerical modeling of in-situ stress 63

Fig. 3.11. In-situ vertical stress distribution with variable thickness of the roof in

Model 3. The coordinates are distances in m, and contours are in-situ vertical

stress in MPa. Negative value in this calculation means compressive stress.

3.6.3 Numerical model for calculating horizontal stresses

Calculation model

The studied area is located in the west side in Fangezhuang colliery, where

the coal seam is going to be exploited in an area of 2 km

. The finite dif-

ference method is used to calculate in-situ stress. The seam floor is chosen

as the calculation plane. The length of model is 2940 m, and the width is

640 m, as shown in Fig. 3.12. The buried depth of coal seam #12 in the

studied area varies from 495.18 to 807.25 m, and the average depth is

659.75 m. The thickness of coal seam is 0.29-5.24m with an average

thickness of 2.51. The calculation model is discretized into 4704 quadran-

gle elements. Stress boundary is applied (Peng and Meng 2002).

64 3 In-situ stress and pore pressure

2940 m

640

8º

Fig. 3.12. Numerical model to calculate horizontal stresses in Fangezhuang Col-

liery of Kailuan Coalfield, China.

Calculation results

The vertical stress in this analysis is obtained by using Eq. 3.10, which is

55.17027.0 z

(MPa)

The horizontal stresses are calculated by using the numerical method.

Figures 3.13-3.15 present the calculated maximum principal horizontal

stress, minimum principal horizontal stress, and maximum shear stress

components, respectively. It can be seen from the figures that the maxi-

mum horizontal principal stress varies from 54.24 to 5.59 MPa with an av-

erage of 24.71 MPa and the minimum principal horizontal stress are 26.89

to 3.80 MPa with an average of 13.53 MPa. The maximum horizontal

principal stress is in EW and NW-SE direction.

In-situ stress measurement was conducted by overcoring method in this

area. The results show that this region belongs to strike-slip faulting stress

regime. The maximum horizontal stress varies from 20.46 to 24.34 MPa,

and direction is N103 - N142. The intermediate principal stress varies from

15.31 to 16.01 MPa, whose direction is near vertical with an inclination of

78.67-81.88q from the horizontal direction. The minimum principal stress

varies from 7.64 to 13.9 MPa. The calculated results are close to the data

from in-situ measurement. The differences are mainly caused by tectonics,

geological structures, and lithology. For instances, the faults cause stress

concentration, causing changes in both stress magnitudes and directions.