GRC Transactions, Vol. 41, 2017

An Integrated Workflow to Design Screen/Slotted Liners in Geothermal Wells

Ruiyue Yang, Zhongwei Huang*, Gensheng Li, Huaizhong Shi, Xianzhi Song, Yu Shi

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China

Keywords

Geothermal wells completion, collapse strength, thermal stress, screen/slotted liner, complementary approach

ABSTRACT

Screen/slotted liners are generally used in geothermal well completions. However, the thermally induced stress by elevated temperature could substantially deteriorate the collapse strength. This paper presents an integrated workflow which complementarily utilizes analytical and numerical methods to design screen/slotted liners in geothermal wells. The collapse rating of a screen/slotted liner is obtained by a modified analytical approach. The thermally induced stress is estimated through the Finite Element Method. Subsequently, the collapse strength assessment for a screen/slotted liner when subjected to high-temperature is made by combining these two approaches. Finally, a selection guide for the schematic of holes/slots configuration is provided. The method is simple and versatile, without complicated mechanical-thermo-coupling process. It can provide guidance for completion engineers to modify the design of screen/slotted liners prior to the actual treatment in geothermal wells.

1. Introduction

Ongoing rapid development of geothermal energy worldwide has led to an increased focus on developing robust tubular design bases for extreme service conditions. High-temperature downhole environment encountered in geothermal wells produces adverse effects on the integrity of the tubulars (Edwards et al. 1982). The associated compressive axial stress caused by constrained thermal expansion can weaken the collapse resistance of the tubulars (Torres 2014).

Screen/slotted liners used in geothermal wells must provide stable structure under extreme thermally-induced loading in order to maintain the wellbore stable and to prevent any unwanted debris. A successful screen/slotted liner design will ensure that the liner provides the maximum inflow area and minimum strength reduction compared to an intact liner. Previous attempts for the design of structural integrity of screen/slotted liners can be categorized into two types:

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numerical simulation (Placido et al. 2005; Yang et al. 2014) and laboratory experimental works (Kumar et al. 2010; Huang et al. 2012; Yang et al. 2017). However, these works neglected the thermal effects, which is acceptable in conventional oil and gas wells. Even API grade degradation defined the mechanical property requirements at room temperature. In heavy oil reservoirs, similar problems resulted from high-operating temperatures occurred. Industry Recommended Practice (IRP) has provided some design guidelines for thermal wells (IPR Volume 2002). Researchers also developed tubular material formulations that were specifically designed for use in slotted liner installations in Steam Assisted Gravity Drainage (SAGD) wells (Slack et al. 2000 ; Dall&apos et al. 2010). However, IRP didn’t present a detailed schematic for slot configurations, and the development of material formulation was based on a series of comprehensive analytical/ theoretical and experimental works which was a time-consuming and complicated process. Torres (2014) discussed the design criteria for tubulars in geothermal wells, including thermally induced axial stress and plastic deformation. However, the method was only valid for intact pipe, which cannot be directly used in the design of a screen/slotted liner. Okech et al. (2015) have discussed the completion design in geothermal wells by reviewing the conventional and unconventional deep geothermal development well concepts. However, there were no systematic analysis for the collapse strength reduction for a screen/slotted liner. Hence, an efficient method to design the screen/slotted liner in geothermal wells where high-temperature effects are considered is still desirable.

The topic of discussion for this paper is a hybrid approach. The collapse rating of a screen/slotted liner is reduced compared to that of intact liner. To quantify this reduction, a simple method of evaluating the collapse strength of a screen/slotted liner developed by Abbassian and Parfitt (1998) is introduced first. Then, we modified the model to consider various patterns of screen/slotted liner. Subsequently, Finite Element Method (FEM) is employed to account for the thermally induced axial stress on the reduction of the collapse strength. Finally, an integrated workflow by combing the analytical and numerical efforts to design the screen/slotted liner in geothermal wells is provided. Based on the workflow, different liners with varied arrangements of holes and slots have been proposed to study its structural response under high-temperature effects.

This approach, although not as conclusive as collecting hard data, offers a cost-efficient workflow to rapidly estimate the collapse resistance for screen/slotted liner in geothermal wells subjected to high-temperature effect. The key findings of the work are expected to provide valuable design criteria for screen/slotted liners completion in geothermal wells.

2. Methodology

2.1 Analytical method

An analytical method developed by Abbassian and Parfitt (1998) for calculating collapse strength of a screen/slotted liner subjected to external pressure is utilized. Then, we modified this model by taking different penetration/slot patterns into account. The original method is based on pre-collapse elastic ovalization and subsequent plastic collapse through the formation of four plastic hinges. The model assumes that the collapse behavior of liners under external pressure consists of two distinct and independent behavior regimes: elastic ovalization and plastic collapse via four-hinge mechanism. Comprehensive descriptions of the model development can be seen in references. Here, we present the calculation outline in a concise manner.

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2.1.1 Elastic Ovalization and Plastic Collapse Pressure

A liner with initial ovality will deform and ovalize further subjected to external uniform pressure. The elastic ovalizaition pressure for a screen/slotted liner is given by Abbassian and Parfitt (1998):

1 oeo e

uP P

uλ = −

(1)

where eoP is the elastic ovalization pressure, MPa; eP is the elastic buckling collapse pressure for

a thin walled liner, MPa; ou is the amplitude of initial ovality, mm; u is the ovality amplitude at

a certain pressure value, and λ is the reduction factor for elastic bending stiffness with respect to that of intact liner.

For a thin walled liner, the elastic buckling collapse pressure eP is expressed as (Abbassian and

Parfitt 1998)

3

2

2

1et

E hP

v d

= −

(2)

where E is the material Young’s modulus, MPa; v is the Poisson’s ratio; h is the tube thickness, mm; td is the tube mean diameter, mm.

The ovality amplitude u , based on small displacement theory of thin cylindrical shells, is given by (Timoshenko and Gere 1961)

1

1o

e

u uPP

=

−

(3)

where P is the external pressure, MPa.

For a screen liner, assuming a uniformly distributed perforation pattern, the reduction factor λ is estimated as (Abbassian and Parfitt 1998)

1 p

p

d

sλ = − (4)

where pd is the perforation diameter, mm; ps is the screen holes’ longitudinal separation, mm.

For a slotted liner, assuming a uniformly distributed slot pattern, the reduction factor λ is estimated as (Abbassian and Parfitt 1998)

1 s

l

l

sλ = − (5)

where sl is the slot length, mm; ls is the slots’ longitudinal separation, mm.

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The plastic collapse pressure is derived base on the four-hinge collapse mechanism, which produces the well-known dog bone final post-collapse configuration (Palmer and Martin 1975). As a function of ovality amplitude, it can be expressed as (Abbassian and Parfitt 1998)

22 2

2 22 1 1 4 1t t

pc yt t t t

d du u u uP P

h d d h d dμ

= − − + + −

(6)

where μ is the reduction factor for plastic bending strength capacity with respect to that of intact

liner, which equals to λ for both screen and slotted liners; yP is the pressure at the onset of yield

from hoop compression, referred to here as yield pressure, MPa, which can be calculated by (Abbassian and Parfitt 1998)

2 yy

t

hP

d

σ= (7)

where yσ is the material yield stress, MPa.

For staggered holes, we expect slightly higher collapse strength than inline ones. Previous research showed that staggered-pattern penetrations could have less strength loss than the inline ones (Yang et al. 2014). Therefore, we modified the model by introducing an effective holes number around the circumference of a staggered screen liner, which is given by Furui et al. (2015)

( )/1 ap hD pN d

ap apN N e δ−′ = + (8)

where apN ′ is the effective holes number around the circumference of a staggered screen liner;

apN is the holes number around the circumference of an inline screen liner; hDd is the

dimensionless hole diameter (= /p wd r ), and wr is the wellbore radius; pδ is the hole penetration

ratio, defined as the diameter of holes per unit length of liner (= /p pd s ).

Similarly, the effective number of slots around the circumference of a staggered slotted liner must be modified. The following equation is introduced (Furui et al. 2015)

( )/1 al sD lN lal alN N e δ−′ = + (9)

where alN ′ is the effective slots number around the circumference of a staggered slotted liner;

alN is the slots number around the circumference of a inline slotted liner; sDl is the dimensionless

slot length (= /s wl r ); lδ is the slot penetration ratio, defined as the diameter of holes per unit

length of liner (= /s ll s ).

2.1.2 Collapse rating

The elastic ovalizaition and plastic collapse pressure expressed by Eqs. (1) and (6) can be plotted for a given screen/slotted liner size as a function of ovality amplitude. Then, the screen/slotted

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collapse rating is defined as the intersection between the above two curves, which is a standard technique used in beam-column buckling analysis (Horne and Merchant 1965).

2.2 Numerical method

The screen or slotted liner completion technique involves setting an uncemented screen or slotted liner assembly below the production casing (Edwards et al. 1982). The thermal expansion of the liners resulting from elevated temperature is simulated by Finite Element Method (FEM). The connected end with production casing is restricted, creating axial stress within the screen/slotted liner when subjected to high temperature. The magnitude of the axial stress is investigated in this section. The FEM model is developed using the commercial software ANSYSTM R16.0.

The accuracy of the numerical model is confirmed by comparing the results with the following equation, which is generally used for estimating the thermally induced stress for an intact liner (Edwards et al. 1982)

z E Tσ β= Δ (10)

where β is the linear thermal expansion coefficient, m./m./ °C-1; E is the Young’s modulus of elasticity, MPa; TΔ is the temperature change, °C. Young’s modulus of elasticity and coefficient of thermal expansion for low carbon steels are different at various temperature (Table 1).

Table 1. Young’s modulus of elasticity and linear thermal expansion coefficient for low carbon steels (C≤0.30%) at different temperatures (Nayyar et al. 2000)

Temperature (°C) Young’s modulus of

elasticity (×105MPa)

Linear thermal expansion coefficient

(×10-6m./m./ °C-1) 21 2.068 11.628 93 2.052 12.960 149 2.022 13.878 204 1.989 14.670 260 1.952 15.354 316 1.906 15.948 371 1.850 16.416 427 1.795 16.794

An intact liner is simulated with various temperatures. The dimension of the model and mechanical properties are shown in table 2. The FEM model was discretized by 57646 nodes and 39495 elements (Figure 1). The boundary condition is that one end of the intact liner is x-y-z direction displacement restricted. The comparison is shown in Figure 2.

Table 2. Input parameters used for model validation.

Length (mm)

Outer diameter (mm)

Thickness (mm)

Poisson’s ratio

1000 177.80 11.50 0.27

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Figure 1. Schematic of the FEM simulation model (intact liner).

Figure 2. Collapse strength of screen liners with various phase angles (120 °C).

The thermally induced axial stress between the established numerical model and analytical formula is compared in Figure 2. A good agreement between them is presented. The average error is 4.45%. The difference is negligible at low temperature, while it becomes larger with the increase of temperature. Consequently, the numerical model can be used to calculate the thermally induced axial stress in the estimation of collapse strength for screen/slotted liners.

2.3 Thermal stress effect

An important consideration must be taken into account to prevent mechanical problems for a screen/slotted liner is high-temperature effect. High-temperature could cause the liner expansion,

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rmal

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ess

(MP

a)

Temperature (°C)

Analytical solutionNumerical solution

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which increases the axial stress and elongation. The collapse resistance of a screen/slotted liner is modified when axial tension stress is considered, which can be expressed as (Li et al. 2009)

1.03 0.74 zcc c

y

P Pσσ

= −

(11)

where is the collapse strength of a screen/slotted liner when axial tension stress is regarded, MPa; is the collapse strength of a screen/slotted liner when axial tension stress is not considered, MPa; is the axial tension stress, MPa.

Based on the above analysis, can be obtained from the collapse-strength-analytical model, and can be gained from the FEM-analysis.

3. Proposed workflow

Figure 3 shows the flowchart of the proposed workflow for screen/slotted liners design in geothermal wells.

Figure 3. Integrated workflow to design screen/slotted liners in geothermal wells

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The proposed workflow consists of the following four steps:

Step 1: Obtain geothermal reservoir and wellbore parameters

• Estimate underground temperature of the target reservoir; • Obtain wellbore parameters, such as wellbore radius, casing size, casing grade, etc; • Obtain material properties and hole/slot parameters of the given screen/slotted liner.

Step 2: Estimate screen/slotted liner collapse ratings

• Calculate the elastic ovalization pressure of a screen/slotted liner; • Calculate the plastic collapse pressure of a screen/slotted liner; • Plot curves of elastic ovalizaition and plastic collapse pressure as a function of ovality

amplitude; • Estimate the collapse ratings of the screen/slotted liner from the intersection point.

Step 3: Estimate thermally induced axial stress

• Calculate the thermally induced axial stress from finite element method.

Step 4: Collapse assessment and design adjustment

• Measure the collapse strength of the screen/slotted liner subjected to high-temperature effect;

• Grade/size/parameters schematic adjustments for the screen/slotted liner; • Repeat steps 2-4, until the collapse strength can meet the requirements.

4. Screen Liner Design

This section discusses the application of the proposed workflow to a screen liner designing in geothermal wells. A series of cases to describe the effects of numerous holes in a screen liner on the collapse resistance when subjected to high-temperature are presented (Table 3). For most of the production wells in geothermal reservoirs, the wellhead temperature is less than 100°C (275 among 290 production wells in China from the year of 2010 to 2014) (Zheng et al. 2015). In this paper, the underground temperature is set to be 120 °C. The material properties of intact liner are listed in Table 4.

Table 3. Values for cases studies of screen liners.

Parameter Value 1 Phase angle, ° 30, 60*, 90, 120, 180 2 Hole diameter, mm 9.525, 15.875*, 25.4 3 Perforation density, holes/m 30, 60*, 90, 120, 4 Pattern Inline, Staggered

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Table 4. Material properties of intact liner.

Grade Outer

diameter (mm)

Wall thickness

(mm)

Young’s Modulus

(×105MPa) (120°C)

Coefficient of thermal expansion

(×10-6°C-1) (120°C)

Poisson’ ratio

Yield strength (MPa)

Collapse strength (MPa)

N80 177.80 11.50 2.04 13.40 0.27 551.52 59.36

First, we obtain the collapse ratings of screen liners with various perforation parameters through the analytical model. Then we established the FEM numerical simulation model. We make a LGR (local grid refinement) around each hole. The schematic of the simulation model for a screen liner is shown in Figure 4, and it is discretized by 100043 nodes and 418452 elements. The boundary condition is that one end of the screen liner is x-y-z direction displacement fully restricted. Subsequently, we make the collapse strength assessment when they are subjected to high-temperature.

Figure 4. Schematic of the FEM simulation model for screen liner (base case, staggered pattern)

4.1 Phase angle

In this section, we make collapse assessment for different phase angles of screen liners. The collapse ratings of screen liners are shown in Figure 5. The collapse strengths when subjected to high-temperature effects are presented in Figure 6.

The result indicated that when hole density is given, the collapse rating reduces with the increase of phase angle (Figure 5). This is because too many holes in the longitudinal direction could reduce the hole’s longitudinal separation, which could severely weaken the collapse rating. For an inline screen liner, phase angle of 30° does not weaken the liner significantly, approximately 7.93% reduction when compared to an intact liner. While 47.62% collapse rating decreases for

11.5 mm

15.875 mm

LGR

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the case of 180° phase angle. Compared with an inline screen liner, a staggered screen liner has higher collapse rating. The phenomenon becomes more profound when phase angle increases.

(a) Inline screen liner (b) Staggered screen liner

Figure 5. Collapse rating of screen liners with various phase angles

Figure 6. Collapse strength of screen liners with various phase angles (120 °C)

When high-temperature effect is considered, the collapse strength of the screen liner further decreases. With the increase of phase angle, the collapse strength reduces linearly (Figure 6). If the underground temperature is 120 °C, the collapse strength of an inline screen liner is 13.12 to 21.43 MPa when phase angle varies from 30 to 180°, and it is 15.92 to 21.43 MPa for a staggered screen liner. Compared with the intact liner, the diminution rate is 60.22 to 75.64% for the inline screen liner, and 60.22 to 70.44% for the staggered screen liner. Therefore, the result suggests that the elevated temperature could substantially impair the collapse strength of the screen liners. Among all the cases, when hole density is given, smaller phase angles have higher

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collapse strength. Besides, a staggered screen liner performs better than an inline screen liner, especially combined with larger phase angles.

4.2 Hole diameter

In this section, we make collapse assessment for different hole diameters of screen liners. The collapse ratings of screen liners are shown in Figure 7. The collapse strengths when subjected to high-temperature effects are presented in Figure 8.

(a) Inline screen liner (b) Staggered screen liner

Figure 7. Collapse rating of screen liners with various hole diameters

The result showed that the collapse rating declines with the rise of hole diameter (Figure 7). For an inline screen liner, when hole diameter increases from 9.525 to 25.4 mm, the collapse rating reduces from 9.80 to 25.40% when compared to an intact liner. Similar to mentioned above, a staggered screen liner has higher collapse rating than an inline screen liner.

Figure 8. Collapse strength of screen liners with various hole diameters (120 °C)

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Intact 9.525 mm15.875 mm 25.4 mm

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ress

ure

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a)

u/dt

Intact 9.525 mm15.875 mm 25.4 mm

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laps

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reng

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Pa)

Hole Diameter (mm)

InlineStaggeredLinear (Inline)Polynomial (Staggered)

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The hole diameter with collapse strength relationship infers that with the increase of hole diameter, the collapse strength reduces linearly for an inline screen liner (Figure 8). While, for a staggered screen liner, the collapse strength will increase first then decrease (Figure 8). The reason could be attributed to the occurrence of higher thermally induced stress-concentration for smaller hole diameters on a staggered screen liner. If the underground temperature is 120 °C, the collapse strength of an inline screen liner is 19.96 to 18.48 MPa when hole diameter changes from 9.525 to 25.4 mm. For a staggered screen liner, the maximum collapse strength is 20.80 MPa when hole diameter is 15.875 mm, and the minimum value is 18.98 MPa for hole diameter with 9.525 mm. Compared with the intact liner, the collapse strength degradation rate is 62.96 to 65.70% for an inline screen liner, and 61.39 to 64.76% for a staggered screen liner. Furthermore, when hole diameter is smaller (less than 12 mm), an inline screen liner performs better than a staggered screen liner. While, with the increase of hole diameter, the differences between these two patterns dwindle.

4.3 Hole density

In this section, we make collapse assessment for different hole densities of screen liners. The collapse ratings of screen liners are shown in Figure 9. The collapse strengths when subjected to high-temperature effects are presented in Figure 10.

(a) Inline screen liner (b) Staggered screen liner

Figure 9. Collapse rating of screen liners with various hole densities

The result indicated that when phase angle is given, the collapse rating reduces with the increase of hole density (Figure 9). This is also because too many holes in the longitudinal direction could reduce the hole’s longitudinal separation, which could severely weaken the collapse rating. For an inline screen liner, the increase of hole density from 30 to 120 holes/m could decrease the collapse ratings from 7.93 to 31.75%. For a staggered screen liner, the growth of hole density from 30 to 120 holes/m could decline the collapse ratings from 7.93 to 26.79%. Therefore, with larger hole densities, a staggered screen liner has higher collapse rating.

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Figure 10. Collapse strength of screen liners with various hole densities (120 °C)

Figure 10 presents that with the increase of hole density, the collapse strength reduces linearly (Fig. 5). If the underground temperature is 120 °C, the collapse strength of an inline screen liner is 21.55 to 18.03 MPa when hole density changes from 30 to 120 holes/m. For a staggered screen liner, the collapse strength is 21.09 to 17.44 MPa when hole density changes from 30 to 120 holes/m. Compared with the intact liner, the reduction rate is 60.00 to 66.54% for an inline screen liner, and 60.84 to 67.63% for a staggered screen liner. From curve above, the staggered screen liner is above the inline screen liner although the difference is less significant when compared to the impact of phase angle. Hence, a staggered screen liner could be induced higher thermal-axial stress than an inline screen liner.

In sum, although a staggered screen liner has higher collapse strength than an inline screen liner when subjected to high temperature, cases with smaller hole diameters (less than 12 mm) and larger hole densities (more than 90 holes/m) should be used with caution.

5. Slotted Liner Design

This section discusses the application of the proposed workflow to a slotted liner designing in geothermal wells. A series of cases to describe the effects of numerous slots in a slotted liner on the collapse resistance when subjected to high-temperature are displayed (Table 5). Similarly, the underground temperature is also set to be 120 °C. The material properties of intact liner are the same as Table 4. The slot width is 0.6 mm.

Table 5. Values for cases studies of a slotted liner.

Parameter Value 1 Phase angle, ° 30, 45, 60*, 90 2 Slot length, mm 40, 60*, 80 3 Perforation density, slots/m 30, 48*, 60, 90 4 Pattern Inline, Staggered

The symbol * represents base case

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e st

reng

th (M

Pa)

Hole Density (holes/m)

InlineStaggeredLinear (Inline)Linear (Staggered)

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First, we obtain the collapse ratings of slotted liners with various slots parameters through the analytical model. Then we established the FEM numerical simulation model. Similar to screen liners, we make a LGR (local grid refinement) around each slot. The schematic of the simulation model for the slotted liner is shown in Figure 11, and it is discretized by 197785 nodes and 904150 elements. The boundary condition is that one end of the slotted liner is x-y-z direction displacement fully restricted. Subsequently, we make collapse strength assessment when they are subjected to high-temperature effect.

Figure 11. Schematic of the FEM simulation model for slotted liner (base case, staggered pattern)

5.1 Phase angle

In this section, we make collapse assessment for different phase angles of slotted liners. The collapse rating of slotted liners is shown in Figure 12. The collapse strength when subjected to high-temperature effects are presented in Figure 13.

(a) Inline slotted liner (b) Staggered slotted liner

Figure 12. Collapse rating of slotted liners with various phase angles

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The result illustrates that when slot density is given, the collapse rating reduces with the increase of phase angle significantly (Figure 12). This is because too many slots in the longitudinal direction could reduce the slot’s longitudinal separation, which could severely weaken the collapse rating. For an inline slotted liner, when phase angle varies from 30 to 90°, the collapse rating reduction changes from 24.00 to 72.00%. While for a staggered slotted liner, when phase angle changes from 30 to 90°, the collapse rating reduction varies from 24.00 to 71.88%. Compared with an inline slotted liner, a staggered slotted liner has higher collapse rating. However, compared with a screen liner, the collapse rating of a slotted liner is considerably lower. Furthermore, the change of collapse strength is more sensitive to the change of phase angle for a slotted liner. Consequently, as expected, slots tend to cause more severe reduction in collapse rating.

Figure 13. Collapse strength of slotted liners with various phase angles (120 °C)

Figure 13 indicates that when high-temperature effect is considered, the collapse strength of the slotted liner could be further decreased. With the increase of phase angle, the collapse strength reduces linearly. If the underground temperature is 120 °C, the collapse strength of an inline slotted liner is 7.40 to 17.18 MPa when phase angle varies from 30 to 90°, and it is 8.07 to 16.29 MPa for a staggered screen liner. Compared with the intact liner, the collapse strength decrease rate is 68.10 to 86.27% for an inline screen liner, and 69.76 to 85.02% for a staggered screen liner. Therefore, the result implies that the elevated temperature could notably degrade the collapse strength of the slotted liners. Different from a screen liner, the collapse strength of an inline slotted liner is higher than a staggered slotted liner when subjected to high temperature, especially at smaller phase angle.

5.2 Slot length

In this section, we make collapse assessment for different slot lengths of slotted liners. The collapse rating of slotted liners is shown in Figure 14. The collapse strength when subjected to high-temperature effects are presented in Figure 15.

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InlineStaggeredLinear (Inline)Linear (Staggered)

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(a) Inline slotted liner (b) Staggered slotted liner

Figure 14. Collapse rating of slotted liners with various slot lengths

The calculation result shows that with the increase of slot length, the collapse rating declines (Figure 14). For an inline slotted liner, when slot length increases from 40 to 80 mm, the collapse rating reduces from 31.99 to 64.00% when compared to an intact liner. For a staggered slotted liner, the collapse rating decreases from 31.79 to 63.89% when compared to an intact liner. Similar to mentioned above, a staggered slotted liner has higher collapse rating than an inline slotted liner.

Figure 15. Collapse strength of slotted liners with various slot lengths (120 °C)

The estimation shows that with the increase of slot length, the collapse strength diminishes linearly (Figure 15). If the underground temperature is 120 °C, the collapse strength of an inline slotted liner decreases from 15.84 to 8.47 MPa when slot length varies from 40 to 80 mm, and it reduces from 12.68 to 8.52 MPa for a staggered screen liner. Compared with the intact liner, the collapse strength decrease rate is 70.60 to 84.28% for an inline screen liner, and 76.45 to 84.18% for a staggered screen liner. The collapse strength of an inline slotted liner is higher than a staggered slotted liner when subjected to high temperature, especially at shorter slot length.

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5.3 Slot density

In this section, we make collapse assessment for different slot densities of slotted liners. The collapse ratings of slotted liners are shown in Figure 16. The collapse strengths when subjected to high-temperature effects are presented in Figure 17.

(a) Inline slotted liner (b) Staggered slotted liner

Figure 16. Collapse rating of slotted liners with various slot densities

The result indicated that when phase angle is given, the collapse rating reduces considerably with the increase of slot density (Figure 16). This is also because too many slots in the longitudinal direction could reduce the slot’s longitudinal separation, which could severely deteriorate the collapse rating. For an inline slotted liner, the increase of slot density from 30 to 90 slots/m could decrease the collapse ratings from 30.00 to 89.99%. For a staggered screen liner, the growth of slot density from 30 to 90 slots/m could decline the collapse ratings from 29.79 to 89.95%. Therefore, for slotted liners with larger slot densities, a staggered screen liner has higher collapse rating. Besides, by comparing Figure 9 with Figure 16, it unequivocally indicates that the collapse ratings of slotted liners reveal much more distinct trends because of a variation in the slot parameters.

Figure 17. Collapse strength of slotted liners with various slot densities (120 °C)

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Pre

ssur

e (M

Pa)

u/dt

Intact30 (slots/m)48 (slots/m)60 (slots/m)90 (slots/m)

0

5

10

15

20

20 40 60 80 100

Col

laps

e st

reng

th (M

Pa)

Slot Density (slots/m)

InlineStaggeredLinear (Inline)Linear (Staggered)

Yang et al.

Figure 17 presents that with the increase of slot density, the collapse strength reduces linearly. If the underground temperature is 120 °C, the collapse strength of an inline slotted liner decreases from 17.27 to 3.07 MPa when slot density changes from 30 to 90 slots/m. For a staggered slotted liner, the collapse strength reduces from 17.06 to 3.38 MPa when slot density changes from 30 to 90 slots/m. Compared with the intact liner, the reduction rate is 67.94 to 94.30% for an inline screen liner, and 68.34 to 93.72% for a staggered screen liner. Moreover, the staggered slotted liner is below the inline slotted liner although the difference is less eloquent with the increase of slot density. Hence, similar to the screen liner, a staggered slotted liner could be induced higher thermal-axial stress than an inline slotted liner.

Consequently, an inline slotted liner with lower slot density (less than 60 slots/m), shorter slot length (less than 80 mm), and smaller phase angle (smaller than 80°) has higher collapse strength than a staggered slotted liner.

Generally, in the real design, when the collapse strength cannot meet the requirement if more-dangerous situation in the field is considered, such as extreme higher-temperature, falling of large rocks, etc, the screen/slotted configurations must be carefully adjusted. Then, the whole process is re-estimated again in order to have a safe and efficient completion approach in geothermal wells. Moreover, field trials in an actual geothermal operating environment are necessary to test the accuracy of the modeling, which require time and energy to perform and evaluate.

6. Conclusions

This work presents an integrated workflow to provide a methodology for the design of screen/slotted liners completion in geothermal wells. The following observations can be made from the applications of the proposed workflow:

• The high-temperature effect could substantially impair the collapse strength of a screen/slotted liner.

• The collapse strength of a slotted liner reveal much more distinct trends because of a variation in the slot parameters than a screen liners. And, slots tend to cause more severe reduction in collapse rating and collapse strength when subjected to high temperature than holes.

• A staggered screen/slotted liner could be inducing higher thermal-axial stress than an inline screen/slotted liner.

• For a screen liner, the staggered pattern with smaller phase angle (less than 120°), larger hole diameters (larger than 12 mm) and smaller hole densities (less than 90 holes/m) is suggested to be used in geothermal wells.

• For a slotted liner, the inline pattern with lower slot density (less than 60 slots/m), shorter slot length (less than 80 mm), and smaller phase angle (smaller than 80°) is viable options in the completion of geothermal wells.

Yang et al.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the National Key Research and Development Program of China (Grant No. 2016YFE0124600). Besides, support from the Program of Introducing Talents of Discipline to Chinese Universities (111 Plan) (Grant NO. B17045) is also appreciated. We also would like to express our gratitude to Dr. Xiaochun Jin for his useful suggestions and ideas for the work.

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