Critical Measurement of Well Thermal Properties to Support Design

A.A. Koenig, Ph.D.ARB/Geowell

NGWA Geothermal ForumDec 10, 2009New Orleans

AbstractFor large tonnage (100 tons or greater) HVAC systems, it is imperative that a test well be drilled and that measurement of the thermal characteristics of the well (as representative) be undertaken prior to a final design. The defining thermal properties include: the “effective” thermal conductivity, K, of the formation surrounding the bore; the thermal diffusivity, α, and the characteristic thermal decay rate, τ. Armed with this knowledge, the geothermal engineer can begin to specify the design (wetted ft per delivered ton) to meet a building heating or cooling load. This paper will demonstrate the measurement, analysis and interpretation required to extract this information, using a number of geothermal installations to exemplify the approach.

A Typical SCW Bore Cross-Section

• 10”-12” bore with 60’-120’ of 8” steel casing grouted into competent bedrock

• 8” open bore to 150’-200’• 6” open bore thereafter to final depth• Final depth range: 800’-1500’ (deeper for urban

constrained areas) Bore can encounter faults, etc. which render

the borehole unstable and subject to collapse

SCW Design Considerations

• How do I recognize a good site opportunity to reduce installed capital cost by specifying open loop SCW design?

• How deep should I go in a single bore?• What should I do if I encounter significant

water while drilling?• How do I specify how many wells and at what

depth to meet a given building load?

Response

• Ideal: fractured hard rock with high effective thermal conductivity (k ≥ 2 BTUH/ft°F); depth to bedrock & water < 70’

• Drilled depth should be left somewhat flexible to allow for termination when large amounts of water preclude economic drilling or there is potential for approaching a salt water interface

• What is important is the total wetted feet of bore supported by thermal & hydro-geologic testing followed by simulation.

Map of Where We Are Going• Measurement needs• Analysis of measurement to yield critical thermal

& hydro-geologic properties that dictate SCW design

• What controls the limits of specified borehole depth?

• How many wells do I need to serve a given load, and how should I specify this?

• A look at some examples.

What Size Project Commands Testing?

• Set aside 5% project cost for testing• With a 2 day thermal test charge of $15,000 per

well, the minimum size installation is then $300,000, or approx. 100 tons

• Additional wells should be drilled and tested for larger tonnage projects; consider the extremes of the well field layout

• The average measured borehole thermal values should be used to support the design.

Purpose of Thermal Testing

Measure the thermal properties of the wellbore rock in order to:

support an informed decision on continued drilling (total no. drilled feet)

develop simulations of the geothermal seasonal system performance

incorporate the building hr x hr block load expectations utilize information on the hydrogeology

(interconnectedness of the wells).

SCW Thermal Test LayoutWhy a propane source? Take the example of a 1000’ well designed to accept 80 ft/ton => 12.5 tons or 150 kBTUH; with a 84% combustion efficiency, the heater will need a heat source of 180 kBTUH for the test duration of at least a day.

Water Heater SelectionFeatures: 84% efficient pool/spa heater rated:

150-250 kBTUH Propane (100 gal) or NG Max temperature 105°F Electronic set: temperature limits and

rise Cuper-Nickel HX Portability (120 lbs) 2” ports Designed for outdoor use Well insulated

Test Basis• 1-2 day continuous test period @ 150-250 kBTUH, depending

on heater selection • You’ll need 50-100 gal. propane (expect to get 32 hrs out of a

100 gal tank for the larger 250 kBTUH heater)• 50 gpm test flowrate => 8°F ΔT (spec)• Followed by 14 hrs cool down• Avg. water temperatures and flowrate tabulated every minute

(3000 data pts)• Typical SCW water temperature rise from 53°F to 87°F

depending on the rock conductivity & water encountered.

Comparison of Thermal Testing Results with Expectations Based on the Carslaw & Jaeger Model

0 200 400 600 800 10005060708090

100

Transient Conduction in Rock

measured C-J model

Time (hr)

Roc

k T(

F)

The thermal test results over 65 hrs. shows good agreement with the C-J model. Note that a typical 48 hr duration overlays the rising portion of the curve and falls short in supporting prediction of seasonal SCW performance, i.e. the flatter portion. It would be beneficial to continue the testing, but this becomes an expense tradeoff.

Thermal Test Equipment Setup

Test Equipment Layout

Labview + NI FieldPoint DAQ

Detailed DAQ Measurements

0 5 10 15 20 25 30 3560

65

70

75

80

85

90

Test Time (hr)

SCW

Tem

p(°F

)

Q° = 209,275 BTUH, L(wetted) = 1460’ => 83.7 ft/ton

Analytical Fit to Test Data:(Tav-T∞) = 4.30 LN(t) + 6

Slope=4.30

k(eff) = 2.65BTUH/ft°F

-5 -4 -3 -2 -1 0 1 2 3 40

5

10

15

20

25

LN(t)-hr

T(av

) - T

(0)

q° = 22.8 BTUH/ft

Keff = q°/(2*Slope) = 2.65 BTUH/ft°F

Slope = 4.30

Intercept = 6.01

Data Analysis Using Graphical Solutions for k & α K-value: measured from slope of data ΔTavg vs. LN(t)

fixed heat flux: q° = Q°(BTUH)/(2πL) = 22.8 BTUH/ftmeasured slope, s = 4.304K = q°/(2s) = 22.8/(2*4.304) = 2.65 BTUH/ft°F

Thermal diffusivity, α (sqf/hr): measured using the intercept value (ΔTo)@ LN(t)=0: α = {ro/δo EXP[ΔTo/(2s)] }2 measured intercept, ΔTo = 6.013α = .068 sqf/hr (1.62 sqf/day)or averaged from individual datum using: α = {ro/2 EXP[½(ΔTi/slope-LN(t))]}2

Check of α: (ρCp) = k/α = 2.65/.068 = 39.2 BTU/cuf°F Is this reasonable? Can it be verified from independent analysis of rock samples taken at various depths during drilling?

Contribution of Mobile Water at the Bore Fracture Face to K(eff)

-5 -4 -3 -2 -1 0 1 2 3 40

5

10

15

20

25

LN(t)-hr

T(av

) - T

(0)

Flatter Slope => Higher K S1

S2

Keff = Q°/(2AboreS2) where S=slopeKrock = Q°/(2AboreS1) =(Q°- qx)/(2AboreS2)Krock = Keff (1- qx/Q°), or Keff = Krock/(1- qx/Q°)

qx

Thermal Relaxation Study Why is this measurement important?

• Temperature decay rate is important to the understanding of what temperatures will be achieved as the building load comes off and the geothermal wells are allowed to relax.

• This time constant goes into a model simulating well performance with time.

Two ways to measure borehole thermal relaxation rate: remove heat load; measure & record SCW temperatures over 14 hours of cool-down by either• allowing wellbore water to circulate while measuring

temperature exiting the well, or• affix temperature probes to the PVC separator at select depths

(e.g. top, mid, bottom) record without circulation.

Thermal Relaxation Discrete Data

0 2 4 6 8 10 12 14 1662646668707274767880

Relaxation Time (hr)

Wat

er T

(F)

Analytical Form for Relaxation

T(t) = T∞ + (Tstart-T∞) EXP(-t/τ)

where T(t) is SCW temp. @ time, t(hr)T∞ is the undisturbed (ambient) ground temp.Tstart is the water temp. @ start of relaxationτ is the time constant (hr) for thermal relaxation.Note: LN[(T-T∞)/(Tstart-T∞)] vs. t is a straight line with

slope = τ.

Thermal Relaxation Study

0 2 4 6 8 10 12 14 16

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Relaxation Time (hr)

LN[(T

-Ta)

/(Ts

-Ta)

] Two Time Constants

Thermal Relaxation Analysis(Early Portion)

0 1 2 3 40

0.2

0.4

0.6

0.8

1

Data

Model

Relaxation Time (hr)

(T-T

a)/(

Ts-T

a)

τ =7 hrs

Thermal Relaxation Analysis(Later Portion) Time Constant: τ ≈ 20 hrs

2 4 6 8 10 12 14

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Relaxation Time (hr)

LN[(T

-Ta)

/(Ts

-Ta)

]

τ =20 hrs

Alternative Form: Semi-log Fit to Relaxation Data

0 2 4 6 8 10 12 14 166264666870727476788082

Relaxation Time (hr)

SCW

Tem

p(°F

)

-5 -4 -3 -2 -1 0 1 2 360

65

70

75

80

85

90

LN(t)-hr

SCW

Tem

p(°F

)

T=77.4-.52 LN(t)

T=77.1-3.48 LN(t)

------ t > 1 hr =>

<= t < 1 hr --------

Another Example: Thermal Relaxation Study

-4 -3 -2 -1 0 1 2 350

60

70

80

90

LN(time-hrs)

Avg.

Wat

er T

(F)

36 minutes

A Comparative Look at Thermal Characteristics Measured at Various Sites

Site Rock Type K(BTUH/ft°F)effective

α (sqf/day)effective

r (thermal recovery rate)

S-F Schools Royersford, PA

red shale with large yield ≈ 250 gpm

2.98 2.35 4.0610.6 (top)

Friends Center Philadelphia

Wissahickon schist with 100 gpm yield

2.65 1.65 3.48

Villanova University

gneiss with few fractures & 5 gpm yield

1.86 1.03 7.375

99th ACE Londonderry, NH

gneiss with 50 gpm yield; num fractures > 200’

3.09 2.10 6.10

General Observations Regarding Thermal Properties

High K values (>2 BTUH/ft°F) are likely due to the presence of significant amounts of mobile ground water present at the bore, which increases the effective conductivity.

In general, ground water infiltration in the bore enhances the effective K-value in a linear contribution: Keff K(rock) + F(Gf), where Gf is the equiv. total infiltrating flow (gpm) over the face of the bore, as it is modeled.

How do you use this information to develop a preliminary SCW design?

Well bore measurements (k, α, τ)

Wellfield-HP Interface

Heating & Cooling Load Considerations

1. Is there a balanced heating & cooling load for this site? Typically, the answer is NO, which means that the designer is forced to make a choice to:a. Meet only the smaller of the two loads using geothermal, in which

case, the additional burden must be supplemented with a conventional HVAC system, or

b. Over-design the system to meet the most demanding load.

2. The most economical solution to (1) is (1a) assuming that the additional first cost of implementing (1b) is an impediment to proceeding with the project. Note also, that (1a) presents an annual balanced load to the ground.

How to Design a SCW Field to Meet a Load

1. Start with the building design LOAD. Is this heating (or cooling) dominated?a. If heating dominated, the SCW design must be cognizant of preventing a

potential freezing condition in the well as water is returned cooler with each circulation

b. If cooling dominated, the SCW field is burdened additionally by having to reject the heat of compression from the heat pumps. This amounts to an additional 20%.

2. Use the thermal test results specific to the site to guide the design:a. If bleed is acceptable, then you will need to determine an optimal design

(capital cost & annual performance) that will minimize the design (ft/ton) at an acceptable bleed percentage, e.g. 10% for “x” hours a year

b. If a NO-bleed design is contemplated, you need to select a conservative design (ft/ton) that is consistent with the measured effective thermal conductivity.

No-Bleed Design Guidance

0.5 1 1.5 2 2.5 3 3.560

70

80

90

100

110

120

K-Factor Guidance on SCW Design (ft/ton)No-Bleed Case

K(BTUH/ft°F)

Desig

n (ft

/ton

)

No-Bleed Design Case Example Let’s assume that one measures & determines a representative

K-value = 1.9 BTUH/ft°F Enter the curve at the bottom at K=1.9 and read across to the y-

axis to arrive at a conservative design basis of 90 ft/ton For example, to meet a building load of 258,000 BTUH (215 tons

heating equiv.), one will require a total wetted bore length of: 215 x 90 = 19,350 ft of bore

Assuming that the ($/ft) risk of drilling is the same down to depths of around 1300’, and static levels are around 40’, then 15 wells will be required, drilled to an average depth of 1330’ (1290’ + 40’). If significant water is encountered during drilling a well, then one will need to re-visit in-situ the design depth for a better economic selection.

Ground Water Flow Coupling to SCW Model

Study of GW Flow Impact on k(eff)

Two Contributions to k(eff)

1. Heat transport of “thermal” water from the bore by advective flow, along with

2. Influx of ground water due to the natural hydraulic gradient[Note: as the rock & water around the borehole store heat, the avg. temperature rises in time: T(SCW) => T(avg)]

Base Case: K(eff) @ Zero GW Flow

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

20

25

30

35

Wellbore Thermal Response (flow = 0 gpm)

LN(t-hrs)

T(SC

W)-T

(sta

rt)

K = 1.89 BTUH/ft°F

GW Flow Modification to Model

0 1 2 3 4 50

5

10

15

20

25

Wellbore Thermal Response (flow = 1.5 gpm)

LN(t-hrs)

T(SC

W)-T

(sta

rt)

k = 2.12 BTUH/ft°F

0 1 2 3 4 50

5

10

15

20

Wellbore Thermal Response (flow = 3 gpm)

LN(t-hrs)

T(SC

W)-T

(sta

rt)

k = 2.37 BTUH/ft°F

Model of 48 hour thermal test (continuous heating): (1) K(eff) increases with

ground water flow rate(2) Non-linear behavior for

t > 1 day

K(eff) Increase with GW Flow

0 1 2 3 4 5 6 7 8 9 101.5

2

2.5

3

3.5

4

4.5

Effective K-Value with Ground Water Flow

Ground Water Flow (GPM)

Effec

tive

k-Va

lue

Gneiss Forma-tion

Friends Ctr Data

K= 1.89 + .161Gx

Modeling & Simulation

Three Elements: hr x hr daily load representation for each month; heat pump

(EWT) characteristics, and SCW dynamic thermal model

Model of Daily Heating & Thermal Relaxation Developed from Testing

0 4 8 12 16 20 2450

55

60

65

70

75

SCW Daily Response to Duty Cycle

DC=50%DC=58%DC=67%DC=75%

Time of Day

SCW

Wat

er T

(°F)

Translation from Building HVAC Daily Peak to Avg. Daily Heating/Cooling Rate

30 40 50 60 70 80 90 100 1100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Influence of Design (ft/ton) on Avg Daily Heating Rate

50% DC25% DC75% DC

Design (ft/ton)

q°(a

v)/q

°

Daily Avg. Load Interpretation

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Influence of Duty Cycle on Avg Heating Rate

Daily Duty Cycle

q°(a

v)/q

°

K = 2.4 BTUH/ft°F

Heat Pump Duty Cycle Approximation

30 Ton w-w Heat Pump Characteristics

20 30 40 50 60 70 80 900

10

20

30

40

30 Ton Heat Pump Heating Capacity

Well Supply T(F)

Capa

city

(Ton

s)

40 50 60 70 80 90 100 110 1201

1.1

1.2

1.3

1.4

30 Ton Heat Pump Cooling

Well Supply T(F)

Rej

ectio

n/C

apac

ity

40 50 60 70 80 90 100 110 1200

10

20

30

30 Ton Heat Pump Cooling Capacity

Well Supply T(F)

Cap

acity

(Ton

s)

30 40 50 60 70 80 900.600000000000001

0.700000000000001

0.800000000000001

0.900000000000001

30 Ton Heat Pump Heating

Well Supply T(F)

Abso

rptio

n/Ca

paci

ty

Daily Cooling Load Simulation

0 5 10 15 20 25 3060

70

80

90

SCW July Daily Performance

Return Supply

Time (hrs)

SCW

Tem

p(F)

0 10 20 30 40 50 6060

70

80

90

SCW July Two Day Performance

Return Supply

Time (hrs)

SCW

Tem

p(F)

One Week Cooling Results

0 20 40 60 80 100 120 140 160 18060

70

80

90

SCW July Weekly Performance

Return

Supply

Time (hrs)

SCW

Tem

p(F)

One Month Cooling Results

0 100 200 300 400 500 600 700 80060

70

80

90

SCW July Monthly Performance

Return Supply

Time (hrs)

SCW

Tem

p(F)

Cooling Season (4 mo.) Results

0 500 1000 1500 2000 2500 300060

70

80

90

100

SCW Seasonal Cooling Performance

Return

Supply

Time (hrs)

SCW

Tem

p(F)

Conclusion

• Measurement of the well bore thermal properties is critical to support a proper design of SCW geothermal field to meet a building load

• Modeling & simulation of the HVAC system operation allows the designer to fine-tune the geothermal design

• For more information, we recommend visiting HeatSpring Institute (www.heatspring.com) for their course offering on SCW Design.