Well Design for Optimal Efficiency by Understanding and Minimizing Well Losses at Source Tanna DeRuyter, EIT and Michael Kenrick, PE, LHG GeoEngineers, Inc. Redmond WA

Outline Current basis for Well Design Components of Well Losses

– Laminar Losses – Turbulent Losses

Step-Drawdown Tests Calculating Well Losses Optimizing Well Design

Well Design and Limiting Well Losses Design paradigms (filter-packed wells):

– Filter pack: D30 4 to 6 times aquifer d30 – Uniformity Coefficient: 2.5 or less – Slot Size: to retain 90% of filter pack – Screen Length: 80 – 90% of Aquifer Thickness – Open Area: > 5% … or more? – Entrance Velocity: < 0.1 ft/s – Upflow Velocity: < 5 ft/s – Casing size > Pump size: by 2, 4, 6 inches

Best Drilling Practices Construction paradigms:

– Generally follow BDPs… – Best Drilling Practices!!! – Balance water head to avoid heave – Flush out fluid / suspended sediment – Avoid wellbore skin – Develop, – Develop, – Develop

Well Losses

Original Piezometric Surface

Water Level in Well

Confined Aquifer Flow

sw

Q

Ground Surface

Well Losses Ground Surface

Original Piezometric Surface

Water Level in Well

Confined Aquifer Flow

BQ

CQ2

sw = BQ + CQ2

Jacob (1946)

Q

sw

Well Losses

Original Piezometric Surface

Water Level in Well

Confined Aquifer Flow

BQ

CQ2

BQ: Laminar flow • head loss ∝ velocity • Darcy’s Law • Aquifer Loss

Q

Ground Surface

sw

Well Losses

Original Piezometric Surface

Water Level in Well

Confined Aquifer Flow

BQ

CQ2

CQ2: Turbulent flow • head loss ∝ velocity2

• Forchheimer • Well Loss

Q

Ground Surface

sw

Step-Drawdown Tests

Step-Drawdown Tests

Step Test Analysis Calculate sw/Q Plot against Q Intercept = B Slope = C Natapoc Example: B = 0.0665 min/ft² C = 0.000136 min²/ft5

Laminar Well Losses

Occurs in: Conventional screened wells with filter pack (or naturally developed)

Calculated by: Aquifer loss/drawdown equation (Thiem, for distance-drawdown)

Laminar Well Losses

Source: Houben (2015)

1. Partial Penetration • Flow path convergence

(blue) • Non-uniform screen inflow

rate (red)

Laminar Well Losses

No Skin Factor

2. Wellbore skin (skin effect)

Laminar Well Losses

No Skin Factor

Positive Skin Factor

Positive skin • Formation damage, clogging • Increases drawdown

Laminar Well Losses

Source: Houben (2015)

Filter Pack

Aquifer Material

Positive Skin

Laminar Well Losses

No Skin Factor

Negative Skin Factor

Negative skin • Filter pack development • Reduces drawdown

Well Screen Losses

3. Slot Convergence (Laminar) • Flow path convergence at

the well screen slots

Turbulent Well Losses Occurs in: Conventional screened wells with filter pack (or naturally

developed) Calculated by: empirical equations

Turbulent Well Losses

1. Turbulent flow caused by the filter pack

Turbulent Well Losses

2. Turbulent flow caused by the screen slots

Turbulent Well Losses

3. Turbulent flow caused by • Upflow inside the well screen • 90-degree momentum change

Turbulent Well Losses

4. Turbulent flow caused by upflow inside the well casing

Turbulent Well Losses

5. Turbulent flow caused by flow around the pump motor • Not yet modelled

Turbulent Well Losses

6. Turbulent flow caused by swirling turbulence at the pump intake • Not yet modelled

Does the Well Diameter make a difference?

“doubling the diameter of a 6-inch well creates an approximate 10% increase in yield (tripling size increases yield by about 17%)” —Sterret (2007); Groundwater and Wells

• But this is based on the Theim equation • And it completely ignores well losses • Turbulent well losses are strongly related to well

and screen diameter

Quantifying Aquifer and Well Losses Houben’s 2015 WellDesigner Spreadsheet Model: Flow system broken down into the above series of stages Equations provided for the identified well losses Losses are grouped as both laminar and turbulent Reynolds Number used to differentiate turbulent flow All losses account for predicted or observed well drawdown Approach verified by comparison with step-drawdown tests

Converting WellDesigner to GoldSim

GoldSim Dashboard

GoldSim Simulated Step Test Output Matrix

Costing out Efficiency Benefits Fixed Variables

– Design Flow Rate – Total Dynamic Head – Aquifer Depth – Pump Size

Sensitivity analysis – Screen open area / number of slots – Length of screen – Diameter of screen – Diameter of casing – Pump setting depth

Sensitivity Analysis

Smaller diameter borehole

Larger diameter borehole

Longer Screen Shorter Screen

Less Expensive More Expensive

Capital Cost versus Operating Cost Larger wells are:

– more efficient – more expensive to construct – less costly to operate

Use WellDesigner in GoldSim to optimize design Include estimated uncertainty in key parameters:

– Aquifer Transmissivity – Wellbore Skin – Filter Pack Conductivity

Future Improvements Transient Flow

– Theis rather than Theim – More complex aquifer hydraulics

Unconfined Aquifers – Reduced Aquifer Thickness – Development of a Seepage Face

Heterogeneous Aquifers – Layered formations – Vertical Anisotropy

Wells with excessive well losses: sw = BQ + CQP

Fractured Rock Aquifers – Non-laminar flow in fissures – Turbulent entry losses – Upflow in open wellbore – (Atkinson, Gale & Dudgeon 1994)

Well deterioration and rehabilitation

– Fines migration – Clogging of the filter pack

Encrustation Precipitation Biofilm

Thank you