Review: Hydraulics of water wells—head losses of individual components

Abstract

Knowledge about the hydraulics of water wells is important to optimize their energy efficiency. By minimizing head losses around the well, energy consumption and ageing processes can be limited, thereby prolonging the well’s service life. The contribution of the individual components to total head loss (drawdown) in the well is analyzed in detail. The single most important contributor to drawdown is commonly the aquifer. Its hydraulic conductivity can only be improved slightly through development. The second most important contributor is the formation of a wellbore skin layer. This occurs if no proper well development was performed after drilling; the layer contains remnants of drilling-fluid additives or mobilized fine aquifer particles. The head loss caused by groundwater flow in the gravel pack, through the screen slots and inside the well, was found to be small. Thus, well development is the most important measure to influence well performance and energy efficiency. For longer operation times and pumped volumes, the energy gains outperform the cost for the development.

Résumé

La connaissance en matière d’hydraulique des puits est importante pour optimiser leur efficacité énergétique. En réduisant les pertes de charge autour du puits, la consommation d’énergie et les phénomènes de vieillissement peuvent être limités, prolongeant ainsi la durée de vie de l’ouvrage. La contribution des différents composants dans la perte de charge globale (rabattement) dans le puits est analysée en détail. Le facteur le plus important à l’origine du rabattement est généralement l’aquifère. Le 2ème facteur le plus important est la formation d’un effet de paroi autour du puits. Cela se produit si un développement du puits n’est pas réalisé correctement à l’issue du forage. La paroi du forage contient les résidus d’additifs du fluide de forage ou des particules fines issues de l’aquifère. Les pertes de charge créées par l’écoulement d’eau souterraine dans le massif filtrant, à travers les fentes de la crépine et à l’intérieur du puits ont été jugées assez faibles. Ainsi, le développement du puits est la mesure la plus importante pour agir sur la performance et l’efficacité énergétique. Pour des temps d’exploitation et des volumes de pompage conséquents, les gains d’énergie surpassent le coût du développement.

Resumen

El conocimiento de la hidráulica de los pozos de agua es importante para optimizar la eficiencia de energía. Al minimizar las pérdidas de carga del pozo, el consumo de energía y los procesos de envejecimiento pueden ser limitados, prolongando así la vida útil de los pozos. Se analiza en detalle la contribución de los componentes individuales a la pérdida total de carga hidráulica (reducción) en el pozo. El factor individual que más contribuye a la reducción de la carga hidráulica comúnmente es el acuífero. Su conductividad hidráulica sólo puede mejorarse ligeramente a través del desarrollo. El segundo factor más importante es la formación de una capa de revestimiento en el pozo. Esto sucede si no hay un desarrollo adecuado después de ejecutarse la perforación; la capa contiene restos de aditivos de los fluidos de perforación o de partículas finas movilizadas en el acuífero. Se encontró que la pérdida de carga causada por el flujo del agua subterránea en el empaque de grava, a través de las ranuras del filtro y el interior del pozo era pequeña. Por lo tanto, el desarrollo del pozo es el aspecto más importante que influye en el rendimiento del pozo y en la eficiencia de la energía. Para mayores tiempos de funcionamiento y volúmenes bombeados, las ganancias de energía superan el costo del desarrollo.

摘要

水井水力学知识对优化其能量效率非常重要。通过最小化井周围的水头损失,可以限制能量消耗和老化过程,从而延长井的使用寿命。本文详细分析了单个组分对水井中总水头损失 (水位降落)的贡献。对水位降深最重要的单个贡献者通常是含水层。通过建井工程其水力传导性只能稍微改善。第二个最重要的贡献者是钻井孔表层的形成。如果钻进后没有进行适当的建井工程,表层就会出现;钻孔表层保留着残余的钻进液体添加剂或松动的细小含水层颗粒。发现过滤填料中通过滤水管开槽的地下水流及水井内中的地下水流造成的水头损失很小。因此,建井工程是影响井性能和能量效率的最重要措施。对于较长运行时间和抽取的水量,能量增益胜过建井工程的成本。

Resumo

Conhecimento a respeito da hidráulica de poços d’água é importante para otimizar sua eficiência energética. Através da minimização das perdas de carga ao redor do poço, o consumo de energia e os processos de deterioração podem ser limitados, prolongando assim a vida útil do poço. A contribuição de componentes individuais à perda de carga total (rebaixamento) em um poço é analisada em detalhe. O mais importante contribuinte individual para o rebaixamento é geralmente o aquífero. Sua condutividade hidráulica só pode ser ligeiramente melhorada através do desenvolvimento. O segundo contribuinte mais importante é a formação de uma camada de revestimento do poço. Isso ocorre se nenhum desenvolvimento bem adequado foi realizado após a perfuração; a camada contém restos de aditivos do fluido de perfuração ou partículas finas do aquífero mobilizadas. A perda de carga causada pelo fluxo das águas subterrâneas no pacote de cascalho, através das ranhuras do filtro e dentro do poço foi pequena. Assim, o desenvolvimento do poço é a medida mais importante para influenciar o desempenho do poço e eficiência energética. Para maiores tempos de operação e volumes bombeados, os ganhos de energia superam o custo para o desenvolvimento.

Appendix

Notation

a _f :

frictional head loss factor screen

a _j :

joint coefficient (a _j = 2 for box and pin joints, a _j = 1.5 for nipple joints)

a _sl :

longer side length of rectangular slot (L)

A :

area (L²)

A _o :

open area (open area / total area) × 100 (%)

A _p :

fractional open area (open area / total area)

A _sc :

area of screen pipe (L²)

A _sl :

area of screen slots (L²)

b _aq :

thickness of aquifer (L)

b _gp :

thickness of gravel pack (L)

b _i :

thickness of individual layer (L)

b _m :

momentum head loss factor screen

b _sk :

thickness of skin layer (L)

b _sl :

shorter side length of rectangular slot (L)

b _tot :

total thickness (sum of individual layers) (L)

B :

full aquifer thickness (L)

C :

constant (numerical value)

C _c :

coefficient of contraction, typically ≈ 0.6

C _CT :

fit parameter used by Clark and Turner (1983) (L⁻¹/T⁻²)

C _sl :

circumference of screen slot (L)

C _v :

velocity coefficient ≈ 0.98 for slots

d :

diameter (L)

d ₁, d ₂ :

diameter of tube sections (d₁ < d₂) (L)

d _gp-in :

thickness inner gravel pack (L)

d _gp-out :

thickness outer gravel pack (L)

d _j :

inner diameter of joint (L)

d _p :

(inner) diameter of pipe (L)

d _rd1 :

upstream internal diameter of reducer (L)

d _rd2 :

downstream internal diameter of reducer (L)

d _s :

diameter of screen (L)

d _s-o :

outer diameter of screen (L)

d _sk :

thickness of skin layer (L)

d _sw :

screen wall thickness (L)

DFP:

dual filter pack

f _j :

friction factor of joint

f _p :

friction factor of pipe section

f _D :

Darcy friction factor (= 4 × Fanning friction factor)

f _r :

surface roughness of slots (f ≥ 1)

F _s :

skin factor

g :

acceleration of gravity (gravitational constant) (L²/T)

kW:

kilowatt (0.746 kW = 1 horsepower (electrical), 1 W = 0.00136 hp)

K :

hydraulic conductivity (L/T)

K _aq :

hydraulic conductivity of aquifer (L/T)

K _gp :

hydraulic conductivity of gravel pack (L/T)

K _i :

hydraulic conductivity of individual layer (L/T)

K _s :

hydraulic conductivity of screen (L/T)

K _sk :

hydraulic conductivity of skin layer (L/T)

K _tot :

hydraulic conductivity of all layers (L/T)

kWh:

kilowatt hour (=3.6 Mega-Joule)

l _sl :

length of individual screen slot (L)

L :

length, usually of low path (L)

L _c :

length of casing section (L)

L _p :

length of pipe (L)

L _s :

length of screen (L)

n :

number (e.g., of layers)

n _c :

number of vertical slots around circumference of screen

n _j :

number of joints

n _rd :

number of reducers (joints)

n _s :

number of slots per length (L⁻¹)

n _se :

number of pipe sections

p :

pressure (M/L · T²)

p _j :

pressure in pipe joint (M/L · T²)

P _gros :

gross (electrical) power consumption (M · L² · T⁻³)

P _net :

net (electrical) power consumption (M · L² · T⁻³)

q :

Q/A = specific discharge (Darcy velocity) (L/T)

Q :

pumping rate, well discharge (L³/T)

r :

radius (L)

r ₀ :

radius of cone of depression = radial distance from well center to location where drawdown is zero (L)

r _b :

radius borehole, drilling diameter (L)

r _crit :

critical radius (L)

r _gp :

radius gravel pack (radial thickness) (L)

r _gp-i :

radius from center of the well to inner edge of gravel pack (L)

r _gp-o :

radius from center of the well to outer edge of gravel pack (L)

r _h :

hydraulic radius screen (L)

r _s :

radius screen (L)

r _s-in :

inner radius screen pipe (L)

r _s-out :

outer radius screen pipe (L)

r _sk :

radius skin layer (radial thickness) (L)

r _sk-i :

radius from center of the well to inner edge of skin layer (L)

r _sk-o :

radius from center of the well to outer edge of skin layer (L)

Re:

Reynolds number

s :

head loss or drawdown (L)

s _aq :

head loss aquifer (L)

s _cv :

head loss convergence (L)

s _gp :

head loss gravel pack (L)

s _gp-in :

head loss inner gravel pack (L)

s _gp-out :

head loss outer gravel pack (L)

s _gp′ :

head loss interface between inner and outer gravel pack (L)

s _in :

head loss at inlet of tube (L)

s _out :

head loss at outlet of tube (L)

s _sc :

head losses screen (L)

s _sk :

head loss skin layer (L)

s _tot :

total head loss or drawdown (m)

s _up :

total head loss or drawdown (m)

S :

storage coefficient

SFP:

single filter pack

t :

time (T)

T :

K/b = aquifer transmissivity (L²/T)

V :

velocity of flow (L/T)

v ₁ etc.:

flow velocity at location x = 1 etc. (L/T)

v _cs :

flow velocity in casing (but not in joint) (L/T)

v _crit :

critical entrance velocity (L/T)

v _e :

entrance velocity (L/T)

v _f :

flow velocity in pipe (L/T)

w _s :

screen slot width (aperture) (L)

w _w :

width of outside wrapping wire (for wire-wound screens) (L)

y :

exponent

β*:

inertial factor or Forchheimer coefficient

δ :

slot/distance ratio

ζ _rd :

loss coefficient for reducer

η _p :

efficiency of pump system

κ :

equivalent surface roughness (L)

μ :

dynamic viscosity of water (M/L · T)

ν :

kinematic viscosity (L²/T)

ρ :

density (of water, if not stated otherwise) (M/L³)

σ :

roughness coefficient (T²/L^2/3)

Ω _s :

resistance coefficient screen

Ω _sl :

resistance coefficient screen slots

Ψ :

(1 – d ₁ ²/d ₂ ²)²

Constants

g :

9.81 m/s²

ρ :

ρ _w = 1000 kg/m³

μ :

0.001 kg/s · m

ν :

1.01 · 10⁻⁶ m²/s