Contribution to head loss by partial penetration and well completion: implications for dewatering and artificial recharge wells

Abstract

A wide variety of well drilling techniques and well completion methods is used in the installation of dewatering and artificial recharge wells for the purpose of construction dewatering. The selection of the optimal well type is always a trade-off between the overall costs of well completion and development, the optimal well hydraulics of the well itself, the hydraulic impact of the well on its surroundings, and the required operational life span of the well. The present study provides an analytical framework that can be used by dewatering and drilling companies to quantify the contribution to head loss of typical dewatering and artificial-recharge well configurations. The analysis shows that the placement of partially penetrating wells in high-permeability layers could promote the use of quick and cheap installation of naturally developed wells using jetting or straight-flush rotary drilling. In high-permeability layers, such wells can be favorable over wells completed with filter pack, which require extensive well development to remove the fines from the filter cake layer. The amount of total head loss during discharge/recharge at a volumetric rate of 20 m³/h per meter of filter length, into or from a gravely aquifer layer, is reduced by factors of 3–4 while using naturally developed well types instead of well types completed with a filter pack that contains a filter cake layer due to borehole smearing.

Résumé

Une grande variété de techniques de forage de puits et de méthodes de complétion d’ouvrages est utilisée dans l’installation de puits de dénoyage et de recharge artificielle à des fins de mise hors d’eau de construction. La sélection du type de puits optimal est toujours un compromis entre les coûts globaux de réalisation et de développement du puits, les caractéristiques hydrauliques optimales du puits lui-même, l’impact hydraulique du puits sur son environnement, et la durée de vie opérationnelle requise du puits. La présente étude fournit un cadre analytique qui peut être utilisé par les entreprises de dénoyage et de forage pour quantifier la contribution à la perte de charge des configurations typiques de puits de dénoyage et de recharge artificielle. L’analyse montre que la mise en place de puits partiellement pénétrants dans des couches à haute perméabilité pourrait favoriser l’utilisation d’une installation rapide et bon marché de puits développés naturellement à l’aide de forage au rotary à jets ou chasse directe. Dans les couches à haute perméabilité, de tels puits peuvent être favorables par rapport aux puits complétés par un ensemble de filtres, qui nécessitent un développement de puits approfondi pour éliminer les fines de la couche de la galette filtration colmatée sur les parois de l’ouvrage. La quantité de perte de charge totale pendant la décharge/recharge à un taux volumétrique de 20 m³/h par mètre de longueur de filtre, dans ou à partir d’une couche aquifère graveleuse, est réduite par des facteurs de 3–4 tout en utilisant des types de puits développés naturellement au lieu de puits types complets avec un massif filtrant qui contient une couche de galette filtrante en raison des projections de boue lors de la foration.

Resumen

En la instalación de pozos de drenaje y de recarga artificial para la construcción de sistemas de drenaje se utiliza una amplia variedad de técnicas de perforación y de métodos de terminación de pozos. La selección del tipo de pozo óptimo es siempre un compromiso entre los costos generales de terminación y desarrollo del pozo, la hidráulica óptima del pozo en sí, el impacto hidráulico del pozo en su entorno y la vida útil requerida del pozo. El presente estudio ofrece un marco analítico que pueden utilizar las empresas dedicadas a la perforación y el drenaje para cuantificar la contribución a la pérdida de carga de las configuraciones típicas de los pozos de drenaje y de recarga artificial. El análisis muestra que la colocación de pozos parcialmente penetrantes en capas de alta permeabilidad podría promover el uso de la instalación rápida y económica de pozos desarrollados naturalmente mediante la perforación por chorro o rotación directa. En las capas de alta permeabilidad, tales pozos pueden ser favorables sobre los pozos completados con prefiltros, que requieren un extenso desarrollo del pozo para eliminar los finos. La cantidad de pérdida total de carga durante la descarga/recarga a una tasa volumétrica de 20 m³/h por metro de longitud de filtro, en o desde una capa de acuífero gravitacional, se reduce en factores de 3–4 al utilizar tipos de pozos desarrollados naturalmente en lugar de los pozos terminados con un pack de filtros que contiene una capa en el filtro debido al arrastre de la perforación.

摘要

为了进行工程疏干, 在疏干和人工补给井的安装中使用了各种钻井技术和完井方法。最佳井型的选择始终需要权衡完井和开采的总成本、井本身的最佳井水力学、井对周围环境的水力影响以及井所需的使用寿命之间的关系。本研究提供了一个可供疏干和钻井公司用来量化典型疏干和人工补给井设计对水头损失贡献的分析框架。分析表明, 将非完整井放置在高渗透率层中, 有便于使用快速和廉价的自然开发井(采用旋喷或垂直冲洗旋钻)进行安装。在高渗透率层中, 采用充填过滤器的完井方式较好, 这需要钻探大量的井才能从滤饼层中除去细颗粒物。使用自然开发的油井类型而不是由于钻孔拖尾而包含滤饼层的充填过滤器的完井类型时, 当每米过滤器的长度的排泄或补给率在20 m³/h时, 总水头损失减少了3到4倍。

Resumo

Uma ampla variedade de técnicas de perfuração e métodos de preenchimento anelar é utilizada na instalação de poços de bombeamento e de recarga artificial para fins de rebaixamento de nível freático para obras de construção civil. A seleção do tipo de poço ideal frequentemente pondera custos de instalação e desenvolvimento do poço, as condições hidráulicas ideais intrínsecas ao poço, o impacto hidráulico do poço no seu entorno, e a vida útil poço. O presente estudo provê um arcabouço analítico que pode ser utilizado por empresas de rebaixamento de nível freático e de perfuração de poços para quantificar a contribuição da perda de carga hidráulica em configurações típicas de poços de rebaixamento de nível freático e recarga artificial. A análise mostra que a alocação de poços parcialmente penetrantes em camadas altamente permeáveis pode promover a utilização de instalação rápida e barata de poços de desenvolvimento natural utilizando jateamento ou sondagem rotativa com circulação direta. Em zonas de alta permeabilidade, tais poços podem ser mais favoráveis do que poços preenchidos com pré-filtro, o qual exige desenvolvimento extensivo para remover materiais finos do envoltório do poço e retido no pré-filtro. A quantidade total de perda de carga hidráulica durante a descarga/recarga volumétrica de 20 m³/h por metro de comprimento do filtro, adentro ou a partir de uma cama aquífera de cascalho, é reduzida entre 3–4 vezes quando utilizado poços de desenvolvimento natural ao invés de poços preenchidos com pré-filtro.

Appendix

Solution for the Darcy-Forchheimer equation for converging flow in filter packs towards screen slots

Inside a filter pack, groundwater flow is affected by the presence of well screens. During abstraction, groundwater has to converge to the screen slots, which causes an additional head called ∆h_cv. Boulton (1947) derived an equation for ∆h_cv based on the ratio (δ_s) of slot aperture (l) and circumference of the well:

$$ {\delta}_{\mathrm{s}}=\frac{n_{\mathrm{s}}l}{2\pi R} $$

(18)

where n_s is the number of slots inside the circumference of a well and R is the radius of the well. The equation by Boulton (1947) is given by (Houben 2015b):

$$ {\Delta h}_{\mathrm{cv}}=\frac{Q}{K_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\ln \left(\frac{2}{1-\cos {\delta}_{\mathrm{s}}\pi}\right) $$

(19)

where K_fp is the hydraulic conductivity of the gravel pack and L_s is the length of the screen. Unfortunately, the derivation of Boulton’s equation is not given in that article and therefore the assumptions behind the equation are unknown; thus, a derivation of the equation for ∆h_cv is given in the following.

The starting point of the derivation is the Darcy-Forchheimer equation, which is given by:

$$ \frac{\partial h}{\partial r}=-\frac{Q}{2\pi r{K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}-\beta {\left(\frac{Q}{2\pi r{K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\right)}^2 $$

(20)

where r is a radial coordinate. By separating variables, one can obtain:

$$ \partial h=-\left(\frac{Q}{2\pi {K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\right)\frac{1}{r}\partial r-\left[\beta {\left(\frac{Q}{2\pi {K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\right)}^2\right]\frac{1}{r^2}\partial r $$

(21)

The Darcy-Forchheimer equation is independent of slot aperture, therefore a geometric consideration is conducted before solving the Darcy-Forchheimer equation.

In order to obtain Boulton’s equation, the distance between the well circumference and the opening (distance D) has to be considered constant (see Fig. 9). This assumption implies that flow remains radial inside the gravel pack until the groundwater is very close to the well. As a consequence, stagnant zones of groundwater arise between the screen slots (see Fig. 9) which forces the remaining groundwater towards the screen openings. Distance D is defined for any circle having a radius r as such that D is constant (based on trigonometry; see Fig. 9):

$$ D=R-H=r\left(1-\cos \frac{\theta }{2}\right)=r\left(1-\cos \pi \delta \right) $$

(22)

Differentiating Eq. (22), yields:

$$ \frac{1}{r}\partial r=\frac{\pi \sin \pi \delta}{1-\cos \pi \delta}\partial \delta $$

(23)

Using Eqs. (22 and 23), the Darcy-Forchheimer equation becomes:

$$ \partial h=-\left(\frac{Q}{2\pi {K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\right)\left(\frac{\pi \sin \left(\pi \delta \right)}{1-\cos \left(\pi \delta \right)}\partial \delta \right)-\left[\frac{\beta }{D}{\left(\frac{Q}{2\pi {K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\right)}^2\right]\pi \sin \left(\pi \delta \right)\partial \delta $$

(24)

In Eq. (24), the radial coordinates are projected on δ coordinates, which represents flow perpendicular to the radius. The boundary conditions for Eq. (24) are:

$$ \left\{\begin{array}{cc}\kern0.5em h={h}_{\mathrm{gp}}& \delta =1\\ {}h={h}_{\mathrm{s}}& \delta ={\delta}_{\mathrm{s}}\end{array}\right. $$

(25)

Defining integration of Eq. (24) yields:

$$ {\int}_{h={h}_{\mathrm{s}}}^{h_{\mathrm{gp}}}\partial h=-\left(\frac{Q}{2\pi {K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\right){\int}_{\delta ={\delta}_{\mathrm{s}}}^1\frac{\pi \sin \left(\pi \delta \right)}{1-\cos \left(\pi \delta \right)}\partial \delta -\left[\frac{\beta }{D}{\left(\frac{Q}{2\pi {K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\right)}^2\right]{\int}_{\delta ={\delta}_{\mathrm{s}}}^1\pi \sin \left(\pi \delta \right)\partial \delta $$

(26)

Finally, one can obtain:

$$ {\Delta h}_{cv}=\frac{Q}{2\pi {n}_{\mathrm{s}}{K}_{\mathrm{fp}}{L}_{\mathrm{s}}}\ln \left(\frac{2}{1-\cos {\delta}_{\mathrm{s}}\pi}\right)-\frac{\beta }{r_s}{\left(\frac{Q}{2\pi {K}_{\mathrm{fp}}{L}_{\mathrm{s}}{n}_{\mathrm{s}}}\right)}^2 $$

(27)

where the Forchheimer coefficient $b=\frac{\beta }{K_{\mathrm{fp}}^2}$

Fig. 9

Schematic overview of flow convergence in the filter pack (assumption by Boulton 1947)