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Hydrogeology Journal

, Volume 27, Issue 3, pp 841–855 | Cite as

Determination of groundwater sustainable yield using a numerical modelling approach for the Table Mountain Group sandstone aquifer, Rawsonville, South Africa

  • Lixiang LinEmail author
  • Haili Lin
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Abstract

Sustainable yield is defined as the amount of groundwater abstraction that can be maintained for an indefinite time without causing unacceptable environmental, economic and social consequences. It is usually determined by monitoring the water-table depth, without the need for costly pumping exercises and subsequent deterioration of the groundwater and ecological environment. Groundwater numerical modelling provides an effective way to determine the yield by analysing the responding water levels to various pumping scenarios. In this study, the natural flow system and flow with pumping scenarios were simulated using FEFLOW for the fractured-rock aquifer in Table Mountain Group, South Africa. Results for different pumping rates show the distinct impact of groundwater abstraction on hydraulic head, which indicates that long-term abstraction slowly increases the well drawdown, but it would stabilize at a level that is dependent on pumping rate and induced recharge. To estimate the aquifer sustainable yield, a relationship between simulated drawdown and pumping rate was established, namely an exponential function with parameters that may change value between sites. This empirical relation, derived from this site-specific study, provides an option for informed decision-making. The issue of how to sustainably abstract groundwater might rely on a compromise between the groundwater user and the governmental authority.

Keywords

Sustainable yield Fractured rocks Numerical modelling Sub-Saharan Africa 

Détermination du rendement durable des eaux souterraines à l’aide d’une approche de modélisation numérique de l’aquifère gréseux de la formation Montagne de la Table, Rawsonville, Afrique du Sud

Résumé

Le rendement durable est défini comme le volume d’eau souterraine extrait qui peut être maintenu pour une durée indéterminée sans engendrer de conséquences environnementale, économique et sociale inacceptables. Il est généralement déterminé par un suivi de la profondeur du niveau de la nappe phréatique, sans que des pompages coûteux soient nécessaires et sans détérioration ultérieurement de l’eau souterraine et de l’environnement écologique. La modélisation numérique des eaux souterraines fournit un moyen efficace de déterminer le rendement par l’analyse de la réponse des niveaux d’eau selon divers scénarios de pompage. Dans cette étude, le régime d’écoulement naturel du système et les écoulements avec scénarios de pompage ont été simulés avec FEFLOW pour l’aquifère fracturé de la formation Montagne de la Table en Afrique du Sud. Les résultats pour différents débits de pompage montrent un impact marqué du volume extrait des eaux souterraines sur la charge hydraulique, indiquant que l’exploitation à long terme augmente le rabattement au puits, mais celui-ci se stabiliserait à un niveau qui est fonction du débit de pompage et de la recharge induite. Afin d’estimer le rendement durable de l’aquifère, une relation entre le rabattement simulé et le débit pompé a été développée, à savoir une fonction exponentielle dont la valeur des paramètres peut changer entre les sites. Cette relation empirique, déduite à partir de cette étude spécifique de cas, fournit une option pour une prise de décision éclairée. La problématique du comment exploiter durablement une eau souterraine, pourrait reposer sur un compromis entre les utilisateurs des eaux souterraines et les instances gouvernementales.

Determinación del rendimiento sostenible del agua subterránea utilizando un enfoque de modelado numérico para el acuífero de areniscas del Table Mountain Group, Rawsonville, Sudáfrica

Resumen

El rendimiento sostenible se define como la cantidad de extracción de agua subterránea que se puede mantener por un tiempo indefinido sin causar consecuencias ambientales, económicas y sociales inaceptables. Por lo general, se determina al monitorear la profundidad del nivel freático, sin la necesidad de costosos ejercicios de bombeo y el subsiguiente deterioro del agua subterránea y del entorno ecológico. El modelado numérico del agua subterránea proporciona una forma efectiva de determinar el rendimiento al analizar los niveles de agua que responden a diferentes escenarios de bombeo. En este estudio, el sistema de flujo natural y el flujo con escenarios de bombeo se simularon utilizando FEFLOW para el acuífero de roca fracturada en el Table Mountain Group, Sudáfrica. Los resultados para diferentes caudales de bombeo muestran el impacto particular de la extracción de agua subterránea en la carga hidráulica, lo que indica que la extracción a largo plazo aumenta lentamente la depresión en el pozo, pero se estabilizaría en un nivel que depende del caudal de bombeo y de la recarga inducida. Para estimar el rendimiento sostenible del acuífero, se estableció una relación entre la depresión simulada y el caudal de bombeo, es decir, una función exponencial con parámetros que pueden cambiar el valor entre los sitios. Esta relación empírica, derivada de este estudio específico del sitio, proporciona una opción para tomar decisiones fundadas. El tema de cómo extraer de manera sostenible el agua subterránea puede depender de un compromiso entre el usuario de agua subterránea y la autoridad gubernamental.

应用数值模拟方法多南非罗森威尔地区桌山群砂岩含水层的可持续产量的确定

摘要

地下水可持续产量可定义为长期抽水而不会对环境,经济和社会造成不可接受后果的取水量。通常通过监测水位深度来确定,而不需要经历昂贵的抽水以及随后产生的地下水和生态环境的恶化。该方法通过分析各种抽水情行的水位响应,地下水数值模拟提供了一种确定该产量的有效方法。本项研究采用FEFLOW分别模拟了南非桌山群中一个裂隙含水层的自然流动和抽水情况下的地下水动态系统。结果显示不同抽水量对含水层水头的影响明显,长期抽水会缓慢增加井的降深,但该含水层的水位最终会稳定在一个深度,这决于单位抽水量和由此引发的地下水补给。同时通过数值模拟来估算含水层的可持续产量,建立了模拟降深和单位抽水量之间的联系,即二者为指数函数关系,其参数可随着含水层的条件变化而不同。这种来自本特定研究的经验关系为决策提供了一个选择,即如何可持续地抽取地下水的取决于地下水用户和水资源管理部门之间的协商结果。

Determinação do rendimento sustentável de águas subterrâneas usando uma abordagem de modelagem numérica para o aquífero de arenito do Grupo Table Mountain, Rawsonville, África do Sul

Resumo

O rendimento sustentável é definido como a quantidade de captação de água subterrânea que pode ser mantida por um tempo indefinido sem causar consequências ambientais, econômicas e sociais inaceitáveis. Geralmente é determinado pelo monitoramento da profundidade do lençol freático, sem a necessidade de exercícios caros de bombeamento e subsequente deterioração do lençol freático e do ambiente ecológico. A modelagem numérica das águas subterrâneas fornece uma maneira eficaz de determinar o rendimento analisando as respostas dos níveis de água à vários cenários de bombeamento. Neste estudo, o sistema de fluxo natural e o fluxo com cenários de bombeamento foram simulados usando o FEFLOW para o aquífero de rocha fraturada no Grupo Table Mountain, na África do Sul. Os resultados para diferentes taxas de bombeamento mostram o impacto distinto da captação de águas subterrâneas na carga hidráulica, que indica que a captação de longo prazo aumenta lentamente o rebaixamento do poço, mas se estabiliza em um nível que depende da taxa de bombeamento e da recarga induzida. Para estimar o rendimento sustentável do aquífero, estabeleceu-se uma relação entre a redução simulada e a taxa de bombeamento, ou seja, uma função exponencial com parâmetros que podem alterar o valor entre os locais. Esta relação empírica, derivada deste estudo em local específico, fornece uma opção para tomada de decisão informada. A questão de como extrair água subterrânea de forma sustentável pode depender de um compromisso entre o usuário de águas subterrâneas e a autoridade governamental.

Introduction

Sustainably developing groundwater resources has been a critical issue in South Africa, where groundwater and surface water are equally important in this arid to semi-arid region. The region has low water abundance and increasing demand on water resources. Persistent problems with water shortage and contamination of water bodies induced by farming, mining and industrial activities have had a negative impact on water resources sustainability and the growth of the economy in the country, which has been experiencing a severe drought since the year of 2015. A nation-wide water shortage is looming, and the pressure on water resources calls for methods of preserving any available water resources by any means possible to ensure sustainability.

The concept of sustainably utilizing groundwater resources has evolved from the concept of safe yield (Meinzer 1923), proposed in the early 1980s (Bredehoeft et al. 1982), which forced the practice of using water budget methods to estimate the available amount of resource for water supply purposes (Bredehoeft 1997). The estimation was largely conducted on the basis of determining groundwater recharge. In South Africa, for instance, the percentage of groundwater recharge in the overall budget was used to determine groundwater harvest potential (Baron et al. 1998; Vegter 1995; DWA 2013), which is closely related to, but different from groundwater sustainability (Lohman 1972a). In the early 1940s, Theis (1940) raised the point that it was not necessary to know the recharge value in order to determine sustainability. Bredehoeft (2002) defined groundwater sustainability as the development and use of groundwater in a manner such that the water use can be maintained for an indefinite period of time without causing unacceptable environmental impacts (Gambolati et al. 1974; Alley et al. 1999; Alley and Leake 2004; Shi et al. 2012) and economic and social consequences (Hunter and Wilcox 2003; Custodio 2005). The definition implies that groundwater resources should be used under the constraint of no degradation of the water quantity and quality (Xu et al. 2003), and it also requires the application of policy for compromises between the governmental authority and groundwater users (Alley and Leake 2004), thus increasing the number of studies on groundwater sustainable yield, groundwater quality and groundwater-dependent ecosystems.

The determination of groundwater sustainable yield requires providing an optimal and quantitative outcome based on groundwater flow and mass balance principles. Much effort through research has contributed to studies on the definition, methods and factors of sustainable yield, either on an aquifer scale or a basin scale (Wang et al. 2001; van Tonder et al. 2001; Alley and Leake 2004; Maimone 2004; Delvin and Sophocleous 2005; Holland and Witthüser 2009; Zhou 2009). It has been commonly acknowledged that groundwater sustainable yield is dependent on the amount of water captured (Seward et al. 2006), which is defined by the increase of recharge and the decrease of discharge of an aquifer due to pumping operations (Lohman 1972b; Zhou 2009). Furthermore, methods of water balance have been widely applied in the determination of sustainable yield for groundwater management purposes. According to Kalf and Woolley (2005), methods for determining the sustainable yield must allow various models to optimize the yield output at a new state of equilibrium, which implies that groundwater sustainable yield is not a fixed but a movable quantity along with aquifer pumping stress.

Because the subsurface aquifer media are not easily conceptualized, and because models are often used to physically simplify a complex system and mathematically represent key phenomena of the system (Chiang and Kinzelbach 2001; Anderson and Woessner 2002), various models have become the tools employed to understand groundwater systems via simulating and predicting its behavior (Water Science and Technology Board 1990). Compared with analytical methods, numerical modelling provides a fast and sometimes effective way to evaluate the bulk behavior and quantity of groundwater resources (Sophocleous and Devlin 2002).

Current three-dimensional (3D) numerical modelling is based on either finite-element or finite-difference model codes to simulate steady or transient flow of groundwater with uniform density (van Heeswijk and Smith 2002). The model is largely calibrated to the monitoring data, including water level, natural or artificial discharge, groundwater recharge, the change of boundary condition over time, etc.; however, model applicability is dependent on the establishment and refinement of a sound aquifer conceptual model.

The purpose of this study is to evaluate groundwater flow and associated sustainable yield via a case study of a fractured-rock aquifer of the Table Mountain Group, South Africa, and through estimating how groundwater flows along a fault where the fault core is impermeable, in light of data derived from field work, which includes core logs of the boreholes and the observations during hydraulic tests (Lin 2008; Lin et al. 2015). Thus, to satisfy this case, a five-borehole network was established at the study site located in Rawsonville, Western Cape, South Africa. To determine the aquifer’s sustainable yield, it is necessary to understand the boundaries and extent of the aquifer, to establish a sound conceptual model, as well as to evaluate how the hypothetical scenarios of future abstractions would affect the groundwater flow system, from which its sustainable yield can be estimated.

Conceptualization and numerical model

Site hydrogeology

The site is located at Gevonden Farm, some 5 km west of Rawsonville, Western Cape, where there are five groundwater boreholes that form a well network for various study purposes (Fig. 1a). A perennial stream runs northwards with the water sourced from a catchment of about 80 km2 in which the mountain elevation mostly reaches 2,000 m above mean sea level (amsl) but it is about 290 m amsl at the site. Geologically, the area consists of Table Mountain Group (TMG), where the majority comprises Peninsula Formation, a sequence of typical marine sandstones, overlaid by Nardouw Subgroup with lithology dominated by siltstones and Cedarberg shale which occur in the very north of the study area.
Fig. 1

Map showing the extent of the Table Mountain Group (TMG) and the location of the study site in South Africa

The site is situated in the center of structural syntaxis of the Cape Fold Belt (De Beer 2002; Newton et al. 2006), backboned by the TMG sandstones. It is bounded by basement rocks in the west and southwest, as well as faults, i.e., Brandvlei-Elkenhofdam megafault and Smiths Kraal fault in the east and southeast (Fig. 1b). The Waterkloof fault, a normal fault, extends northeastwards some 15 km, cutting through the well site (Fig. 1c). Controlled by both this fault structure and the NE-trending TMG formations, geomorphologic features of the area are mainly characterized by the steep bare rock slopes on the Peninsula outcrop; a stepwise watercourse (stream) on which there are three waterfalls with height drops of 14–40 m; and a 6-m thick pluvial boulder soil that covers the site area. Several springs in the stream are identified, but are not linked to one another in a regional flow system because the water head gradient may reach more than 1/20. The phenomenon is also familiar in the other adjacent catchments where some more field surveys were initiated to gain a better understanding of the boundary conditions of the study area. This suggests that the fractured rock groundwater systems on the surface are localized ones that seem to be controlled by fractured blocks (National Research Council 1996).

This groundwater research and monitoring site was established with a five-borehole network in the TMG fractured rock aquifer (Fig. 1c), of which boreholes BH-1 and BH-2 are cored holes with complete logging records and BH-3 and BH-4 are percussion-drilled holes, while BH-5 is an existing one (Table 1). The hydrogeological cross section (Fig. 2) shows that groundwater largely originates from the fractured sandstone of the Peninsula Formation, while to the west of the Waterkloof fault, it is a confined aquifer with artesian water emanating from three conductive fractures intercepted by borehole BH-1; however, the aquifer to the east of the fault is unconfined and the boreholes are connected to each other through groundwater flow. To have a better understanding of the fractured-rock groundwater system, some observations obtained from drilling and monitoring at the study site are listed as follows.
  1. 1.

    Borehole BH-1, which inclines to the west with a plunge of 60°, was drilled to the depth of 250 m (270 m in length). This borehole penetrates through the bottom of Nardouw Formation and Cedarberg (shale) Formation, tapping the top of Peninsula Formation, with an artesian flow of 0.3 L/s, identified from three conductive zones at the depths of 67.5, 95.3, and 213.0 m, respectively. In order to conduct long-term monitoring of the Peninsula groundwater, a 179-m-long steel casing was installed into the bottom of the Cedarberg shale to seal the former two conductive zones, resulting in a remaining flow of about 0.2 L/s (Fig. 2).

     
  2. 2.

    Borehole BH-2 was drilled to a depth 201 m and the casing depth is 65 m. Similar to BH-1, this borehole is sited on the fault core zone and was drilled to examine the rock formations of both the fault core and fault fracturing zone. Water level in borehole BH-2 is 1.8 m deep. The groundwaters of the two boreholes (BH-1, BH-2) were found to have different origins, and they are both different from the stream water.

     
  3. 3.

    Based on the groundwater observations in BH-1 and BH-2, percussion borehole BH-3 was installed in between borehole BH-2 and the existing borehole BH-5. During the percussion drilling, water level and flow rate in boreholes BH-2, BH-5 and the BH-1 were monitored; and it was found that when the air-lift water was pumped out of BH-3, water levels subsequently dropped in both BH-2 and BH-5, while the flow did not change in artesian borehole BH-1.

     
Table 1

Basic information of the boreholes at the study site

Borehole No.

Drill type

Ground elevation (m amsl)

Depth (m)

Inclination

Formations

Bore

Casing

BH-1

Core drilling

286.83

250

156

60°W

Nardouw to Peninsula

BH-2

Core drilling

285.92

201.1

65

Vertical

Peninsula

BH-3

Percussion

283.34

200

16

Vertical

Peninsula

BH-4

Percussion

284.63

8.0

6

Vertical

Regolith

BH-5

Percussion

285.45

175

7

Vertical

Peninsula

Fig. 2

Schematic hydrogeological cross section, showing the construction of the boreholes and the fault zone and rock formations of the site

In addition, field observations from the core logs and site surveys show that the normal fault plays a key role in controlling the occurrence of groundwater with good quality (Table 2). It was observed that the 80-m-wide fault core (Fig. 2), identified to be cemented cataclasites, acts as a groundwater barrier that separates the fractured-rock aquifers into the eastern and western ones. In the eastern wall (hanging wall) of the fault, groundwater only occurs with a static water level, but there appears to be artesian flow in the western wall (foot wall). It was also observed that the conductive zones intercepted by the boreholes did not fall in the fault core but at the fracture zones of the fault.
Table 2

Physical properties of borehole groundwater and surface water

Property

Water source

BH1

BH2

BH3

BH4

BH5

Stream

Temperature (°)

20.15

19.25

18.5

18.9

20.05

14.50

Water level

Depth (m)

0

1.8

3.05

2.59

5.57

Elevation (m amsl)

286.83

284.12

280.29

282.04

pH

6.8

5.5

5.8

5.6

5.2

4.41

EC (uS/cm)

50–60

40–70

36–40

130–160

43–50

<10

Rock formation

Nardouw

Peninsula

Peninsula

Regolith

Peninsula

Surface water

Model description and data processing

Previous studies conducted at this site include rock core and percussion drillings, and packer and pumping tests, as well as the examination of fracture characteristics, with the objective of establishing site-specific characterization of the aquifer’s hydraulic properties (Lin 2008), groundwater resources (Jia 2007), surface-water/groundwater interaction and resources protection features (Nel 2011), and the hydraulic properties of the confined aquifer (Sun 2014). These assist in developing a better understanding of the fractured-rock aquifers with the involvement of fault structures, and in constructing a sound conceptual model on the site scale.

The study focuses on the determination of the sustainable yield of the unconfined aquifer via flow simulation with different pumping rates. Based on aquifer setting analysis, field observations and aquifer characterization, the study enabled refinement of the initial conceptual model, as discussed before, to produce a sound conceptual model for the site-specific groundwater problem. This study used the software FEFLOW 6.0 (Diersch 2014) with model codes based on the finite element method (Trefry and Muffels 2007; DHI-WASY GmbH 2009) to:
  1. 1.

    Simulate natural groundwater flow at the damage zone by characterizing the distribution of aquifer hydraulic head.

     
  2. 2.

    Examine the effects of pumping alternatives on the resource.

     
  3. 3.

    Determine the sustainable yield, through analyzing the impact of groundwater abstraction on the change of groundwater resource quantity, which is important for groundwater management purposes.

     

Hypothesis

It is assumed that at the site, groundwater occurs in the fracture-damage zones, but not in the fault core, in alignment with the fault architecture proposed by Caine et al. (1996). This suggests that the hydraulic properties of the fault core can be assigned as nil; however, during the simultaneous simulation of groundwater flow on both fault damage zones, an advanced simulation result showed that the fault core somehow continued to dewater while the water levels rose in both zones. Moreover, field observation has evidenced that the aquifer in the western damage zone is a typical fracture flow system and the current model is perhaps unsuitable to evaluate the type of flow. These observations lead to the following hypotheses:
  1. 1.

    The confined aquifer to the west of the fault is where groundwater originates from a single conductive zone; and the unconfined aquifer in the east is closely connected to the surface water system.

     
  2. 2.

    The fault core, in this case, is an impermeable body with hydraulic conductivity of nil.

     
  3. 3.

    Aquifers of both damage zones cannot be simulated at the same time.

     

Thus, in recognition of the independent groundwater flow system on each side of the fault, in this study only the unconfined aquifer in the east is extracted for the modelling process.

In terms of aquifer medium, the anisotropy in both material and hydraulic properties is a common phenomenon. In order to achieve good modelling results for a fractured-rock aquifer, it is often necessary to have such an assumption that groundwater is flowing through a geological continuum, or the aquifer may be simplified into a fractured porous medium with an appropriate size of discretized elements (Svensson 2001; Berkowitz 2002).

Surface-water/groundwater interaction

It is assumed that the dominant mechanism for the discharge of groundwater from the unconfined system is through the stream bed and via spring flows to the rivers, and that the river and groundwater are in dynamic connection. Based on this assumption, it is possible at the modelling stage to use the observational result on the stream which perennially runs through the site area with the stream bed roughly riding along the fault core. Additional groundwater flow information collected by Nel (2011) showed that the borehole flow changed seasonally due to the interaction between groundwater and the stream and precipitation.

Model and data preparation

The model area is highlighted in Fig. 3. In the east part of the fault, the shallow hole BH-4 installed in the fault core regolith is not involved in the fractured rock flow system (Fig. 2). The size of the model area is 1,500 m latitudinally by 500 m longitudinally, or 0.7 km2, with elevation ranging from 275 m amsl in the north to 570 m amsl in the south. The model area is defined to fit the groundwater problem studied at the site scale. Furthermore, considering the constraint of damage zone width, its east boundary is defined to be along the slope divide, which will be discussed later.
Fig. 3

Model area of the site where the unconfined aquifer is east of the fault

The development of the model is based on the conceptual understanding of the aquifer, as discussed in the preceding. To establish a conceptual model, first, relevant geometrical data which include the area extent, borehole position and depth, and a digital elevation model (DEM), etc., are necessary. All the geometrical data, including polygons and points and lines were prepared with the same projection in ArcGIS because they can be directly recognized by FEFLOW, as the software is flexible in the spatial discretization—for example, the surface topographical data were extracted from the site DEM and then converted into a relief point table before it was loaded up and integrated after model discretization by the modelling software.

Figure 4a shows the discretized initial conceptual model and Fig. 4b shows associated model geometry, where there are 6,988 mesh elements and 4,640 mesh nodes in total. In the vicinity of each borehole and model boundary, the mesh element density is enhanced. It is noted that the model is divided into four layers, in light of possible changes in aquifer hydraulic properties at depth according to the results from previous packer tests conducted in borehole BH-2 (Lin 2008). The model bottom is defined by the bottom of borehole BH-3 with a total length of 200 m. With this initial conceptual model, it is possible to specify other modelling data such as hydraulic boundary conditions, the initial water head and aquifer hydraulic properties.
Fig. 4

Results of the model configuration

Model refining and hydraulic boundary conditions

By default, the model takes all the nodes on the model boundary to be inactive or a no-flow boundary. It is critical to define the model geometric/physical boundary components and subsequently determine the model extent in three dimensions.
  • Bottom boundary. As the model is built to fit the groundwater condition on a site scale, its bottom is defined by the bottom of borehole BH-3 with a total whole length of 200 m.

  • West boundary. The fault core, where hydraulic conductivity is assumed as nil, naturally forms a boundary with inactive mesh nodes on the 4-layer border.

  • North boundary. The boundary at the northern limit is defined by the stream which is topographically the lowest zone of the model area. According to the results of borehole and stream leveling, the stream level at the northern boundary is around 280 m amsl.

  • South boundary. The southern boundary is topographically restricted to the first 40-m high waterfall on the stream with perennial flow. Geologically, the throw of the fault seems to be drastically reduced. It is hence assumed that the aquifer at the damage zone, in terms of both geometry and hydrogeological properties, may also change, which separates the site aquifer from the others along the fault zone.

  • East boundary. Physically, there is no evidence to define the east boundary. According to previous studies conducted in brittle rock formations (Gudmundsson and Geyer 2006; Johri 2012), there is a generally close relationship between the thickness of the fault damage zone and displacement. Using fault throw to represent the displacement, Shipton and Cowie (2001, 2003) estimated that the thickness of the fault damage zone is around two and half times that of the fault throw, on the basis of their research on the evolution of the fault at a meter- to kilometer-scale on brittle sandstones.

The aforementioned method may be adapted to the case of the fault developing in the TMG sandstone. Through the examination of the borehole cores of BH-1 and BH-2 and surface landform, which indicate the position of the bottom of the Cedarberg shale, the fault throw near the groundwater research site is about 180–250 m, but that value reduces to the south. Therefore, the thickness of the fault damage zone for this modelling exercise is estimated as 500 m, forming the basis of the eastern no flow boundary determination.

The hydraulic head in FEFLOW is defined as the head for the modelling process (such as initial head) and the hydraulic boundary condition. It is assumed that in a natural condition, inflow to the system as groundwater recharge and outflow from the system as groundwater discharge are controlled by the stream located on the western edge of both the south and north boundary lines, as marked with circles in Fig. 5, with associated hydraulic head in Table 3. A constant head at either boundary may be assigned to the nodes where the stream, in reality, is located at the start of the simulation. The imposition of the constant head boundary around the model area is based on the assumption that the groundwater flow system in the area is relatively independent. This simplifies the interaction between surface water and groundwater within the modelled area, which allows for flux exchange between the local groundwater flow system and the outside.
Fig. 5

Refined conceptual model with the distribution of hydraulic conductivities assigned to aquifer layers

Table 3

Boundary and initial conditions for model simulation

Model parameter

Water source

BH-1

BH-2

BH-3

BH-4

BH-5

Stream

Ground elevation (m amsl)

286.825

285.924

283.341

284.634

284.983

Water level elevation (m amsl)

287.30

283.92

282.24

283.18

Boundary condition (m amsl)

North

281.00

South

291.00

Modelling process, hydraulic head

Initial head

From the observed water levels of boreholes BH-2, BH-3 and BH-5, the hydraulic head in these boreholes has changed over time since the drilling was completed—for example, the initial water level of 2.5 m below ground level (blg) in BH-3 was recorded in 2007, whereas it was 0.9 m blg in Oct 2013; and the same trends were observed in BH-2 and BH-5. Therefore, an average value of the water levels for each borehole was assigned to the modelling process with respect to hydraulic head. The time–drawdown observations have confirmed that these three boreholes have hydraulic connection with each other. Furthermore, in the case of future operation of BH-3 or BH-5 with different pumping rates, and in the simulation of a pumping condition in this area, boreholes BH-3 and BH-5 could not be assumed as an initial head boundary; therefore, borehole BH-2 was taken as a head boundary.

Hydraulic properties

Besides the need to understand the aquifer’s hydrogeological setting and thus refine the conceptual model, the determination of aquifer hydraulic properties is essential for numerical modelling. In 2006 and 2013, a number of pumping tests were conducted in boreholes BH-3 and BH-5, while in October 2014 a constant head test was done in borehole BH-1, resulting in a range of hydraulic conductivity K and specific storage S values. During the core hole drilling, packer tests were carried out in both BH-1 and BH-2 with an interval length of 6 m. The K values derived from the pumping tests fall in the range of 10−5 to 10−7 m/s—estimated using a well image method (Lin et al. 2015)—while the packer test yielded K values ranging from 10−2 to 10−5 m/s (Lin 2008). Moreover, the hydraulic conductivities estimated by the hydraulic tensor method, by using three-dimensionally interconnected fractures (Lin and Xu 2006), is in the order of 10−6 m/s.

To perform the modelling and associated analysis in the fractured porous media aquifer, it was assumed that aquifer parameters of a layer in the horizontal (x, y) direction are uniform but not in the vertical (z) direction. Considering the change of hydraulic conductivity at depth (Fig. 6), the K values were assigned on a layer basis by Kx = Ky and Kz = 0.5Kx. The K and S values input to the model are listed in Table 4 and the K value are also shown in Fig. 5; these values are based on the results of the packer test and pumping tests.
Fig. 6

Hydraulic conductivity (K) values plot against depth, from packer tests in a BH-1 and b BH-2

Table 4

Layer elevation and associated hydraulic conductivity and specific storage

Layer No.

Bottom elevation (m amsl)

Kx = Ky (m/s)

Kz (m/s)

S

1

230

1.90E-05

9.50E-06

1.2E-04

2

180

5.70E-05

2.85E-05

2.0E-05

3

130

9.80E-06

4.90E-06

9.5E-06

4

80

8.00E-07

4.00E-07

1.7E-07

Results

Because both the site-scale pumping test and borehole-scale packer test determine the bulk aquifer hydraulic properties, and because there is hydraulic connection between the boreholes, it is possible to use the fractured porous media with a horizontal-element cell size of 5–20 m to simulate the flow system. In this study, both the cases of groundwater natural flow and aquifer response to pumping operation at BH-3 are simulated using FEFLOW.

Natural flow

By using the data of model geometry, boundary condition and hydraulic properties as the input, the natural condition of groundwater flow was simulated under an unconfined environment. During this process:
  • A 10-year time period was used to simulate the flow; a maximum iteration of 12 steps was included in each period in the model calibration process.

  • In the 4-layer model domain, elevation of the top layer ranged from the surface to 230 m amsl. This implies that the layer might be partially dewatered in the case of well abstraction; therefore, a free and movable water table was assigned to this layer.

  • In the modelling process, the forward prediction corrector scheme was set up for the groundwater problem.

  • Because the model domain water budget was checked in an advanced modelling process, the change of hydraulic head was the major parameter which was extracted and discussed in the study.

The groundwater level was used to simulate the natural groundwater flow in the unconfined aquifer in transient state, with the hydraulic gradient initially defined by the observed water levels. As can be seen during the model run, a state of equilibrium over the groundwater domain was attained within 1,900 days or 5.28 years. The migration of the water body starts at the hydraulic boundary and the initial head area, and the flow is controlled through actual hydraulic heads. The simulated hydraulic head is shown in Fig. 7, where the isoline of the head indicates a horizontal direction of flow from the south to the north. Figure 7 also shows the recharge area with the natural hydraulic head located in the area above 285 m amsl, while the boreholes are located on the major flow-path near the top of the discharge area.
Fig. 7

Modelling result with balancing water-table elevation calibrated from initial and boundary conditions in an unconfined environment

Comparing the simulated hydraulic head with the observed ones (Table 5), it was noted that the % error values for hydraulic head at BH-2 and BH-5 seem acceptable (although not for borehole BH-3). This perhaps suggests that the conceptual model was well refined. However, the error would perhaps be attributed to the iteration errors arising from model configuration, or the fact that both BH-2 and BH-3 are very close to the fault core which is actually inclined to the west with a dip of 60°, but in the model it was treated as a vertical surface.
Table 5

Comparison of measured and simulated water levels (WL) in a natural flow condition

Borehole

Observed WL (m amsl)

Simulated WL (m amsl)

Error (%)

BH-2

283.92

284

2.8

BH-3

282.24

284

6.2

BH-5

283.18

283

0.6

Aquifer response to pumping scenarios

Because the wellfield with a five-borehole network was initially developed as a monitoring and research base, it has not yet experienced any continuous groundwater abstraction for water supply. However, as one of the resource options in the dry season, it is necessary to assess the resource for management purposes. One of the key issues associated with resource management is the determination of sustainable yield. Therefore, a number of pumping scenarios were set up at the capture zone to examine the impact of groundwater abstraction on the capture zone and to determine an estimate of sustainable yield for the specific aquifer.

In this case, groundwater recharge can be regarded as a constant, which is defined by hydraulic boundary conditions in the model. This ensures that the aquifer has a sustainable induced supplement to the capture zone when the borehole is continuously pumped. The deep percussion-drilled borehole BH-3 was selected to simulate the pumping process at the pumping rates of 15 and 20 L/s. The simulation results are shown in Figs. 8, 9 and 10, from which it can be seen that the stabilized drawdown at a pumping rate of 15 L/s is 38 m (Fig. 10) and for the 20 L/s pumping rate is 53 m. The cone of depression on the fault zone seems to be time-dependent and restricted to a half circle. In addition, the development of the depression cone slowly changes the original groundwater dynamics as the flow direction is gradually influenced by the pumping well.
Fig. 8

Effect of abstraction on hydraulic head in BH-3 at a flow rate of 15 L/s: a modelling result, b graph of hydraulic head vs. elapsed time

Fig. 9

Effect of abstraction on hydraulic head in BH-3 at a flow rate of 20 L/s: a modelling result, b graph of hydraulic head vs. elapsed time

Fig. 10

Drawdown from the long-term well abstraction at the flow rate of 15 L/s

Determination of sustainable yield

As can been seen in Figs. 8, 9 and 10, along with continued pumping, the water table will arrive at a stable level. The sustainable yield of the aquifer, achieved with a sustainable induced recharge, seems to be a dynamic parameter, reflected by the relation of borehole abstraction quantity and its hydraulic head. Therefore, it can be determined by monitoring the water table without the need for costly pumping exercises and subsequent deterioration of the adjacent groundwater and ecological environment (Ponce 2007).

In order to determine the sustainable yield for the aquifer at this particular site, aquifer simulations at multiple pumping rates (ranging from 2 to 25 L/s) and all durations up to 10 years were performed. Considering the top portion of the aquifer that might be dewatered by the higher well discharge, the simulated pump was installed in the lower part of the aquifer, i.e., layers 3 and 4. Data on the hydraulic heads and step time durations were extracted after a pumping scenario was completed, from which the modelling results could be converted into the relationship between the drawdowns and associated time durations as shown in Fig. 11, which indicates that the higher the pumping rate, the larger the drawdown—for example, Fig. 11 shows that due to various pumping rates, the minimum stabilized drawdown is 4.9 m for the rate of 2 L/s and the maximum one is 76.8 m for the rate of 25 L/s.
Fig. 11

Simulated drawdown associated with a 10-year well abstraction scenario at various pumping rates

Time duration to arrive at the stable water level or a new equilibrium state seems to be a complex process that depends on pumping rate, aquifer setting and recharge and hydraulic conditions. Table 6 shows that there is no systematic relationship between the pumping rates and the time durations. In this study, when the drawdown is less than 2% of the final one, the water table is considered to be stabilized, and the length of time for equilibrium can be presented as
$$ {T}_i={T}_n,\kern0.5em \mathrm{when}\kern0.5em \Delta {S}_{\mathrm{w}}=\frac{S_{\mathrm{w}n}-{S}_{\mathrm{w}i}}{S_{\mathrm{w}n}}\times 100\%\le 2\%,\kern3em i=1,\cdots, n-1 $$
(1)
Table 6

Stabilized drawdown and time duration at different pumping rates

Pumping rate (L/s)

Stabilized drawdown (m)

Time to reach new equilibrium (day)

2

4.90

917.10

4

9.74

737.59

6

14.68

814.89

8

19.73

989.61

10

24.91

675.17

12

30.21

681.83

15

38.44

633.66

20

52.92

686.91

25

76.82

1447.05

where, Swi is the drawdown corresponding to the ith simulation step, Swn is stabilized drawdown of the final simulation step, Ti the time duration of the ith simulation step, and Tn is the time to arrive at the new equilibrium.
For the determination of sustainable yield, the relation of Sw and pumping rate (Qp) is established as shown in Fig. 12, using the data from Table 6. By using the curve fitting, the following formula is derived, to represent the relationship between Sw and Qp.
$$ {S}_{\mathrm{w}}=a\cdotp {Q}_{\mathrm{p}}^b\kern1.25em \mathrm{or}\kern1em {Q}_{\mathrm{p}}={\mathrm{e}}^{\frac{\ln {S}_{\mathrm{w}}-\ln a}{b}} $$
(2)
Fig. 12

Relationship between pumping rate and stabilized drawdown

In this case, a = 2.2189 and b = 1.0653. This provides an option for groundwater managers to make informed decisions on the desired resource abstraction rate.

Discussion

Equation (2) gives a nonlinear relationship between the pumping rate and groundwater level at a new equilibrium state, which is different from the linear state derived from pumping tests and which solves the problem in relation to recommended yield for a production well (van Tonder et al. 2001). According to Ponce (2007), to work out how to sustainably pump an aquifer is dependent on the compromise between the groundwater user and associated stakeholders, which can been seen from the relation of Sw and Qp, the proposed yield and the predicted water level, but these are a series of variable parameters but not fixed ones. This provides an option for multiple parties to make a sustainability decision in terms of social, environmental and economic impacts of continuous aquifer pumping, in which the determination of sustainable yield is a key issue especially in areas with water shortage.

In general, long-term abstraction slowly increases the well drawdown, but it would stabilize at a certain level which is dependent on pumping rate. With multiple pumping rates and associated stabilized drawdowns, it is possible to estimate the aquifer sustainable yield. In this case and based on Eq. (2), the proposed drawdowns and associated pumping rates are listed in Table 7, from which a deliberative pumping rate may be reached in accordance with aquifer setting, the regional water users’ regulations, and in agreement with neighboring groundwater users.
Table 7

A series of proposed drawdowns and associated pumping rates for the option of sustainable yield

Drawdown (m)

Pumping rate (L/s)

1

0.47

2

0.95

3

1.42

4

1.89

5

2.37

6

2.84

7

3.31

8

3.79

In terms of model applicability, the relation of Sw and Qp was derived from the site-specific study and its parameters may differ from one aquifer to another, although the model does provide an option for informed decision-making in determining a sustainable yield. The formula heavily relies on good understanding of the aquifer setting, hydraulic properties, and groundwater recharge and abstraction magnitudes, i.e., conceptual model. Thus, numerical modelling can best describe aquifer response to external stresses either on a basin scale or on an aquifer scale, because the modelling is performed on the basis of a groundwater depression cone under varied boundary and hydraulic conditions, as well as because the modelling can simulate the aquifer response over long periods of time length, which cannot be done using aquifer hydraulic tests.

Conclusions

Sustainable yield is a key parameter in the determination of groundwater sustainability. Determining the sustainable yield of an aquifer is of importance in managing the water resource in an effective manner for the arid- and semi-arid regions such as South Africa. In many areas of the nation, groundwater has been the sole source of water supply. The amount of water supply through borehole abstraction is used to adopt the recommended yield derived from the pumping test, which is different from sustainable yield.

In this study, a 3D model was performed for a fault-controlled aquifer using FEFLOW. The modelling process started with an understanding of the aquifer setting and the establishment of a conceptual model, with data derived from borehole drillings, field measurements and hydraulic tests, with the intention of:
  • Simulating natural groundwater flow on the damage zone by characterizing the distribution of aquifer hydraulic head

  • Examining the effects of pumping scenarios on the change in hydraulic drawdown and pumping rate

  • Determining aquifer sustainable yield through analyzing the impact of groundwater abstraction rate on the change of stabilized groundwater level in the long term

To meet the objectives, it is critical to establish a sound conceptual model, which requires model refinement. Based on this refined model, the natural flow system and the flow associated with pumping scenarios were simulated. Results for natural flow simulation show a balancing groundwater dynamic, with groundwater in the fault damage zone flowing from the south and discharging in the north, and there is a four-borehole network located on the upper end of the discharge area; note that simulated water level is well correlated with the observed water levels at these boreholes.

Due to its advantage in simulating various-scale domains with different time lengths, numerical modelling provides an effective tool towards predicting groundwater behaviour, including sustainable yield, through determining aquifer characteristics and taking the cone of depression as a unit into account. Results of simulations with different pumping scenarios show the distinct impact of groundwater abstraction on the aquifer hydraulic head (drawdown). In fact, during the modelling process, the drawdown was dependent on pumping rate and time duration, and groundwater level would reach a new equilibrium state reflected by a stabilized water level. This implies that there is a relationship between the pumping rate and associated stable drawdown, and this relationship is a key to determining the sustainable yield of an aquifer. However, the proposed yield and predictive water level is a series of movable figures but not a fixed one. The issue of how to sustainably pump might rely on the compromises made between the groundwater users and associated stakeholders, who together must make a decision regarding sustainability in consideration of the social, environmental and economic impacts of continuous aquifer pumping.

Notes

Acknowledgements

We are grateful to Prof. Y Xu from University of the Western Cape for his generous support in this research.

Funding information

The author would like to acknowledge the Water Research Commission of South Africa who has funded this study.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Water Conservancy and HydropowerHebei University of EngineeringHandanChina
  2. 2.Council for GeosciencePretoriaSouth Africa

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