Modreck Gomo Institute for Groundwater Studies (IGS), University of the Free State

1. On the Methods to Determine Borehole Sustainable Yield Modreck Gomo Institute for Groundwater Studies (IGS), University of the Free State

2. Presentation outline • Introduction, • Why borehole sustainable yield matters? • Methods/Approaches to determine borehole sustainable yield • Numerical groundwater flow models, • Use of the Classical Theis (1935) Equation, • 20-year safe yield (Q20) of wells, • Flow Characteristics Method (FCM) • Use of Operational data,

3. Introduction • Anyone who owns a borehole is interested to knowing the maximum discharge rate at which they can abstract/pump groundwater in such a way that they can be assured of continuously getting that yield from their borehole (assuming the quality is good/great). • This is irrespective of the fact that the prescribed pumping rate can still be turned down when they apply for the water use licence. What is Sustainable? • Toenable something to continue for a period of time (Cambridge Dictionary), • To enable to continue for an extended period or without interruption (Oxford Dictionary) • Despite decades of research and development, there are different opinions about the concept of sustainable/safe yield in groundwater and this serves as an illustration of the conceptual and technical challenges surrounding the subject.

4. Introduction • It is important also to differentiate between sustainable yield of a production borehole and sustainability in the context of the basin/catchment (or any other defined groundwater entity) in terms of principles and practicability of assessments • Basin/Catchment Sustainability – derived from on the water balance of the whole entity, • Borehole sustainable yield – derived from aquifer pumping test to stress the localised aquifer, • These aspects are still very difficult to reconcile (not the focus of the presentation)

5. Why borehole sustainable yield matters? • Determine if demand can be satisfied from the drilled borehole, • Sizing and costing of pumping units (perhaps for Engineers), • Operation of the the borehole, • Managment of the the borehole • Irrespective that pumping has been authorised/allocated at basin/catchment level - the borehole still requires good managment, • Borehole sustainable yield can have huge cost implications, which can sometimes defeat the whole purpose of sustainability (See example on the next slide)

6. Why borehole sustainable yield matters? • Say a village has a need/demand of 20 L/s 4 L/s 4 L/s Qs = 20 L/s Qs = 4 L/s 4 L/s 4 L/s Less conservative but cheaper Conservative but expensive X 5 Cost Risk of failure is relative, could be same or different depending aquifer characteristics

7. Methods/Approaches to determine borehole sustainable yield • A number of methods/approaches exist to determine borehole sustainable yield but very few are direct • This presentation does not claim to provide an exhaustive list all the methods to estimate borehole sustainable yield but rather what the author could find and synthesize as standardised approach after a thorough literature review. • The presentation will only give a quick overview about some of the established methods given the available time, • The idea is not to try promote and suggest any of the methods as the most appropriate but just discussion about some of these approaches as reflection of the developments in the grroundwater field.

8. Numerical groundwater flow models • Can be used to generate various pumping regime scenarios and to assess the impacts of those scenarios. • But it is not practically and economically feasible to conduct groundwater flow numerical modelling for a single borehole situations, • Analytical models are therefore often used.

9. Use of the Classical Theis (1935) Equation • Methods typically based on the Cooper-Jacob (1946) approximation of the Theis equation because of its simplicity • Such methods have been applied in different ways, but typically requires a constant aquifer discharge test to be performed to determine aquifer storativity and transimissivity • To calculate the maximum pumping rate (regarded as sustainable) that enables maintaining of drawdown (s) above a specific (often above the aquifer), after a long duration of pumping, the Cooper-Jacob equation can used as follows: • Where: Q = sustainable yield (L3/T); T = transmissivity (L2/T); s = available drawdown (L); t = Planned pumping duration (T); r = radius of influence (L); S = storativity In practice aquifers rarely conform to the Theis conditions, approach also applied with other analytical models for different aquifer conditions

10. 20-year safe yield (Q20) of wells • The 20-year safe yield (Q20) for a well is defined as the rate at which a well can be pumped continuously for a period of 20 years so that the pumping water level does not fall below the top of the aquifer (Available drawdown). • Farvolden (1959) introduced the concept of the safe pumping rate of a well for 20 years in Alberta, • Calculations based on the Copper-Jacob approximation, • The equation to derive the apparent transmissivity and safe yield was then described as: • Where: Q is the pumping rate (metric units) of the well and Δs is the drawdown of the well.

11. 20-year safe yield (Q20) of wells • For 20-year safe yield (Q20) of wells, the straight-line drawdown curve was extrapolated by calculation to 8 log cycles (10 million minutes = 19 years): • Where: where T is the transmissibility (transmissivity), H is the available head (difference between static non-pumping water level and the top of aquifer), and 0.7 is a safety factor reducing the Q value to 70%. • Maathuis and van der Kamp (2006) modfied the method to include constant discharge test rate and and also drawdown measured during phases of pumping test and various aquifer models

12. Flow Characteristics Method (FCM) • Flow Characteristics Method (FCM), sometimes referred to “FC method” was developed to estimate the sustainable yields of boreholes in fractured rock formations (van Tonder et al. 2001). • According to this method Borehole Sustainable Yield defined as: The discharge rate at which a borehole must pumped in such a way that the water level must not drop below a specified level (e.g. fractures – main water strike) in the borehole after abstracting water from the borehole for a long time (e.g. 2 years) without any recharge taking place

13. Basis of the FC Method

14. Basis of FC Method • Estimates the sustainable yield (Qsustainable) of a borehole in fractured-rock aquifer based on the following equation: • Wheretlongdescribes the maximum operation time in which the drawdown s shall not exceed a maximum drawdown savailable during operation period of the borehole, • The extrapolation of the measured pumping test drawdown (spump test ) is used to determine the Qsustainable

15. Extrapolation of pumping test drawdown • The drawdown measured during a pumping test ((spump test)is the sum of the drawdowns due to the production well (swell) and the boundaries (sboundary) Where swellis extrapolated by a Taylor series expansion • Image well theory is applied to analyse the effects of the boundaries on the drawdown (sboundary) • (sboundary) - 4 types of impermeable boundary conditions

16. FC Method – Main Result • A borehole yield that does not result in the groundwater level going below the main yield fracture(s) thereby protecting the fracture (s), • Takes into account the potential influence of unforeseable, impemeable boundaries, but could also understimate the yield, • Optionally consider influence of other pumping wells, • Meant for fractured-rock aquifers, and • Has not included the influence of well losses on available drawdown

17. Use of operational data • Due to the risk of overestimating or underestimation of borehole sustainable yield, a studies have started to advocate for the use of operational data to establish the sustainable yield relative to analytical prediction (Misstear and Beeson 2000; Hammond 2017). The idea according to Hammond (2017) is to: • Use step tests and short-term, single-well, aquifer pumping tests that are commonly used to determine well capacities for water system design for establishing an initial conservative operational yield. • Such an initial rate should still not exceed available drawdown (should not cause water levels to go below the main yielding aquifer layers).

18. Use of operational data The idea according to Hammond (2017) is to: • Use step tests and short-term, single-well, aquifer pumping tests that are commonly used to determine well capacities for water system design for establishing an initial conservative operational yield. • Such an initial rate should still not exceed available drawdown (should not cause water levels to go below the main yielding aquifer layers). • The well can be on operation on a temporary licence based on this initial rate • When in operation, cost effective long-term operational data can be collected by water systems operators for the groundwater experts to firmly establish its yield relative to the analytical prediction.

19. Use of operational data • Hammond (2017) recommends that “data should be taken over a period of several years that includes a drought and the records from the well should include; the daily production, the number of hours pumped each day, and the depth of any stable operating water level near the end of each daily pumping cycle. • This data can then be used to establish an informed sustainable yield for the borehole (well).

20. Summary • Sustainable borehole yield is a very important parameter for operation, impact on overal cost of groundwater development and borehole managment, • Few direct established approaches/methods exist to determine sustainable borehole yield, • Due to risk of failures, more stress on groundwater resources and uncertainities, use of operational data to determine borehole sustainable yield appears to be recently recieving interests and might to need to be further explored, but has its disadvantages and advantages: • Advantages - Ensures the groundwater experts are involved in operational phases and Can save cost on unnecessary and unreliable once off pumping tests • Disadvantages - Less jobs/income with regard to once long sustainable yields and failure also to provide a concrete/reliable yield for decision makers before the borehole can be operated (But it could be what it is)

21. References • Kalf FRP and Woolley DR (2005). Applicability and methodology of determining sustainable yield in groundwater systems. Hydrogeology Journal 13, 1: 295–312. • Van Tonder GJ, Botha JF, Chiang WH, Kunstmann H, Xu Y (2001). Estimation of the sustainable yields of boreholes in fractured rock formation. Journal of Hydrology 241:70-90. • Cooper HH Jr, Jacob CE (1946) A generalized graphical method for evaluating formation constants and summarizing well field history, Transactions-American Geophysical Union 27. doi: 526-534. 10.1029/TR027i004p00526.

22. References • Theis CV (1935). The relation between the lowering of the piezeometric surface and the rate and duration of discharge of a well using groundwater storage. Transactions-American Geophysical Union, 16:519-524. • Farvolden, R.N., 1959. Groundwater supply in Alberta. Alberta Research Council. • Maathuis H and van der Kamp G (2006). The Q20 Concept: Sustainable well yield and sustainable aquifer yield. Saskatchewan Research Council. SRC Publication No. 10417-4E06