Report

Performance Evaluation of Deep Tubewells of Muktagacha , ,

M. A. Mojid*, M. Ahmed*, M. S. U. Talukder* and M. M. Ali**

Summary The performance characteristics of a well are important for proper design, operation, maintenance, and rehabilitation and in estimating the well's long-term maximum yield. Step-drawdown pumping test data for 30 deep tubewells were analyzed using Labadie's optimization and Jacob's approxi- mation techniques. The aquifer and welll oss factors, well efficiency, specific capacity and specific drawdowns were calculated. Most of the wells showed reasonably acceptable values for aquifer and well loss factors . Twenty-four wells were found to be hydraulically efficient; four were inefficient, and two produced meaningless results. The specific capacity and specific drawdown were suitable for good performance of the wells. However, these parameters governing well performances were adequate to justify proper design and development of the wells. The results may be used for future evaluation of the wells in the study area.

I. Introduction Groundwater is a valuable natural resource which is one of the vital inputs for agricultural production in Bangladesh. The cost of extracting groundwater is largely dependent on the performance characteristics of the wells, which deter- mine the economic viability of irrigated agriculture. Knowledge of initial perfor- mance of a new well provides a basis for evaluating future performance of wells and for design, operation, maintenance, and rehabilitation programs for the technology. Most of the deep tubewells in Bangladesh have the problems of low discharge capability, clogging, and sand pumping (Khan et al., 1987). Though some mea- sures are being taken to improve tubewell performance, the physical constraints inherent in tubewell design cannot be solved by improved management practices alone. The design of a well, in particular the diameter, percent open area associated with slot size, and shape and screen length, controls its performance (Johnson, 1966). But unfortunately, very little attention is given, particularly to

*Department of Irrigation and Water Management , Bangladesh Agricultural University, Mymensingh, Bangladesh. **Department of Mathematics , Bangladesh Agricultural University, Mymensingh, Bangladesh. (Manuscript Received June 26, 1991, Accepted May 7, 1992)

Irrigation Engineering and Rural Planning No.23, 1992 PERFORMANCE EVALUATION OF DEEP TUBEWELLS 71 the aquifer and well loss factors, in designing tubewells. The effect of well loss on drawdown in the pumping well is important both in determining aquifers' hydraulic characteristics and in design of supply wells (Heath, 1984). The two principal well characteristics of well performance, yield and draw- down, are measures of the capacity of the well to yield water. The step- drawdown pumping test helps to determine the well performance by estimating general adequacy prior to completion and normal functioning of the well. It can also suggest correct pump capacity and pump setting by relating discharge and drawdown and determine deterioration of the well following a period of use (USDIBR, 1985). Well efficiency is an important consideration both in well design and in well construction and development. A reasonable efficiency makes a well hydrauli- cally efficient; excessive energy consumption is avoided by designing and con- structing wells that will yield the required water with least drawdown (Heath, 1984). Determining the efficiency of a new well is necessary for predicting its loss in efficiency over time. Efficiencies for a number of pumping rates are also necessary to normalize the efficiency of the well in future (Helweg et al., 1983). Thus, it is observed that the formation loss (aquifer loss) and well loss factors are critically important for determining the performance of a well both at the initial stage and in future stages. Likewise, the objectives of this study were to evaluate the performance of some deep tubewells at in , Bangladesh, by determining the hydraulic efficiency asso- ciated with the aquifer loss and well loss factors and to justify the design and construction details of deep tubewells which are presently being built in the study area.

II. Methodology This study was conducted at the Muktagacha upazila in Mymensingh district, Bangladesh, during the period 1990-1991. Four constant-rate step-drawdown tests were conducted with the existing deep tubewells installed during the last two years. In addition, step-drawdown data on 26 deep tubewells tested by the International Development Agency (IDA) were also collected. These data were used to determine the performance characteristics of the tested wells.

Methods of Well Evaluation The discharge-drawdown relationship is very important in determining the per- formance of a well. Assuming turbulent flow in the vicinity of a pumping well, the total drawdown in a well may be expressed by the following equation, which i the basic formula for step-drawdown test data analysis (Jacob, 1947):

(1) where S=drawdown in the well (m) B=head loss coefficient due to laminar flow, usually assumed to be caused by the aquifer (m/m3/min)

Irrigation Engineering and Rural Planning No.23, 1992 72 M. A. MOJID, M. AHMED, M. S. U. TALUKDER & M. M. ALI C=head loss coefficient for turbulent flow, usually caused by flow into the borehole and screen (m1-3p sp pvaries from 1 to 4). p=exponent which indicates the severity of the turbulence; and Q=discharge of the well (m3/min) The first term BQ in the above equation is roughly the laminar head loss term, and the second term CQp indicates the head loss due to turbulent flow (Figure 1), because the total drawdown observed at a well consists of laminar head loss, referred to as aquifer or formation loss, and a well loss component. The aquifer or formation loss is caused by travel of water towards the well, representing a logarithmic drawdown curve at the well face, while the well loss component is caused by, the resistance to turbulent flow of groundwater through the well screens, violating the Darcy's law (Johnson, 1966). When there is slight turbulent head loss, it is difficult to ascertain the adequacy of design and development of the well since laminar well losses can also occur (Mogg, 1959; Sheahan, 1971). Rather it may be said that minimum turbulence is necessary but not enough to indicate good well design and development. The efficiency of a well, which is a function of head loss resulting from flow through the gravel pack, screen and axially in the well to the pump, represents the hydraulic effectiveness of the well. Well efficiency can be defined as the ratio of the drawdown in the aquifer at the radius of the pumping well to the drawdown inside the well. Thus, well efficiency may be expressed as

E=[BQ/(BQ+CQp)]•~100, in percent where BQ and CQp approximately represent the laminar and turbulent head loss terms, respectively, with the parameters explained earlier. Thus, well efficiency associated with well loss factor is a way of expressing the adequacy of a constructed well. In a 100% efficient well, not all drawdown resulting from head loss in the aquifer would be related to the design of the well. But well efficiency

Figure 1 The drawdown characteristics of a pumping well in a semi-confined aquifer

Irrigation Engineering and Rural Planning No.23, 1992 PERFORMANCE EVALUATION OF DEEP TUBEWELLS 73 is considerably affected by partial penetration of the well and anisotropy of the formation (USDIBR, 1985). However, analysis of step-drawdown data and deter- mination of the apparent efficiency by Jacob's method (Eq. 1) may be useful in comparing variations in apparent efficiency of an individual well over time as an aid in recognizing the degree of deterioration and possible need for rehabilitation.

Solution of Step-Drawdown Equation The step-drawdown pumping test consists of a series of constant discharge tests in which the discharge is increased incrementally to obtain corresponding incre- ments of drawdown. The steps or increments of discharge increase are arranged in such a way that three or more steps are possible before the design capacity of the pump or well is reached. The basic concept for solution of the step- drawdown equation (Eq. 1) is to find those particular values of B, C, and p at which the actual drawdown observed in the field from the step-drawdown test is as close as possible to the drawdown computed by Eq. 1. The parameter p, being an exponent, provides a highly nonlinear solution to the equation. In order to simplify the equation, Jacob (1947) suggested an average value of 2 for p which facilitates the determination of B and C by graphic solution. But Rora- bough (1953) and Lennox (1966) strongly questioned the justification of Jacob's value for p. Later a range for p was proposed by Sheahan (1971). A least-square curve-fitting analysis developed by Labadie and Helweg (1975) was used in this study for determining the unknown coefficients and exponent. The technique was formulated as an optimization problem of the following form:

(2)

where N= the total number of steps, i=1•cNi Qi=discharge during step i of the test; Si=drawdown observed after step i of the test; and E(B,C,p)=the squared fitting error as a function of chosen B, C, and p for given step-drawdown test data. The solution of the optimization equation (Eq. 2) requires known values of the exponent p for which the equation reduces to

(3)

Cramer's rule (Labadie et al., 1975) was then applied for solution of B and C for known values of p as

(4) and (5)

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The error function E(p) being a smooth convex function, an efficient and simple one-dimensional grid-search technique was used for solving this problem to determine the optimal p for which Eq. 3 was optimized. For the above process, the value of p was restricted between 1 and 4 (Sheahan, 1971). However, provision was made in the algorithm to find the minimum error by avoiding the lower and upper limits of p values if necessary. The algorithm used in this study was derived iteratively by increasing the value of p between its lower and upper limits (1 and 4), avoiding any subjective input of p value from the user.

III. Results and Discussion

The aquifer condition of the study area was investigated by using borelogs of 54 existing deep tubewells, soil samples collected during the installation of observa- tion wells, and the data obtained from pumping tests. The lithologic investiga- tion performed to determine the vertical stratification of the study area showed that on average the top 20 m soil of the study area consisted mainly of silty clay and hard clay layers. The hard clay layer was observed at all the locations. In some places, a 5 to 10 m thick purely fine sand layer was found below the clay layer. The subsurface lithology below the clay formation was layered with fine, medium coarse, and coarse sands and gravels. Almost all the layers were actually a mixture of different graded sands. The existing deep tubewells were installed at depths ranging from 65 to 100 m below the ground surface, hence the lithology beyond these depths is not known. On the basis of geologic study and pumping test, it was found that the main aquifer was semi-confined (leaky type) in nature. The analysis of hydrological and geological data revealed the study area to be hydrogeologically homogeneous. The average values of aquifer's hydraulic properties, viz., transmissivity, stora- tivity, aquifer permeability, aquitard permeability, leakage factor and hydraulic resistance were found to be 1755m2/d, 0.0074, 29m/d, 0.45m/d, 385m and 93 days, respectively. All the deep tubewells used in this study to evaluate their performance were operating in the aforesaid aquifer. The performance of deep tubewells is basically evaluated in terms of their discharge. The major factors governing well performance are aquifer and well loss factors, specific capacity, specific drawdown, and efficiency of the well. The aquifer and well loss factors of 30 deep tubewells calculated by Labadie's optimiza- tion technique and Jacob's approximation method are presented in Table 1. The aquifer loss factor (B) is related to the aquifer's transmitting capacity, the higher value of which indicates a lower transmissive aquifer and vice-versa. This parameter may be used to estimate act-lifer transmissivity where long- duration pumping test data are not available. Table 1 shows that 8 wells (TW- 3, IW-63, IW-67, IW-70, IW-71, IW-73, IW-81, and IW-84) indicating higher aquifer loss factor were operating in a lower transmissive zone whereas the others were operating in a higher transmissive zone. However, these values were indicative of an acceptable transmissive aquifer in the study area.

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Table 1 Drawdown parameters computed by Labadie's optimization technique (p>=1) and Jacob's approximation (p=2)

*TW: Well tested under this study **IW: Well tested by IDA

The well loss factor (C) is closely related to the well condition. In Labadie's optimization, the parameter C varies with the value of p, but in Jacob's approxima- tion C is always in min2/m5, since p is always constant. It was observed that wells no. IW-63 and IW-73 produced negative values of C by both methods, which is meaningless. This happened probably due to inaccurate data recording. The well loss increased with increasing discharge (Figure 2). The reason was more turbulence in the vicinity of the well at higher discharges, which increased the turbulence factor (p), ultimately increasing well loss. The difference between total drawdown (Se) and aquifer loss (Sa) was attributed to head loss as water moved from an aquifer into a well and up the well bore. These losses can be

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Figure 2 Relation to pumping rate, drawdown and well efficiency

Table 2 Relation between well loss coefficient (C) and well condition (after Walton,1962)

minimized by reducing the entrance velocity of water, which can be done by installing the required length of screen and pumping at the lowest acceptable rate. The well loss factor, when expressed in min2/m5, may be used to explain the existing condition of a well by comparing it to Walton's (1966) value (Table 2). It was observed that for all the wells the well loss factor remained below 0.334 min2/m5 (Table 1), indicating that the wells were designed and developed properly. The hydraulic efficiencies of the wells under study were calculated at various

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Table 3 Well efficiencies at various discharge rates as computed by Labadie's optimization technique

discharge rates (Table 3). It can be seen that the efficiency decreased gradually with increasing discharge rates (Table 3 and Figure 2) due to increasing well losses. At the two wells (IW-63 and IW-73) the efficiencies were above 100%. But obviously a well cannot be more efficient than 100%. The discrepancy was due to incorrect recording of data by the concerned authority. Under ideal conditions, an efficiency of about 80% is the maximum that can usually be achieved in most screened wells, but under normal conditions, an efficiency of 60% is probably more realistic (Helweg et al.,1983). In this study, the wells (except for IW-79, IW-80, and IW-86) were found to be hydraulically efficient. The specific capacities and specific drawdowns for the wells under investiga- tion were calculated and are presented in Table 4 . The specific capacity of a well is the yield per unit of drawdown, and is determined by dividing the pumping rate at any time during pumping by the drawdown at the same time , the specific drawdown is the inverse of specific capacity, and indicates drawdown per unit discharge of a well. However, the results indicate that the specific capacity

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Table 4 Specific capacities (SP.C) in litre per second per meter and specific drawdowns (SP.DD) in meter per litre per second of 30 deep tubewells

decreased with increasing discharge rate and length of pumping period, except in a few cases where the value initially increased and then decreased. The decline at increasing discharge rates was due to greater well loss for increased turbulence, while the initial increase of specific capacity over time probably indicated that the well was continuing to develop and that the original development was inadequate. The specific capacity may be used to estimate aquifer transmissivity, for which long-duration pumping test data are not available. For expected and smooth performance, a tubewell should have specific capacity between 6.2 e/s/m and 18.5 /s/m (IDA, 1988). However, the specific capacity as obtained in this study e (except for wells no. TW-3, IW-81, and IW-84 in Table 4) showed that the aquifer of the study area had reasonable transmitting capacity for water. The specific drawdown is a useful indication for selecting well capacity for the particular aquifer. For expected and smooth performance, a tubewell should have specific drawdown between 0.054m/l/s and 0.162m/l/s (5 to 15 ft/cusec) (IDA, 1988). The specific drawdowns obtained in this study had values that were

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within reasonable limits. The yield of most wells declines with use because of normal deterioration due to buildup of incrustation on screen and plugging of aquifer and gravel packs. Comparing the drawdown parameters obtained from step-drawdown test at any time to those obtained from new wells reveals the extent of deterioration. For a partially deteriorated well, the pumping rate may be adjusted to obtain reasonable efficiency for minimizing pumping costs. Determining the long-term yield of a well from data collected during an initial short-period well test is one of the most important practical problems in ground- water hydrology. The problem may partially be solved based on specific capacity and behavior of static water level fluctuation. The long-term yield is approxi- mated as the product of specific capacity obtained from a new well and available drawdown and may be reduced as and when necessary to compensate for long- term decline of static water level. The available drawdown at the time of initial testing of a well is the difference between the static water level at that time and the lowest pumping level that can be imposed on the well, for a screened well which is normally two meters above the top of the screen. To predict the maximum continuous long-term yield, it is necessary to estimate how much the static water level and thus the available drawdown may decline from the position that it occupies during the initial testing of a well.

IV. Conclusion It may be concluded that the step-drawdown pumping test is a useful technique (i) for evaluating the existing performance status of a tubewell and hence (ii) for suggesting possible remedial measures if necessary. This ultimately would help increase the efficiency of the pumping unit and optimize groundwater utilization.

References 1) Helweg, O. J., V. H. Scott and J. C. Scalmanini (1983): Improving Well and Pump Efficiency. American Water Works Association, USA 2) Heath, R. C. (1984): Basic Groundwater Hydrology. US Geological Survey Water Supply Paper 2220, USA 3) IDA (1988): Well Design and Construction Manual. Guide to Supervisory Staff. IDA Deep Tubewell II Project, November, 1988 4) Jacob, C. E. (1947): Drawdown Test to Determine Effective Radius of Artesian Well. Trans. ASCE, Vol. 112, pp.1047-1070 5) Johnson, E. E. (1966): Groundwater and Wells, First edition, Edward E. Johnson Inc. St. Paul, Minnesota 6) Khan, L. R., S. Dass and M. R. Biswas (1987): Determination of Deep Tubewell Performance from Step-Drawdown Tests. Bangladesh. J. of Water Resources Res. Vol. 8. No.1, pp.19-28 7) Lennox, D. H. (1966): Analysis and Application of Step-Drawdown Test . J. of the Hydraulics Div. ASCE, HY6. DD.25-48 8) Labadie, J. W. and O. J. Helweg (1975): Step-Drawdown Test Analysis by Computer. Groundwater, Vol. 13. No.5. September-October

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9) Mogg, J. L. (1959): Effect of Aquifer Turbulence on Well Drawdown. J. of the Hydrau- lics Div_ ASCE_ HY11. Nov. DD.19-112 10) Rorabaugh, M. I. (1953): Graphical and Theoretical Analysis of Step-Drawdown Test of Artesian Well. ASCE Proc., Hydraulics Div. Vol. 79. December pp.362-385 11) Sheahan, N. T. (1971): Type Curve Solution of Step-Drawdown Test. Groundwater, Vol.9. No.1. January-February, pp.25-29 12) USDIBR (1985): Groundwater Manual. A Water Resources Technical Publication. U. S. Department of the Interior Bureau of Reclamation 13) Walton, W. C. (1962): Selected Analytical Method for Well and Aquifer Evaluation. Illinois State Water Survey, Bulletin No.49

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