Determination of the Costs of Potable Water Extraction in the Municipality of Villagran, Guanajuato, Mexico ^†

Abstract

In this work, the costs generated from the extraction of water from the wells of the operating body of the Potable Water Board of the Municipality of Villagrán, Guanajuato (JUMAPAV) were determined, in which the characteristics of each well were considered for evaluation and analysis. The unit costs were determined through the unit price analysis methodology proposed by the Regulation of the Law of Public Works and Related Services (RLOPSRM, 2012), the electromechanical efficiency of the wells was calculated and the influence on its value in energy costs and on the volume extracted was evaluated. Finally, the price of the agency’s fixed rate for 10 m³ of water was compared with the price obtained from the proposed analysis.

1. Introduction

The responsibility for providing drinking water, sewage and sanitation services, in accordance with Article 115 of the Political Constitution of the United Mexican States, corresponds to the municipalities, for which each municipality possesses entities that provide the above water services. For this reason, drinking water rates are set differently in each municipality, depending on what is established by the legislation of each federal entity. In some, the rates are approved by the local congress of the entity, while in others they are approved by the governing body or directive congress of the drinking water operating agency of the municipality or locality, or the state water commission [1].

In this work, the costs generated from the extraction of water from the wells operated by the drinking water board of the municipality of Villagrán, Guanajuato (JUMAPAV) were determined, and the characteristics of each well were considered for evaluation and analysis. Unit costs were determined through the unit price analysis methodology proposed by the Regulations of the Law of Public Works and Services Related Thereto [2]. The electromechanical efficiency of the wells was also calculated and the influence of its value on energy costs and the volume extracted was evaluated. Finally, the price of the agency’s fixed rate for 10 m³ of water was compared with the price obtained from the proposed analysis.

2. Materials and Methods

This study was carried out in JUMAPAV, in the municipality of Villagrán, Guanajuato. The INEGI [3] reports that the total population of the municipality of Villagrán is 65,791 and the number of private homes is 21,920, of which 16,201 are inhabited and 16,125 have piped water in their housing area. JUMAPAV has 7 deep wells dedicated to the extraction of groundwater for drinking water use.

The total costs of the wells were calculated, dividing them into fixed and variable costs according to article 195 of the RLOPSRM. For the fixed costs, the establishment and equipment costs were determined; the former were estimated with the Catalog of Direct Costs of Drilling Wells for Drinking Water [4], updating them to the year 2021. From these, the fixed costs for depreciation, investment and maintenance were calculated, and for the latter they were quoted with a private company. The equation to determine depreciation costs is as follows:

$$D={\displaystyle \frac{(V_m-V_r)}{V_e}}$$

(1)

where D is the hourly cost for depreciation of the drilling and well equipment, V_m is the value of the drilling (P) or equipment (E) of the well, V_r is the salvage value of the P or E of the well and V_e is the economic life of the drilling or well.

The cost per investment is obtained from the following equation:

$$I_m={\displaystyle \frac{(V_m+V_r)i}{{2H}_{ea}}}$$

(2)

where I_m is the hourly cost per investment, V_m and V_r are defined in Equation (1), H_ea is the effective hours of operation per year and i is the annual interest rate.

The maintenance cost considers a value of 4% of the cost of drilling. Therefore, the fixed cost is integrated as follows:

CF = D + I + CM

(3)

where CF: annual fixed cost, D: annual depreciation cost, I: annual investment cost and CM: maintenance cost.

The variable costs are a function of the operating time of the well; the costs were considered for electrical energy, oil, labor and maintenance:

CV = CE + CO + CM + CA

(4)

where CV: annual variable cost, CE: electric energy cost, CO: operating cost, CM: maintenance cost and CA: oil consumption cost.

For the cost of electrical energy, it is necessary to determine the electromechanical efficiency of each well, which is the total efficiency of the pumping equipment considering energy consumption and pumping expenses. This was calculated in accordance with NOM-006-ENER-2015, with the electrical and hydraulic variables; the power consumed by the engine and the power used were determined using the following formulas:

$$Powerconsumed={\displaystyle \frac{\sqrt{n}\ast f_p\ast I_m\ast T_m}{745}}$$

(5)

where f_p: power factor, n: 3 for three-phase motors, 745: conversion factor to HP, I_m: average intensity measured in amperes and T_m: average voltage measured in Volts.

$$Powerused={\displaystyle \frac{\ast Q\ast CDT}{76}}$$

(6)

where specific weight of water, 1000 kg/m³, Q: flow rate in m³/s, CDT: total dynamic load and 76: conversion factor to HP.

$$\mathrm{E}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{e}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}\left(\mathrm{\%}\right)={\displaystyle \frac{Powerused}{Powerconsumed}}\ast 10$$

(7)

The power used is less than the power consumed due to losses caused by hydraulic friction in the column and discharge, among others.

The calculation of the total cost is the sum of the fixed costs and the variable costs:

CT = CF + CV

(8)

where CT: total annual extraction cost, CF: fixed cost and CV: annual variable cost.

To determine the unit extraction cost, and to obtain a cost per m³ and hourly extraction cost:

$$CAS={\displaystyle \frac{CT}{V_e}}$$

(9)

where CAS: cost of groundwater per m³, CT: total cost of exploitation and V_e exploitation volume, m³/year.

$$C_h={\displaystyle \frac{CT}{TO}}$$

(10)

where C_h: hourly cost of groundwater extraction, EUR/h, CT: total cost of exploitation and TO: annual operation time.

3. Results

The drilling and equipment costs were estimated with the Catalog of Direct Costs of Drilling Wells for Drinking Water [4], updating them according to annual inflation until 2021; see

Table 1. Characteristics of three wells with drilling and equipment costs.

Well Name	Depth	PEP 1	Spent	Drilling	Equipment
	m	HP	lps	EUR	EUR
Las Flores	189	75 HP	25	83,352.82	41,379.34
Salida a Juventino	94	75 HP	21	60,461.27	36,394.09
Praderas	255	100 HP	19	105,683.21	69,785.62

¹ Pumping Equipment Power. Note: Exchange rate is 18.53 pesos per euro at 28 February 2024.

.

To obtain the fixed cost, Equations (1)–(3) were applied.

Table 2. Fixed costs for every well in euros.

Well Name	Depreciation (EUR)		Investment (EUR)		Maintenance (EUR)	Fixed Costs (EUR)
	Drilling	Equipment	Drilling	Equipment
Las Flores	3334.11	2648.28	6643.22	3429.85	3334.11	19,389.57
Salida a Juventino	2418.45	2329.22	4818.76	3016.63	2418.45	15,001.52
Praderas	4227.33	4466.28	8422.95	5784.39	4227.33	27,128.28

Note: Exchange rate is 18.53 pesos per euro at 28 February 2024.

presents the costs for depreciation, investment and maintenance and the fixed cost for three wells in order to illustrate them.

In the variable costs, for the consumption of electrical energy, the hours that the equipment operates in a year and the power it consumes were considered. The annual operating time was 8 h a day for 365 days a year, resulting in 2920 h. Equations (5)–(7) were applied, and

Table 3. Energy costs.

Well Name	Input Power	Output Power	EE 1	PC 2	AEC	Price kW-h	TCE 3
	HP	HP	%	Kw	Kw-h	EUR	EUR
Las Flores	66.09	46.18	69.68	49.3	143,964.60	0.0475	7922.76
Sal. a Juventino	72.97	24.44	33.5	54.44	158,953.61	0.0475	8747.65
Praderas	103.36	59.77	57.59	77.1	225,140.33	0.0685	17,913.54

¹ Electromechanical efficiency, ² power consumed, ³ total energy cost.

shows the results for three wells and the annual energy consumed (AEC) in kW hours. For oil consumption, only the “Salida a Juventino” well has vertical turbine-type equipment; its cost for annual oil consumption was EUR 228.95. For the maintenance cost, 10% of the cost of drilling each well was considered. The cost of labor was calculated considering a salary of 15.92 EUR/day, resulting in an annual cost of EUR 727.87.

Total and unit costs: The total annual cost is the sum of the fixed and variable costs (Equation (8)), the unit cost for the extraction of one cubic meter of water was obtained by applying Equation (9) and the cost for one hour of extraction was obtained by applying Equation (10); see

Table 4. Total and unitarian costs for every well.

Well Name	Fixed Costs/Year (EUR)	Variable Costs/Year (EUR)	CTA 1 (EUR)	Volume	Cost m3/Year	Cost Per Hour
				m3/Year	EUR/m3	EUR/h
Las Flores	19,389.57	12,788.58	32,178.15	262,800	0.12	11.02
Sal. a Juvent	15,001.52	13,343.89	28,345.41	220,752	0.13	9.71
Praderas	27,128.28	25,619.99	52,748.26	199,728	0.26	18.06

¹ Total annual costs.

.

The JUMAPAV operating body charges a rate according to use: domestic, commercial, industrial, mixed or special. If the sum of the total costs of the wells is taken as a direct cost (EUR 246,311.90) and the indirect costs are added to this (the cost of administration of the organization), reaching a total of EUR 1,383,668.42 (year 2021), these are divided by the total annual volume multiplied by a driving efficiency of 70%, and a cost per 10 m³ of 11.94 EUR/m³ is obtained.

4. Discussion

The wells with greater depth were the wells with the highest drilling cost; it was observed that the greater the depth, the greater the influence on the fixed cost. The extraction expense has a direct relationship with the equipment costs and the establishment cost. In the case of smaller depths with considerable expenses, a greater influence of the equipment cost on the fixed cost is reflected.

5. Conclusions

The power consumption of the well pumping equipment directly influences the electromechanical efficiency, so low values generate higher variable costs. In the “DIF” and “Salida a Juventino” wells with efficiencies of 32.27% and 33.24%, respectively, it is recommended that rehabilitation or replacement of the pumping equipment be carried out. In the total costs, when relating them to the volume extracted, it is observed that the greater the expense, the lower the price per cubic meter generated, since the greatest impact of the costs occurs mainly in the fixed costs and when comparing the operation time with the costs. It was observed that the price was higher when the efficiency in the wells is low. The cost of the annual domestic rate (2021) of 10 m³ of the operating organization was EUR 121.02; the estimate in this proposal is EUR 11.94, and if considering direct plus indirect cost, there is a lack of financing and utility costs; therefore, it is recommended to review the methodology used for the cost of obtaining rates from the operating organization since the rate for this work represents 9.8% of what is charged.