# Simultaneous Energy and Water Optimisation in Shale Exploration

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}kJ/m

^{3}of water, which is found to be less than the range of thermal consumption values reported for membrane distillation in the literature. Although the obtained results are not generally applicable to all shale gas plays, the proposed framework and supporting models aid in understanding the potential impact of using scheduling and optimisation techniques to address flowback wastewater management.

## 1. Introduction

^{3}of water to fracture and drill a typical well [3,4,5]. A main challenge associated with water usage in hydraulic fracturing is the relatively short time within which the large volume of fracturing fluid is needed [4]. Another issue of contention that has impeded the ongoing progress in shale gas production processes is water contamination. Two categories of wastewater are generated: flowback water and produced water. Flowback water is the wastewater that returns to the surface within the first few weeks after hydraulic fracturing, and is characterised by a high flowrate and volume generated in the range between 10% and 40% of the initial injected fluid [4]. The contaminants found in flowback water include total suspended solids (TSS), metals, organics, and total dissolved solids (TDS), with the TDS value ranging between 20,000 mg/L and 300,000 mg/L depending on the shale formation and how long the water remains underground [3,4]. Produced water, on the other hand, is the wastewater generated in the production stages. It is made up of the formation water and the injected fracturing fluid generally characterised by high salinity. In selecting appropriate options for the effective management of the high volume of the generated flowback water, several factors have to be considered. These include environmental regulation, the amount and types of contaminants in the wastewater, and economics factors. Thus, water consumption in shale gas production is a serious matter, making water resource management an important operational and environmental issue [6]. The increase in the cost of freshwater and the disposal of generated wastewater, limitations in providing fresh water for fracturing, and the concerns about the negative environmental impact of shale gas wastewater have spurred the interest in identifying cost-effective technologies that can reduce the usage of fresh water and the discharge of wastewater in shale gas production [7].

- Low-level heating and the ability to operate with moderate temperature and pressure; this is a very crucial factor in shale exploration due to the availability of wasted energy from flaring which can be used as an energy source for MD.
- The ability to treat a highly concentrated feed, which is the case with water, generated from hydraulic fracturing.
- Compact size and modular nature: MD is characterised with a small footprint due to the high surface area to volume ratio of the membrane. It can also be easily adjusted to the required capacity by the removal or addition of MD modules, which allow for easy movement from one well pad to another. All of these factors make MD a candidate desalination technology in this study.

^{3}(48 billion ft

^{3}) of natural gas. The estimated rate of flare based on these figures can be set at 9600 m

^{3}per well per day, though variation might occur based on a particular well [18]. In general, flaring is found to be a waste of resources globally, resulting in serious environmental problems such as air, thermal, and light pollution [19]. Studies available in the literature for the utilisation of the co-produced gas that is flared after well completion is either focused on onsite atmospheric water harvesting [19] using the captured gas or using it as a source of heat [18] for heat-based regenerators. However, it needs to be mentioned that the work by Glazer et al. [18] was conducted based on analytical framework and not in the context of mathematical optimisation.

## 2. Problem Statement

- Number of freshwater sources (interruptible and uninterruptible);
- Set of well pads S to be fractured with a known volume of water required for fracturing and a maximum allowable contaminant concentration in the fracturing fluid;
- Total number of frac stages for each well pad;
- Earliest fracturing date for each well pad;
- Set of wastewater injection wells D;
- Volume of water required per stage;
- Minimum and maximum number of stages that can be fractured per day;
- Time horizon of interest;
- Network of regenerator;
- Gas storage facility;
- Historical stream data for the interruptible source,

- Optimal fracturing schedule of the well pads;
- Minimum freshwater intake and wastewater generation;
- Optimal operation and design conditions of the regenerator such as the number of membrane modules and the energy consumption;
- Feasibility of using captured flared gas as an energy source for the regenerator.

- The wells in each well pad are aggregated [4];
- Each well pad is connected to exactly one of the impoundment through piping [4];
- The number of fracturing stages that could be fractured per day is kept constant at 4 instead of allowing it to be variable between 2 and 4 stages [4];
- The flowback water from the fractured well pad is assumed to be 25% [10] of the initial water used;
- The capacity of the wastewater tank and fracturing tank on each well pad varies depending on its water requirement;
- The water treatment unit is located onsite and can be moved from one well pad to the other;
- The historical flowrate data for the interruptible water source from each calendar year is treated as a scenario, and each year is treated with equal probability [4].

## 3. Superstructure Representation

- The transfer of water from the wastewater tank to the regenerator R is conducted provided that there is a well pad to be fractured. Whenever the regenerator starts operation, it operates continuously until the wastewater tank becomes empty.
- The regenerator only operates if there is a well pad to be fractured, otherwise it remains inactive.
- The performance of the regenerator is specified based on a variable removal ratio.

## 4. Model Formulation

#### 4.1. Mass Balance Constraint

#### 4.1.1. Mass Balance around Well Pad s

_{s,t}between impoundment t and well pad s. The volume $v{i}_{t,n,y}$ of impoundment t at time point n for a given scenario year $y$ is described by Equation (8). The equation states that the volume of freshwater stored in the impoundment consists of the volume stored at the previous time point and the difference between the amount of water entering the impoundment through trucking and piping and the total water leaving the impoundment to well pads. ${f}_{t,n,y}^{pump}$ is a continuous variable which specifies the amount of water supplied through piping from an interruptible source to the corresponding impoundment at time point n and ${f}_{t,n,y}^{truck}$ is the amount of water supplied through trucking.

#### 4.1.2. Mass Balance around the Wastewater Storage Tank and the Fracturing Tank

#### 4.1.3. Mass Balance around the Regenerator

#### 4.2. Scheduling Model

- well pad scheduling,
- wastewater storage tank scheduling, and
- regenerator scheduling.

#### 4.2.1. Well Pad Scheduling

#### 4.2.2. Storage Tank Scheduling

#### 4.2.3. Regenerator Scheduling

#### 4.2.4. Tightening Constraint

#### 4.3. Membrane Distillation (MD) Model

#### 4.4. Additional Constraints

#### 4.5. Objective Function

- ${A}_{m}$: Total area of membranes (m
^{2}), defined by Equation (65). - ${f}_{t,n,y}^{pump}$: Water pumped from an interruptible source at time point n in scenario year y (m
^{3}), defined by Equation (8). - ${f}_{t,n,y}^{truck}$: Water trucked from an uninterruptible source at time point n in scenario year y (m
^{3}), defined by Equation (8). - ${f}_{s,n}^{fw}$: Freshwater required to fracture well pad s at time point n (m
^{3}), defined by Equation (2). - ${f}_{s,n}^{ww}$: Wastewater required to fracture well pad s at time point n (m
^{3}), defined by Equation (2). - ${f}_{n}^{reg}$: Total flowback water to be treated at time point n (m
^{3}), defined by Equations (15). - $f{f}^{MD}$: Total flowrate into MD (m
^{3}/day), defined by Equation (43). - ${i}_{t,n}^{fw}$: Total freshwater required from impoundment t for fracturing at time point n (m
^{3}), defined by Equation (7). - $Jw$: Water flux across the membrane (kg/(m
^{2}·s)), defined by Equation (46). - ${p}_{wf}^{vap}$: Water vapour pressure of the feed in MD (pa), defined by Equation (47).
- ${p}_{wp}^{vap}$: Water vapour pressure of the permeate in MD (pa), defined by Equation (48).
- $Q$: Heat required by the feed into MD (kJ/day), defined by Equation (55).
- $RR$: Regenerator removal ratio, defined by Equation (64).
- ${T}_{mf}$: Temperature of the feed on the membrane (K), defined by Equation (60).
- ${T}_{mp}$: Temperature of the permeate on the membrane (K), defined by Equation (60).
- ${T}_{m}$: Membrane average temperature (K), defined by Equation (51).
- ${T}_{bf}$: Temperature of the feed in the bulk (K), defined by Equation (55).
- ${T}_{bp}$: Temperature of permeate in the bulk (K), defined by Equation (51).
- $v{i}_{t,n,y}$: Volume of impoundment t at time point n in scenario year y (m
^{3}), defined by Equation (8). - ${\gamma}_{wf}$: Activity coefficient of water in the feed for membrane distillation, defined by Equation (49).

## 5. Case Study

^{3}. The results encourage the use of freshwater from interruptible sources, which is achieved through piping, thereby reducing the high cost and environmental issues that are associated with trucking. It should be noted that Scenario 1, which involved the use of freshwater only, does not take into account the extra cost associated with the water network such as the cost of treatment and storage. Thus, no comparison with regard to profit is conducted between the three scenarios, as shown in Table 3. The total revenue for both Scenarios 2 and 3 is found to be $261.24 million and the total profit for Scenario 3 is found to be 0.6% higher than the profit obtained in Scenario 2. This is mainly due to the fact that the costs of wastewater disposal and treatment cost are higher in Scenario 2 compared to Scenario 3.

^{3}of freshwater is achieved out of the total volume of 818,800 m

^{3}required for the 14 well pads. The saving is found to be 21.23% higher than those of a previous study in literature [4] that uses discrete time formulation. In Scenario 2, 96.7% of the flowback water is sent to the regenerator (R) and the remaining 3.3% is sent to the injection well to be disposed, while in Scenario 3, 99.4% of the flowback water is sent to the regenerator (R) while the remaining 0.6% is disposed.

^{3}m

^{2}. The permeate flux, thermal efficiency, thermal energy required, and the removal ratio are also given in Table 5. The model prediction of 0.013 kg/(m

^{2}s) fow Much Water Does U.S [9], as well as the experimental data of 0.0125 kg/(m

^{2}s) at 351 K reported by Yun et al. [20].

^{6}kJ (equivalent to 18,250 m

^{3}of natural gas) to 610 × 10

^{6}kJ (equivalent to 15,926 m

^{3}of natural gas). The value of energy consumed by the regenerator is 244 × 10

^{3}kJ/m

^{3}of distillate, which is found to be less than the range of thermal energy reported in the literature for membrane distillation. The range of thermal energy required by membrane distillation is between 120 and 1700 kWh/m

^{3}, equivalent to between 432 × 10

^{3}kJ/m

^{3}and 6.12 × 10

^{6}kJ/m

^{3}[23,33]. The average volume of flared gas per unit time based on literature [18] is used in this study and this is compared to the energy requirement of the regenerator. Gas that would otherwise be flared is used as the source of heat for the regenerator, thereby, making the heating cost in the objective function to become zero.

## 6. Conclusions and Recommendations for Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Sets | |

$D$ | {d | d = injection well} |

$N$ | {n | n = time point} |

$S$ | {s | s = well pad} |

$T$ | {t | t = an interruptible source and its corresponding impoundment} |

$T{P}_{s,t}$ | Match between well pad s and source t |

$Y$ | {y | y = historical river flowrate data year} |

Parameters | |

$A{T}_{s}$ | Availability time of well pad s, day |

$AOT$ | Annual operating time, h |

${B}_{wb}$ | Temperature independent base value for the permeability, kg/m^{2}.s.pa.K^{1.334} |

${C}_{p}$ | Specific heat capacity of the feed stream, KJ/(kg K) |

${C}^{\mathrm{max}}$ | Maximum inlet concentration in the treatment unit, mg/L t |

$C{f}^{feed}$ | Concentration of the feed water in MD, mg/L |

$C{S}^{\mathrm{max}}$ | Maximum inlet concentration in well pad s, mg/L |

$C{S}_{s}$ | Flowback water concentration in well pad s, mg/L |

$C{T}_{S}^{{S}^{\prime}}$ | Crew transition time between well pads, day |

$D{I}^{\mathrm{max}}$ | Maximum capacity of injection well d, m^{3} |

$D{S}_{s}$ | Distance from well pad s to a treatment facility, km |

$H$ | Time horizon of interest, day |

$LR$ | Liquid recovery for the regenerator |

$NY$ | Number of historical year, year |

$O{C}_{s}^{pump,fw}$ | Freshwater pumping cost, $/m^{3} |

$O{C}_{s}^{truck,fw}$ | Freshwater trucking cost, $/m^{3} |

$O{C}_{s}^{pump,ww}$ | Wastewater pumping cost, $/m^{3}/km |

$O{C}^{dis}$ | Cost of wastewater disposal, $/m^{3} |

$O{C}_{s}^{st,ww}$ | Cost of wastewater storage, $/m^{3} |

$O{C}^{ht}$ | Cost of heating, $/(10^{9} J) |

${P}_{s}$ | Gas production of well pad s, m^{3} |

$S{P}^{gas}$ | Unit price of natural gas, $/m^{3} |

$S{T}_{s}$ | Availability date of well pad s, day |

$T{R}_{s}$ | Time required fracturing well pad s, day |

${T}_{sf}$ | Temperature of feed water in the treatment unit, K |

$u$ | Ratio of recycled reject to raw feed |

${V}^{\mathrm{max}}$ | Maximum capacity of storage, m^{3} |

${V}^{\mathrm{min}}$ | Minimum capacity of storage, m^{3} |

$W{R}_{s}$ | Amount of water required to fracture well pad s, m^{3} |

${X}_{NaCl}$ | Molar concentration of NaCl in the feed |

$\delta $ | Membrane thickness, mm |

${\partial}_{ED}$ | Energy density, kJ/ m^{3} |

${\rho}_{water}$ | Density of water, kg/ m^{3} |

Binary variables | |

${w}_{s,n}$ | Defines the beginning of stimulating each well pad s at time point n |

$w{v}_{s,n}$ | Transfer of water from well pad $s$ to storage at time point n |

$w{r}_{n}$ | Transfer of water from storage to the regenerator at time point n |

Continuous variables | |

${A}_{m}$ | Required membrane area, m^{2} |

$AFC$ | Annualised fixed capital cost for the regenerator, $/year |

$AHC$ | Annualised heating cost for the regenerator, $/year |

$AOC$ | Annualised operating cost for the regenerator, $/year |

$Bw$ | Membrane permeability, kg/(m^{2} pa) |

${c}_{s,n}^{fbw}$ | Flowback water concentration of well pad s at time point n, mg/L |

${c}_{n}^{st,ww}$ | Contaminant concentration in the treatment unit at time point n, mg/L |

${c}_{n}^{perm}$ | Outlet concentration of contaminant from the regenerator at time point n, mg/L |

${c}_{n}^{con}$ | Contaminant concentration removed from the water by the regenerator at time point n, mg/L |

$c{p}^{perm}$ | Permeate concentration from MD, mg/L |

$c{r}^{con}$ | Retentate concentration from MD, mg/L |

$d{u}_{s,n}$ | Duration of well pad s at time point n, day |

${E}^{cons}$ | Thermal energy consumption per unit of water treated, kJ/m^{3} |

${E}_{n}^{total}$ | Thermal energy required at time point n, kJ |

${f}_{s,n}$ | Total water required to fracture well pad s at time point n, m^{3} |

${f}_{t,n,y}^{pump}$ | Water pumped from interruptible source at time point n in scenario year y, m^{3} |

${f}_{t,n,y}^{truck}$ | Water trucked from uninterruptible source at time point n in scenario year y, m^{3} |

${f}_{s,n}^{fw}$ | Freshwater required to fracture well pad s at time point n, m^{3} |

${f}_{s,n}^{ww}$ | Wastewater required to fracture well pad s at time point n, m^{3} |

${f}_{s,n}^{fbw}$ | Flowback water from well pad s at time point n, m^{3} |

${f}_{s,n}^{st}$ | Flowback water sent to storage tank from well pad s at time point n, m^{3} |

${f}_{s,n}^{dis}$ | Flowback water sent to disposal from well pad s at time point n, m^{3} |

${f}_{n}^{reg}$ | Total flowback water to be treated at time point n, m^{3} |

${f}_{n}^{perm}$ | Amount of water collected as permeate from the regenerator at time point n, m^{3} |

${f}_{n}^{con}$ | Amount of retentate from the regenerator at time point n, m^{3} |

$f{d}_{n}$ | Total water sent to disposal at time point n, m^{3} |

$f{f}_{d,n}^{dis}$ | Throughput of an injection well d at time point n, m^{3} |

$f{f}^{MD}$ | Total flowrate into MD, m^{3}/day |

$f{f}^{feed}$ | Total flowrate into MD, kg/day |

$f{f}^{perm}$ | Permeate flowrate from MD, kg/day |

$f{f}^{con}$ | Retentate flowrate from MD, kg/day |

${i}_{t,n}^{fw}$ | Total freshwater required from impoundment t for fracturing at time point n, m^{3} |

$Jw$ | Water flux across the membrane, kg/(m^{2}·s) |

${k}_{m}$ | Membrane thermal conductivity, kW/(m·K) |

${p}_{s,n}$ | Expected gas production of well pad s at time point n, m^{3} |

${p}_{wf}^{vap}$ | Water vapour pressure of the feed in MD, pa |

${p}_{wp}^{vap}$ | Water vapour pressure of the permeate in MD, pa |

$Q$ | Heat required by the feed into MD, kJ/day |

$RR$ | Regenerator removal ratio |

$t{s}_{s,n}$ | Start time of well pad s at time point n, day |

$t{f}_{s,n}$ | Finish time of well pad s at time point n, day |

$t{t}_{n}$ | Time that corresponds to time point n, day |

$t{r}_{n}$ | Start time of regeneration at time point n, day |

$tt{r}_{n}$ | Duration of regeneration at time point n, day |

$t{v}_{s,n}$ | Time at which water is transferred from well pad s to storage tank at time point n, day |

${T}_{mf}$ | Temperature of the feed on the membrane, K |

${T}_{mp}$ | Temperature of the permeate on the membrane, K |

${T}_{m}$ | Membrane average temperature, K |

${T}_{bf}$ | Temperature of the feed in the bulk, K |

${T}_{bp}$ | Temperature of permeate in the bulk, K |

$v{i}_{t,n,y}$ | Volume of impoundment t at time point n in scenario year y, m^{3} |

${v}_{n}^{ww}$ | Capacity of wastewater tank at time point n, m^{3} |

${v}_{s,n}^{ft}$ | Capacity of fracturing tank on well pad s at time point n, m^{3} |

${v}_{n}^{nat}$ | Volume of natural gas needed to produce the required energy at time point n, m^{3} |

${x}_{wf}$ | Mole fraction of water in the feed |

${\gamma}_{wf}$ | Activity coefficient of water in the feed for membrane distillation |

$\eta $ | Overall thermal efficiency of the regenerator |

$\Delta {H}_{vw}$ | Latent heat of vaporisation for water, kJ/kg |

$\theta $ | Temperature polarisation coefficient |

Superscript | |

con | Concentrate |

cons | Consumption |

dis | Disposal |

feed | Feed |

ft | Fracturing tank |

fw | Freshwater |

fbw | Flowback water |

gas | Gas |

ht | Heating |

max | Maximum |

min | Minimum |

nat | Natural gas |

pump | Pumping |

perm | Permeate |

reg | Regenerator |

st | Storage |

total | Total |

truck | Trucking |

vap | Vapour |

ww | Wastewater |

Subscript | |

bp | Permeate bulk |

bf | Feed bulk |

m | Membrane |

mp | Membrane permeate |

mf | Membrane feed |

wf | Feed water |

wp | Permeate water |

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**Table 1.**Well pad data [4].

Well Pads | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | S11 | S12 | S13 | S14 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Match with takepoints TP_{s,t} | t2 | t1 | t1 | t1 | t1 | t2 | t2 | t2 | t2 | t2 | t2 | t1 | t1 | t2 |

Earliest fracturing day | 1 | 1 | 1 | 1 | 1 | 39 | 1 | 273 | 273 | 273 | 396 | 379 | 379 | 1 |

No. of stages | 57 | 61 | 54 | 55 | 64 | 26 | 97 | 88 | 86 | 76 | 63 | 100 | 100 | 87 |

Parameter | Value |
---|---|

Crew transition time (day) | 5 |

Volume of fracturing fluid used per stage (m^{3}) | 950 |

Freshwater used (%) | 85 |

Storage cost ($/m^{3}) | 0.59 |

Freshwater trucking cost ($/m^{3}) | 29.35 |

Freshwater pumping cost ($/m^{3}) | 15.93 |

Disposal cost ($/m^{3}) | 134.18 |

Wastewater pumping cost ($/km/m^{3}) | 0.28 |

Wastewater storage cost ($/m^{3}) | 0.59 |

Temperature-independent base value of membrane permeability B_{WB}(kg/(m ^{2} s pa K^{1.334})) | 3.9 × 10^{−10} |

Membrane thickness (mm) | 0.65 |

Membrane life time (year) | 4 |

Annual operation time (h) | 8000 |

Heating cost ($/(10^{9} J)) | 5 |

Supply temperature (K) | 293 |

Specific heat capacity (kJ/(kg K)) | 4 |

Average TDS concentration of the feed into membrane distillation (MD) (mg/L) | 200,000 |

Scenario 1 | Scenario 2 | Scenario 3 | |
---|---|---|---|

Freshwater pumped (1000, m^{3}) | 818.80 | 640.30 | 635.30 |

Freshwater trucked (1000, m^{3}) | 0 | 0 | 0 |

Regenerated water (1000, m^{3}) | 0 | 178.53 | 183.53 |

Freshwater saved (%) | 0 | 21.80 | 22.42 |

Freshwater trucking cost ($1000) | 0 | 0 | 0 |

Freshwater pumping cost ($1000) | 13,043 | 10,019 | 10,012 |

Disposal cost ($1000) | 0 | 2119 | 1450 |

Wastewater pumping cost ($1000) | 0 | 10.01 | 11.65 |

Wastewater storage cost ($1000) | 0 | 1740 | 1747 |

Treatment cost ($1000) | 0 | 11,307 | 10,575 |

Revenue ($1000) | - | 261,240 | 261,240 |

Profit ($1000) | - | 235,860 | 237,340 |

Scenario 1 | Scenario 2 | Scenario 3 | |
---|---|---|---|

No. of constraints | 5698 | 9324 | 9418 |

No. of continuous variables | 3796 | 6023 | 6103 |

No. of binary variables | 210 | 435 | 435 |

Non-linear terms | - | 1458 | 1514 |

CPU time (s) | 0.11 | 51.82 | 458.59 |

No. of slots | 14 | 14 | 14 |

No. of time points | 15 | 15 | 15 |

Design Variables | Optimum Values |
---|---|

MD feed temperature (K) | 354 |

Required membrane area (m^{2}) | 186.67 × 10^{3} |

Thermal efficiency | 0.98 |

Thermal energy (kJ/day) | 610 × 10^{6} |

Permeate flux (kg/(m^{2} s)) | 0.013 |

Removal ratio (RR) (%) | 1 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Oke, D.; Majozi, T.; Mukherjee, R.; Sengupta, D.; El-Halwagi, M.M. Simultaneous Energy and Water Optimisation in Shale Exploration. *Processes* **2018**, *6*, 86.
https://doi.org/10.3390/pr6070086

**AMA Style**

Oke D, Majozi T, Mukherjee R, Sengupta D, El-Halwagi MM. Simultaneous Energy and Water Optimisation in Shale Exploration. *Processes*. 2018; 6(7):86.
https://doi.org/10.3390/pr6070086

**Chicago/Turabian Style**

Oke, Doris, Thokozani Majozi, Rajib Mukherjee, Debalina Sengupta, and Mahmoud M. El-Halwagi. 2018. "Simultaneous Energy and Water Optimisation in Shale Exploration" *Processes* 6, no. 7: 86.
https://doi.org/10.3390/pr6070086