In this section, we present the detailed converging process for the solution point B using the proposed tailored global optimization algorithm. As can be seen in Figure D1, the proposed tailored global optimization algorithm takes four outer loop iterations to converge. Apart from the first outer loop iteration that converges in one inner loop iteration, all the remaining outer loop iterations take two inner loop iterations to converge. In the last outer loop iteration, the reformulated linear objective function F(q) converges to 0, indicating the convergence of this tailored global optimization algorithm. The total computational time is 38,973 CPU seconds, and the computational time of each inner loop iteration ranges from 4,126 to 7,973 CPU seconds.
Figure D1. Converging process for the solution of point B.
3.9 Nomenclature
Sets
G Set of power plants indexed by g I Set of shale sites indexed by i M Set of processes indexed by m N Set of number of wells indexed by n NS Set of industrial sectors indexed by ns
O Set of onsite treatment technologies indexed by o (o1: MSF; o2: MED; o3: RO)
P Set of processing plants indexed by p
R Set of capacity levels for gas pipelines indexed by r T Set of time periods indexed by t
Subsets
e
( )
I i
Subset of existing shale sites indexed by in
( )
I i
Subset of potential shale sites indexed by in
( )
P p
Subset of potential processing plants to be constructed indexed by p'( )
T t Subset of time periods when wells are drilled indexed by t’
Parameters
, ' ns ns
aio Technical coefficient connecting industrial sector ns and ns’ in the EIO table
,
cns m Upstream technical coefficient linking industrial sector ns and process m
cc
i Correlation coefficient for shale gas production and wastewater production of a shale well at shale site icca
t Capacity for wastewater treatment at CWT facility in time period t,
dglg t Minimum demand of electricity at CCGT power plant g in time period t
,
dgupg t Maximum demand of electricity at CCGT power plant g in time period t
dr Discount rate per time period
pro
em Environmental impact factors of basic process m
IO
ens Environmental impact factors of industrial sector ns
fac Unit acquisition cost of freshwater _ i m,
inv cwt Amount of input from process m for treating unit amount of wastewater from shale site i at CWT facilities
_ o m,
inv onsite Amount of input from process m for treating unit amount of wastewater with onsite treatment technology o
_ i m,
inv drill Amount of input from process m for drilling a shale well at shale site i.
_ i m,
inv prod Amount of input from process m for producing unit amount of shale gas at shale site i
_ p m,
inv proc Amount of input from process m for processing unit amount of raw shale gas at processing plant p
_
minv trans
Amount of input from process m for transporting unit amount of shale gas for unit distance_ g m,
inv power Amount of input from process m for consuming unit amount of shale gas to generate electricity at CCGT power plant g
lc
i NGL composition in shale gas at shale site ilo
o Recovery factor for treating wastewater of onsite treatment technology o,
lpgp g Distance from processing plant p to power plant g lsp,i p Distance from shale site i to processing plant p
mc
i Methane composition in shale gas at shale site imn
i Maximum number of wells that can be drilled at shale site i per time periodne
i Number of existing shale wells drilled at shale site iocl
o Minimum treatment capacity for onsite treatment technology oocu
o Maximum treatment capacity for onsite treatment technology o pcep Capacity of existing processing plant ppci Chemical engineering plant cost index for processing plant
pcl Minimum capacity of processing plants pcup Maximum capacity of processing plants
pef NGL recovery efficiency at processing plants
pl
t Average unit price of NGLs in time period t prc Reference capacity of processing plantpri Reference capital investment of processing plant
price
m Unit price input from process mrf
o Ratio of freshwater to wastewater required for blending after treatment of onsite treatment technology orpci Chemical engineering plant cost index for processing plant of the reference year
sdc,it Unit cost for shale well drilling and completion at shale site i in time period t
sfp Size factor of processing plants
spc,it Unit cost for shale gas production at shale site i in time period t
,
sppi t Shale gas production of a shale well with age t at shale site i
tmn
i Maximum number of wells that can be drilled at shale site i over the planning horizontprc
r Reference capacity of gas pipeline with capacity level rtpri
r Reference capital investment of gas pipeline with capacity level rue Amount of electricity generated per unit natural gas input
vc Unit cost for wastewater treatment at CWT facility
veg Unit cost for electricity generation from natural gas at CCGT power plant g
vo
o Unit cost for wastewater treatment of onsite treatment technology ovpp Unit processing cost at processing plant p
vtp Unit transportation cost of shale gas via pipelines
wd
i Average drilling water usage for each well at shale site iwrd
i Recovery ratio of water for drilling process at shale site iwrf
i Recovery ratio of water for hydraulic fracturing process at shale site iNonnegative Continuous variables
,
FDWi t Freshwater demand of shale site i in time period t
,
FWi t Amount of freshwater acquired from water source to shale site i in time period t
,
GEg t Amount of electricity generated at power plant g in time period t
,
NNi t Number of wells drilled at shale site i in time period t
P
ns Total output of industrial sector ns in the EIO systems PCp Capacity of processing plant pQ
m Total net input of process m from all activities in the process systems, water m
Q Total input of process m associated with water management activities
, drill m
Q Total input of process m regarding drilling activities
, prod m
Q Total input of process m associated with shale gas production activities
, proc m
Q Total input of process m associated with shale gas processing activities
, trans m
Q Total input of process m associated with gas transportation activities
, power m
Q Total input of process m associated with electricity generation activities
,
SPi t Shale gas production rate at shale site i in time period t
, , i p t
STP Amount of shale gas transported from shale site i to processing plant p in time period t
, , p g t
STPG Amount of sales gas transported from processing plant p to CCGT power plant g in time period t
,
SPLp t Amount of NGLs produced at processing plant p in time period t
,
SPMp t Amount of methane produced at processing plant p in time period t
, , i p r
TCP Capacity of gas pipeline with capacity level r between shale site i and processing plant p
, , p g r
TCPG Capacity of gas pipeline with capacity level r between processing plant p and CCGT power plant g
UP
ns Upstream input from industrial sector ns to the process systems,
WPi t Wastewater production rate at shale site i in time period t
,
WTCi t Amount of wastewater transported from shale site i to CWT facilities in time period t
, , i o t
WTO Amount of wastewater treated by onsite treatment technology o at shale site i in time period t
Binary variables
, , i p r
XP 0-1 variable. Equal to 1 if gathering pipeline with capacity level r is installed to transport shale gas from shale site i to processing plant p
, , p g r
XPG 0-1 variable. Equal to 1 if gathering pipeline with capacity level r is installed to transport sales gas from processing plant p to CCGT power plant g
, , i n t
YD 0-1 variable. Equal to 1 if n shale wells at shale site i are drilled in time period t
YO,io 0-1 variable. Equal to 1 if onsite treatment technology o is applied at shale site i
YPp 0-1 variable. Equal to 1 if processing plant p is constructed Equation Chapter (Next) Section 1
CHAPTER 4
DYNAMIC MATERIAL FLOW ANALYSIS-BASED LIFE CYCLE OPTIMIZATION
4.1 Introduction
Sustainability has received increasing research attention in design and operations of energy systems. Thus, tools and indicators are developed for assessing and benchmarking sustainability performance of different systems [159]. Among these tools, LCA is one of the most widely applied methods to systematically quantify the environmental impacts of a product from a life cycle perspective [138, 160]. As an analysis tool, LCA is designed to evaluate the environmental impacts based on a certain or a collection of design alternatives. However, the sustainable design and operations of energy systems generally involve substantially large number of design alternatives [161]. Using LCA approach to manually analyze each alternative system can be tedious or even infeasible. Therefore, it is imperative to develop an optimization framework that can automatically identify sustainable alternatives in energy systems design and operations.
To tackle this challenge, the LCO methodology was developed, which integrates LCA with multiobjective optimization technique into a holistic optimization model [151, 162]. In an LCO model, both the design and operational decisions are connected to their corresponding environmental consequences through mathematical constraints. By solving the resulting LCO problem, we can obtain the optimal design and operational decisions considering both economic and environmental performances [155, 163].
Despite the successful application of LCO in various energy systems, the framework
itself has its shortcomings inherited from LCA approaches [129, 161]. First, LCA is normally designed for general product systems based on simplified models, and the corresponding inventory data are estimated based on average values [17, 79-81, 84, 86, 95, 118]. This leads to the loss of precision and lack of customization in the investigation of specific systems. Additionally, it is challenging to depict the material flow relationships in systems with complex recycling flows using LCA. Consequently, the benefits of recycling for improving sustainability in certain complex energy systems may not be properly addressed with traditional LCO. More importantly, LCA might not holistically recognize resource depletion as a potential sustainability concern [164-166].
By solely evaluating the environmental impacts, the optimal design obtained in traditional LCO could not be truly sustainable, especially in terms of resource efficiency. To tackle these research challenges, it is necessary to develop a novel LCO framework that can effectively overcome the shortcomings of LCA by integrating with dynamic material flow (MFA) analysis.
In this study, we propose a dynamic MFA-based LCO framework in pursuit of sustainable design and operations of energy systems. MFA is considered as a complementary tool to LCA that can capture flows and stocks of materials with high-fidelity models and sufficient details for specific complex systems [167-170].
Moreover, dynamic MFA enables establishment of life cycle material flow profiles and investigation of detailed environmental mechanisms for more sustainable decisions [171-174]. Therefore, with the integration of dynamic MFA and LCA, we expect to overcome their shortcomings and contribute to better sustainable designs of energy systems [175-177]. Specifically, in this dynamic MFA-based LCO framework, various
input, output, and recycling material/energy flows of processes are captured with precision throughout their life time. Meanwhile, by introducing an extra dimension of resource sustainability in addition to economic and environmental performances, we aim to provide a more comprehensive evaluation of sustainable system designs. Based on the functional unit, we define three fractional objective functions, corresponding to the economic, environmental, and resource sustainability performances, respectively.
The resulting optimization problem is formulated as a multiobjective mixed-integer linear fractional programing (MILFP) problem that is computationally challenging due to the fractional objective functions. Thus, we further adopt an efficient parametric algorithm to facilitate the solution [107]. To illustrate the applicability of proposed modeling framework and solution algorithm, we consider an application to a Marcellus shale gas supply chain. In this application, major design and operational decisions, including shale pad development, well drilling schedule, water treatment and recycling, pipeline network design, allocation and capacity selection of processing plants, production planning, transportation arrangement, and more, are fully addressed. The corresponding key material flows, such as concrete, steel, barite, bentonite, organic/inorganic chemical additives, proppant, water diesel, electricity, heat, steam, and more, are taken into account and incorporated into the MFA-based LCO model.
Through a detailed result analysis, a Pareto optimal solution balancing economic, environmental, and resource performances can be recognized, and the corresponding optimal material flow profiles are obtained.