In the manufacturing sector, sand casting services form a foundational pillar, enabling the production of complex metal components across industries such as automotive, aerospace, and machinery. As global emphasis on sustainability grows, sand casting services face increasing pressure to reduce their carbon footprint while maintaining efficiency and quality. I have developed a comprehensive methodology to model and analyze carbon emissions in sand casting services, focusing on process-level carbon sources. This approach not only quantifies emissions but also provides insights for optimizing sand casting services towards low-carbon operations. The core of this work lies in transforming traditional sand casting processes into a structured representation using process carbon sources, which can be systematically calculated and managed.
Sand casting services involve multiple stages, from mold preparation to pouring and finishing, each contributing to overall energy consumption and emissions. To address this, I propose a process carbon source model specifically tailored for sand casting services. This model categorizes emissions into five types: Material Consumption Carbon Source (MC), Non-Expectation Carbon Source (UC), Idle (Standby) Carbon Source (PC), Load Carbon Source (LC), and Energy Consumption Carbon Source (EC). Each type captures distinct aspects of sand casting services, such as resource usage, waste handling, and equipment operation. The mathematical formulations for these carbon sources are summarized in Table 1.
| No. | Process Carbon Source Type | Symbol | Description | Calculation Model |
|---|---|---|---|---|
| 1 | Material Consumption Carbon Source | MC | Carbon emissions from consuming materials during process execution in sand casting services. | $$C_{MC} = \sum_{i=1}^{n} \sum_{k=1}^{i} (ES_k \cdot U_i) \cdot E_e$$ |
| 2 | Non-Expectation Carbon Source | UC | Carbon emissions from handling pollutants during process execution in sand casting services. | $$C_{UC} = \sum_{i=1}^{n} \sum_{k=1}^{i} (ES_k \cdot Q_i \cdot \phi_i) \cdot E_e$$ |
| 3 | Idle (Standby) Carbon Source | PC | Carbon emissions from equipment in idle or standby mode in sand casting services. | $$C_{PC} = P_o \cdot t \cdot E_e$$ |
| 4 | Load Carbon Source | LC | Carbon emissions from equipment under load in sand casting services. | $$C_{LC} = (P_o + \mu \cdot W_e \cdot P_w) \cdot t \cdot E_e$$ |
| 5 | Energy Consumption Carbon Source | EC | Carbon emissions from non-electric energy consumption in sand casting services. | $$C_{EC} = \sum_{i=1}^{n} V_i \cdot E_i$$ |
In these models, $P_o$ represents idle power, $t$ is operating time, $E_e$ is the carbon emission factor for electricity, $\mu$ is power loss coefficient, $W_e$ is load weight, $U_i$ is material consumption, $ES_k$ is energy consumption at processing stage $k$, $V_i$ is energy consumption volume, $E_i$ is carbon emission factor for energy type $i$, $Q_i$ is pollutant quantity, and $\phi_i$ is treatment difficulty factor. These equations form the basis for quantifying emissions in sand casting services, allowing for detailed analysis at each process step. To further refine this, I identify eight characteristic elements that describe process carbon sources in sand casting services, as shown in Table 2.
| No. | Characteristic Element | Symbol | Meaning |
|---|---|---|---|
| 1 | Time Element | TCE | Duration of process states: idle time ($t_p$), load time ($t_l$), standby time ($t_s$). |
| 2 | Load Element | WCE | Magnitude of load during process execution in sand casting services. |
| 3 | Load Power Element | LCE | Power characteristics under load in sand casting services. |
| 4 | Idle Power Element | PCE | Power characteristics in idle mode in sand casting services. |
| 5 | Standby Element | SCE | Power characteristics in standby mode in sand casting services. |
| 6 | Non-Expectation Element | UCE | Characteristics of pollutants like waste gas, slag, sand, and water in sand casting services. |
| 7 | Material Element | MCE | Resources consumed: materials, water, air, oil, etc., in sand casting services. |
| 8 | Energy Element | ECE | Non-electric energy objects consumed in sand casting services. |
These elements help in mapping process activities to carbon emissions, enabling a granular view of sand casting services. However, to systematically apply this model, I need to represent sand casting processes in a structured way. This leads to the development of an event procedure node model for sand casting services. In sand casting services, each process activity triggers events that change the state of objects like materials, equipment, and products. An event procedure node (EPP) is defined as a collection of procedures that reflect information states under operational events. For the $i$-th node, it is expressed as:
$$EPP_i = \{ EP_i, P_i, WU_i, EO_i \}$$
where $EP_i = (ep_1, ep_2, \dots, ep_l)$ is the event set, $P_i = (p_{i1}, p_{i2}, \dots, p_{io})$ is the procedure set, $WU_i = (wu_{i1}, wu_{i2}, \dots, wu_{iu})$ is the work unit set (e.g., equipment), and $EO_i = (eo_{i1}, eo_{i2}, \dots, eo_{iv})$ is the resource object set (e.g., materials, energy, emissions). This model captures the hierarchical relationships in sand casting services, as illustrated in the node structure. Each procedure event $ep$ is described by:
$$ep = ep(eid, ea, esc, tm, es)$$
Here, $eid$ is event ID, $ea$ is attribute set, $esc$ is event type set, $tm$ is time stamp, and $es$ is state set. For a procedure $p_i$, it comprises event sets: $p_i = (pid, EP, pat, T)$, where $pid$ is ID, $EP$ is event set, $pat$ is attribute set, and $T$ is duration set. To manage event relationships in sand casting services, I define operators such as AND ($\land$), OR ($\lor$), NOT ($\neg$), SEQUENCE ($;$), and CONDITION ($WITHIN$). For example, a lifting procedure in sand casting services might be formalized as $p_{\text{lift}} = \{ ep_1; ep_2; ep_3; ep_4 WITHIN(ep_3, WTI); ep_5(ep_3 \lor ep_2) \}$, representing start, lift, transport, pause, and stop events with conditional logic.
To track state changes, I construct an event state matrix (ESM) for procedures in sand casting services. If a procedure has $n$ states (e.g., start, run, pause, interrupt, stop) and $m$ events, the state vector for event $ep_i$ is:
$$esm(ep_i) = [t(ep_i)_1, t(ep_i)_2, \dots, t(ep_i)_j, \dots, t(ep_i)_n]$$
where $t(ep_i)_j$ is the duration of state $j$ for event $ep_i$. The full ESM for procedure $p$ is:
$$ESM(p) =
\begin{bmatrix}
esm(ep_1) \\
esm(ep_2) \\
\vdots \\
esm(ep_i) \\
\vdots \\
esm(ep_m)
\end{bmatrix}
\times
\begin{bmatrix}
s(p)_1 & s(p)_2 & \cdots & s(p)_j & \cdots & s(p)_n
\end{bmatrix}^T
=
\begin{bmatrix}
t(ep_1)_1 & t(ep_1)_2 & \cdots & t(ep_1)_j & \cdots & t(ep_1)_n \\
t(ep_2)_1 & t(ep_2)_2 & \cdots & t(ep_2)_j & \cdots & t(ep_2)_n \\
\vdots & \vdots & \ddots & \vdots & \ddots & \vdots \\
t(ep_i)_1 & t(ep_i)_2 & \cdots & t(ep_i)_j & \cdots & t(ep_i)_n \\
\vdots & \vdots & \ddots & \vdots & \ddots & \vdots \\
t(ep_m)_1 & t(ep_m)_2 & \cdots & t(ep_m)_j & \cdots & t(ep_m)_n
\end{bmatrix}$$
This matrix allows analysis of event durations and total run time, e.g., $t_{ep_i} = \sum_{j=1}^{n} t(ep)_{ij}$. Integrating this with a directed graph model, I build a comprehensive sand casting process model for sand casting services. The model is defined as $GPM = (EPP, \{R, RPP, REP\}, \{PF, EP\}, \{IFP, WP_p, WE_p\})$, where $RPP$ and $REP$ are directed edge sets, $PF$ is the characteristic element set (TCE, WCE, LCE, PCE, SCE, UCE, MCE, ECE), $EP$ is the event set, and $WP_p$ and $WE_p$ are weights. The relationship matrix $R_{GPM}$ describes connections between event procedure nodes, with weights reflecting conditions. For instance, if $ifp = \emptyset$, $r_{EPP}(i,j) = 1$ if $EPP_i \to EPP_j$, else 0; if $ifp \neq \emptyset$, it depends on condition satisfaction.
Based on this model, I propose a method to construct process carbon sources for sand casting services using event procedure nodes. The steps are as follows:
- Establish Event Sets: For an event procedure node, define the event set $EP = (ep_1, ep_2, \dots, ep_m)$.
- Build Event State Matrix: Construct $ESM$ as per the above formulation.
- Construct Process Carbon Source Matrix (PCSM): Map events to carbon source types (PC, LC, MC, EC, UC). The matrix is:
$$PCSM =
\begin{bmatrix}
r_{pcs11} & r_{pcs12} & r_{pcs13} & r_{pcs14} & r_{pcs15} \\
r_{pcs21} & r_{pcs22} & r_{pcs23} & r_{pcs24} & r_{pcs25} \\
\vdots & \vdots & \vdots & \vdots & \vdots \\
r_{pcs i1} & r_{pcs i2} & r_{pcs i3} & r_{pcs i4} & r_{pcs i5} \\
\vdots & \vdots & \vdots & \vdots & \vdots \\
r_{pcs m1} & r_{pcs m2} & r_{pcs m3} & r_{pcs m4} & r_{pcs m5}
\end{bmatrix}$$
where $r_{pcs i j} = 1$ if event $i$ involves carbon source type $j$, else 0. - Transform to Process Carbon Source Expression: The carbon source set for the node is $EP_{pcs} = PCSM \cdot [PCS]^T$, where $[PCS] = [PC, LC, MC, EC, UC]^T$. For event $i$, it becomes:
$$ep_{pcs i} \to \{ r_{pcs i1} \cdot PC, r_{pcs i2} \cdot LC, r_{pcs i3} \cdot MC, r_{pcs i4} \cdot EC, r_{pcs i5} \cdot UC \}$$
The node’s carbon emission form is:
$$EP_{pcs} \to \left\{ \left[ \sum_{i=1}^{m} r_{pcs i1} \right] \cdot PC, \left[ \sum_{i=1}^{m} r_{pcs i2} \right] \cdot LC, \left[ \sum_{i=1}^{m} r_{pcs i3} \right] \cdot MC, \left[ \sum_{i=1}^{m} r_{pcs i4} \right] \cdot EC, \left[ \sum_{i=1}^{m} r_{pcs i5} \right] \cdot UC \right\}$$
Carbon emissions for node $j$ with $m$ events are calculated as:
$$C_{EPP_j} = [C_{ep1}, C_{ep2}, \dots, C_{epi}, \dots, C_{epm}]^T = C_{PCSM} \gamma EP_{pcs} = C_{PCSM} \gamma (PCSM \cdot [PCS])$$
where $C_{PCSM}$ is the relationship matrix between events and characteristic elements, and $\gamma$ denotes mapping and summation. For event $i$:
$$C_{ep_i} = C_{PCSM_i} \gamma EP_{pcs_i} = C_{PCSM_i} \gamma (PCSM_i \cdot [PCS])$$
This enables precise emission tracking in sand casting services.
To illustrate this methodology, I apply it to a sand molding production line in sand casting services. The process includes steps like sand mixing, transportation, molding, and finishing. For the mixing event procedure node (EPP1), events are feeding ($ep_1$), mixing ($ep_2$), pause ($ep_3$), and discharge ($ep_4$). The event state matrix is:
$$ESM(EP) =
\begin{bmatrix}
0.01 & 0.14 & 0.08 & 0 & 0.01 \\
0.08 & 0.50 & 0.07 & 0 & 0.01 \\
0 & 0.07 & 0 & 0 & 0 \\
0 & 0.05 & 0 & 0 & 0.01
\end{bmatrix}$$
with states: start, run, pause, interrupt, stop. The PCSM is derived as:
$$PCSM =
\begin{bmatrix}
1 & 1 & 1 & 0 & 1 \\
1 & 1 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 1
\end{bmatrix}$$
Thus, the node’s carbon source expression is $EP_{pcs1} \to \{ [4] \cdot PC, [3] \cdot LC, [1] \cdot MC, [0] \cdot EC, [3] \cdot UC \}$. Using operational data from sand casting services—idle power 0.4 kW, load power 0.6 kW/t, material consumption 2 t, etc.—I compute emissions. The characteristic element matrix $C_{PCSM}$ is populated with times, loads, and powers. For example, for $ep_1$: $t_{p1}=0.01$ h, $t_{l1}=0.14$ h, $t_{s1}=0.09$ h, load 2 t, idle power 1 kW, load power 0.1 kW/t, standby power 0.1 kW, non-expectation 0.0001 t. Calculations yield:
$$C_{EPP1} =
\begin{bmatrix}
C_{ep1} \\
C_{ep2} \\
C_{ep3} \\
C_{ep4}
\end{bmatrix}
=
\begin{bmatrix}
31.68105 \\
3.57412 \\
0.11298 \\
0.91909
\end{bmatrix} \text{ kg CO}_2$$
Breaking down by carbon source: $C_{PC} = 1.90856$ kg CO$_2$, $C_{LC} = 2.59718$ kg CO$_2$, $C_{MC} = 31.4358$ kg CO$_2$, $C_{EC} = 0$ kg CO$_2$, $C_{UC} = 0.1668$ kg CO$_2$. This analysis highlights that material consumption dominates emissions in this sand casting service, guiding reduction strategies.
The event state matrix also facilitates aggregation of multiple events in sand casting services, which is crucial for optimizing complex procedures. For two procedures $p_a$ and $p_b$ with event sets $EP_a$ and $EP_b$, the aggregated ESM is $ESM_{EPP} = [ESM^*_a; ESM^*_b]$, where $ESM^*$ includes extended attributes like event type $esc$, time stamp $tm$, and run time $t_{ep}$. The matrix can be sorted by event type and time, then simplified by merging similar states. For instance, if procedures share $k$ similar events in a type, the aggregated matrix is:
$$EPM^{i}_{p_a+p_b} = [EPM^{i}_{p_a}(k) + EPM^{i}_{p_b}(k)] \oplus [EPM^{i}_{p_a}(u-k) \oplus EPM^{i}_{p_b}(v-k)]$$
where $\oplus$ denotes concatenation. This approach reduces complexity and enhances efficiency in modeling sand casting services. In practice, sand casting services often involve repetitive events, such as multiple transport or heating cycles, and aggregation helps in consolidating carbon emission calculations for better management.
In conclusion, this methodology provides a robust framework for carbon emission modeling in sand casting services. By leveraging event procedure nodes and process carbon sources, sand casting services can transition from traditional process descriptions to structured emission analysis. The use of matrices and formulas enables precise quantification, while aggregation techniques support scalability. For sand casting services aiming to achieve low-carbon operations, this approach offers actionable insights, such as identifying high-emission events like material consumption or idle states. Future work could integrate real-time monitoring and machine learning to dynamically optimize sand casting services, further reducing their environmental impact. As the demand for sustainable manufacturing grows, such tools will be essential for sand casting services to remain competitive and compliant with global carbon reduction targets.