Logical Operations

Recycle

Principle of Operation

At each iteration k, the Recycle block reads the inlet stream properties (coming from downstream) and compares them against the outlet stream properties (going upstream). The convergence errors are defined as:

\[ \varepsilon_{T}^{(k)}=T_{\mathrm{in}}^{(k)}-T_{\mathrm{out}}^{(k)} \]

\[ \varepsilon_{P}^{(k)}=P_{\mathrm{in}}^{(k)}-P_{\mathrm{out}}^{(k)} \]

\[ \varepsilon_{W}^{(k)}=\sum_{i=1}^{N_{c}}\left|\dot{m}_{i,\mathrm{in}}^{(k)}-\dot{m}_{i,\mathrm{out}}^{(k)}\right| \]

where \(T\) is temperature, \(P\) is pressure, \(m_{i}\) is the mass flow rate of component i, and \(N_{c}\) is the number of components.

Convergence is achieved when all errors fall below their respective tolerances simultaneously:

\[ \left|\varepsilon_{T}^{(k)}\right|\leq\delta_{T}\quad\wedge\quad\left|\varepsilon_{P}^{(k)}\right|\leq\delta_{P}\quad\wedge\quad\left|\varepsilon_{W}^{(k)}\right|\leq\delta_{W} \]

Smoothing (Non-Legacy Mode)

When Legacy Mode is disabled, the Recycle block applies a smoothing factor alpha to dampen oscillations:

\[ T_{\mathrm{out}}^{(k+1)}=\alpha\,T_{\mathrm{in}}^{(k)}+(1-\alpha)\,T_{\mathrm{in}}^{(k-1)} \]

\[ P_{\mathrm{out}}^{(k+1)}=\alpha\,P_{\mathrm{in}}^{(k)}+(1-\alpha)\,P_{\mathrm{in}}^{(k-1)} \]

\[ \dot{m}_{i,\mathrm{out}}^{(k+1)}=\alpha\,\dot{m}_{i,\mathrm{in}}^{(k)}+(1-\alpha)\,\dot{m}_{i,\mathrm{out}}^{(k)} \]

where alpha is in (0, 1] (default alpha = 1.0, equivalent to direct substitution).

Parameters

Parameter	Symbol	Default	Unit
Temperature Tolerance	\(\delta_{T}\)	0.1	K
Pressure Tolerance	\(\delta_{P}\)	0.1	Pa
Mass Flow Tolerance	\(\delta_{W}\)	0.01	kg/s
Maximum Iterations	\(N_{\max}\)	50	–
Smoothing Factor	\(\alpha\)	1.0	–

Recycle Block Parameters

Parameter	Default	Description
Acceleration Frequency	4	Apply acceleration every \(n\) iterations
Acceleration Delay	2	Initial iterations before acceleration begins
\(q_{\max}\)	0	Upper bound for the Wegstein \(q\) factor
\(q_{\min}\)	\(-20\)	Lower bound for the Wegstein \(q\) factor

Wegstein Acceleration Parameters

Property	Description
Temperature Error	$\left
Pressure Error	$\left
Mass Flow Error	$\left
Iterations Taken	Number of iterations to converge

Recycle Block Output Properties

Energy Recycle

Overview

The Energy Recycle logical block is analogous to the Recycle block but operates on energy streams instead of material streams. It is used when an energy stream from a downstream unit must feed back to an upstream unit.

Principle of Operation

The block compares the energy flow of the inlet and outlet energy streams. The convergence error is:

\[ \varepsilon_{E}^{(k)}=\dot{E}_{\mathrm{in}}^{(k)}-\dot{E}_{\mathrm{out}}^{(k-1)} \]

Convergence is achieved when:

\[ \left|\varepsilon_{E}^{(k)}\right|\leq\delta_{E} \]

Wegstein Acceleration

The Wegstein acceleration method is available and applied identically to the material Recycle case, but operating on the single energy flow variable:

\[ s_{E}^{(k)}=\frac{\varepsilon_{E}^{(k)}-\varepsilon_{E}^{(k-1)}}{\dot{E}^{(k)}-\dot{E}^{(k-1)}} \]

\[ q_{E}^{(k)}=\frac{s_{E}^{(k)}}{s_{E}^{(k)}-1} \]

\[ \dot{E}_{\mathrm{out}}^{(k+1)}=\varepsilon_{E}^{(k)}\left(1-q_{E}^{(k)}\right)+\dot{E}^{(k)}\,q_{E}^{(k)} \]

The same bounding conditions on \(q_{E}\) and the delay/frequency parameters apply as in the material Recycle block.

Parameters

Parameter	Symbol	Default	Unit
Energy Tolerance	\(\delta_{E}\)	0.1	kW
Maximum Iterations	\(N_{\max}\)	100	–

Energy Recycle Block Parameters

Adjust

Overview

The Adjust logical block implements a feedback controller that manipulates a variable in one object to drive a controlled variable in another object to a desired set point. It is conceptually equivalent to a single-loop controller and can be used, for example, to adjust a heater duty until a stream reaches a target temperature.

Definitions

The Adjust block involves three objects:

Role	Description
Manipulated Variable (MV)	The variable that the solver modifies (e.g., heat duty)
Controlled Variable (CV)	The variable driven toward the target (e.g., outlet temperature)
Reference Variable (RV)	Optional. When referenced, the target becomes \(\mathrm{RV}+\Delta\)

Adjust Block Object Roles

Objective

The solver seeks to satisfy CV = Set Point, where the set point is defined as:

\[ \mathrm{Set\;Point}=\begin{cases} V_{\mathrm{adj}} & \text{if no reference object is used}\\ \mathrm{RV}+V_{\mathrm{adj}} & \text{if a reference object is used} \end{cases} \]

and \(V_{a}dj\) is the user-specified adjust value.

Parameters

Parameter	Default	Description
Adjust Value (\(V_{\mathrm{adj}}\))	1.0	Target value or offset from reference
Step Size	0.1	Perturbation step for numerical derivatives
Tolerance	0.0001	Convergence tolerance for $\left
Maximum Iterations	10	Maximum solver iterations
Minimum Value	–	Optional lower bound for the manipulated variable
Maximum Value	–	Optional upper bound for the manipulated variable

Adjust Block Parameters

Simultaneous Adjust Mode

When enabled, multiple Adjust blocks are solved simultaneously as a system of equations rather than sequentially. This is recommended when the manipulated variables of different Adjust blocks interact with each other (e.g., two controllers affecting the same unit operation).

Specification (Spec)

Overview

The Specification (Spec) logical block establishes an algebraic relationship between a source variable and a target variable using a user-defined mathematical expression. Unlike the Adjust block (which iterates), the Spec block directly computes and assigns the target variable value from the expression.

Expression Evaluation

The user defines an expression f(X, Y) where X is the current value of the source variable (read-only) and Y is the current value of the target variable (before assignment). The target variable is then set to:

\[ Y_{\mathrm{new}}=f(X,Y) \]

The expression supports all standard mathematical functions from System.Math, including Abs, Sqrt, Log, Log10, Exp, Sin, Cos, Tan, Pow, Min, Max, among others.

Example Expressions

Expression	Meaning
X	Target equals source directly
X ``*`` 1.05	Target is 5% higher than source
X + 10	Target is source plus 10 (in display units)
Sqrt(X ``*`` Y)	Target is the geometric mean of source and previous target
Max(X, 300)	Target is at least 300

Example Spec Expressions

Value Clamping

Optional minimum and maximum bounds can be specified. When bounds are active, the assigned value is clamped:

\[ Y_{\mathrm{new}}=\begin{cases} Y_{\min} & \text{if }f(X,Y)<Y_{\min}\\ Y_{\max} & \text{if }f(X,Y)>Y_{\max}\\ f(X,Y) & \text{otherwise} \end{cases} \]

Parameters

Parameter	Description
Source Object / Property	The object and property to read as \(X\)
Target Object / Property	The object and property to write as \(Y\)
Expression	Mathematical expression \(f(X,Y)\)
Minimum Value (\(Y_{\min}\))	Optional lower bound for the target
Maximum Value (\(Y_{\max}\))	Optional upper bound for the target

Spec Block Parameters

Information Carrier

Overview

The Information Carrier logical block transfers a property value from a source object to up to three target objects. It is used to propagate information across the flowsheet without requiring a physical stream connection, enabling non-standard data flows between unit operations.

Configuration

Parameter	Description
Source Object / Property	The object and property to read
Target Object 1 / Property	First target: the object and property to write
Target Object 2 / Property	Second target (optional)
Target Object 3 / Property	Third target (optional)

Information Carrier Block Configuration

Behavior

The Information Carrier reads the specified property from the source object and writes it directly to the corresponding property of each configured target object. No mathematical transformation is applied. This block supports both steady-state and dynamic simulation modes.

Summary

Block	Stream Type	Purpose	Dynamic Support
Recycle	Material	Converge material recycle loops	Yes
Energy Recycle	Energy	Converge energy recycle loops	Yes
Adjust	–	Feedback control (MV \(\to\) CV)	No
Spec	–	Algebraic variable assignment	Yes
Information Carrier	–	Property propagation to multiple targets	Yes

DWSIM Logical Blocks Summary