pressure flow theory, aspen tech, 2005.pdf

Pressure Flow Theory 1

Pressure Flow Theory

@2005 AspenTech -AII Rights reserved. EB1017.04.05 Document1

2 Pressure Flow Theory

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Workshop The Pressure Flow Theory module introduces you to the 1U1derlying concepts necessary for developing your own dynamic simulations with Aspen HYSYS Dynamics. Sorne ofthe things you will leam :from this module are:

• The underlying assumptions of dynamic simulation with Aspen HYSYS

• How to analyze your Flowsheet to make appropriate pressme flow specifications

• Which pressure-flow specifications make sense

• How to troubleshoot the process Flowsheet for inconsistent pressure-flow specifications

Learning Objectives Once you have completed this section, you wil11U1derstand:

• The basic concepts of dynamic simulation in Aspen HYSYS

• Dynamic pressure flow specifications

• Process Flowsheets

Since pressure gradients are lhe dñving fon::e for flow In Allpen HYSYS, care should be taken to ensure that the preesure prollle of the flowsheet has been propaty speclfted.

Preuure Flow Thaory 3

Theoretical Foundations

The Pressure-Flow Solver: A Boundary Value Problem In tams of pressmes and flows, perhaps tb.e simplest way to view tbe pressure tlow solver in Aspen HYSYS Dynamics is to consider tb.e Flowsheet as a Boundary Value Problem.

lf you were to make pressure or tlow specifications on all tb.e boundary streams (feedslproduct s1reams in a Flowsheet), tb.m all tb.e intemal pressures and flows would be solved Sllllultaneously at eacb. integra1ion step by tbe pressure-flow solver. The intema1 stteam pressures and flow rates are calculated ftom tb.e pressure grad.ients in tb.e Flowsheet. Flow rates are detennined ftom:

1. Changes in vapour pressure nodes (vessels with hold-ups) witb.in tb.e Flowsheet system.

2. Resistance across valves

3. Conductance through equipment (coolers, heaters, heat exchangers)

Pressure Nodes All unit operatims (witb. hold-up) represent pressure nodes. Some unit operations may con.tribute to one or more nodes. For example:

• Heaters/Coolers witb. multiple zones

• Heat Exchanger- shell side/tube side

• Columns witb.multiple stages (ttays)

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4 Pruaure Flow Thaory

Thia concept i8 fundamental to perforrring dynamic simulation analyses with Aspen HYSYS.

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Fundamental Principie Vessel equipment has a fixed geometty and thus a fixed volume. Ma1hema1ically, this means that:

dV -O dt

(1)

Therefure, fura fixed volume, a pressure node (vessel pressure) is calculated as a fimctian ofthe vessel temperature and the vessel hold up.

In dynamic mode, the rate of cbange in vessel pressure is related to the rate of change of temperature (enthalpy) and the rate of change of material hold-up Qevel):

dP dt = fn(V, F, T)

where: Y= Fixed volume

F = Clumge in tlow (hold-up)

T= Temperature (dlange in en1halpy)

A volumetric flow balance around the vessel can be expressed as follows:

where: AY¡.= Volume change dueto pressure cbange

ll.VF = Volume change du.e to flow clumges

ll.Vr= Volume cbange du.e to temperature diange

The total volume change must always be zero.

(2)

(3)


Example

Consider the operation of a separator in dynamic mode that is initially at steady state with a level of 60%:

Figura 1

Remember:

------Assume fixed flow

Flowin

Fixed geometry 60%

------Assume fixed flow

In Steady State,

Flow into separator = Flow out of separator,

no accumulation.

But in Dynamics, if the separator feed flow increases with the product flow rates (vapour and liquid) remaining oochanged, the level (hold up ), temperature ( enthalpy) and pressure of the vessel must all change from the steady state condition.

Liquid Level lncreases

Sin ce

Liquid Flow In - Liquid Flow Out = Accumulation (hold-up ),

an increase in the feed liquid Flowrate with a constant liquid product Flowrate results in the liquid level (hold-up) increasing.

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Vessel Pressure lncreases

The vessel pressure would increase for two reasons.

l. Vapour Flow In - Vapour Flow Out= Accumulation.

An increase in the feed vapour Flowrate with a constant vapour product Flowrate results in the vapour (hold up) increasing. Because vapour is a compressible fluid, the accumulation ofvapour, occupying a smaller volume, will cause the vessel pressure to rise.

2. The increase in liquid level also causes the vapour hold-up to occupy a smaller volume within the vessel, causing the vessel pressure to rise.

Distributed and Lumped Models Most chemical engineering systems have thermal and component gradients in three dimensions (x, y, z) as well as in time. This is known as a distributed system. Thus, in the formulation of chemical engineering problem equations, we obtain a set of partial differential equations in the x, y, z and t domains.

Ifthe x, y, and z gradients are ignored, the system is lumped and all the physical properties are considered to be equal in space. In such, an analysis in which only the time gradients are considered, the chemical engineering system equations are represented by a set of ordinary differential equations (ODE's). This method saves calculation time and provides a solution that is reasonably close to the distributed model solution.

Aspen HYSYS uses lumped models for all unit operations. For instan.ce, in the development ofthe equations describing the separator, it is assumed that there are no thermal, pressure or concentration gradients present In other words, the temperature, pressure, and component gradients are the same throughout the entire separator.

Aspen HYSYS does take into account the static pressures in the fluid and vapour phases. This can result in a dP/dz effect in a vessel. However, Aspen HYSYS does not solve any partial differential equations.


Pressure-Flow Relationship for Valves In any Flowsheet, the valve unit operation describes the resistance to flow between two material streams by the Turbulent Flow equation:

where: P 1 = upstream pressure (pressure of stream 1)

P2 = downstream pressure (pressure of stream 2)

(4)

C., = the valve coefficient, Aspen HYSYS will calculate this value on request

Pressure-Flow Relationship for Other Operations More generally, flow rates in Aspen HYSYS Dynamics are related to delta P. Ali process equipment relates the flow between its feed and product streams with flow equations that are similar to the turbulent flow equation. Toe form ofthese equations is:

F = k J pAP

where: k = Conductance, which is a constant representing the reciprocal of resistance to flow

p = Stream bulk density

AP = Pressure gradient across the operation

(5)

Specifying Cv or k values, rather than a fixed delta P, across valves and process equipment provides for a more realistic simulation. By specifying these variables, the pressure drop through valves and process equipment can change with changes in flow, as would happen in an actual plant. This allows the Dynamic simulator to more accurately model the actual operating conditions of the plant

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The reelatance to flow lhrough valves and lhe conductance lhrough process equipment determlnee atream flow rales between nodes.

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Pressure/Flow Networks In Aspen HYSYS Dynamics the pressure/flow network is described in terms of nodes, resistance and canductance. Flow takes place in stteams from one node tD anotber. Thus there are two basic sets of equaticms 1hat define the pressure/flow network:

1. Equations tbat define 1he material balance at 1he nodes

2. Equations tbat define 1he flow- condw:tance and resistance tD flow

The simplest case is tbat of incompressible tlow with no accumulation at 1he nodes. In this situation, the tlow equations are a fimction ofthe pressure gradient ancl equipm.ent parameters su.ch as 1he pipe diameter and rougbness. The material balance at the nodes is simply that the accmnulation is zero.

In a more comprehensive dynamic simulatim the pressure tlow equations are more complex. They account for:

• Multi-phase tlow with 1he potential for slippage between pbases

• The rate of change of pressure at the nodes as a fimction of 1he equipment geom.etry, hold-op and mthalpy of the pbases

• Flow rates 1hat are determined not mly bypressure gradient but also by weir heigb.ts ( columns) and density differences

Simultaneous Solution Approach to Pressure Flow Balances Since pressures at nodes are a fimction of the flow rates in.to and out of the nodes ancl the flow rates through equipment are fimctions of the opstream ancl downstream pressures, the relatimships between pressure and Flowrate equations in Aspen HYSYS Dyna.mics are significantly coupled. To find a solution to 1he pressure-flow relationships in Aspen HYSYS Dynamics, a simultaneous solution of the Flowsheet is performed. Solving for 1he tlows ancl pressures requires the simultaneous solutim of a set of linear ancl nm-Jinear equations..


Figura 2

• Pl, P2, P3 etc. represent Pressme Nodes (Vessels with hold up)

• Fl, F2, F3 etc. represent streams with flow rates

Moreover, in order to epitomize computational effort, Aspen HYSYS Dynamics partitions the equations describing any unit operation into three classes:

• Pressme/flow relationships

• Energy relationships

• Compositional relationships

These groups of equations can then be integrated/solved with different frequencies. Typically, the pressme flow relationships will have the smallest step size and the composition relationships the largest.

The grouping of the equations also permits a different solution strategy to be applied to each group. In particular, it is possible to solve the pressme/flow relationships simultaneously across the entire Flowsheet while the other equations ( composition, enthalpy) are solved on a module-by-module basis.

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lfyou suspect tbat 1he P/F solver is failing because ofthe interaction wi1h the VLE correlation, then you can do one ofth.e following:

• Reduce tbe integration step size-1bis can be accessed ftom 1he mmu bar: SimulatiGD - lntegrator-Generd.

• Change tbe ftequmcy of integration steps pee step size (composition and cmthalpy). This can be accessed ftom the menu bar: Simulation -lntegrator- ExeeutiGD.

Figure 3

• lntegrator ~ lü IB) lnlegralion Conbo

ro A1.1lomatic (" Manyal

lnlegration Tim

Unils minutes Cur,entTime 6 07.3917 Acceleralion Tf End Time <Ñoo-Sto'T Real time _J

Dis la lnlerval. 000000 Real lime factor - 20.38

lnlegration Step·

Units seconds Ste Size r - floooo Minimum r_ Maximum ~ 000-

General E xecutii:m O ptii:ms Heat loss

Continue !! esel Display

• lntegr<1.tor l~J51~ Calculalion Execution Rales·~-------

E.xecution rates as per integrator time step:

Pressure Flow Solver Control and Logical Ops

Ener C.alculations Composilion and Flash Calculations Use these defaull periods for ali operalions

-=---General Execution Oplions Heat loss

! ... Conlinue .. j B,eset DisJ>lay

Preuure FlowThaory 11

Degrees of Freedom Analysis In Module 2 we in1roduced 1he cancept of dynamic specificaticms. The simultaneous solution of 1he pressure-flow rela1ionships wi1hin the Flowsheet requires the user to make a number of dynamic operating specificaticms.

• P = Pressure

• F=Flow

In 1bis Flowsheet, 1here are 7 variables in total that will define the system. These are:

Figure 4

-.... ---~ ~ ~~-=+--~--..~ Feed 1 1 VLV-100

l. Feedl (pressure, flowrate- 2 variables)

Vapo1..1r

V-100 Separator

Liquid

2. Productl (pressure, flowrate- 2 variables)

3. Product2 (pressure, flowrate- 2 variables) and

4. V-100 (Pressure - 1 variable)

VLV-101

VLV-102

Product 1

Product 2

In addition, there are 4 equations that define the pressure-fl.ow relationships in the Flowsheet. 1hese are:

l. VLV-100: Resistance to Flow equation FVLv-100 = fn(Cv, Pi, P2)

2. VLV-101: Resistance to Flow equation FVLv-101 = fn(Cv,P1, P2)

3. VLV-102: Resistance to Flow equation FVLv-102 = fn(Cv, Pi, P2)

4. V-100: Pressure Node Relationsbip dP/dt = fn(V,F,T)

With 7 variables and 4 equatians, the OOF = 7-4 = 3. Therefore, 3 P/F specifications need to be made te define 1his system.

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Understanding the Placement of P/F Specifications Why do some P/F specifications work while others don't?

Aspen HYSYS Dynamics is equipped with a Dynamics Assistant that analyzes the Flowsheet to identify problems. (We will discuss this simulation aid later in this module). However, with a greater understanding ofthe role ofthe P/F solver and the P/F calculations you will be better able to:

• Specify the process Flowsheet correctly

• Troubleshoot the process Flowsheet to identify P/F problems

• Use the power of Aspen HYSYS Dynamics to its full capabilities

Making Consistent Pressure or Flow Specifications

As mentioned earlier, Aspen HYSYS Dynamics users can select from a variety of pressure-flow specification combinations to solve the process Flowsheet. These include:

• Pressure specifications on material streams

• Flow specifications on material streams

• Fixed pressure drop specifications across equipment

• Pressure/Flow calculations for valves -resistance to flow (Cv)

• Conductance calculations (k) for process equipment

In the previous example, we had three Degrees ofFreedom, requiring that three specifications be made to define the system.

Preuure Flow Thaory 13

One Posslble Solutlon

Specify:

Figure 5

~ --....---,..¡ Feed VLV-100 1 P,F?

• Feed 1 Pressure

• Stream 1 Pressure

• VLV-100 DeltaP

Vapour

V-100 Separator

P?

Liquid

VLV-101

... Product 1 P, F?

Product VLV-102 2

P.F?

A11hough making 1hese 1hree specifications will satisfy the DOF analysis, the choice of specifications would not make sen.se. P,ee41, P1 and Pvi.v-100 are ali related by the following equation:

PFeedl -P¡ -APYLY-100 = O (6)

Specifying the Flowsheet in this manner would lead toan inconsistent solution. In filct, 1he Flowsheet would be unda--specified because one of1he specifications is redundan.t

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Anothar Posslble Solutlon

Specify:

Figure 6

_..,..,.._~ ~ ~~...+ ..... ~--.1 Feed 1 1 VLV-100

• Feedl Pressure

• Productl Pressure

• Product2 Pressure

Vapour

V-100

Separator

Liquid

VLV-101

VLV-102

Product 1

Product 2

Consider the same Flowsheet with pressure specifications made on all the boundary streams. This solutlon is consistmt because the pressure in the vessel is calculated by 1he hold-up equation. (The stream fl.ow rates were calculated using the turbulent equation or 1he resistance to fl.ow equation).

Guidelinea to Remember:

• One P/F apecificalion ahould be made on each boundary atream (feeda/producta)

• Maka preuure speclflcallons on boundary streams attached to process equlpment that UN reslstance to ftowlconductance 19latlonshlps.

• Aapen HYSYS Dynamica will uae the equipmant conductanca or Cv valua combinad with the preaaure of tha inlet and outlet atreama to detannina a Flowrate through the equlpment.

• lntemal ftow ratea will be calculatacl by prauura gradianta (reaiatanca to ftowlconductance equations) throughout the Flowaheet.


Summary of P/F Theory and Specifications: 1. The flow tbrough the plant, or operation, is driven by the pressure gradient.

2. P/F theory defines the relationship between flow and pressw-e.

3. The Aspen HYSYS P/F solver solves a set oflinear and non-linear equations simultaneously to determine the P/F relationship.

4. In order for the P/F solver to solve the Flowsheet, there must be a pressure gradient established over the entire Flowsheet.

5. The pressure gradient exists dueto a specified pressure flow relationship (ora speci:fied pressure drop) over all operations in the Flowsheet.

6. The P/F solver works by finding P from F, according to the P/F theory, or by solving the pressure node equation.

7. Following any flow path tbrough the Flowsheet, the user should be able to see the pressure gradient, or expect to see a pressure gradient established along the path. If the pressure gradient cannot be seen, an additional pressure specification may be needed.

8. If the user follows a flow path to the boundary of the Flowsheet, they should see that at such a location, a pressure gradient does not exist, nor can it be established. This means that a pressure ( or flow) specification is always needed on boundary streams.

Other Possible Solutions Ifwe modeled the same unit operation without using valves on all product streams, then we could not make P specifications on all boundary streams. Remember the lumped parameter model - the model assumes there are no pressure gradients inside the unit operation. Thus, if a pressure specification is made on the vapour product stream it is best not to make pressure specifications on the other unit operation streams. This can lead to an inconsistent solution because once one stream pressure is known they all become known, resulting in no pressure gradients in the unit operation.

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1& Pruaure Flow Thaory

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Figure 7

Feed 1

Vapour Product

Separator

Liquid Product

It is possible to have flow specifications on all unit operation streems as lcmg as the vessel pressure is controlled.

Figure 8

Feed 1

Separator

,--------w Vapour Product

Sep PC

.._ ______ .. Liquid Product


Exercise Modifying the Flowsheet in dynamics

Load the saved case FHT _ Dynl.hsc.

Modify the Flowsheet such that there is a Cooler downstream of the Sep Vap 1 stream.

1. Add a Cooler and move the P/F specifications.

2. Calculate the resistance to flow for the Cooler. Like the Valve, the flow through the Cooler is calculated as a fimction of delta P.

Using the conductance equation provides a more realistic simulation. Toe pressure drop across the Cooler can change with increases or decreases in flow. Ifthe Cooler pressure drop were fixed, then it would not vary. Because we specify the resistance to flow as the dynamic specification, then we can make a pressure specification as the boundary specification. Toe flow rates are calculated by the resistance equation.

Save your case as Exercise.hsc.

Save your case! 1

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pressure flow theory, aspen tech, 2005.pdf

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