Final Report for Chevron

Vapor Recovery Unit Project

Submitted to:

Wesley Brubaker, Project Engineer

Chevron

Houston, Texas

Prepared by:

Leslie Esparza

Krisha Mehta

Sean Swearingen, Team Leader

Mechanical Engineering Design Projects Program

The University of Texas at Austin

Austin, Texas

Fall 2009

Final Report for Chevron

Vapor Recovery Unit Project

Submitted to:

Wesley Brubaker, Project Engineer

Chevron

Houston, Texas

Prepared by:

Leslie Esparza

Krisha Mehta

Sean Swearingen, Team Leader

Mechanical Engineering Design Projects Program

The University of Texas at Austin

Austin, Texas

Fall 2009

i

ACKNOWLEDGMENTS

Over the course of semester we received much guidance and technical advice from both the

engineers at Chevron and the faculty at the University of Texas at Austin. We would like to

extend our thanks to those who helped make our project possible and call attention to their

contributions.

First, we would like to thank Wesley Brubaker, Chris Kurr, and Zachary Schneider at

Chevron for sponsoring our senior design project and giving us the key information and

counseling necessary to execute our project.

We would also like to think Dr. Crawford for heading the UT-SDP program which gives us

and our classmates the opportunity to work on real world projects with major companies, such as

Chevron.

Dr. Kiehne, our Mechanical Engineering faculty advisor, provided us with valuable feedback

on our project. Dr. Bommer, from UT’s Petroleum Engineering department, was also kind

enough to review our vapor recovery unit design and give us insight into critical problems that

occur in the field during oil and gas production. Dr. Krueger, our graphics advisor, reviewed our

reports helped us to improve their professionalism.

John Montgomery, our teaching assistant, played a central role in our project’s

development and provided us with advice and coaching throughout the semester.

iii

TABLE OF CONTENTS

Acknowledgments................................................................................................................ i Table of Contents ............................................................................................................... iii

List of Figures ......................................................................................................................v

List of Tables .................................................................................................................... vii

Executive Summary ........................................................................................................... ix 1 INTRODUCTION ..........................................................................................................1

2 BACKGROUND ............................................................................................................1

2.1 Chevron ................................................................................................................... 1 2.2 Project Overview .....................................................................................................2

2.3 Standard Vapor Recovery Unit ...............................................................................5

3 PROBLEM STATEMENT ..............................................................................................6

4 REQUIREMENTS AND CONSTRAINTS ....................................................................6

4.1 Requirements ...........................................................................................................6

4.2 Constraints ..............................................................................................................8

5 SUBFUNCTION DEFINITION ......................................................................................9

5.1 Function Structure and Morphological Matrix .......................................................9

5.2 Patent Search .........................................................................................................11

6 DESIGN EMBODIMENT AND ANALYSIS ............................................................. 12

6.1 VRU Design Overview ........................................................................................ 12

6.1.1 Determining Gas Compression Stages Required ................................... 13

6.1.1.1 Tank 1 Gas Compressions Feasibility Calculation ................... 14

6.1.1.2 Combined Gas Flow Compression Feasibility Calculation ...... 16

6.1.2 Interstage Cooling ................................................................................. 17

6.1.3 Water and Gas Phase Separation ............................................................ 17

6.1.4 Equipment Drivers ................................................................................. 18

6.1.5 Valve Systems ........................................................................................ 18

6.2 MATLAB Model ................................................................................................. 19

6.3 Individual Component Design ............................................................................. 20

6.3.1 Compressors ........................................................................................... 20

6.3.1.1 Compressor Selection Justification ........................................... 21

6.3.1.2 Design Calculations .................................................................. 24

6.3.2 Gas Coolers ............................................................................................ 24

6.3.2.1 Cooler Selection Justification ................................................... 25

6.3.2.2 Air-Cooled Heat Exchanger Design ......................................... 25

6.3.3 Gas-Liquid Separators ............................................................................ 28

6.3.3.1 Separator Selection Justification ............................................... 29

6.3.3.2 Vertical Separator Design ......................................................... 30

6.3.4 Water Disposal System .......................................................................... 31

6.3.5 Drivers .................................................................................................... 34

6.3.5.1 Compressor Drivers .................................................................. 34

6.3.5.2 Cooler Drivers ........................................................................... 34

6.4 MATLAB Results and Sensitivities..................................................................... 34

6.4.1 Separator and Cooler Results ................................................................. 36

6.4.2 Compressor Results and Sensitivities ..................................................... 37

iv

TABLE OF CONTENTS CONTINUED

6.5 Bill of Materials ................................................................................................... 39

6.6 Solid Skid Model ................................................................................................. 40

7 FINANCIAL ANALYSIS ........................................................................................... 43

7.1 Annual Sales Loss ................................................................................................ 43

7.2 Investment Costs .................................................................................................. 44

7.3 Payback and Return on Investment ...................................................................... 45

7.4 Net Present Value ................................................................................................ 47

8 COST ESTIMATE....................................................................................................... 49

9 FUTURE WORK AND RECOMMENDATIONS ..................................................... 49

10 CONCLUSION ............................................................................................................ 50

REFERENCES ................................................................................................................. 51

APPENDIX A: DESIGN FEASIBILITY CALCULATIONS ............................... A-1

APPENDIX B: DETAILED VRU DESIGN FLOW DIAGRAM ......................... B-1

APPENDIX C: MATLAB FLOW CHARTS......................................................... C-1

APPENDIX D MATLAB CODE .......................................................................... D-1 APPENDIX E: COOLER SAMPLE CALCULATIONS ...................................... E-1

APPENDIX F: VERTICAL SEPARATOR SAMPLE CALCULATIONS .......... F-1

APPENDIX G: GANTT CHART .......................................................................... G-1

v

LIST OF FIGURES

Figure 1. Production Platform Flow Diagram. ...............................................................4

Figure 2. Standard Vapor Recovery Unit Schematic. ....................................................5

Figure 3. VRU Function Structure .............................................................................. 10

Figure 4. Air Cooled Exchanger with Wind Shields ................................................... 11

Figure 5. VRU Design Flow Process Diagram ........................................................... 13

Figure 6. Single Stage Compressions from Tank 1 ..................................................... 14

Figure 7. Two Stage Compressions from Tank 1 ........................................................ 15

Figure 8. Combined Gas Flow Compression .............................................................. 16

Figure 9. Compressor Chart ........................................................................................ 21

Figure 10. Compressor Selection Chart ........................................................................ 22

Figure 11. Component Layout of Air Coolers .............................................................. 26

Figure 12. Vertical and Horizontal Two Phase Separator Schematic ........................... 29

Figure 13. Vertical Scrubber Design Dimensions ......................................................... 31

Figure 14. Two Dimensional Skid Layout .................................................................... 41

Figure 15. Three Dimensional Skid Layout .................................................................. 42

Figure 16. Value of Recovered Gas vs. Natural Gas Spot Price ................................... 46

Figure B.1. Detailed VRU Process Flow Diagram .......................................................B-1

Figure C.1. Main VRU MATLAB Program Flowchart ................................................C-1

Figure C.2. Vertical Separator MATLAB Function Flowchart ....................................C-2

Figure C.3. Cooler MATLAB Function Flowchart .......................................................C-3

Figure C.4. Heat Capacity Calculator MATLAB Function Flowchart .........................C-4

Figure G.1. Gantt Chart ................................................................................................ G-1

vii

LIST OF TABLES

Table 1. Specification Sheet: Function Requirements. ................................................7

Table 2. Specification Sheet: Constraints. ....................................................................9

Table 3. Thermodynamic Property Table. ..................................................................13

Table 4. Compression stage flow rate and discharge pressures ............................... 22

Table 5. Compressor Selection Decision Matrix ...................................................... 23

Table 6. Condensate Water Piping Results .............................................................. 33

Table 7. Sensitivity Cases ......................................................................................... 35

Table 8. Separator Design Outputs ........................................................................... 36

Table 9. Cooler Design Outputs ............................................................................... 37

Table 10. Compressor Design Outputs ....................................................................... 38

Table 11. Bill of Materials .......................................................................................... 40

Table 12. Past and Predicted Natural Gas Spot Prices ............................................... 43

Table 13. VRU Costs .................................................................................................. 44

ix

EXECUTIVE SUMMARY

The Vapor Recovery Unit project focuses on one of Chevron’s oil and gas

production platforms in the Gulf of Mexico continental shelf. Our team’s objective is to

configure a Vapor Recovery Unit (VRU) for this platform that will increase two low-

pressure gas flows to a sufficient pressure and re-route the gas to enter the sales stream.

This system will compress gas coming from both an existing bulk surge tank on the

platform as well as a new tank that has not yet been installed. Chevron wants to maintain

compliance with applicable environmental laws and regulations to minimize gas losses

and increase profits. To reduce hazardous emissions on the platform, an efficient and

economical system is needed to capture hydrocarbon vapors which are currently being

“flared” or burnt off into the atmosphere. Further detail on our project’s background and

design requirements can be seen in the Background, Problem Statement, and

Requirements and Constraints sections of the report.

Overall VRU and detailed individual component designs have been developed

through research and analysis. Our final VRU design recommendation incorporates the

following key components: gas compression and cooling, water and gas separation,

piping systems for condensate water removal, equipment drivers, and key valve systems.

Reciprocating compressors, powered by natural gas engines, are used for gas

compression. Hot gas at the compressor outlet is cooled using air-cooled heat exchangers,

which are powered by electric motors. Vertical liquid-vapor separators use gravity to

separate condensate water from dry gas after cooling, where the water is piped from the

scrubbers to a water collection point. The key valve systems include valves for the

compressor inlet and discharge, control valves for the scrubber, and a three way valve to

combine gas flows. Because of the significantly low gas pressures, multiple compression

stages are needed considering individual and combined gas streams. As a result, three

sets of compressors, coolers, and scrubbers are modeled in our overall VRU design.

Thermodynamic feasibility calculations and justifications are presented to support

our findings and component selections. A MATLAB computer model of our system

provides design simulation and verification using engineering analysis. Equipment sizing

and power specifications from the model, along with a compiled bill of materials, are

used to create a solid skid model of our design layout for visualization. A full discussion

of these topics concerning our overall VRU design and its key components can be seen in

the Design Embodiment and Analysis section of the report.

An important aspect of the proposed design solution is our financial analysis,

addressing annual sales loss, investment costs, payback, ROI, and net present value. The

Financial Analysis section in the report provides further detail on these topics. Based on

average values, considering the short payback period of 4 months, high return on

investment of 243%, and positive annual revenue of $4 million, our analysis shows

implementing our final design solution is financially sound and would be a favorable

investment for Chevron.

1 INTRODUCTION

The Vapor Recovery Unit project focuses on one of Chevron’s oil and gas

production platforms in the Gulf of Mexico continental shelf. Our team’s objective is to

configure a Vapor Recovery Unit (VRU) for this platform that will increase two low-

pressure gas flows to a sufficient pressure to enter the sales gas stream. In addition to

conveying our understanding of the project background and problem, we will describe

and justify our decisions made when generating ideas for design. Our primary focus will

be on outlining the design analysis, embodiment, and results for our final design model

and individual component designs. Our team will discuss the financial analysis associated

with our project solution, as well as provide recommendations for further solution

improvements and future studies for the project. Also included in this report is a project

Gantt Chart outlining our project time schedule, and a specification sheet detailing the

project-specific design requirements and constraints for implementing a VRU system.

2 BACKGROUND

2.1 Chevron

Our sponsor, Chevron, is a major oil and gas company that has over 62,000

employees and operates in over 100 countries. It is one of six “super major” oil

companies that are involved in all aspects of upstream and downstream activities,

including the exploration, production, refining, distributing, and marketing of

hydrocarbons as finished oil and gas products. In addition to producing oil and gas,

2

Chevron is also involved with power production and is the world’s leader in producing

geothermal energy. Chevron also has mining and chemical production divisions and

invests in researching renewable fuels. Outside of oil and gas production, Chevron is

well known for its fuel additive Techron, which acts as a detergent and prevents engine

build-up [1].

Chevron is one of the largest producers of oil and natural gas on the Gulf of

Mexico shelf. In addition to being the largest lease holder on the outer continental shelf,

Chevron owns 313 major structures in the Gulf of Mexico and in 2008 maintained an

average daily net production of 76,000 barrels of crude oil, 439 million cubic feet of

natural gas and 10,000 barrels of natural gas liquids. Working with engineers in Houston,

TX and Covington, LA, our team will be focusing on one of Chevron’s oil and gas

production platforms in the Gulf of Mexico continental shelf [2].

2.2 Project Overview

Our project involves increasing the reliability and efficiency of gas production,

presenting a unique set of cost drivers and environmental concerns due to its offshore

location. Offshore equipment reliability is a high priority because loss of production and

equipment replacement present financial liabilities for Chevron. Environmental factors

are also of concern and Chevron wants to reduce its carbon emissions on this platform by

recovering excess low pressure gas and adding it to the sales gas stream rather than

burning it off, also known as “flaring.” Gas flaring and venting are highly regulated in the

Gulf of Mexico by the Minerals Management Service (MMS).

3

Our team will focus on one of Chevron’s offshore production platforms in the

Gulf of Mexico, where oil and gas are produced and processed from underground

deposits. A general flow diagram of this platform, as seen in Figure 1 on the following

page, gives a basic overview of how oil, water, and gas are separated from the well

streams. The gas and liquids flow from the well head through high, medium, and low

pressure separators. The liquids, consisting of oil and water, eventually exit the low

pressure separator and enter the oil dehydration unit. At this stage the water is sent for

treatment to be dumped back into the ocean, while the dry oil is pumped to shore. The

excess gas needs to be compressed to be sent to shore and must go through the inlet of the

sales compressor. The high and medium pressure gas flows are at sufficient pressures to

enter the second and first stages of the sales gas compressor, respectively. Currently, the

excess low pressure gas must flow from the low pressure separator to a bulk surge tank,

where the gas is then flared to the atmosphere rather than going through a Vapor

Recovery Unit (VRU). This VRU would allow for excess low pressure gas to achieve a

sufficient pressure to enter the first stage of the sales compressor, recovering some of the

gas.

4

Figure 1. Production Platform Flow Diagram.

Our project’s focal point will be designing and analyzing a VRU system to add to

the production platform. Currently, all of the excess low pressure gas is being vented to

the atmosphere since there is no VRU installed on the platform. Additionally, due to

other production platforms in the area being damaged from a hurricane, a larger volume

of production will be brought to our platform to compensate for the incurred losses.

Bringing more oil and gas to the platform places greater emphasis on maximizing

productivity, efficiency, and the sales compressor’s capabilities, while increasing the

demand for other separating equipment. At the same time, environmental and cost factors

need to be considered. Thus, adding a vapor recovery system to feed into the compressor

will address these issues by capturing low pressure gas and compressing it to add to the

sales gas stream rather than venting/flaring. Flaring less of the low pressure gas and

Clean H2O

High Pressure Separator

VRU

OilDehydration

Sales Compressor

Dry Oil

1000 psig

200 psig

35 psig

1st

stg2nd

stg

Well Stream

BulkSurge

Tank

Liquid Flows

Gas Flows

Alternate LP Gas Flow

Medium Pressure Separator

Low Pressure Separator

Flare toAtmosphere

Clean H2O

High Pressure Separator

VRU

OilDehydration

Sales Compressor

Dry Oil

1000 psig

200 psig

35 psig

1st

stg2nd

stg

Well Stream

BulkSurge

Tank

Liquid Flows

Gas Flows

Alternate LP Gas Flow

Liquid Flows

Gas Flows

Alternate LP Gas Flow

Medium Pressure Separator

Low Pressure Separator

Flare toAtmosphere

5

incorporating it into the sales stream will recover vapors and boost sales while

maintaining compliance with applicable laws and regulations.

2.3 Standard Vapor Recovery Unit

A standard VRU includes three key components including a suction scrubber, a

compressor, and a liquid transfer pump (with its associated drivers). Figure 2 below

depicts a standard single stage VRU attached to a crude oil storage tank. Initially,

hydrocarbon vapors are drawn out of the storage tank under low pressure and sent to a

suction scrubber which separates excess water from the gas. The condensed water is then

sent back to the storage tank via the liquid transfer pump while the gas in the suction

scrubber flows through a compressor. From the compressor, the vapors are metered and

transported to either the sales gas line or back to the production facility to drive other

equipment. The control pilot that separates the stock tank from the suction scrubber

prevents the formation of a vacuum in the top of the stock tank by shutting off the

compressor and allowing back flow into the tank [3].

Figure 2. Standard Vapor Recovery Unit Schematic [4].

6

3 PROBLEM STATEMENT

Our team will research various Vapor Recovery Unit (VRU) equipment to develop

design recommendations and select the optimal configuration for incorporating a VRU

system on the platform while meeting key design criteria. This VRU will need to

compress excess low pressure gas coming from both an existing bulk surge tank as well

as a new tank that has not yet been installed. This gas must be brought up to a sufficient

pressure in order to enter the inlet of the sales gas compressor.

4 REQUIREMENTS AND CONSTRAINTS

4.1 Requirements

The first page of the specification sheet shown in Table 1 outlines the functional

requirements that we will use to gauge the success of our design.

The first functional requirement listed is to reduce carbon emissions. This

environmental factor, which is one of the key drivers for installing the VRU, will be

achieved by taking low pressure gas that that would normally be burned off or “flared”

and increasing its pressure so that it can be added to the sale’s gas stream and sold or

rerouted back to the platform for use on-site.

Another significant requirement for this project is to bring the low pressure gas

from the new bulk surge tank and add it to the gas from the existing bulk surge tank.

This is done to recover the low pressure gas from a damaged facility by integrating it

with a functional facility.

7

Other key requirements for the VRU include making it easy to install and

minimizing its size and weight due to the limited space available on the platform. It is

also important to ensure that the design operates within safe temperature and pressure

limits. This will ultimately prevent the need for costly repairs and extend the useful life

of the gas processing equipment that makes up the VRU. The VRU design must also be

judged on its financial merits and should provide a cost-benefit to Chevron in addition to

complying with environmental regulations.

Table 1. Specification Sheet: Function Requirements.

8

4.2 Constraints

The second page of the specification sheet, Table 2, details the five categories of

constraints associated with our VRU design: pressures, temperatures, flow rates,

equipment sizes, and gas properties. The specifications for some pressures, temperatures,

and flow rates were determined by first locating where the VRU would be integrated with

the existing equipment, and then looking up the relevant information from our facility’s

process and instrumentation diagrams (P&ID). The rest of the pressures, temperatures,

and flow rates were found by asking our sponsor what could generally be expected from

the additional low pressure gas that would be brought in from the damaged facility. The

limitations on equipment size and placement can be found by looking at the equipment

location diagrams for our platform. The gas properties found in the specification sheet

were determined by reviewing the results of a gas sample analysis test and will be

assumed constant for all further models and analysis.

9

Table 2. Specification Sheet: Constraints.

5 SUBFUNCTION DEFINITION

5.1 Function Structure and Morphological Matrix

By linking the various energy, material, and signal inputs from the black box to

key functional requirements, we were able to develop a function structure as shown in

Figure 3. Some lessons learned from the function structure were based on available

resources and cycles. We learned that gravity could be used as a key energy source for

facilitating liquid and gas separation in the VRU. Also, the process of separating,

compressing and cooling gas is iterative and will most likely require multiple stages. We

10

also learned that the process of transferring condensed water and compressing gas

pressure may require a driver. Due to the flow process, if one of the components fail, the

entire process will need to be shut down until the component is repaired.

Figure 3. Function Structure of VRU.

A morphological matrix was created to review all possible ways to achieve the

desired subfunctions from the function structure. We used the morphological matrix as a

tool to discover new technologies and determine which components we could

recommend for future VRU configurations. We were also able to use the matrix to select

which components we would like in our final VRU design.

11

5.2 Patent Search

Throughout the design process our team has performed a patent search to generate

ideas for selection and design of VRU components and alternative vapor recovery

systems. The following section is a description of two patents that we found to be the

most relevant for the systems we considered in our project design.

The first patent, “Air Cooled Exchanger,” describes an improved air-cooled heat

exchanger with shields attached to each tube bank to deflect wind entering the exchanger

without affecting cooling air flow on the tube exterior [5]. This proposed system seen in

Figure 4, which has shields comprised of a wind deflecting front wall and triangular side

walls, would be advantageous for improving control of exchanger operations in difficult

weather with high wind velocities. This invention is significant for the project because

certain design aspects were adopted for modeling the inter-stage gas coolers in our VRU

system. It also provided insight into reflecting adverse atmospheric conditions in our

design sensitivity analysis, which is especially relevant considering our project’s offshore

location.

Figure 4. Air Cooled Exchanger with Wind Shields [5].

12

The second patent, “Eductor System and Method for Vapor Recovery,” outlines a

system for recovering discharged vapors from hydrocarbon processing systems to prevent

or minimize harmful emissions [6]. This design uses venturi eductor technology to

combine a high-pressure motive fluid with low-pressure vapors to discharge gas at an

intermediate pressure and inject it into existing process equipment. Considering our

project’s objective of economically capturing hydrocarbon emissions, while maintaining

Chevron’s compliance with environmental regulations, this non-mechanical alternative

vapor recovery system is relevant for our project’s gas production and processing

application. However, due to the lack of a high-pressure gas source on the offshore

facility, we have only utilized this idea for future project recommendations.

6 DESIGN EMBODIMENT AND ANALYSIS

6.1 VRU Design Overview

After reviewing our function structure, standard vapor recovery unit designs, and

input from our sponsor we created the VRU layout shown in Figure 5. The

thermodynamic properties associated with states 1-9 can be found in Table 3. The

following sections will outline the process that led us to this design.

13

Figure 5. VRU Design Flow Process Diagram.

Table 3. Thermodynamic Property Table.

6.1.1 Determining Gas Compression Stages Required

The first step toward creating a vapor recovery unit is to become familiar with the

process of natural gas compression. The Handbook of Natural Gas Transmission and

Processing (HNGTP) provides much information on the subject and served as our source

for determining the number of compression stages required for the gas flows from each of

our two stock tanks. In particular, the handbook recommends keeping the compression

14

ratio for each stage of compression less than 4. This prevents the gas from reaching

critical temperatures in excess of 300 oF which will damage compressors [7]. To create

our design we performed design feasibility calculations for both the 5-45 psig gas

compression from stock tank 1 and the 45-90 psig gas compression for the combined

3MMSCFD flow stream.

6.1.1.1 Tank 1 Gas Compression Feasibility Calculation

Figure 6 details the thermodynamic constraints associated with gas compression

from tank 1.

Figure 6. Single Stage Compression from Tank 1.

Assuming negligible changes in potential and kinetic energy and adiabatic compression,

the first law of thermodynamics reduces to [7]:

If we assume constant specific heat for the gas, the isentropic outlet temperature can be

found by the relation [7]:

15

Where (P2/P1) is the compression ratio, K is the gas heat capacity ratio, and T2s is the

isentropic compressor outlet temperature. Once the isentropic temperature at the

compressor outlet has been determined the actual outlet temperature can be found from

the relation [7]:

Where ηc is the isentropic compressor efficiency which we have assumed to be 83% for a

reciprocating compressor [8]. As expected, the outlet temperature for the compressor

was in excess of 300oF. With this in mind we decided to add a second compression stage

and an interstage cooler to the design as seen in Figure 7.

Figure 7. Two Stage Compression from Tank 1.

To minimize the compression ratios across the compressors we decided to make

each of the compression ratios three, resulting in an intermediate pressure of 15 Psig.

16

From the Handbook of Natural Gas Transmission, we found a rule of thumb relation that

said that interstage air cooling could result in output cooler temperatures of 25oF above

ambient temperature. Assuming Steady State Steady Flow isentropic compression and

negligible pressure drop across the cooler, we followed a similar procedure to the single

stage compression and determined the intermediate temperature T3 as well as T5. This

procedure resulted in compressor operating temperatures safely below the critical

temperature of 300oF. The detailed calculations for both single and two stage

compression feasibility can be found in Appendix A.

6.1.1.2 Combined Gas Flow Compression Feasibility Calculation

Figure 8 details the thermodynamic constraints associated with the combined gas

flow from tank 2 and tank 1.

Figure 8. Combined Gas Flow Compression.

Performing the same calculation as the single stage compression from tank 1 we

found that the compressor operating temperature was safely below the critical

temperature of 300oF. This makes it clear that only one compression stage is required for

the combined 3MMSCFD gas flow from 45Psig to 90Psig. The feasibility calculations

for this section can also be found in Appendix A.

17

6.1.2 Interstage Cooling

The interstage coolers CLR 1-3 on Figure 5 are included in the design for the

purpose of both lowering the potentially damaging high temperatures associated with gas

compression and minimizing the horsepower requirements for the compressors. As we

have mentioned before, gas flows over the critical temperature of 300oF can damage

equipment especially by degrading lubricants used in compressors [7]. Minimizing

compressor power requirements is another important consideration in our design and

interstage cooling decreases the temperature of the gas entering the compressor which in

turn decreases the power required to run the compressor [7].

6.1.3 Water and Gas Phase Separation

Since water is an incompressible fluid, large quantities of water vapor in a natural

gas flow stream can have catastrophic effects on gas compressors. To extract water from

natural gas, two phase gravity separators (also called scrubbers) are often used in gas

processing and our design includes one before every compression stage. Initially, our

design also included scrubbers after each stock tank, but we were informed by our

sponsor that they were not required because the stock tanks included mist extractors that

removed excess water. Since condensate water is produced by each of the three

scrubbers in our design it is necessary to transport the excess water to a holding tank to

be cleaned and disposed of. On the bottom deck of the production facility where the VRU

will be installed, there is a holding vessel called a sump tank where excess water

produced at the facility can be stored. Since the VRU will be installed on the top deck of

the facility, condensate water will be piped from the scrubbers to the sump tank using

18

gravity and internal scrubber pressure as a driving force. It is important to note that we

have assumed that changes in pressure, temperature and volumetric gas flow rates across

the scrubbers will be negligible.

6.1.4 Equipment Drivers

Compressors and coolers are the only two pieces of equipment in the VRU that

require an outside power source. As a requirement from our sponsors, the compressors in

the VRU will be powered with natural gas drivers. These natural gas drivers typically

come in the form of internal combustion engines and will provide power to all three of

our compressors. The cooling systems typically have a low horsepower requirement and

will be powered electrically from the production facility.

6.1.5 Valve Systems

To set limits on the scope of our design we have decided not to design the valves

in the VRU in detail but to simply show the placement of key valve systems in a detailed

VRU design flow diagram found in Appendix B. There are three key valve systems

found on the VRU design in Appendix B including compressor valves, scrubber valves

and a three way valve. In order to control fluctuating gas flows and prevent damage, each

compressor in the VRU is equipped with an inlet valve and discharge valve, labeled CIV

and CDV respectively. In addition to controlling gas flows through the use of a pressure

control valve (PCV), scrubbers must also be able to control the condensate liquid flow to

the sump tank. This will be achieved through the use of a liquid control valve or LCV.

A three way valve between state 7 and 8 on the VRU flow process diagram will be used

19

to combine the gas flows from stock tank 1 and 2 so that they may enter the final

compression stage.

6.2 MATLAB Model

A critical aspect of our engineering analysis for the project was to apply

principles of thermodynamics, heat transfer, fluid mechanics, and gas separation to verify

our proposed VRU configuration. As a result, we have created a computer model to

simulate our developed VRU design using MATLAB. From this model, we automated

our final design and obtained significant outputs by running simulations with varying key

parameters. It also allowed us to examine and evaluate each individual component design

in greater detail and adjust assumptions made as necessary. This feature facilitated the

troubleshooting process for our design since each key component is modeled as a

separate entity that can be modified individually.

These computer simulations provided us with a collection of valuable data for our

design: temperatures at all key states including compressor outlet temperatures;

compressor and cooler brake horsepower to determine overall power required to drive the

system; scrubber and cooler sizing specifications; and effects of deviating ambient

temperatures, and flow rates. Some of this data, particularly the power requirements and

dimensions, were important factors in sizing our VRU system for the platform and

determining capital expenditure cost estimates for our financial analysis.

The inter-stage coolers and vertical separators in our VRU configuration are

modeled as separate sub-functions that are called in from the main MATLAB function,

where the overall VRU program incorporates the isentropic compression analysis of the

three compressors to reflect different compression stages in our design. The MATLAB

20

flow chart for the main function can be seen in Appendix C.1, while the separator and

cooler flow charts are in Appendices C.2 and C.3, respectively. Another function was

created to calculate the specific heat capacity of the gas at variable temperatures, using

both the specific heat polynomial expression and, assuming the gas is treated as an ideal

gas mixture, mass composition for the individual gas components. This function, whose

MATLAB flow chart can be seen in Appendix C.4, proved to be extremely beneficial in

easing the automation process of our model algorithms. The MATLAB code for these

four functions can be seen in Appendices D.1-D.4.

The key input variables for our program included the temperatures, pressures, and

flow rates of the gas streams from both stock tanks, as well as the specific gravity and

molecular weight of the gas. To verify the feasibility and output values of our model, we

produced sample calculations for the compressors, coolers, and scrubbers, and provided

justifications for assumptions made in our analysis; these calculations can be seen in

Appendix A and Appendices E-F. Each of these components will be discussed in further

detail in the next section of this report.

6.3 Individual Component Design

6.3.1 Compressors

Compression is the central element in VRU design and successful compressor

selection is vital to a VRU’s operation. Figure 9 divides natural gas compressors into

three distinct groups: positive displacement, dynamic, and thermal type compressors.

Though ejectors have been used in onshore gas pressure boosting, they require a high

21

pressure motive gas flow that is not available at our offshore site and will not be

considered in our compressor selection.

Figure 9. Compressor Chart [8].

6.3.1.1 Compressor Selection Justification

The Gas Processors Suppliers Association Engineering Data Handbook is a

valuable resource for compressor selection and provides many useful charts and tables

that compare various gas compressor types across wide volumetric flow rate and pressure

regimes. Figure 10 compares reciprocating, rotary, centrifugal, and axial compressors

based on their ability to handle various input flow rates and discharge pressures.

When the flow rates and discharge pressures for each of the three compression

stages are plotted on Figure 10 below, it becomes apparent that reciprocating, rotary, and

centrifugal compressors are all acceptable choices. For offshore gas processing however

rotary compressors are rarely used so we will further limit our compressor selection to

only reciprocating and centrifugal compressors [8].

22

Figure 10. Compressor Selection Chart [8].

Table 4. Compression Stage Flow Rate and Discharge Pressures.

Though reciprocating and centrifugal compressors are both capable of increasing

the pressure of natural gas, they operate under different mechanical principles which give

rise to different operating characteristics. Reciprocating compressors, which consist of a

piston that compresses gas in a fixed volume cylinder, tend to have lower capital costs

23

and power costs than centrifugal compressors while maintaining higher adiabatic

efficiencies [8]. Centrifugal compressors, which use radial impeller movement to

increase the pressure of a gas stream, require less maintenance than reciprocating

compressors (due to having fewer moving parts) and have lower installation costs [8].

The benefits of each compressor type are summarized in Table 5 below. Since adiabatic

efficiency and maintenance are both key concerns in compressor selection, there is no

clear choice based on the aforementioned criteria. After running our MATLAB model

for each type of compressor we found that the brake horse power (horse power adjusted

for mechanical losses) requirements for the compressors were similar (within 5%), which

also prevented us from using power requirements as a deciding criteria. Our final

decision to use reciprocating compressors came after finding that using centrifugal

compressors led to higher interstage temperatures, resulting from their lower adiabatic

efficiencies. Since larger coolers are needed to offset the damaging high interstage

temperatures and production floor space is limited, we found reciprocating compressors

to be the preferred choice.

Table 5. Compressor Selection Decision Matrix.

24

6.3.1.2 Design Calculations

Brake horsepower (BHP) is the primary parameter for compressor design. The

formula for calculating BHP can easily be adjusted to model reciprocating or centrifugal

compressors, and is given below [7]:

Where Zavg is the average compressibility factor; QG,SC is the standard volumetric

flow rate of gas (MMSCFD). T is the compressor suction temperature (R). P2 and P1 are

the discharge and suction temperatures (Psia). E is the parasitic efficiency (for

reciprocating: 0.72-0.82, for centrifugal: 0.99), and η is the compression efficiency (1 for

reciprocating, 0.8-0.87 for centrifugal units) [7].

6.3.2 Gas Coolers

Gas coolers are typically used as intercoolers for multiple compression stages or

for compressor suction and discharge [9]. Gas cooling is a significant aspect of our VRU

design by helping prevent equipment damage and lower compressor power requirements.

These coolers cause minor pressure losses of the gas depending on the design [7].

However, for our design this pressure drop is considered negligible and gas cooling is

assumed to be done at constant pressure. Based on our research, calculations, and

selected cooler size, this critical assumption can safely be made and has been approved

by our Chevron sponsors and faculty advisor, Dr. Thomas Kiehne.

25

6.3.2.1 Cooler Selection Justification

The two primary types of cooling media used for gas cooling are air and water,

where air cooling is achieved by air-cooled heat exchangers and water cooling is

typically done using water-cooled heat exchangers or cooling towers. Since water has

more favorable thermal properties than air, water coolers have a higher cooling capacity

and require less heat-transfer surface area [8]. However, because water coolers require an

adequate supply of cooling water, they have significantly higher operation and

maintenance costs due to water pumping, treatment, and disposal [10]. Other concerns

associated with water coolers include equipment corrosion and limited water availability,

while air coolers require less frequent cleaning and have unlimited air quantities available

with no preparation costs [11]. Although seasonal variations in ambient temperature can

make temperature control difficult, air has become the more viable and economical heat

transfer media for achieving industrial cooling requirements [8].

Overall, air-cooled heat exchangers are viewed as more cost-effective than water

coolers over the system’s projected lifespan, especially with their well-established and

reliable design [8]. Considering our project’s low design pressures, temperatures, and

flow rates, as well as other factors including offshore location, cost sensitivity, and strict

environmental regulations in the Gulf of Mexico, air-cooled heat exchangers are the ideal

choice for modeling our cooler designs.

6.3.2.2 Air-Cooled Heat Exchanger Design

The fundamental principle behind air-cooled heat exchangers (ACHEs) involves

transferring heat from the gas to a cooling ambient airstream via finned tubes, where air

movement is achieved by mechanical fans [11]. ACHEs consist of the following basic

26

components: tube bundle, axial fan, fan drive assembly, and supporting structure [8]. Hot

gas flows through tubes in the tube bundle, the heat-transfer device for the cooler, where

fins are applied to increase heat-transfer effectiveness by providing an extended surface

on the air side [12]. We used the most typical fan configuration for our design, known as

forced-draft, where the fan below forces air up across the tube exterior; a basic layout of

this configuration can be seen in Figure 11.

Figure 11. Basic Component Layout of Air Coolers [9].

To optimally model our three cooler designs, we assumed standard values in

terms of tube geometry and tube bundle layout. These assumptions include fin length and

spacing, tube pitch and diameter, and the number of tube passes and rows [12]. To keep

the designs conservative we used a minimum ratio of 0.40 for fan coverage, which

measures air distribution across the tube bundle face [8]. Using the ACHE design

procedure outlined in the GPSA Engineering Data Book, we determined the key sizing

and power requirements to model the coolers. These parameters, along with our cooler

results, will be discussed in detail further along in the report. The key principles

27

underlying ACHE thermal design involve basic heat transfer analysis, where heat and

material balances are performed for the air and gas sides of the exchanger.

The heat dissipated by the gas (Qgas), absorbed by the air (Qair), and transferred from gas

to air (Q) are all equal [9]:

Qgas = Qair = Q

which can also be expressed as [9]:

mgas Cpgas ΔTgas = mair Cpair ΔTair = U A F (LMTD)

where m is the mass flow rate, Cp is the specific heat capacity, ΔT is the temperature

change, U is the overall heat-transfer coefficient, A is the heat transfer area, F is the

LMTD correction factor, and LMTD is the log mean temperature difference that acts as

the driving force of heat transfer.

Using the relationship above, we calculated the total extended surface heat

transfer area and converted this value to a bundle face area depending on the tube

geometry and bundle layout. These parameters also allowed us to calculate the air mass

flow rate and velocity. The minimum fan area and fan diameter were calculated using the

bundle face area and fan coverage ratio. To determine the total pressure loss across the

fan, we summed the calculated dynamic fan and air static pressure drops. Finally, the fan

driver brake horsepower was estimated using average fan and speed reducer efficiencies,

total fan pressure drop, and the actual volumetric flow rate of air at the fan inlet [8].

Sample calculations and key assumptions detailing this cooler design methodology are

outlined in Appendix E.

28

6.3.3 Gas-Liquid Separators

Liquid-vapor separators are one of the most common types of process equipment.

As discussed in the VRU design section of the paper, water vapor extraction is crucial for

prolonging compressor life and preventing equipment damage. Though there are three

main types of gravity phase separators (horizontal, vertical and spherical) we will be

limiting our discussion to horizontal and vertical scrubbers because spherical separators

are only used for high pressure service which does not apply to our project constraints

[8]. For both horizontal and vertical scrubbers, gas-liquid separation is accomplished in

three stages. Primary separation, section A in Figure 12, occurs when incoming gas hits

the inlet diverter plate causing large water droplets to coalesce and fall into section D

from gravitational forces. In section B, secondary separation takes place as gravity

causes the smaller water droplets in the gas flow to fall through the disengagement area

into section D. Finally, the smallest droplets of water are collected by the mist extractor

in section C before the gas exits the separator [13].

29

Figure 12. Vertical and Horizontal Two Phase Separator Schematic [8].

6.3.3.1 Separator Selection Justification

Though vertical and horizontal separators achieve gas-liquid separation in the

same manner, they have inherent advantages and disadvantages from one another that

make them ideal for different situations. For example, vertical separators are ideal for

offshore applications because they require less production floor space than horizontal

separators. It is also easier to clean vertical separators and control their fluid levels [7].

Horizontal separators, on the other hand, are ideal for applications where large volumes

of gas and surging are key concerns [7]. Since floor space on the production facility is

severely limited and we do not require a separator that can handle large throughputs and

surging volumes, we have decided to implement vertical separators in our design.

30

6.3.3.2 Vertical Separator Design

When designing a two phase separator, the key dimensions required include the

inner vessel diameter and seam-to-seam height. Other important dimensions include the

liquid level height and vessel wall thickness. After reviewing numerous sources on

separator design, we found a paper by Svrcek that takes multiple industry standard

separator sizing methods and streamlines the process into a simple step by step

methodology. A brief outline of the steps required to size a two phase separator will be

covered here while the detailed sample calculations can be found in Appendix F.

The first key dimension that must be calculated is the vessel diameter and it is found by

the relation [13]:

where QV is the volumetric flow rate of gas in ft3/sec and UV is the vertical terminal vapor

velocity of a single water droplet falling through the disengagement area of the separator

in ft/sec. Once the vessel inner diameter has been found, the seam to seam height of the

separator HT in Figure 13 must be determined, where HT is simply the sum of the heights

HD, HLIN, HS, HH, HLLL and 1.5 ft. The lower liquid level height (HLLL), distance between

inlet nozzle and liquid level (HLIN ), and distance between inlet nozzle and mist extractor

HD are easily determined from pressure dependent sizing charts given in the paper by

Svrcek. Other heights that deal with the liquid level in the separator such as HS and HH,

require more detailed calculations and are outlined in Appendix F.

31

Figure 13. Vertical Scrubber Design Dimensions [13].

6.3.4 Water Disposal System

To transport the condensed water coming out of the water separators and exiting

the VRU system, we found the most viable and economical choice for our project would

be to model a piping system that disposes the water into a sump tank, which is a mass

tank vessel at atmospheric pressure that contains collected water from other equipment on

the facility.

Since water flow from our three scrubber designs is substantially low, we

eliminated the need for liquid transfer pumps and their associated drivers in our system,

simplifying our overall VRU design. Instead, this piping system uses the pressure

difference from gravity to push the liquids out of the scrubbers and into the sump tank,

32

which is currently located on the bottom deck level of the platform. According to

Chevron, our VRU system will be installed above the tank, allowing us to utilize this

height difference and use gravity as the key driving force of this piping system.

Our analysis for determining the required pipe sizing for each scrubber’s water

flow in our design was based on applying Bernoulli’s principle, assuming an

incompressible and non-viscous water flow. Standard pipe sizes vary from ½” to 2” in

diameter with ½” increments, as per Chevron. We have also accounted for pressure losses

in the pipe due to friction, which depends on the average water velocity, pipe length and

diameter, and a friction factor obtained from the Moody diagram. The friction factor is

based on pipe roughness and the Reynolds number for determining turbulent or laminar

flow [9]. To account for losses from expected bends and valves in the piping, Chevron

has provided us with an equivalent pipe length of 300 ft from each scrubber to the sump

tank for our calculations.

Using Bernoulli’s equation to combine the fluid energy in terms of elevation (h),

velocity (v), and pressure (P) between the scrubber and sump tank, the total energy can

be expressed as [9]:

P1 + ½ ρv1² + ρgh1 = P2 + ½ ρv2² + ρgh2 + Ploss

The pressure loss, using the D’Arcy-Weisbach Equation, is expressed as [9]:

Ploss = (f Leq /D)(½ ρvavg²)

where f is the friction factor, Leq is the equivalent pipe length, D is the pipe diameter, and

vavg is the average water velocity in the pipe. For the height difference between the

33

scrubbers and sump tank, we assumed the VRU would be installed two deck levels above

the tank based on our system’s skid dimensions and the equipment location diagram of

the platform. Provided that the pipe inlet at the sump tank is located 6” from the bottom

as per Chevron, and using the known height of 18’ per deck level, we calculated the

elevation difference to be 35’5”. Using these equations and assumptions, along with the

pressures and calculated water velocities for each scrubber, we created an Excel

spreadsheet to determine the average water velocity in the pipe for each scrubber design

at different standard pipe diameters. These results are summarized in Table 6.

Table 6. Condensate Water Piping Results.

The feasibility analysis of our piping system was based on ensuring that the water

velocity in the pipes remained between 5 to 15 ft/s to avoid pipe damage. According to

Chevron, high water flows cause pipe erosion, while low velocities cause pipe corrosion.

Using our data in Table 6, we were able to select the feasible pipe diameter for each

scrubber depending on which average pipe velocity fell within this velocity range. As a

result, both scrubbers 1 and 2 require ½” diameter piping, while scrubber 3 requires a 1”

pipe diameter for water condensate removal.

34

6.3.5 Drivers

In order to power our compressors and air coolers, we need to look at what types

of drivers are applicable for our designs.

6.3.5.1 Compressor Drivers

Gas compressors are typically driven by electric motors, gas engines, or gas

turbines. While electric motors must rely on the availability of electric power, both gas

engines and gas turbines can use pipeline gas as fuel. Since an abundant supply of natural

gas fuel already exists on the production facility, we have only considered engines fueled

by natural gas to drive the compressors in our VRU design. We have also discussed this

decision with our sponsors at Chevron and have received their approval.

6.3.5.2 Cooler Drivers

Fan drivers for air-cooled heat exchangers are typically electric motors, steam

turbines, hydraulic motors, or gas engines. After further research and analysis, our team

decided that an electric motor would be the ideal driver selection for our air coolers, as

this is commonly used and would be most appropriate for our coolers considering the

relatively low amount of brake horsepower required to drive the cooler fans. Electricity

would power these motors using the extra capacity from the generator on the facility. We

have also verified this selection with Chevron, and other types of drivers for our cooler

designs will not be considered.

6.4 MATLAB Results and Sensitivities

Using our methodology for detailed design and the MATLAB model, we obtained

key parameters to determine power and sizing requirements for each of the compressors,

35

scrubbers, and coolers in our VRU design. To run the overall MATLAB VRU program at

average conditions, we used the pressures, temperatures, and flow rates listed earlier in

the report in Table 3. These base conditions consist of an ambient air temperature of 80oF

at average gas flow rates.

From a practical standpoint, certain aspects associated with our design change on

a daily basis. To simulate these variations, we used our MATLAB program to run

multiple cases with varying parameters to reflect realistic conditions and analyze the

effects on key model outputs. Performing this sensitivity analysis allowed us to refine our

model and adjust assumptions made based on our design’s feasibility in extreme

conditions. Two key fluctuations are modeled in our VRU design: ambient air

temperatures and gas flow rates. A summary of these sensitivity cases can be seen in

Table 7, and these cases will discussed in further detail in the compressor results section

of the report. We have considered sensitivity effects solely on the three compressors in

our model because altering these conditions only had a significant impact on the

compressor output values. The results presented for the scrubber and cooler designs were

obtained at average conditions using the values for case 2, or the base case, as seen in

Table 7.

Table 7. Sensitivity Cases.

36

6.4.1 Separator and Cooler Results

From the MATLAB output, we populated an Excel spreadsheet for the scrubbers

containing the inner separator diameters (Dvd) and seam to seam lengths (Lss) in feet.

These values can be seen in Table 8. Since vendors only make separators with diameters

and lengths in 6-inch increments, the dimensions were converted to inches and then

rounded up to the next multiple of six inches. The slenderness ratio (Lss / Dvd) for each

separator was then calculated based on the rounded dimensions; these values can also be

seen in Table 8. Typical slenderness ratios for two-phase separators fall in the range of 3

to 5, and all three of our separators meet these criteria [8].

Table 8. Separator Design Outputs.

We obtained the necessary outputs from the model to determine the horsepower

and size requirements for our three cooler designs, providing data for the cost analysis

and skid model. These values, as seen in Table 10, include the fan driver brake

horsepower, total extended surface heat-transfer area of tubes (Ax), tube bundle face area

(Fa) which represents the heat-transfer surface available to airflow, and fan blade

diameter (Dfan) rounded up to the next available fan size. The total power required to

37

drive our entire VRU system was determined using the cooler and compressor brake

horsepower values.

Table 9. Cooler Design Outputs.

6.4.2 Compressor Results and Sensitivities

To simulate hot and cold day (daytime vs. nighttime) conditions, we used ambient

air temperature to model three cases: minimum (cold), average, and maximum (hot)

temperatures. After simulating these cases, also referred to as cases 1-3 in Table 7, our

results showed that both the outlet temperature and brake horsepower for compressors 2

and 3 increased with ambient temperature, as seen in the compressor outputs for cases 1-

3 of Table 10. When compared to our base case conditions, the outlet temperature and

brake horsepower changed by an average 11% and 4%, respectively. The outlet

temperature is a critical aspect of our design as it determines compression feasibility. For

the hot conditions (case 3), we observed that the outlet temperature for compressor 2 was

slightly above the critical temperature of 300oF, illustrating that our design may not be

feasible for extremely hot weather without making key changes. To minimize these

compressor outlet temperatures for extreme conditions, many future modifications can be

made to our design: add more air cooling, use or add water cooling, increase number of

38

compression stages, change compressor type, increase compressor efficiency, and/or re-

size the existing compressors.

Surging effects were also considered, as the gas flow rates coming from both

stock tanks are constantly fluctuating, especially with the presence of excess liquids or

pipeline pressure changes. To model these deviations in flow, the given gas flow rates

were used as averages, while ±30% of these values provided the maximum and minimum

flow rates; these conditions are indicated as cases 2, 4, and 5 in Table 7. According to our

design results, the brake horsepower for all three compressors significantly increased

with gas throughput, as seen in Table 10. Compressor power changed by an average 30%

when compared to our base case values, which stresses the importance of accounting for

extreme conditions in our design. Compressor brake horsepower is a key design output

because it not only determines minimum sizing and power requirements for the

compressor designs, but also affects compressor selection, equipment cost analysis, VRU

skid layout for the platform, and the total power required to run our system.

Table 10. Compressor Design Outputs.

39

6.5 Bill of Materials

Before creating a skid layout of our proposed design, we had to list all

components with their dimensions in a Bill of Materials (BOM) as shown in Table 11.

Dimensions were determined using product catalogs from vendors, MATLAB models,

and calculations described above [14,15]. The BOM was also needed to determine part of

the financial costs concerning capital expenses, where costs for the specific components

were obtained using values from 2003 [16]. We doubled the cost values to account for the

recent increase in raw materials and labor rate costs. The total equipment cost was

estimated to be approximately $750,000, which was also used for further financial

analysis. The BOM provides a layout of the type and quantity of individual components

needed for the VRU system as well as their estimated costs.

40

Table 11. Bill of Materials.

6.6 Solid Skid Model

The VRU system will need to be placed on a skid, which represents a base

platform that will be able to withstand the weight of components placed on top. The VRU

components will be placed on a skid, transported, and finally be placed on the production

platform offshore. To fit on the production platform, we had to focus on reducing the skid

size as much as possible. From the BOM, we were able to lay out a two-dimensional

sketch of the VRU on the skid. Figure 14 shows the two-dimensional sketch from the top

view.

41

Scrubbers

Coolers

Compressors

Key

Cooler 2 Cooler 3

2 MMSCFD 1 MMSCFD

3 MMSCFD

29 ft.

12 ft.

S1 S2S3

Com 3Com 1&2

Cooler 1

Figure 14. Two Dimensional Skid Layout.

Looking at this skid layout above, we can see the overall relative dimensions as

well as the streams entering and exiting the VRU. The process starts with the 2MMSCFD

flow running first through the two-stage compressor to increase the pressure from 5psig

to 15psig, cooler 1, scrubber (S1), and returning to the same two-stage compressor

(Com1&2) to be recompressed from 15psig to 45psig. Since the first compressor

(Com1&2) is a two-stage compressor, it is able to simultaneously compress two flows at

one time. From there, it passes through cooler 2, scrubber (S2), and then enters the

second compressor (Com3). The 1 MMSCFD stream is added into the stream to be

compressed from 45psig to 90psig in the second compressor (Com3). Finally the

combined stream of 3 MMCFD is cooled, separated (S3), and rerouted to the sales

compressor.

90 psig

45 psig 5 psig

42

The final dimensions for the skid will be 29 ft. long and 12 ft. wide with a

maximum height of 10 ft due to scrubber 3’s height. The components are spaced 2 ft.

apart from each other and 6 in. from the edges of the skid to allow access for piping and

maintenance.

Figure 15 is a three-dimensional model of our proposed design following the

same layout, from left to right, as the two-dimensional model in Figure 14. As seen in

Figure 15, the two stage reciprocating compressor on the left is much larger in

comparison to the single stage reciprocating compressor because it will have to

recompress two streams. The heat exchangers shown in the back are the largest pieces of

equipment in our final design while the vertical scrubbers are the tallest.

Figure 15. Three Dimensional Skid Layout.

43

7 FINANCIAL ANALYSIS

7.1 Annual Sales Loss

Now that we have covered the key aspects of sizing components, we shift our

focus to financial costs. Currently the gas stream of 45psi (1 MMSCFD) is being burnt

off into the atmosphere, so we calculated the value of the gas that was being lost. To do

this, we needed a cost estimate of how much the natural gas is worth in today’s market,

also known as spot price. Since the spot price of natural gas changes every day, we chose

to look at the spot trends over the last year, published on online markets, as well as future

price predictions from natural gas price traders and the Energy Information

Administration. These prices per million British thermal units (MMBtu) for November

11th

can be seen in Table 12.

Table 12. Past and Predicted Natural Gas Spot Prices [17,18,19].

To estimate the value of natural gas being lost in a given day, we took the Henry

Hub spot price on the day of November 11, 2009, since this is the closest value to

present day, which was $4.18 per million British thermal units [18]. To calculate the sales

amount that is lost due to flaring, we had to account for the natural gas heating value

which is 1,028 Btu/SCF. Using the equation below we are able to compute the value of

the original 1 MMSCFD stream being burnt off:

44

Annual Sales Loss = Flowrate (Q)* Heating Value (HV)* Spot Price* Days in a year

Annual Sales Loss = 1 MMSCF/day * 1,028 Btu/SCF* $4.18/MMBtu * 365 days/year

From our calculations, the annual sales loss from the 1 MMSCFD stream alone is

approximately $1,568,400 a year. Instead of earning this profit amount, Chevron is

currently burning off the 1 MMSCFD gas stream.

7.2 Investment Costs

Capital, installation, and operations and maintenance (O&M) costs are related to

the design flow capacity of the stream. We determined the costs for a VRU system for

the 3MMSCFD flow capacity leaving the VRU. Due to Chevron’s request we were not

able to contact vendors for specific prices on equipment; therefore, we derived our

financial values from extrapolating capital, installation, and O&M costs available from

EPA’s Natural Gas Star Program [20]. Capital costs were also compared to values of the

specific equipment costs [16]. Table 13 lists the capital, installation, and O&M costs

derived.

Table 13. VRU Costs [3].

45

Since the above values were obtained in 2004, we doubled the cost estimate to

take into account recent increases in labor rates, installation costs, deck differences, cost

of raw materials, and equipment costs. Therefore, the cost estimates we focused on for

our design were based on the 6000 MSCFD design capacity, rather than the 3000

MSCFD, to have a more conservative and accurate representation of today’s prices.

Design capacity is the maximum fluid flow the VRU will experience while

running. As fluid capacity increases, the investment cost also increases. Capital costs

include the cost of the equipment: compressors, separators, and coolers. Installation costs

include the cost of a crew to install the system and any extra equipment needed to

transport the skid onto the platform. In the above example, installation cost is calculated

as 75% of the capital cost [20]. Operation and maintenance costs incorporate the cost of

the crew to maintain the VRU, as well as the operating cost to keep the VRU in working

order. The investment cost is the sum of the capital and installation cost. As seen in

Table 13, the investment cost for our project is approximately $1.3 million. Equipment

cost was the major factor in contributing to the investment cost and unavoidable since it

relies on the capacity flow.

7.3 Payback and Return on Investment

To continue our financial analysis, we calculated the value of recovered gas, the

payback period, and the return on investment after the installation of the VRU. The value

of recovered gas is the annual value that Chevron may potentially earn by selling off the

natural gas recovered by the VRU. The price range of the recovered gas was based on a

low and high range from past and future natural gas spot prices from Table 12. To

46

calculate the value of recovered gas, we used the same annual sales loss equation as

stated previously.

Figure 16 graphs the predicted value of recovered gas at 75% runtime versus the

natural gas spot price. A 75% runtime was chosen to take into account the annual

downtime from maintenance on the VRU equipment [21]. The value of recovered gas for

our range of $4.18/MMBtu to $6.50/MMBtu (highlighted in Figure 16) varied from $3.5

million to $5.5 million. In comparison to the initial investment cost of $1.3 million, the

profit exceeds the initial cost by double to triple the cost.

Figure 16. Value of Recovered Gas and Net Present Value vs. Natural Gas Spot Price.

Now that we know the investment cost and the value of recovered gas, we were

able to calculate payback and return on investment. The payback period tells us how

long it will take for incoming cash flow to equal the amount invested on implementing

$0

$5,000,000

$10,000,000

$15,000,000

$20,000,000

$25,000,000

$0.00 $2.00 $4.00 $6.00 $8.00 $10.00

Do

llar

Am

ou

nt

Natural Gas Spot Price

Value of Recovered Gas and Net Present Value

Value of Recovered Gas at 75%

NPV 5yrs

47

the VRU system. The payback period was calculated by dividing the initial capital and

installation costs by the annual value of the recovered gas. For our low and high range

for natural gas spot prices, we calculated payback to be from about 3 months to less than

5 months. This is a considerably short payback and favors the installation of our VRU on

the platform.

The return on investment differs from the payback period because it determines

how much profit is gained in comparison to the initial investment. The return on

investment (ROI) was calculated using the equation:

ROI = (Value of Recovered – Initial Investment)/Initial Investment.

For the low and high range spot prices, return on investment varied from 168% to 317%.

This is a very high return on investment and if natural gas prices continue to climb, so

will Chevron’s return on investment. Fast payback and high return on investment makes

installing the VRU on the platform a favorable option for Chevron.

7.4 Net Present Value

Since Chevron would still like to implement the VRU for environmental reasons

even if implementing the VRU on the platform does not add much financial contributions

we chose a small discount rate (i) of 10%. The discount rate is the minimum percentage

price a company would like to be returned by an investment. By using the 10% discount

rate, we calculated the net present value (NPV) of the project for five years.

48

To calculate NPV, we used the equation:

NPV = AVRG *(PVIFA,n) – CC – IC – O&MC*(PVIFAi,n)

NPV = Net present value

AVRG = Annual value of recovered gas

PVIFA = Present value of an annuity

n = Number of years

i = Discount rate

CC = Capital cost

O&MC = Operation and maintenance cost

The present value of an annuity was obtained from economic tables [22] and based on the

discount rate of 10% for a five year span.

Again, we took a range considering the changes in natural gas prices. Figure 16

also depicts the linear increase in net present value in relation to the natural gas price.

For our low/high range, net present value ranged from $11.3 million to $18.8 million.

Since net present value is greater than zero, this project can be deemed a good investment

because the company would not be losing any money; in fact, they can still make $11 to

$18 million dollars more than the 10% return desired.

Almost as important, is the annual revenue Chevron can expect to see after

installing the VRU system, also known as annuity. Taking the net present value, we

back-calculated to obtain the annual revenue. By knowing the interest rate and the

number of years, we determined the annuity of the present value using the conversion

factor (1/PVIFA). The equation used the equation:

Annuity = Net Present Value * (1/PVIFA).

After calculation, for the low and high gas spot prices, the annuity ranged from $3

million to $5 million. After incorporating the VRU system on the platform, Chevron can

expect positive annual revenue from the recovered natural gas.

49

Considering the short payback, high return on investment, and positive values of

net present value and annuity, the financial analysis proves to benefit Chevron financially

and would be a great investment if the VRU is implemented. If natural gas prices

continue to increase, Chevron will be able to obtain more revenue in the years to come.

8 COST ESTIMATE

No costs were associated with our project. A prototype was not required for our

project, eliminating material costs. The MATLAB and SolidWorks software we used

were available free of charge at the university. Due to resources through the university’s

libraries, we also did not need to buy technical papers.

9 FUTURE WORK AND RECOMMENDATIONS

For future purposes, implementing liquid transfer pumps after each scrubber may

be a critical addition to the proposed VRU system to account for surging and the presence

of excess liquids in the gas when restarting the VRU. This will help prevent damage to

the compressors and decrease downtime when gravity is not sufficient to drain all the

liquids to the sump tank. If there is access to a high pressure gas source on the platform,

an alternative for vapor recovery could be to use venturi jet ejector technology, which

takes a high pressure gas flow and combines it with the low pressure vapors to create an

intermediate pressure flow which can then enter the sales compressor or other processing

equipment. Currently, venturi jet ejectors have only been implemented onshore, but may

50

be used offshore in the future. In addition, venturi jet ejectors have no mechanical

moving parts resulting in significantly lower maintenance costs [23].

10 CONCLUSION

In conclusion, our team has developed overall VRU and detailed individual

component designs through research and utilization of applicable design tools, along with

supporting feasibility calculations and justifications for our selections. A critical

component of our engineering analysis included creating a MATLAB computer model to

simulate and verify our VRU design, applying principles of thermodynamics, heat

transfer, fluid mechanics, and gas separation. A three-dimensional solid model was also

created to provide detailed visualization of our VRU design components and overall

layout. This VRU system will recover hydrocarbon vapors and re-route the gas to sales

on one of Chevron’s offshore production platform in the Gulf of Mexico, minimizing gas

losses and increasing profits while complying with environmental regulations.

Considering the short payback period, high return on investment, and annual revenue of

about $4 million associated with the proposed VRU design, our analysis shows this final

design solution is financially sound and would be a favorable investment for

implementing in the project. We have also provided Chevron with recommendations for

future work in terms of further improvement of the final solution and potential

investments in new and existing technologies.

51

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1. Our Businesses. (n.d.). Retrieved September 3, 2009, from Chevron:

http://www.chevron.com/about/ourbusiness/

2. Chevron. (2009). Gulf of Mexico Business Unit Fact Sheet. Houston: Chevron

North American Exploration and Production.

3. Natural GasSTAR Program. (n.d.). Retrieved September 10, 2009, from

http://www.epa.gov/gasstar/documents/workshops/houston-2005/instal_v.pdf

4. Evans, N. (n.d.). Retrieved from http://www.vaporrecoveryunits.net/

5. Rothenbucher, R. K. (1976). U.S. Patent No. 3,939,906. Washington, DC: U.S.

Patent and Trademark Office.

6. Goodyear, M. A. (2002). U.S. Patent No. 6,418,957. Washington, DC: U.S. Patent

and Trademark Office.

7. Mokhatab, S., Poe, W., & Speight, J. (2006). Handbook of Natural Gas

Transmission and Processing. Burlington: Gulf Publishing

8. Gas Processors Suppliers Association. (1994). Engineering Data Bok. Tulsa: Gas

Processors Association.

9. Mohitpour, M., Golshan, H., & Murray, A. (2003). Pipeline Design &

Construction: A Practical Approach. New York: American Society of Mechanical

Engineers.

10. Hewitt, G. (1998). Heat Exchanger Design Handbook. New York: Begell House

Inc.

11. Kroger, D. G. (2004). Air-Cooled Heat Exchangers and Cooling Towers.

PennWell Books.

12. Kuppan, T. (2000). Heat Exchanger Design Handbook. New York: Marcel

Dekker Publishing .

13. Svrcek, W., & Monnery, W. (1993). Design Two-Phase Separators Within the

Right Limits. Chemical Engineering Progress , 53-60.

14. Ariel Corporation. (n.d.). Ariel JGM, JGP, JGN, JCQ Compressors [Brochure].

Retrieved from http://www.arielcorp.com/uploadedFiles/Products/JGMPNQ.pdf

52

15. Air-X-Changers. (n.d.). AXC Model H [Brochure]. Retrieved from

http://www.airx.com/Uploads/All/Air-X-Changers/Publications/

AXC_ModelH_11-06.pdf

16. Process Equipment Cost Estimates. (2003, October 15). Retrieved from

http://www.matche.com/EquipCost/index.htm

17. Oilnergy. (n.d.). NYMEX Henry Hub Natural Gas Price. Retrieved November 19,

2009, from http://www.oilnergy.com/1gnymex.htm

18. Bloomberg. (n.d.). Energy Prices. Retrieved November 11, 2009, from

http://www.bloomberg.com/markets/commodities/energyprices.html

19. CME Group. (2009, November 19). Natural Gas Henry Hub Futures. Retrieved

November 19, 2009, from http://www.cmegroup.com/trading/energy/natural-

gas/natural-gas.html

20. EPA's Natural Gas STAR Program, Shell, GCEAG, API, & Rice University.

(2004, June 8). Installing Vapor Recovery Units to Reduce Methane Losses

[PowerPoint slides].

21. Quincy Compressor. (n.d.). Cost of Ownership: The Definitive Guide [Brochure].

22. National Council of Examiners for Engineering and Surveying (Ed.). (2008).

Fundamentals of Engineering Supplied-Reference Handbook (8th ed.). Author.

23. Goodyear, M. A., Graham, A. L., Stoner, J. B., Boyer, B. B., Zeringue, L. P., &

Society of Petroleum Engineers International. (2003, March). Vapor Recovery of

Natural Gas Using Non-Mechanical Technology (SPE No. 80599). Society of

Petroleum Engineers Inc.

24. Schmidt, P., Baker, D., Ezekoye, O., & Howell, J. (2006). Thermodynamics: An

Integrated Learning System. Hoboken: Wiley.

25. Kline, P. E., Fahlgren, C. E., & Kitchen, M. R. (1971). U.S. Patent No. 3,565,164.

Washington, DC: U.S. Patent and Trademark Office.

26. Artemov, L. N., & Bakanov, A. F. (1977). U.S. Patent No. 4,002,444.

Washington, DC: U.S. Patent and Trademark Office.

27. Longardner, R. L. (1990). U.S. Patent No. 4,936,109. Washington, DC: U.S.

Patent and Trademark Office.

28. Raseley, L. J., Collier, S. J., & McCarty, H. G. (1980). U.S. Patent No. 4,214,883.

Washington, DC: U.S. Patent and Trademark Office.

53

29. Hewitt, P. J. (1991). U.S. Patent No. 5,006,138. Washington, DC: U.S. Patent and

Trademark Office.

30. Grimmer, J. E., & Ketcham, E. T. (2004). U.S. Patent No. 6,695,591.

Washington, DC: U.S. Patent and Trademark Office.

31. Brown, R. (2005). Compressors: Selection and Sizing. Boston: Gulf Publishing.

A-1

APPENDIX A: DESIGN FEASIBILITY CALCULATIONS

545 psig: Stock Tank 1 Single Stage Gas Compression

Figure 6. Single Stage Compression from Tank 1.

o Assumptions

Steady State Steady Flow

No change in KE, PE

Adiabatic

Isentropic Compression

Constant ratio of specific heats (K)

K=1.27, evaluated at T1 using specific heat calculator MATLAB

function

Compressors are reciprocating with adiabatic efficiencies of

𝜂𝑐 = .83 [31]

o 1st Law of Thermodynamics reduces to:

𝑤𝑐 ,13 = ℎ3 − ℎ1

o For Isentropic compression the inlet temperature and adiabatic outlet

temperature are related by:

𝑇3𝑆 = 𝑇1 𝑃3

𝑃1

𝑘−1𝑘

− 1 + 𝑇1 = 849.40 𝑅 = 390𝑜𝐹

o The actual compressor outlet temperature is found by the following

relation:

𝑇3 =𝑇3𝑆 − 𝑇1

𝜂𝑐+ 𝑇1 = 908.68 𝑅 = 448.68𝑜𝐹

o Operating temperature T3>300oF, so cooling phase and multiple

compression stages are required for 5 45spig pressure increase

545 psig: Stock Tank 1 Two Stage Gas Compression with interstage cooling

A-2

Figure 7. Two Stage Compression from Tank 1.

o Set each compression ratio per stage =𝑃3

𝑃1=

𝑃5

𝑃4= 3 to evenly distribute

compression load

o Assumptions:

Steady State Steady Flow

No change in KE, PE

Adiabatic

Isentropic Compression

Constant K=1.27, evaluated at T1 using specific heat calculator

MATLAB function

Compressors are reciprocating with adiabatic efficiencies of

𝜂𝑐 = .83

Pressure change across cooler is negligible

Tambient=80oF

o 13: Following same isentropic compression analysis as for single stage

compression

𝑇3𝑆 = 𝑇1 𝑃3

𝑃1

𝑘−1𝑘

− 1 + 𝑇1 = 707.33 𝑅 = 247.33 𝐹

𝑇3 =𝑇3𝑆 − 𝑇1

𝜂𝑐+ 𝑇1 = 737.51𝑅 = 277.51 𝐹

o 34: Cooler rule of thumb

For air cooling assume discharge temperature of 25oF above

ambient dry bulb temperature [8]

𝑇4 = 𝑇𝑎𝑚𝑏 + 25𝑜𝐹 = 105𝑜𝐹

A-3

o 45: Following same isentropic compression analysis as with single stage

compression

𝑇5𝑆 = 𝑇1 𝑃5

𝑃4

𝑘−1𝑘

− 1 + 𝑇4 = 713.65 𝑅 = 253.65𝑜𝐹

𝑇5 =𝑇5𝑆 − 𝑇4

𝜂𝑐+ 𝑇4 = 744.10 𝑅 = 284.10𝑜𝐹

o Since both T3 and T5 are safely below 300oF, 2 stage compression with

intercooling will boost the gas pressure without damaging the equipment

o Now we will check the feasibility of single stage compression for the

combined 45 psig gas flow stream

4590 psig: combined Gas flow Stream

Figure 8. Combined Gas Flow Compression.

o Same assumptions as Stock Tank 1 Single Stage Gas Compression

𝑇8𝑆 = 𝑇7 𝑃8

𝑃7

𝑘−1𝑘

− 1 + 𝑇7 = 648.91 𝑅 = 188.91𝑜 𝐹

𝑇8 =𝑇8𝑆 − 𝑇7

𝜂𝑐+ 𝑇7 = 667.12 𝑅 = 207.12𝑜 𝐹

o The operating temperature T8<300oF, so the compression can be achieved

in one stage without cooling

Based on these feasibility calculations, we must have two compression stages for

the 2MMSCFD gas flow from stock tank 1 and only one compression stage for

the combined 3MMSCFD gas flow.

B-1

APPENDIX B: DETAILED VRU PROCESS FLOW DIAGRAM

Figure B-1. Detailed VRU Process Flow Diagram.

C-1

APPENDIX C.1: MAIN VRU MATLAB PROGRAM FLOWCHART

Figure C-1. Main VRU MATLAB Program Flowchart.

Inputs: Comp 1-3 Efficiencies, Q 1&2

TambientCalculate T3-T9

Calculate COM BHP’s

Calculate SCR Dimensions

Calculate CLR BHP’s and Dimensions

Print Out Results

Outputs: T1-9, BHP’s: COM & CLR,

Dimensions: CLR and SCR

C-2

APPENDIX C.2: VERTICAL SEPARATOR MATLAB FUNCTION

FLOWCHART

Figure C-2. Vertical Separator MATLAB Function Flowchart.

Function Inputs: P, T,

Qgas

Calculate SCR inner vessel

diameter (Dvd)

Calculate SCR Nozzle

Diameter (Dn)

Calculate SCR Lss

Output array with Dvd, Dn,

Lss

C-3

APPENDIX C.3: COOLER MATLAB FUNCTION FLOWCHART

Figure C-3. Cooler MATLAB Function Flowchart.

Inputs: Comp 1-3 Outlet T's & P's,

Q 1&2, Tambient

Calculate Total Extended Surface

Area

Calculate Tube Bundle Face Area

Calculate Fan Diameter

Calculate Fan Driver BHP

Outputs: Extended Surface & Bundle

Face A's, Fan D, Fan Driver BHP

Send Outputs to Main VRU Function

C-4

APPENDIX C.4: SPECIFIC HEAT CAPACITY CALCULATOR MATLAB

FUNCTION FLOWCHART

Figure C-4. Specific Heat Capacity Calculator MATLAB Function Flowchart.

Inputs: Temperature, Gas

Properties & Composition

Calculate Cp's for Individual Gas Components

Convert Molar Fractions to Mass

Fractions

Calculate Overall Gas Cp

Send Cp to Main VRU & Cooler

Functions

D-1

APPENDIX D.1: MATLAB CODE: MAIN VRU PROGRAM

% Variable Inputs

SG=.625;%input('Enter the Specific gravity of your natural gas ');

T1F=100;%input('Enter the natural gas temperature of the stock tanks in Deg F');

T2F=T1F;

T1R=T1F+460;%Rankine

T2R=T1R;

EffComp1=.835;

EffComp2=.835;

EffComp3=.79;

Tinf=80;%input('Enter the ambient air Temperature in Deg F');

E=.785;%input('Enter parasitic efficiency for compressors (.785 for low speed recip, .99

for centrifugal):');

CompEff=1;%input('Enter Compression efficiency for compressors (1 for low speed

recip, .835 for centrifugal):');

%Constants

P1=5; %[Psig]

P2=45; %[Psig]

P3=15; %[Psig]

P4=15; %[Psig]

P5=45; %[Psig]

P6=45; %[Psig]

P7=45; %[Psig]

P8=90; %[Psig]

P9=90; %[Psig]

Q1=1.4; %[MMSCFD]

Q3=Q1;

Q4=Q1;

Q5=Q1;

Q6=Q1;

Q2=0.7; %[MMSCFD]

Q7=Q1+Q2; %[MMSCFD]

Q8=Q7;

Q9=Q7;

Rbar=1.9858; %[btu/lbm*R]

MW=18.06;

%Calculate K (Specific heat ratio)

%K=CPcalc(T1F)/(CPcalc(T1F)-Rbar/MW);

K=1.3-0.31*(SG-0.55); %Campbell relation (1992)

%1-3: Compressor 1

%Find T3S

T3SR=T1R*(((P3/P1)^((K-1)/K))-1)+T1R;

%Find T3

D-2

T3R=((T3SR-T1R)/EffComp1)+T1R;

T3F=T3R-460;

%3-4: Cooler 1: Rule of thumb- discharge pressure @ cooler exit is ~25Deg F

%above ambient temp

T4F=25+Tinf;

T4R=T4F+460

%4-5: Compressor 2

T5SR=T4R*(((P5/P4)^((K-1)/K))-1)+T4R;

T5R=((T5SR-T4R)/EffComp2)+T4R;

T5F=T5R-460; %[Deg F]

%5-6: Cooler 2

T6F=25+Tinf;

T6R=T6F+460;

%6-7: Combine Gas Streams

cp6=CPcalc(T6F); %[Btu/lbm-degR]

cp2=CPcalc(T2F);

cp7=CPcalc((T6F+T2F)/2); %Evaluated at average of inlet temperatures

mdot6=(Q6*10^6*MW)/(379*24*3600);%Mass flowrate from stock tank 1 [lbm/sec]

mdot2=(Q2*10^6*MW)/(379*24*3600);%Mass flowrate from stock tank 2 [lbm/sec]

mdot7=(Q7*10^6*MW)/(379*24*3600);%Mass flowrate of combined gas streams

[lbm/sec]

T7R=((mdot6*cp6*T6R)+(mdot2*cp2*T2R))/(mdot7*cp7);

T7F=T7R-460; %[Deg F]

%7-8: Compressor 3

T8SR=T7R*(((P8/P7)^((K-1)/K))-1)+T7R;

T8R=((T8SR-T7R)/EffComp3)+T7R;

T8F=T8R-460; %[Deg F]

%8-9: Cooler 3

T9F=25+Tinf;

T9R=T9F+460;

%Outputs

T1F

T2F

T3F

T4F

T5F

T6F

T7F

D-3

T8F

T9F

% BHP for Compressors

KRatio=(K/(K-1));

BhpComp1=0.0854*((Q1*T1R)/(E*CompEff))*KRatio*(((P3/P1)^(1/KRatio))-1)

%[hp]

BhpComp2=0.0854*((Q4*T4R)/(E*CompEff))*KRatio*(((P5/P4)^(1/KRatio))-1)

%[hp]

BhpComp3=0.0854*((Q7*T7R)/(E*CompEff))*KRatio*(((P8/P7)^(1/KRatio))-1)

%[hp]

%Scrubber Designs

%Scrubber 1 Design

A1=VertSepFunction(T4F,P4,Q4)

%Scrubber 2 Design

A2=VertSepFunction(T6F,P6,Q6)

%Scrubber 3 Design

A3=VertSepFunction(T9F,P9,Q9)

%Cooler Designs

%Cooler 1 Design

B1=CoolerFunction(T3F,Tinf,P3,Q3)

%Cooler 2 Design

B2=CoolerFunction(T5F,Tinf,P5,Q5)

%Cooler 3 Design

B3=CoolerFunction(T8F,Tinf,P8,Q8)

D-4

APPENDIX D.2: MATLAB CODE: VERTICAL SEPARATOR FUNCTION

function A = VertSepFunction (TF,Pg,Qsc)

%User Input

%TF=input('Enter the temperature of natural gas entering separator in Deg F: ');

TR=TF+460; %Temp in Rankine

%Pg=input('Enter the Pressure of natural gas entering separator in Psig: ');

Pa=Pg+14.7; %Atmospheric Pressure [Psia]

%Qsc=input('Enter the Volumetric Flow Rate of natural gas entering separator in

MMSCFD: ');

%Constants

R=10.73; %Universal Gas constant

MW=18.064; % Molecular weight of Natural Gas

RhoL=62.4; % Density Natural Gas [lb/ft^3]

Th=5; %Hold up time [Min]

Ts=3; %Surge time [Min]

%Calculate Gas Density at Given Temp and Pressure

RhoV=(Pa*MW)/(R*TR); %lb/ft^3

%Calculate Separation Constant K

Kprime=0.35-0.01*((Pg-100)/100);

K=Kprime*0.75; %Includes correction factor for suction scrubbers

%Step 1: Calculate Vertical Terminal Vapor velocity

Ut=K*((RhoL-RhoV)/(RhoV))^.5; %ft/s

Uv=0.75*Ut; %ft/s

%Step 2: Calculate Vapor and Liquid Volumetric Flow Rates

mdot=(Qsc*10^6*MW)/(379*24*3600);%Mass flowrate of gas converted from

Volumetric Flowrate [lb/sec]

Qv=mdot/RhoV; %volumetric flowrate of gas [ft^3/s]

Qlprime=mdot/RhoL; %volumetric flowrate of liquid water [ft^3/s]

%Step 3: Calculate Vessel ID

Dvdprime=((4*Qv)/(pi()*Uv))^.5; %[ft]

Dvd=Dvdprime+(6/12);%Vessel Diameter with 6" added for mist extractor [ft]

%Step 4: Convert Liquid Flow Rate to ft^3/min

Ql=Qlprime*60; %[ft^3/min]

%Step 5: Calculate hold up volume

Vh=Th*Ql; %ft^3

%Step 6: Calculate Surge Volume

Vs=Ts*Ql; %Ft^3

D-5

%Step 7: Find HLLL

%From chart Svrcek (1993)

HLLL=15/12; %[ft]

%Step 8: Calculate HH

HH=((Vh)/((pi()/4)*(Dvd^2))); %[ft]

%Step 9: Calculate HS

HS=((Vs)/((pi()/4)*(Dvd^2))); %[ft]

%Step 10 Calculate dn and HLIN

Qm=Qlprime+Qv;%[ft^3/s]

lambda=Qlprime/(Qlprime+Qv);

Rhom=(RhoL*lambda)+(RhoV*(1-lambda)); %[lb/ft^3]

dn=((4*Qm)/((pi()*60)/(Rhom^.5)))^.5; %[ft]

HLIN=1+dn; %[ft]

%Step 11 Calculate HD

HD=2+(.5*dn);%[ft]

%Step 12 Calulate Mist extractor Extra Height

HME=1.5; %[ft]

%Step 13 Calculate HT

HT=HLLL+HH+HS+HLIN+HD+HME;%[ft]

% %Outputs

% disp('The diameter of the separator in feet is:')

% Dvd

%

% disp('The diameter of the input nozzle in feet is:')

% dn

%

% disp('The height of the separator in feet is')

% HT

A=[Dvd,dn,HT];

D-6

APPENDIX D.3: MATLAB CODE: COOLER FUNCTION

function B = CoolerFunction (TinF,Tinf,Pg,Qsc)

%User Input

%TinF=input('Enter the natural gas temperature entering cooler in Deg F: ');

TinR=TinF+460; %Temp in Rankine

%Tinf=input('Enter the ambient air temperature in Deg F: ');

%Pg=input('Enter the natural gas pressure entering cooler in Psig: ');

%Qsc=input('Enter the Volumetric Flow Rate of natural gas entering cooler in

MMSCFD: ');

%Constants

EffFan=.70;

EffSpeedReducer=.92;

MW=18.064; %Molecular weight of natural gas

N=3; %Number of rows of tubes

L=6; %Tube length in ft

F=1; %Mean Temperature Difference correction factor for 3 tube passes

APSF=80.4; %Total Available External Area/Bundle Face Area for 3 rows of tubes

cpAIR=0.24; %[Btu/lbm-degR]

FCmin=0.40; %Minimum Fan Coverage ratio

RhoDryAir=0.0749; %Density of Dry Air at 70degF, 14.7psia [lb/ft^3]

%Determine Overall Heat Transfer Coefficients for Air Coolers based on extended

surfaces – values from GPSA table for hydrocarbon vapors

if (Pg == 15)

Ux=1.39;

elseif (Pg == 45)

Ux=1.57;

elseif (Pg == 90)

Ux=1.87;

else

Ux=1.61;

end

%Cooler outlet temp: Rule of thumb- discharge temp @ cooler exit is ~25Deg F above

ambient temp

ToutF=25+Tinf;

D-7

ToutR=ToutF+460; %Rankine temp

%Approximate air temperature rise in Deg F

TavgF=(TinF+ToutF)/2;

TavgR=460+TavgF; %Rankine temp

TinAIR=Tinf; % deg F

DeltaTa=((Ux+1)/10)*(TavgF-Tinf);

ToutAIR=DeltaTa+TinAIR; % deg F

%Calculate Log & Corrected Mean Temperature Differences

LMTD=((TinF-ToutAIR)-(ToutF-TinAIR))/log((TinF-ToutAIR)/(ToutF-TinAIR)); %deg

F

CMTD=F*LMTD; %deg F

%Calculate outside extended surface heat transfer area

%Determine specific heat constant of gas mixture

cpgas=CPcalc(TavgF); %[Btu/lbm-degR]

%Calculate mass flowrate of gas

mdot=(Qsc*10^6*MW)/(379*24*3600);%Mass flowrate of gas converted from

Volumetric Flowrate [lbm/sec]

%Calculate heat transfer rate (Qdot)

Qdot=mdot*cpgas*(TinF-ToutF)*3600; %[BTU/hr]

Ax=Qdot/(Ux*CMTD); %[ft^2]

%Convert heat transfer area to bundle face area

Fa=Ax/APSF; %[ft^2]

UnitWidth=Fa/L; %[ft]

%Calculate air mass flow rate & air face mass velocity

mdotAIR=Qdot/(cpAIR*DeltaTa); %[lbm/hr]

Ga=mdotAIR/Fa; %[lb/ft^2-hr]

%Calculate minimum fan area & fan diameter

FAPF=FCmin*Fa;

df=ceil(sqrt(4*FAPF/pi));

%Calculate fan total pressure & cooling air rate

%Determine density ratio at average air temperature

TavgAIR=(TinAIR+ToutAIR)/2;

Dr1=-0.002*TavgAIR+1.14; %using linear relationship for air-density ratios for

temperature range 40degF-120degF

D-8

%Determine pressure drop factor from air face mass velocity

Fp=7e-5*Ga-0.065; %using linear relationship for air static-pressure drop

%Calculate air static pressure drop

DeltaPs=Fp*N/Dr1; %[in H2O]

%Determine density ratio at fan inlet air temperature

Dr2=-0.002*TinAIR+1.14;

%Calculate actual air volumetric flow rate at fan inlet

ACFM=mdotAIR/(RhoDryAir*60*Dr2); %[ft^3/min]

%Calculate fan dynamic pressure drop

DeltaPd=(ACFM/((pi*df^2)/4))^2*(Dr2/4005^2); %[in H2O]

PF=DeltaPs+DeltaPd; %Total Fan Pressure [in H2O]

%Calculate fan brake horsepower

bhp=(ACFM*PF)/(6356*EffFan); %[hp]

Actualbhp=bhp/EffSpeedReducer; %[hp] actual fan motor bhp

%Outputs

%disp('The fan driver brake horsepower is: ')

%Actualbhp

%disp('The extended surface area in square feet is: ')

%Ax

%disp('The fan diameter in feet is: ')

%df

%disp('The bundle face area in square feet is: ')

%Fa

B=[Actualbhp,Ax,df,Fa];

D-9

APPENDIX D.4: MATLAB CODE: SPECIFIC HEAT CALCULATOR

FUNCTION

function B= CPcalc(TF)

format short g

%User Input

%TR=610.316;

TR=TF+460;

%Constants

M=18.064;

% Coefficient matrix contains the Cp polynomial constants a,b,c and d

% From First Row to last the gases are: Methane, Ethance, CO2,Propane,

% Isobutane, n butane, isopentane,npentane,hexanes+

CeoffMatrix=[4.75,.6666e-2,.09352e-5,-.451e-9; 1.648,2.291e-2,-.4722e-5,.2984e-

9;5.316,7.94e-3,-2.58E-06,3.06E-10;-0.966,4.04E-02,-1.16E-05,1.30E-09;-1.89,5.52E-

02,-1.70E-05,2.04E-09;0.945,4.93E-02,-1.35E-05,1.43E-09;1.618,6.03E-02,-1.66E-

05,1.73E-09;1.618,6.03E-02,-1.66E-05,1.73E-09;1.657,7.33E-02,-2.11E-05,2.36E-09];

%Calculate Cp bar using polynomial expression from Schmidt Thermo Text book

%page 369

CPbar=[CeoffMatrix(1,1)+(CeoffMatrix(1,2)*TR)+CeoffMatrix(1,3)*(TR^2)+CeoffMatr

ix(1,4)*(TR^3);CeoffMatrix(2,1)+(CeoffMatrix(2,2)*TR)+CeoffMatrix(2,3)*(TR^2)+Ce

offMatrix(2,4)*(TR^3);

CeoffMatrix(3,1)+(CeoffMatrix(3,2)*TR)+CeoffMatrix(3,3)*(TR^2)+CeoffMatrix(3,4)*

(TR^3);

CeoffMatrix(4,1)+(CeoffMatrix(4,2)*TR)+CeoffMatrix(4,3)*(TR^2)+CeoffMatrix(4,4)*

(TR^3);

CeoffMatrix(5,1)+(CeoffMatrix(5,2)*TR)+CeoffMatrix(5,3)*(TR^2)+CeoffMatrix(5,4)*

(TR^3);

CeoffMatrix(6,1)+(CeoffMatrix(6,2)*TR)+CeoffMatrix(6,3)*(TR^2)+CeoffMatrix(6,4)*

(TR^3); CeoffMatrix(7,1)+(CeoffMatrix(7,2)*TR)+CeoffMatrix(7,3)*(TR^2)+CeoffMat

rix(7,4)*(TR^3);

CeoffMatrix(8,1)+(CeoffMatrix(8,2)*TR)+CeoffMatrix(8,3)*(TR^2)+CeoffMatrix(8,4)*

(TR^3);

CeoffMatrix(9,1)+(CeoffMatrix(9,2)*TR)+CeoffMatrix(9,3)*(TR^2)+CeoffMatrix(9,4)*

(TR^3)];

%Cpis by dividing cpbars by their molecular weights

CPi=[CPbar(1)/16.043;CPbar(2)/30.07;CPbar(3)/44.01;CPbar(4)/44.094;CPbar(5)/58.124

;CPbar(6)/58.124;CPbar(7)/72.151;CPbar(8)/72.151;CPbar(9)/86.178;(2.5*1.98586)/28.0

13];

Mi=[16.043;30.07;44.01;44.094;58.124;58.124;72.151;72.151;86.178;28.013];%Molecul

ar Weights of gasses [Btu/lbmol*R]

yi=[92.407;3.352;4.79e-1;1.45;4.12e-1;5.18e-1;2.16e-1;1.84e-1;4e-1;5.84e-1];%Molar

composition of each gas

xi=(yi.*Mi)*(1/(100*M))

D-10

Cpix=CPi.*xi;

SumCpix=sum(Cpix);

B=SumCpix;

E-1

APPENDIX E: COOLER SIZING AND POWER SAMPLE CALCULATIONS

Givens

P=15 psig

T1=280.33oF (Compressor 1 outlet temperature)

T2= T∞ + 25 oF = 105

oF (Rule of thumb for cooler outlet temperature)

𝑇𝑎𝑣𝑔 =𝑇1+𝑇2

2= 192.67℉

T∞=80 oF

MWNatural Gas= 18.064

Cpair=0.24 𝐵𝑡𝑢

𝑙𝑏𝑚 −𝑅

Cpgas=0.5534 𝐵𝑡𝑢

𝑙𝑏𝑚 −𝑅

ρdry air =0.0749 𝑙𝑏

𝑓𝑡 3

Qsc=2MMSCFD

F=LMTD Correction Factor=1

FCmin=Minimum Fan Coverage=0.40

𝐴𝑃𝑆𝐹 =𝑇𝑜𝑡𝑎𝑙 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝐸𝑥𝑡𝑒𝑟𝑛𝑎𝑙 𝐴𝑟𝑒𝑎

𝐵𝑢𝑛𝑑𝑙𝑒 𝐹𝑎𝑐𝑒 𝐴𝑟𝑒𝑎= 80.4

Average efficiencies: 𝜀𝑓𝑎𝑛 = 0.70, 𝜀𝑠𝑝𝑒𝑒𝑑 𝑟𝑒𝑑𝑢𝑐𝑒𝑟 = 0.92

Assumptions

Fan Configuration: Forced-draft, horizontal, 1 fan

Ideal gas mixture with constant specific heats

Negligible gas pressure drop across cooler

N=3 rows of tubes

Number of tube passes = 3

Tube pitch & diameter

o Triangular pitch ~ 2 ½”

o 1” outside diameter

Fin length & spacing

o 5/8” high fins

o 10 fins/in spacing

Procedure

Step 1 : Determine overall heat transfer coefficient for extended surfaces

Extrapolate from GPSA Table:

E-2

50 − 15

1.6− 𝑈𝑥 =

100 − 50

1.9− 1.6

𝑈𝑥 = 1.39

Step 2: Approximate air temperature rise

∆𝑇𝑎 =𝑈𝑥 + 1

10 𝑇𝑎𝑣𝑔 − 𝑇∞

∆𝑇𝑎 = 29.93 ℉ = 𝑇𝑎𝑖𝑟 ,𝑜𝑢𝑡 − 𝑇∞

𝑇𝑎𝑖𝑟 ,𝑜𝑢𝑡 = 106.93 ℉

Step 3: Calculate log & corrected mean temperature differences

𝐿𝑀𝑇𝐷 = 𝑇1 − 𝑇𝑎𝑖𝑟 ,𝑜𝑢𝑡 − (𝑇2 − 𝑇∞)

ln𝑇1 − 𝑇𝑎𝑖𝑟 ,𝑜𝑢𝑡

𝑇2 − 𝑇∞

𝐶𝑀𝑇𝐷 = 𝐹 𝐿𝑀𝑇𝐷 = 76.62 ℉

Step 4: Calculate outside extended surface heat-transfer area

𝑚𝑑𝑜𝑡 ,𝑔𝑎𝑠 =𝑄𝑆𝐶 𝑀𝑊 106

379 24 3600 = 1.103

𝑙𝑏𝑚

𝑠𝑒𝑐

𝑄 = 𝑚𝑑𝑜𝑡 ,𝑔𝑎𝑠 𝐶𝑝𝑔𝑎𝑠 𝑇1 − 𝑇2 3600𝑠𝑒𝑐

𝑕𝑟 = 3.8528 𝑥 105

𝐵𝑡𝑢

𝑕𝑟

𝑄 = 𝐴𝑥 𝑈𝑥 𝐶𝑀𝑇𝐷

𝐴𝑥 =𝑄

𝑈𝑥 𝐶𝑀𝑇𝐷= 3627.57 𝑓𝑡2

Step 5: Convert heat transfer area to bundle face area

𝐹𝑎 =𝐴𝑥𝐴𝑃𝑆𝐹

= 45.12 𝑓𝑡2

E-3

Step 6: Calculate air mass flow rate & air face mass velocity

𝑄 = 𝑚𝑑𝑜𝑡 ,𝑎𝑖𝑟 𝐶𝑝𝑎𝑖𝑟 ∆𝑇𝑎

𝑚𝑑𝑜𝑡 ,𝑎𝑖𝑟 =𝑄

𝐶𝑝𝑎𝑖𝑟 ∆𝑇𝑎= 53784.21

𝑙𝑏𝑚

𝑕𝑟

𝐺𝑎 =𝑚𝑑𝑜𝑡 ,𝑎𝑖𝑟

𝐹𝑎= 1192.03

𝑙𝑏

𝑓𝑡2 − 𝑕𝑟

Step 7: Calculate minimum fan area & fan diameter

𝐹𝐶𝑚𝑖𝑛 =𝐴𝑓𝑎𝑛

𝐹𝑎

𝐴𝑓𝑎𝑛 = (𝐹𝐶𝑚𝑖𝑛 ) 𝐹𝑎 =𝜋

4 𝐷𝑓𝑎𝑛

2 = 18.05 𝑓𝑡2

𝐷𝑓𝑎𝑛 = 4

𝜋 𝐴𝑓𝑎𝑛 = 4.79 𝑓𝑡 ≈ 5 𝑓𝑡 (𝑅𝑜𝑢𝑛𝑑 𝑢𝑝 𝑡𝑜 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑓𝑜𝑜𝑡)

Step 8: Determine air static pressure drop

From GPSA Air-Density Ratio Chart:

𝐷𝑟 ,1 = 𝐷𝑟 @𝑇𝑎𝑣𝑔 ,𝑎𝑖𝑟 = 0.96

𝐷𝑟 ,2 = 𝐷𝑟 @𝑇∞ = 0.98

From GPSA Air Static-Pressure Drop Chart: 𝐹𝑝 = 𝐹𝑝 @ 𝐺𝑎 = 0.03

∆𝑃𝑠𝑡𝑎𝑡 =𝐹𝑝 𝑁

𝐷𝑟 ,1= 0.094 𝑖𝑛 𝐻2𝑂

Step 9: Calculate actual air volumetric flow rate at fan inlet

𝐴𝐶𝐹𝑀 =𝑚𝑑𝑜𝑡 ,𝑎𝑖𝑟

(𝜌𝑑𝑟𝑦 𝑎𝑖𝑟 ) (𝐷𝑟 ,2)

1 𝑕𝑟

60 𝑚𝑖𝑛= 12212.25

𝑓𝑡3

𝑚𝑖𝑛

Step 10: Calculate fan dynamic pressure drop

∆𝑃𝑑𝑦𝑛 =1

2 𝜌𝑓𝑎𝑛 𝑎𝑖𝑟 𝑣𝑓𝑎𝑛

2

E-4

𝑣𝑓𝑎𝑛 =𝐴𝐶𝐹𝑀

𝐴𝑓𝑎𝑛=𝐴𝐶𝐹𝑀𝜋4 𝐷𝑓𝑎𝑛

2

∆𝑃𝑑𝑦𝑛 = 𝑣𝑓𝑎𝑛2

𝐷𝑟 ,2

40052=

𝐴𝐶𝐹𝑀𝜋4 𝐷𝑓𝑎𝑛

2

2

𝐷𝑟 ,2

40052 = 0.0236 𝑖𝑛 𝐻2𝑂

(𝑤𝑕𝑒𝑟𝑒 40052 = 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 @ 70℉)

Step 11: Calculate total fan pressure drop

𝑃𝐹 = ∆𝑃𝑠𝑡𝑎𝑡 + ∆𝑃𝑑𝑦𝑛 = 0.1176 𝑖𝑛 𝐻2𝑂

Step 12: Calculate fan driver brake horsepower

𝐹𝑎𝑛 𝐵𝐻𝑃 = 𝐴𝐶𝐹𝑀 (𝑃𝐹)

6356 𝜀𝑓𝑎𝑛= 0.341 𝑕𝑝

(𝑤𝑕𝑒𝑟𝑒 6356 = 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟)

𝐹𝑎𝑛 𝐷𝑟𝑖𝑣𝑒𝑟 𝐵𝐻𝑃 =𝐹𝑎𝑛 𝐵𝐻𝑃

𝜀𝑠𝑝𝑒𝑒𝑑 𝑟𝑒𝑑𝑢𝑐𝑒𝑟= 0.371 𝑕𝑝

F-1

APPENDIX F: VERTICAL SEPARATOR SAMPLE CALCULATIONS

Givens

P=15 psig= 29.7 psia

T=105oF=565 R

Z~1

MWNatural Gas= 18.064

Rbar=10.73 𝑝𝑠𝑖𝑎 −𝑓𝑡 3

𝑙𝑏𝑚𝑜𝑙 −𝑅

ρL= ρwater=62.4 𝑙𝑏

𝑓𝑡 3

Qsc=2MMSCFD

Figure 13. Vertical Scrubber Design Dimensions [13].

Procedure

Step 1 : Calculate Vertical Terminal Vapor Velocity

𝑈𝑉 = 0.75 𝑈𝑡 = 5.329 𝑓𝑡

𝑠𝑒𝑐

F-2

𝑈𝑡 = 𝐾 𝜌𝐿 − 𝜌𝑉𝜌𝑉

12

= 7.105 𝑓𝑡

𝑠𝑒𝑐

From GPSA:

𝐾 ′ = .35 − 0.01 𝑃 − 100

100 = 0.342

𝐾 = 0 .075 𝐾 ′ = 0.256

𝜌𝑉 =𝑃

𝑇𝑍 𝑀𝑊

𝑅𝑏𝑎𝑟 = 0.088

𝑙𝑏

𝑓𝑡3

Step 2: Calculate Vapor and Liquid Volumetric Flow Rates

𝑚𝑑𝑜𝑡 =𝑄𝑆𝐶 𝑀𝑊 106

379 24 3600 = 1.103

𝑙𝑏

𝑠𝑒𝑐

𝑄𝑉 = 𝑚𝑑𝑜𝑡

𝜌𝑉= 12.534

𝑓𝑡3

𝑠𝑒𝑐

𝑄𝐿 = 𝑚𝑑𝑜𝑡

𝜌𝐿= 0.018

𝑓𝑡3

𝑠𝑒𝑐

Step 3: Calculate Vessel Inner Diameter

𝐷𝑉𝐷 = 4 𝑄𝑉𝜋 𝑈𝑉

= 1.731 𝑓𝑡

For a mist eliminator add 3-6” to DVD to accommodate support ring and round

up to the next 6”:

𝐷𝑉 = 𝐷𝑉𝐷 + 6" = 2.23 𝑓𝑡 ~ 2.5 𝑓𝑡

Step 4: Convert Liquid Volumetric Flow Rate Units

𝑄𝐿 = 𝑚𝑑𝑜𝑡

𝜌𝐿= 0.018

𝑓𝑡3

𝑠𝑒𝑐 60 𝑠𝑒𝑐

1 𝑚𝑖𝑛= 1.08

𝑓𝑡3

𝑚𝑖𝑛

Step 5: Select Holdup Time and Calculate Holdup Volume

𝑇𝐻 = 5 min (𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)

𝑉𝐻 = 𝑇𝐻 𝑄𝐿 = 5.4 𝑓𝑡3

F-3

Step 6: Select Surge time and Calculate surge Volume

𝑇𝑆 = 3 min (𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)

𝑉𝑆𝐻 = 𝑇𝑆 𝑄𝐿 = 3.24 𝑓𝑡3

Step 7: Find HLLL From Chart

o For Inner Diameter <= 4 ft and Pressure < 300 psia HLLL= 15”

Step 8: Calculate HH

𝐻𝐻 = 𝑉𝐻

𝜋4 𝐷𝑉

2= 1.383 𝑓𝑡

Step 9: Calculate HS

𝐻𝑆 = 𝑉𝑆

𝜋4 𝐷𝑉

2= 0.830 𝑓𝑡

Step 10: Calculate HLin

𝐻𝐿𝑖𝑛 = 12 𝑖𝑛 + 0.5 𝑑𝑛 𝑊𝑖𝑡𝑕𝑜𝑢𝑡 𝑖𝑛𝑙𝑒𝑡 𝑑𝑖𝑣𝑒𝑟𝑡𝑒𝑟 = 21.55 "

𝑑𝑛 = 𝑛𝑜𝑧𝑧𝑙𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 4 𝑄𝑚

𝜋 60 𝜌𝑚= 9.55 "

𝑄𝑚 = 𝑄𝐿 + 𝑄𝑉 = 12.552

𝑓𝑡3

𝑠𝑒𝑐

𝜆 =𝑄𝐿

𝑄𝐿 + 𝑄𝑉= 0.001434

𝜌𝑚 = 𝜌𝐿𝜆 + 𝜌𝑉 1− 𝜆 = 0.177 𝑙𝑏

𝑓𝑡3

Step 11: Calculate HD

𝐻𝐷 = 24 𝑖𝑛 + 0.5 𝑑𝑛 𝑊𝑖𝑡𝑕 𝑚𝑖𝑠𝑡 𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑜𝑟 = 28.775 𝑖𝑛

F-4

Step 12: Allow 6in for mist eliminator and 1 ft between mist eliminator and top

seam

𝐻𝑀𝐸 = 0.5𝑓𝑡 + 1 𝑓𝑡 = 1.5 𝑓𝑡

Step 13: Calculate HT

𝐻𝑇 = 𝐻𝐿𝐿𝐿 + 𝐻𝐻 + 𝐻𝑆 + 𝐻𝐿𝑖𝑛 + 𝐻𝐷 +𝐻𝑀𝐸= 8.44 𝑓𝑡 ~ 8.5 𝑓𝑡 (𝑅𝑜𝑢𝑛𝑑 𝑡𝑜 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 6")

G-1