The Topic of Essay For Class

The Topic of Essay For ClassThe topic of the essay for class is often an important factor in determining whether the student is successful or not. Writing essays is very similar to writing short stories. The most important thing is to write the essay clearly and logically. A well written topic essay will be a good step towards getting an average grade.The first most important thing to consider when writing an essay for class is to organize it well. A topic of essay for class will always be constructed from two parts. First you need to begin with an introduction and lastly the topic. The introduction should not only state what the class is about but also what is expected of the students.A general introduction on a particular topic should make it easier for students to decide on the subject matter they would like to discuss. A title should also be used, which would provide more detail on the subject matter to be discussed. When writing an essay for a class, you need to be clear in orde r to get better grades.Essay for class can also be divided into several topics. The first one is to focus on the subject as mentioned above. Then you can provide some details to introduce the essay itself.An essay can also contain a great addition on the history of a particular topic. A history of the bible is a good one to put in the topic. This also will give the students a better understanding on the book. In addition, a history of a certain term is also good as it gives the students the understanding about the subject matter.When writing the essay you need to analyze the general material in an essay and when the same subject is to be taken up again, you can rearrange the information and give it a new twist. Thisis the most effective way to get a better grade.There are also certain points you need to pay attention to when writing the essay. You need to have a clear idea about the target audience, the purpose of the course and other important matters. Some students do not have the patience to go through all these and therefore they get the very lowest grade in the class.

Writing A Good College Application Essay

Writing A Good College Application EssayOne of the biggest concerns among students and parents is about what an example good college application essay should look like. While there are many people that write great essays, and often find them easily enough, not everyone has the same skills. So, what does an example good college application essay look like?The most common techniques used to do this are things like simple to the point and content centered. However, it should be said that this is not the only technique you should use. There are also the more unconventional approaches that can be equally effective. The following are just a few of the techniques that can be useful when it comes to college essays.The first technique is to do your research into how other students have tackled this very same task when writing their own good college application essay. Although you will need to spend a little time doing this, once you have done so you will discover that it will help tremendousl y in determining whether you will succeed or fail. This will save you a lot of time and help ensure that you do not need to go through the stress and strain of writing that final college essay.Another thing that can help you if you want to get a good college application essay is to create your own story. By creating your own story and using examples of how others have tackled the same topic, you will realize that this is an essential skill for anyone who is trying to write a good college application essay. By doing this, you will find that you have created your own story and that makes it easier for you to present your ideas.Finally, by thinking about the areas that you are considering when you are trying to write a good college application essay, you will be better prepared to accomplish this. For example, if you are an English major, you may want to consider the different methods of writing that English majors use in dealing with concepts. So by thinking about how you may be using these strategies, you will be better able to create your own writing style.When you start to use these techniques, you will soon find that you have more success when it comes to writing a college application essay. All of these techniques that I am going to discuss are generally used by successful writers.So if you are ready to write a good college application essay, it will help to think about the different things that you can do. Whether you choose to use the aforementioned techniques or choose to come up with your own, you should use them all. This will make the task that much easier and you will be much more likely to write a good college application essay.

How to Write a Sample APA Essay With Citations

How to Write a Sample APA Essay With CitationsWhen you are preparing a sample APA essay with citations, you will find that this may seem like an easy task. With the help of a little research, you can learn how to write a sample with citations so that you will have a proper idea about what you are trying to achieve. It is a good idea to study the APA sample with citations and you should be able to use it when writing your own essays as well.In order to get a better idea about how to write a sample APA essay with citations, you will first want to choose an appropriate topic for your essay. You will want to choose a topic that is meaningful to you, such as career, school, or career goals. This will provide you with something that you want to write about. This also gives you a reason to give specific details about yourself, your life, and your experiences.As you begin to write the sample APA essay with citations, you will want to begin by looking at the general topic. You can look for a topic that you have some knowledge about so that you can apply this knowledge. If you do not have much knowledge about this subject, you will want to do some research. One way that you can do this is to ask for recommendations or information from friends who have used APA topics. Remember, if you are writing for the APA exam, your subject matter should be in-depth.After you find a topic that you know about, you will want to choose a theme for your sample APA essay with citations. You can start with the content of the essay and go from there. In the example above, you would start by examining the career issue and give details about your experiences with the term 'career.' After you finish this section, you can continue by giving the details of what you learned from your references.One of the ways that you can write a sample APA essay with citations is to avoid relying on details. Instead, you can include more details about what you learned. For example, you could put in detail about why you needed to add a particular term to your writing. If you use this technique, you will give the reader more information and they will be more likely to remember what you wrote in your sample with citations.You will need to learn how to use your sources when writing your sample APA essay with citations. If you do not know where to find this information, you can visit the APA website. They will have a list of reference materials that you can use. One of the resources that you will want to include in your sample is the university's information office.The APA website is a great resource when you are writing a sample APA essay with citations. You can use it to save time, research the right information, and find out how to create your own version of this article. When you begin this process, you will find that you will be able to achieve a high grade on your APA essay with citations.

Strategic Brand Management Final Notes Essay Example

Strategic Brand Management: Final Notes Essay Strategic Brand Management Final Study Guide Entire Book, but focus on Chpt 8-15 Reading: The Anatomy of Buzz- How to Create Word of Marketing- (Has taken significance due to 3 reasons: noise, information overload, skepticism-don’t believe message from companies and connectivity-internet). Takes a network approach. The importance of Buzz depends on the 1. Nature of your product (paperclips vs. movies) 2. The people that you’re trying to reach (younger people are more influenced by peers) 3. Your Customer’s connectivity 4. Your marketing strategy (if you have a contract, buzz is less important) 1. Buzz is an invisible network-You will never really see how buzz moves from person to person. You just need to understand that people need to communicate with one another, and figure out how to get them talking. 2. There are thousands of networks through which buzz flows-These networks are loosely connected with one another. Buzz can start one, but might not jump to another without a push. 3. In every network, there is a person who is the hub-Opinion Leaders(Regular Hub, Mega Hub-celebrity, press, Expert Hub, Social Hub)that person needs to be cultivated so he can spread the work about your product or service. Learn how to identify and engage this person. Reach the hub early! 4. A great product is essential- Contagious products- products that evoke an emotional response (blair witch), products that advertise themselves (wheeled luggage bags), products that leave traces, products that become more useful as more people use them (phones), products that are compatible, products that do the rest. We will write a custom essay sample on Strategic Brand Management: Final Notes specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Strategic Brand Management: Final Notes specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Strategic Brand Management: Final Notes specifically for you FOR ONLY $16.38 $13.9/page Hire Writer There is no reason to spread buzz if the product isn’t compelling. 5. Networks must be seeded-Before word-of-mouth can take off, each network must be seeded with suggestion, maybe through first-time or free offer, put the product in their hands, reduce price barrier, listen for silence Rules of Networks- networks are invisible, people link with others like them, similar people form clusters, buzz spreads through common nodes, information gets trapped in clusters, network hubs and connectors create shortcuts, we talk to those around us, weak ties are surprisingly strong, the net nurtures weak ties, networks go across markets. Ads and Buzz can work together- be careful because the wrong kind of advertizing can kill buzz. Distribution and Buzz can work together- seed retailers, or create mystery Reading: Brand Asset Management (–In phases) 1. Develop a Brand Vision- a statement of overall goal for the brand, the target market, the POD, and financial goals, all of which involves senior management approval and that fills in a financial growth gap. 2. Determine Your Brand Picture-determine your brand’s image (association and persona), create your brand’s contract (promises the brand makes to the customer), craft a brand-based customer model (why do they chose one brand over another, how does your brand stack up, what are the opportunities for growth) 3. Develop a Brand Asset Development Strategy- positioning your brand for success, extending your brand, communicating your brand’s position, leveraging your brand to maximize channel influence, and pricing the brand at a premium. 4. Supporting a Brand Asset Management Culture- measuring the ROBI and establishing a brand-based culture Final Review- Building Customer-Based Brand Equity Tools and ObjectivesChoosing Brand Elements(Must be memorable, meaningful, favorable, transferable, adaptable andProtectable)Marketing ProgramsProduct-tangible/intangible BenefitsPrice-value perceptionDistribution Channel- Communications-Leverage Brand Association(company, country of origin,event, etc)| Knowledge EffectBrand AwarenessDepth-Recall and RecognitionBreadth- Purchase and ConsumptionBrand Associations (ex. ountry of Origin)Strong-relevant/consistentFavorable-Unique-POD, POP| 9 Brand OutcomesPossible outcomes are-Loyalty -Less vulnerable to competition and marketing crisis-Lower/Higher margins-Elastic/Inelastic Pricing Response-Increased marketing comm. Efficiency-Licensing Opportunities-Greater trade Cooperation-More Favorable Brand Extension Opportunities| Stages of Brand Development- Customer-Based Brand Equity Pyramid Customer-Based Brand Equity Pyramid-Branding Objectives at Each Stage Managing Customer-Based Brand Equity Define Brand-Product Matrix-Brand Extensions: establish new equity and enhance existing equity. Brand Portfolio: maximize coverage and minimize overlap Enhance Brand Equity Over Time- Brand Reinforcement, Brand Revitalization Establish Brand Equity over Market Segments- Identify Differences in Consumer Behavior, Adjust Branding Programs Brand Positioning (Why is it better, how it is different, the solution to the buyer’s problem, its unique selling proposition) The Process 1. Target Audience (be very focused to have more brand resonance)(D,B,P,G) and must be sizable, identifiable, accessible, responsive. . Competitive Frame of Reference (how do customers relate to you and others)-direct competitors indirect competitors, perceived competitors 3. Benefits-(rational- features-often with tech products/emotional-connection Apple IPod)-POD must be feasible, communicable, sustainable, relevant, distinctive, believable- is desired by target consumer, company can deliver on promise POP 4. Brand Values- abstract brand associations 5. Brand Personality-5 Factors sincerity, excitement, competence, sophistication, ruggedness 6. Brand Essence/Mantra- McDonalds: Food, Folks, Fun=Brand function, Descriptive, Emotional Brand Positioning Matrix: Mapping Differentiation- Relevance and Differentiation Positioning Statement For target audience, brand name is the product description that product payoff 1/Reason Why and product payoff 2/Reason Why. For the Asian or Asian American grocery store consumer, Ranch 99 is the Asian grocery store that has the largest selection of Asian food products and the lowest prices in the San Diego region. Guidelines for Building Brand Equity: 1. Mix and match brand elements 2. Ensure high quality by creating rich images and linking tangible and intangible brand elements 3. Adopt a value-based pricing strategy (customers pay a premium) 4. Consider direct/indirect distribution options (push/pull) 5. Mix up marketing communications 6. leverage secondary associations Why Brand Management Fails- failure to communicate meaning of brand, to live up to brand promise, adequately support brand, be patient, balance consistency and change, to understand the complexity of brand equity measurement and management. Highlights: Chpts 8-10 Brand Value Chain: To Trace the value creation process for brands to better understand the financial impact of the brand to better understand the financial impact of brand marketing expenditures and investments. Brand Value Stage MultipliersProgram QualityMarketplace ConditionsInvestor Sentiment (Clarity, Relevance, (Competitive Reaction, Channel Support(Market Dynamics, Growth potential Distinctiveness, Consistency)Customer Size and profile)risk profile, brand contribution) Brand Tracking Studies Brand Audits-Provide in-depth information and insights for long-term strategy and positioning development Tracking Studies-involve information collection from consumers on a routine basis over time. We should track: Awareness/image, sources that make brand equity, corporate family tracking. Brand Tracking Survey Format: Follow the Customer-Based Brand Equity Pyramid from bottom to top!! How: Who to track: Current customers (light, medium and heavy users) loyal customers vs. rice sensitive customers, non-customers rejecters, When and Where to track: continuous and regular interval tracking-frequency depends on frequency of product purchase. Interpreting tracking studies: shifts are often subtle, what are the minimum threshold numbers. Brand Context Measures: Your brand does not live in a vacuum. What’s happening in the environment (competitive frame of reference) will impact brands long-term value. Examine 8 factors: economic indicators, retail trends, t echnology, media indicators, demographic profile, other products and service, personal attitudes and values, attitudes to brands and shopping. Brand Equity-Who’s responsible? Senior management who develops a brand review process: review brand sensitive material, review status of brand initiatives, review new brand positioning conflicts, etc. Understanding Consumer Behavior: Why do people buy our brand? Or see other brands? See â€Å"Brand Asset Management Measuring Sources of Brand Equity: Qualitative Research Techniques: focus groups, free association, brand personality and values, Projective Techniques: (ex. Maxwell House vs. Nescafe example) (ex . Presidents and products) experiential methods. Quantitative Research Techniques: Awareness, recognition, recall, image, attitude and usage, product-concept, brand relationship. Quantitative Techniques: n 200, generally between 400-1000. Can test 2 things. Awareness- recognition of packing on shelf (eye tracking technique), recall-identify the brand under different circumstances (aided and unaided),( techniques: fake branding, false guesses etc. ) Image-(Strong, Favorable and Unique)- Forced choice, purchase intent, 3 measures of consumer beliefs. -Free choice (which attributes they prefer -Scaling (agree disagree scale 1-6) Ranking (how close is a brand associated with a attribute) Types of Brand-Focused Quantitative Studies Attitude and Usage Survey (AU)-measures attitudes toward brands, describes category involvement, how consumers use the products, track trends. Brand Segmentation Studies- Net Promoter Score-Promoters-Detractor=Net Promoters. Scale of 1-10, 9-10 promoters, 7-8 passives, 1-6 detractors, Asks â€Å"Would you re commend brand X? † Brand Loyalty Studies-Past purchase percentage mix/future purchase mix Brand Substitutability-What brand did you buy last time? , If not available, which brand would you buy? Track repeat rate. YR Brand Asset Valuator Model-Important!! Five Measures of Brand Equity (Pillars) 1. Differentiation-how a brand is different 2. Energy-ability to meet future consumer needs, attract new customers (momentum, dynamic) 3. Relevance-Brand’s appeal (size of franchise, not necessarily profitability) 4. Esteem-How a brand is regarded and respected 5. Knowledge-how familiar and intimate customers are with brand Developed in 1993 and updated in quarterly waves in the US. Its global, 400,000 consumers, 20,000 brands, 72 parameters. Assesses different categories simultaneously vs. one category. Brand Health Indicator- Brand strength: leading indicator future values, Brand Stature: lagging indicatorpast performance. High Brand Strength(Future Performance, Differentiation, Energy and Relevance)| Niche/Unrealized Potential/Growing| Power Leaders vs. Declining Leaders| Low Brand Strength (Future Performance, Differentiation, Energy and Relevance)| New or Unfocused Brands| Eroded| YR Brand Asset Valuation Model| Low Brand Stature (Current Performance Esteem and Knowledge)| High Brand Stature(Current Performance Esteem and Knowledge)| Introducing New Products and Line Extensions New Product Strategic Matrix Current Products| New Products| Current Markets| Market PenetrationStrategy| Product Development Strategy| New Markets| Market DevelopmentStrategy| DiversificationStrategy| Branding Options: 1. Develop a new brand 2. Apply an existing brand (Brand extension) 3. Combine a new brand with an existing brand (Levi’s Dockers) (Brand extension) Brand Extension: 1. Line extensi on 2. Category extension. Why Products Fails: market too small, product is poor match for the company, inadequate product research, entered too early or too late in the market, provided insufficient ROI, product not new or different, unrecognizable/limited capability. Advantages of Brand Extensions: 1. Facilitate New Product Acceptance 2. Provide Feedback Benefits to the Parent Brand Company Disadvantages of Brand Extensions: 1. Possible customer confusion 2. Retailer resistance 3. Can fail and hurt parent brand 4. Can Cannibalize parent brand,5. Can hurt image 6. Can dilute brand meaning Brand-Building Situations Chpt. 12 1. Managing a Corporate Brand, 2. Building a Sub-Brand, 3. Branding an Ingredient 4. Branding a Commodity (coffee, milk, a location ex. Juan Valdez) 5. Managing a Portfolio 6. Building a Corporate Brand 7. Managing a High Growth Brand. Brand-Product Portfolio Strategy Brand-Product Matrix: Brand Portfolio is the set of all brands and brand lines the firm sells in a particular category and the product line. Breadth Vs. Depth of the Product Line: Different lines vs. variants Breadth is how many lines Depth is the variances within Ex. Product from PG | Laundry Detergent| Other Product line| Brand 1| Tide| | Brand 2| Cheer| | Brand 3| Dreft†¦and so on| | Determine the Breadth of a Branding Strategy-Category Attractiveness: 1. Review aggregate market factors 2. Category/industry factors 3. Environmental factors. Reasons for Introducing Multiple Brands: 1. Any one brand is NOT viewed equally favorable by all market segments, increase shelf presense, to attract customers who might switch to another brand. Ex. Mother switches from Tide to Dreft. Special Roles of Brands in a Brand Portfolio: 1. Attack market segments not being served by other brands 2. Flanker to protect flagship brand (5 different brands of beer for Miller) 3. Cash Cow (Milk for Profit)-Funyons 4. Low to end entry level to attract new customers (100 series of BMW) 5. High end prestige product to enhance credibility of entire portfolio (Olay Microdermabrasion) 6. To increase internal competition within firm 7. To leverage economies of scale Ideal Brand Portfolio: Eight Categories of Brand Definition 1. Power -needs to be defended ex. Tide 2. Sleeper -with support, can grow into a power brand 3. Slider -has-been brand, needs attention! 4. Soldier -needs no management attention ex. Funyons 5. Black Hole -Resource suck, no payback 6. Rocket- quickly on its way to be a power brand 7. Wallflower- underappreciated brand with loyal customers (Payday candybars) 8. Discard- should have been tossed Brand Hierarchy: permits companies to focus their communication on key brand elements: Corporate Brand (top) (GM)Family Brand (Chevy)Individual Brand (El Camino) Modifier (SS) Importance Corporate Image Associations: When the brand is primary corporate (GE/HP/BP), then the corporate brand image has to reflect certain associations 1. Common Product attributes, benefits or attitudes 2. People and relationships 3. Values and Programs (CSR) 4. Corporate Credibility (expertise, trustworthiness, likeability) Designing a Brand Strategy: 3 options Corporate Dominant (16%)- corporate brands, house brands -Mixed Brands (52%)- ex. Kellogs corn flakes-dual brands, endorsed brands -Dominant Brand (32%)- mono brands, furtive brands (corporate identify undisclosed Global Marketing (Now a Prerequisite for Success) Why Go Global? 5 Reasons 1. Perception of slow growth and increased competition in domestic markets 2. Belief in enhanced oversees growth and opportunities (BRIC) 3. Desire to reduce costs from economies of scale 4. Need to diversify risk 5. Recognition of global mobility of customers Four Major Decisions to Make Before Going Global 1. Decide which markets to enter (India,EU? ) 2. Decide how to enter the market- (J. V, FDI, exports? ) 3. Decide on the marketing strategy (global or multinational? ) 4. Decide on the marketing organization (centralized or decentralized) Some Advantages of Going Global: lower marketing costs, consistency in brand image, power and scope, economies of scale, etc. Some Disadvantages of Going Global: differences in consumer needs/wants (Venezuela/Colombia), differences in consumer responses to marketing, differences in competitive scope, differences in legal environments, differences in marketing institutions, etc. Selecting Global Markets and Devising Market Entry Strategies Global Market Selection Criteria: economic environment, cultural environment, demographic environment, political/legal environment. 3 Global Market Entry Strategies (Important! ): 1. Export existing brands 2. Acquiring existing brands 3. Creating some form of brand alliance with another firm. Trade-Offs in Market Entry Strategy Strategy| Speed| Control| Investments| Geographic Extension(exporting existing brands)| slow| High| Medium| Brand Acquisition| fast| medium| high| Brand Alliance| Moderate| low| Low| Designing Global Marketing Programs: Standardized or customized? Leverage global PODs and Advantages Global Positioning Considerations: Create mental maps, define core brand values and identify POP, POD/ 10 Commandments of Global Branding: 1. Understand similarities and differences in the global branding landscape 2. Don’t take short-cuts in brand building 3. Establish marketing infrastructure 4. Embrace integrated marketing communications 5. Cultivate brand partnerships 6. Balance Standardization and Customization 7. Balance global and local control 8. Establish operable guidelines 9. Implement a global brand equity measurement system 10. Leverage brand elements Criteria to Develop Successful Global Brands and Viable Industries 3 Essential Criteria: 1. Global positioning and branding, 2. Technology that can be applied globally 3. Capabilities for local implementation Global Branding: Setting the Stage: Centralized: Power at HQ, strong creative theme. Conditions for success= education across the company, global appeal, global recognition of benefits, strong communication. Decentralized: Power in the field, positioning varies with markets, multiple creative directions, create different consumer messages. Conditions for success=strong marketing leader, excellent communication across markets, strong localization opportunities Issues/Learning From Working Internationally: 1. Limited competitive information 2. Quality and training of staff (improving) 3. Limited understanding of research, media and alternative marketing techniques 4. Speed to market 5. Listen to locals 6. Logical vs. emotional consumers

Fluid Temperature Distributation in Oil Gas Wells †Engineering Essay

Fluid Temperature Distributation in Oil Gas Wells – Engineering Essay Free Online Research Papers Fluid Temperature Distributation in Oil Gas Wells Engineering Essay Predicting accurate temperature Profiles in flowing wells can improve the design of production facilities in petroleum engineering. Temperature Profiles in wellbore have application in cementing operations, accurate 2-phase flow pressure drop prediction, Gas lift designs. Gas lift design can be enhanced by more accurate prediction of temperature at valve depth. In this way, the valves dome pressure can be set more accurately thereby improving the predictability of valve thorough put. Existing temperature correlations are often inaccurate because they do not consider the effects of different fluids in the annullus and cooling and heating of the fluid resulting from phase change. Rigorous theoretical model are often complex and in convenient. They depend on many variables and require information about fluid composition. This project work describes a method of predicting temperature distribution in a flowing wells. A model is derived from the steady-state energy equation that considers the heat transfer mechanisms found in the wellbore. An extensive data bank of temperatures from 3 wells was used in the model validation. TABLE OF CONTENTS Page Title page†¦ . †¦. †¦ †¦ †¦. †¦ †¦ †¦. †¦. Certification †¦. †¦. †¦ †¦.. †¦.. †¦. †¦. †¦. †¦. Dedication †¦ †¦. †¦. †¦. †¦ †¦.. †¦. †¦. †¦. Acknowledgement †¦ †¦. †¦. †¦ †¦ †¦ †¦. Abstract †¦ †¦ †¦. †¦. †¦. †¦. †¦. †¦. †¦. CHAPTER ONE Introduction †¦ †¦. †¦. †¦. †¦. †¦. †¦. †¦.. CHAPTER TWO Literature Review †¦. †¦. †¦. †¦. †¦. †¦. †¦.. †¦. CHAPTER THREE Theoretical Background and model development †¦. †¦. CHAPTER FOUR Result of Model Validation CHAPTER FIVE Analysis of Result Conclusion Recommendation References Nomenclature Appendix A Appendix B Appendix C: Computer Programs and Output results CHAPTER ONE INTRODUCTION Heat loss from wellbore fluid depends on the formation temperature distribution. Fluid temperature distribution in wellbore is determined by rate of heat loss from the wellbore to the surrounding formation, which is a function of depth and production/injection time. A model to predict fluid temperature during a steady-state 2-phase flow incorporates a thermal diffusivity solution. Convective and conductive effect is also incorporated in this solution. Ramey and Edwardson et al were the first to present theoretical model for estimating fluid Temperature as a function of depth and producing time. This model is only applicable to single phase fluids flow-because kinetic energy, friction and Joule-Thompson expansion were neglected. Ramey’s work was improved by incoporating the effect of phase charge in fluid injection well. A presentation of excellent model on various resistances to heat transfer between the wellbore and the formation was also constructed by Ramey. An expression for fluid temperature distribution in single-phase flow has the limitation of being applied when multiphase flow is encountered. Interpretation of temperature logs for estimating water and gas injection profile was proposed. Noting, the usefulness, kirkpatrick presented a flowing gradient chart, though simple, lacked generality and accuracy. This inaccuracy and thermal stress failure of casing in steam-injection wellbores, demands a proper understanding of wellbore heat transfer and accurate estimation of flowing fluid temperature. Procedure for estimating wellbore fluid temperature has been suggested, model has been presented as the function of depth and producing time. The problem, however remains that since Kinetic energy and friction was neglected, is therefore only applicable for single-phase flow. Also, the assumption by Ramey of microscopic well radius in solving the temperature formation temperature distribution cannot be defended. Resistances to heat transfer between wellbore fluid and formation, was ignored and consequently rendering the model inaccurate and stream lined. Even qualitative estimation of flow rate from various producing wells depends on establishment of constant temperature different between the wellbore fluid and the formation. Ramey’s method is of limited use especially for estimating flow rate in multiple zones. Fluid temperature distribution in wellbore is very crucial and can be used to estimated flow rate and Gas top Oil ratio in vertical and deviated wellbores. In short a higher flow rate results in a lower temperature drop. A less complex algorithm which avoid complex calculation of overall thermal coefficient has been presented for estimating wellbore fluid temperature distribution which will in -coporate conductive, convective and radiative heat transfer and can be used predict temperature at various depths and production time. CHAPTER TWO LITERATURE REVIEW In recent years, considerable attention has been given to fluid temperature distribution in wellbores. There has been many studies on this subject ranging from heat transfer during two- phase flow in wellbores (Formation Temperature) to wellbore fluid Temperature. And later proposing a unified model for predicting flowing Temperature Distribution in Wellbores. Various aspects of heat transfer between the wellbore fluid and the formation has been studied by many over the last few decades. The usefulness of fluid Temperature measurement was realized as early as 1937 by Schlumberger et al ; Interpretation of temperature log for estimating gas and water injection profiles was proposed by Nowak2 and Bird3 in the early 1950s. Noting the importance, KirkPatrick4 Presented flowing Temperature gradient chart, though simple, lacked generality and accuracy . These deficiency and thermal stress failure of casing in steam injection wells emphasized the importance of proper understanding of wellbore heat transfer and accurate estimation of flowing fluid Temperature. Lesem et al5 and Moss and White6 were the first to suggest procedures for estimating wellbore fluid temperature. However, Ramey7 and Edwardson et al8 were the first present a theoretical model for estimating fluid temperature as a function of producing time and depth. However, both works neglect the effect of friction and kinetic energy. Thereby making them only applicable for flow of single phase fluids. In addition, the assumption of in -finitessimal well radius by Ramey in solving the formation temperature distribution can be unreliable in some cases. The classical method for temperature prediction in wellbore proposed by Ramey coupled the heat transfer mechanisms in the wellbore and transient thermal behaviour of the formation. Temperature equations for the case of injection of either single phase incompressible hot liquid or single phase ideal gas flow were derived. In Ramey’s method, the transient thermal behaviour of the formation was determined by solutions of radial heat conduction problem in an infinite cylinder. The resistances to heat flow in the wellbore due to presence of tubing wall and cement is incoporated in the overall heat transfer coefficient. Griston and Willhite9 extended the application of Ramey’s approach by evaluating the usefulness of steam injection well and taking note of radiative heat transfer during steam injection. Witterholt and Tixier10 employed the influence of fluid flow rate on temperature of the fluid in Ramey’s equation to measure the fluid temperature. Witterholt and Curtis also employed effect of qualitative estimation of flow rate from various producing zones. The method depends on the effect of fluid flow on the inverse Relaxation distance, A, in Ramey’s model for fluid temperature Distribution. This method is of limited use , especially for estimating flow rates from multiple zones, because of its limited accuracy and its dependence on the establishment of constant temperature difference between wellbore fluid and formation. An empirical calculation was developed by Shiu and Beggs for producing wells, to determine the relaxation distance defined by Ramey. This method is actually an attempt to avoid complex calculation of overall heat transfer coefficient and transient heat transfer behaviour of the formation . Since application of Ramey’s equation are restricted to single phase flow in the wellbore, sagar et al extended Ramey’s method for wells with multiphase flow, accounting for kinetic energy effects and Joule-Thompson’s expansion. This simplified method is based on field data., all these methods include severe assumption related to the thermodynamic behaviour of the flowing fluids and thus applicable only for limited operating conditions. Alves et al12 presented a unified model for flowing Temperature prediction which can also be applied to producing and injection wells, under single-phase or two-phase gas liquid conditions over the entire inclination angle range from horizontal to vertical wellbores: the diverse application of the aspects of heat transfer in both formation and wellbore necessitated the development of a Rigorous approach. The model below allows computation of temperature at the formation/wellbore interface, when undisturbed formation temperature and wellbore heat flow rate are input. This represents the relationship between wellbore heat loses and wellbore temperature for steady-state, 2-phase flow: where I wellbore fluid Temperature: Expression for variation of fluid temperature with depth has been obtained: where using appropriate boundary conditions on the above, Hassan and kabir13 modeled the expression as a function of well depth and also producing time. CHAPTER THREE THEORETICAL BACKGROUND AND MODEL DEVELOPMENT Heat loss experience by the fluid as if flows up the well results in lowering its temperature. As this fluids moves through the wellbore, there is transfer of heat between fluid and the earth due to the difference between fluid and geothermal temperatures. This type of heat transmission is involved in drilling and production operations. This solution would assure that heat transfer to the earth will be unsteady radial conduction and that in the wellbore will be steady state. In other to derive a model which predict heat flow in a 2-phase system (e.g Oil well), it would be necessary to obtain, first, the wellbore fluid energy balance. The temperature difference between the formation and wellbore fluid causes a transfer of heat from the fluid to the surrounding formation with decrease in fluid temperature and depth. At any depth formation temperature would vary with radial distance and production time. However, when steady-state flow has been attained, there is constant fluid temperature at any given depth due to turbulence. Heat loss from fluid, therefore declines with time and is dependent on various resistances to heat flow between the hot fluid in the tubing and the surrounding earth. To derive a model for temperature as a function of depth and time, we must as necessity establish the formation temperature distribution as a function of radial distance and time, given a constant heat flux from the well. For a 2-phase system, first obtained the wellbore fluid energy balance, which would relate the fluid temperature with wellbore/ formation interface temperature and the heat flux, given the overall heat transfer coefficient in terms of well configuration shown in Appendix A. 3.1 FORMATION TEMPERATURE DISTRIBUTION Assuming symmetry around the heat source or sink (Producing or injection well); In a short time-step, heat flux from wellbore may be assured to remain constant. Then an energy balance of the formation leads to the following partial differential equation derived in cylindrical coordinates for formation temperature variation with radial distance from well and production time: (1) where: Te – earth temperature; t time, r –distance measured from the wellbore center is thermal diffusivity. Initial condition is that formation temperature at any depth is constant, leading to : Lim Te = Tei (2) At the infinite or outer boundary, formation is also constant with radial distance. (3) The third boundary condition is derived from the heat flow rate at the wellbore/formation interface which is governed by Fourier Law of heat conduction. Heat flow rate per unit mass of wellbore fluid per unit length of well, dq/dz is given by: (4) rwb- outer radius of wellbore and W is the wellbore fluid mass flow rate. To facilitate solution and have a more general applicability of solution, equations 1,3 and 4 are recast in dimensionless variables of rD (dimensionless radial distance)= r/rwb, thermal diffusivity = Ke/PeCe , and tD (dimensionless time =. Equations 1,3 and 4 becomes: (5) (6) (7) I can now introduce a dimensionless temperature, TD, analogous to dimensionless pressure in pressure transient analysis: (8) 3.2 WELLBORE FLUID ENERGY BALANCE An energy balance of fluid for a differential length, dz, for a 2-phase system would lead to the following equation: (9) where gc and J represent appropriate conversion factors (gc= 32.2 lbm.ft/lbf-Sec2, unity in S.I units, dimensionless.) H-fluid enthalpy fluid enthalpy, H, depends on its pressure and temperature, which allows us to write the following expression, for dH/dz: = (10) Cpm is the heat capacity at constant pressure, Cpm where CJ is the Joule- Thompson coefficient. Combining equation (9) and (10), yields: (11) the radial heat transfer between the fluid and the surrounding earth, expressed in overall heat transfer coefficient based on transport phenomena and transient heat transfer. Heat is transferred from the wellbore fluid to the earth overcoming the resistance offered by the tubing wall, tubing insulation, casing wall and cement as shown in fig1. The resistances are in series, and, except for the annulus, the only mechanism of transfer involved is conductive transfer. At steady state, the rate of heat flow through a wellbore per unit length of well, dq/dz, can be expressed: (12) uto ¬- Overall heat transfer coefficient based on tubing –inside surface area, 2 to and temperature difference between the wellbore fluid and wellbore/ formation interface (Tf-Twb). Therefore, the heat transfer rate per total mass flow rate W is: (13) the overall heat transfer coefficient based on tubing outside surface area, uto, depends on resistance. In general, the resistance to heat flow through tubing or casing metal may be neglected. Natural convection is the dominant heat transfer mechanism for fluid in the annulus. Resistance through cement layer could be important depending on its thickness. Using the dimensionless temperature, TD obtained in equation (8), we may write the expression for heat transfer from the wellbore/formation interface to the earth: (14) combining (13) and (14) to eliminate wellbore temperature, Twb, yields: (15) 3.3 WELLBORE FLUID TEMPERATURE The next is to obtain an expression for variation of fluid temperature with well depth by substituting the expression for dq/dz from equation (15) into (11): (16) letting, (17) expressing (16) in terms of A, yields: (18) if the undisturbed formation temperature is assumed to vary directly with depth, thus, Tei= Teibh gTZ (19) Where gT represents the geothermal gradient and Teibh is the undisturbed (Static) formation temperature at the bottom hole: Equation (19) can also be applied when different geologic formation are encountered. At various depths with differing values of geothermal gradient. In this case, the computation may be divided into a number of zones with constant geothermal gradient being applied to each zone. If it is assured that the test two terms in equation (18) does not vary with well depth, equation (18) becomes a linear differential equation: (20) Where (21) Equation (20) can be integrated for a constant, A, and boundary conditions: (a) For a producing well at bottom hole, Z=Zbh (b) Fluid and earth temperatures are generally known Tf =Tfbh and Tei =Teibh giving the expression for fluid temperature as a function of well depth and production time: (22) the value of the parameter, ,in equation(22) would depend on a number of variables, such as flow rates, gas/liquid ratio, wellhead pressure. The calculation of is shown in Appendix A. The earth temperature at wellhead can be assumed to be equal to the surface fluid temperature (i.e. Tewh =Tfwh). The geothermal gradient, gT can be determined by dividing the temperature drop of the formation and the fluid by the measured depth (i.e(Tformation –Tsurface )/depth acceleration due to gravity, g and the appropriate conversion factors, g both has the value of 32ft/sec2 and 32.17 lbf-ft/1bm-sec2 J and Cpm are respectively the mechanical equivalent of heat, 778ft-1bf/Btu and specific heat capacity at constant pressure. =900 for vertical wells. It must be noted that the variable depths are measured in negative values which is a generally accepted convention. Having set these constraints: equation (22) can further be simplified to yield: simply: (23) j=1,2,3,†¦.. J, mechanical equivalent of heat, has a value of 778ft-1bf/Btu and A is the thermal Relaxation distance, in feet. From equation (17) shown below: Aj = The overall thermal coefficient Uto can be computed using the model below ;for differential length and a unit mass flow rate; for tubing: (24) and for casing flow; The equation is shown in appendix (B) The inverse relaxation distance, A, can be estimated using equation (17) but bearing in mind the existence of equality between dimensionless temperature, TD and transient heat conduction time function for the formation (earth) developed by Ramey: (25) is the thermal diffusivity of the earth, ke/CePe, ke, Ce and pe are the formation conductivity, heat capacity and earth (formation) density. And rto , the tubing –inside radius. Using equation (23), the wellbore fluid temperature, Tf can be estimated. The working is shown in Appendix A. Shown in Chapter four are data of 5355-ft deep flowing well used to validate my fluid Temperature calculation. The assumption of f(t)=TD does not affect the solution at large times. Besides the equality of f(t) and TD is not surprising because both functions attempt to describe the temperature distribution in formation based on the same differential equation. CHAPTER FOUR 4.0 RESULTS OF MODEL VALIDATION The following data were used to test the efficiency of the derived model in predicting temperature at any depth and production time. Temperature data from Amerada Hess of west Texas. 4.1 THE FLUID TEMPERATURE DISTRIBUTION Fluid temperature distribution at any depth can be computed using the relations below: where A= the former equation can easily be converted to deviated well, for vertical wells ( =900 )Sin 90=1. and geothermal gradient, gT gT = (Tebh-Ts)/ZSin for deviated wells where = angle of deviation , g and gc are equivalent and acts as a conversion factor. Variables Data report by Sagar etal Amerada Hess cooperation Nafta Gas of Yugoslavia Chevron Escravos Nigeria N 12 15 18 Tebh(F) 108 237.2 172 Ts(F) 76 50.1 89.5 ?(ft2/hr) 0.04 0.04 0.04 Zbh(ft) 5355 6,792 8250 Ke(Btu/hr/ft/F) 1.4 1.4 1.4 dto(Inches) 3.375 2.875 3.875 GLR(scf/bbl) 68.2 APIG (gravity) 34.3 35 30 Yg 1.05 0.75 0.79 dti(Inches) 2.875 2.375 3.375 pwh(Psia) 113 174 215 dwh(Inches) 9.0 7.5 12 dco(Inches) 7.5 5.8 8.304 dci(Inches) 7.0 5.5 8.0 Kan(Btu/hr/ft/F) 0.383 0.383 0.383 Kcem(Btu/hr/ft/F) 4.021 4.021 4.021 tp( hours) 158 165 160 qo (BBL) 59 6.8 1720 qw (BBL) 542 13.3 236 qg (SCF) 41000 3100 1899000 rw 101 1.o 1.0 CHAPTER FIVE ANALYSIS OF RESULTS While the figure 1 shows a very good agreement between the model prediction, measured temperature and Hassan Kabir. The 2 data points nearest to the surface (0 and 500ft depth) shows higher fluid temperature than are predicted the model can accurately predict these temperature if a higher conductivity of 1.4 Btu/hroF is used for the formation near surface. The model allows conduction and convection as heat transfer mechanism for fluid in the tubing casing annulus . The deviation between measured and predicted temperatures is more at the surface and near surface and reduces as depth increases and eventually meet at the bottom hole. This is because gas expansion occurs as multiphase fluid flows up to the surface and that enhances cooling due to Joule-Thompson and Kinetic energy effect and provides room for heat exchange. As depth increase, pressure and temperature increases. The concordance among the proposed Hassan Kabir multiphase prediction with measured temperature and the correlation developed is shown figure 1. and figure 3 for fluid temperature distribution in wellbores and represented in the coloured legend on the profile. The three models in each of the three profiles :(Hassan kabir), the developed model and measured temperature matches as depth of wellbore increases. It could not tally at the surface and 500ft depth with measured temperature due to Joule Thompson cooling as multiphase fluid flows up and pressure is reduced giving rise to gas expansion. The percentage error between the model prediction and that of measured temperature (at 0-500ft.) is 4.1%. Therefore, using correlation developed we must make a correction of predicted temperature at the surface by multiplying it by 4.1% and subtract from the predicted temperature. Example 1: Fluid temperature @ 0ft = 91.64F corrected measured temperature =91.640*(1-4.1/100) = 87.88F There is a high agreement between predicted fluid temperature and that of Hassan Kabir prediction. The profile matches as depth increases and almost coincides showing that there is high agreement amongst both models. Figure 2. is a temperature profile for a flowing gaslift well, the predicted temperature of model and that of Hassan Kabir for multiphase flow agrees with tend to twist. This is as a result of gas injection at 4200ft, this point of gas injection. The temperature is lowered due to presence of gas, gas expansion and Joule-Thompson cooling. WHY FLUID TEMPERATURE DISTRIBUTION ? ? Accurate temperature prediction is necessary in the effective design and execution of cementing programme choosing suitable cement slurry properties: placement and setting time during completion and worker operations ? It is important to know the wellbore fluid temperature before gas lifting operation at various depths to enable us know the temperature at various value depth. ? Also temperature profile of a well must be known before enhanced or secondary recovery: Steam injection. Gas and hot water injection among others. ? Packer design and selection. ? To enable in designing of Logging tool and for log interpretation ? Prediction of Wax and scale depositions in production tubing ? Determination of region in the tubing and casing liable to Corrosion. Wellhead and production equipment design CONCLUSION An algorithm is presented for estimating wellbore fluid temperature. It allows wellbore heat transfer by conduction and convection and evaluate the formation by assuming that fluid temperature at the wellhead is equal to the earth temperature at wellhead. Here, the importance of convective heat transfer is demonstrated. The need for radiation is eliminated due to unavailability of fluid emissivity which depend on surface finish and view factor among other variables. The algorithm can easily be applied to deviated wells. This algorithm was developed from basic thermodynamic principles to predict temperature profiles in two-phase and multiphase flows in wells. The simplified model represents an extension of the latest multiphase fluid temperature distribution correlation. The developed model eliminates the need to estimate fluid temperature at wellhead. And to iterate for overall thermal co-efficient at various depths. RECOMMENDATION I recommend that when using the model. Accurate temperature at the near surface (0-500ft) would be determined by: accurate temperature = Calculated temperature* (1-% error) This would account for the Joule-Thompson cooling and expansion of gas and pressure reduction that occurs as a result of upward flow of multiphase fluid in wellbore. NOMENCLATURE A Inverse relaxation distance, ft Cpm Heat capacity of wellbore fluid, Btu/lboF Ce Heat capacity of the earth, Btu/lboF Cj Joule-Thompson coefficient, dimensionless d Pipe diameter, ft f(t) Ramey’s solution for wellbore earth/interface temperature, dimensionless g Acceleration due to gravity, ft/sec2 gc Conversion factor, 32.2lbmft/lbf sec2 gT Geothermal gradient oF/ft H Fluid Enthalpy Btu/lb K Conductivity, Btu/ft oF Ka Conductivity of Annulus, Btu/ft oF Kcem Cement Conductivity, Btu/ft oF Ke Formation conductivity, Btu/ft oF q Heat flow rate from or to the wellbore, Btu/hr r Radial distance of the wellbore, ft T Temperature, oF TD Dimensionless temperature Tei Formation temperature at any given depth and radial distance from well,oF Teibh Formation temperature at Bottom hole, oF TeWh Formation temperature at wellhead, oF Tf Wellbore fluid temperature, oF W Total mass flow rate, lbm/sec Z Variable depth from surface, ft Zbh Total measured depth from surface, ft J Mechanical equivalent of heat, 778ft-lbf/Btu Kan Thermal conductivity of annulus material, Btu/hr-ft-oF PWh Wellhead pressure q0 oil flow rate, STB/D qg Gas flow rate, SCf/D qw Water flow rate, STB/D uc Heat transfer coefficient of casing ut Tubing heat transfer coefficient of casing U Overall heat transfer coefficient, Btu/hr.ft2 oF Yg Gas specific gravity Yo Oil specific gravity Yw Water specific gravity Dci Casing Internal diameter Dti Tubing Internal diameter Dto Tubing external diameter Dco Casing outside diameter Dwb Diameter of well bore GREEK LETTERS Heat diffusivity of earth ft2/hr Specific gravity of produced gas Oil specific gravity dimensionless Water specific gravity dimensionless Parameter which combines Joule-Thompson and Kinetic Energy effects. Wellbore inclination with horizontal, degree fluid viscosity, Cp Density, lbm/ft3 Earth density, lbm/ft3 REFERENCES Sagar, R.K., Dotty, D.R., and Schmidt, Z: â€Å"Predicting Temperature Profiles in a flowing well,† Paper SPE 19702 presented at 1989 SPE Annual Technical Conference and Exhibition, San Antonio, TX Oct.8 –11 Hassan, A.R. and Kabir, C.S.: â€Å"Heat transfer during 2 –phase flows in wellbores –part II- wellbore fluid Temperature† Hassan, A.R. and Kabir, C.S.: â€Å"Heat transfer during 2 –phase flows in wellbores –part I-Formation Temperature† Ramey, H.J. Jr.: â€Å"wellbore Heat transmission,† JPT (April 1962) 435 Trans AIME, No. 225. Alves, I.N. Alhanati and Shiham, U.: â€Å" A Unified Model for predicting flowing Temperature distribution in wellbores and pipelines â€Å"SPE 20632. G.J Plisga, â€Å"Temperature in wells,† Sohio Alaska Petroleum company. Farouq Ali, S.M.: â€Å"A comprehensive wellbore steam/water flow model for steam injection wells,† Paper 196337 presented at the SPE California Regional meeting, Ventura, CA, April 8 –10,1987 Shiu,K.C. and Beggs, H.D.: â€Å" Predicting Temperatures in Flowing Oil wells,† J. Energy Resources Tech, (March 1989 1- 11) Lesem, I.B. et al.: â€Å"A method of calculating the Distribution of temperature in flowing Gas wells,† Trans, AIME (1957) 210,pg 169. Nowak,T.J.: â€Å"The Estimation of water injection profiles from Temperature surveys,† JPT (Aug. 1953) 203,Trans AIME,198. Gany R. Wooley; â€Å"Computing Downhole temperature in circulating, injection and production wells†. SPE, Enertech Engineering and Research Co. Willhite, G.P; â€Å"Overall Heat Transfer Coefficient in steam and Hot Water injection Wells†, JPT (May 1967) 607-615 Schlumberger, M., Doll, H. G., ‘Temperature Measurement in oil wells,† J. Inst. Pet. Technologist (Jan, 1937) 13, 159 Kick Patrick, C.V: â€Å"Advance in Gaslift Technology†, Drill. Prod. Prac. (March 1959) 24 60. Moss J.T and White, P.D; How to calculate Temperature Profile in a Water Injection Well,† Oil Gas Journal. (March 9, 1959) 57, NoII, 174. Willterholt, E. J. andd Tixier, M.P.: â€Å"Temperature Logging in Injetion Wells,† Paper SPE 4022 presented at the 1972 SPE Annual fall Meeting San Antonio, TX Oct. 8-11. Edwardson, M.J et al: â€Å"Calculation of formation Temperature Disturbances caused by mud circulation, â€Å"JPT (April 1962) 416-26; Trans., AIME, 225. APPENDIX A There are certain parameters we must compute before finally calculating the wellbore fluid temperatures, Tf , These parameters are itemized: a. Geothermal gradient, gT b. , dimensionless correction parameter which depends on Joule-Thompson expansion and GLR c. dimensionless transient heat conduction time function of the formation, f(t) = TD d. The overall thermal transfer coefficient, Uto e. The inverse Relaxation distance, A , ft. f. Using the model (23) to estimate the wellbore fluid temperature. a. GEOTHERMAL GRADIENT, gT The undisturbed temperature of the formation, Tei, is generally assumed to vary linearly with depth.Thus, Tei=Teibh-gTZ†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.. A1 where gT represents the geothermal gradient and Teibh is the undisturbed formation temperature at the bottom hole, Z gT = (Teibh – Tei)/Z†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦.A2 Numerically, using the data in chapter 4 gT = (108oF – 760F)/5355ft Geothermal, gT = 0.0059757oF/ft b. DIMENSIONLESS CORRECTION PARAMETER, This parameter depends on Joule-Thompson expansion and cooling effects and can be estimated by empirical correlation for a unit mass flow rate W=1Lb/sec: =-0.002978+1.006X10-6Pwh+1.906X10-4W-1.047X10-6GLR-0.3551gT+3.229X10-5API +0.004009Yg†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..A3 Gas –to-liquid Ratio, GLR = GLR = qg /(qo+qL)=41X103scf/(542+59)STB GLR =69.374 scf/STB Thus, upon substitution into A2, can be estimated: c. THE SPECIFIC HEAT CAPACITY OF TUBING FLUID, Cpm In other to compute the fluid temperatures at various depths, we need to compute first the specific heat of tubing fluid which is determined by : †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..A4 where typical values for oil, Cpo and water, Cpw are respectively 0.485 and 1.0 Btu/1bm.oF d. THE MASS FLOW RATE, W The mass fluid flow rate is calculated by: †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦A5 where Oil, water and gas flow rates are: qo, qW, qg respectively .†APIG† is used to represent the API Gravity of oil. e. THE OVERALL HEAT TRANSFER COEFFICIENT, U During exchange of heat in the wellbore, heat is transfer from earth/formation to the fluid is in two parts: (i) Overall heat transfer for fluid through tubing is given by: (ii) For casing flow, we have: therefore, the overall heat transfer coefficient is thus: or explicitly: f. THE THOMPSON COEFFICIENT, To account for cooling and expansion as a result of gas in the well bore a dimensionless constant, Joule-Thompson correction factor is introduced, computed by Sagar et al : =1.006X10-6Pwh+1.906X10-4W-2.978X10-3-1.047X10-6 GLR+3.229X10-5APIG+4.009X10-3Yg-0.35511gT where PWh, W and gT are wellhead pressure , mass flow rate and geothermal gradient of earth. g. TRANSIENT HEAT CONDUCTION TIME FUNCTION, f(t) from equation (25) f(t)= using the data provided: f(t)=T f(t)= 2.306 h. WELLBORE FLUID TEMPERATURE, Tf Model (23) permits the estimation of the temperature of fluids as a function of depth and producing times. This model is suitable for slide-rule calculation. Where j=1,2,3†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦N Temperature profiles can therefore be obtained at various depths using the thermal conductivity of the earth to be 1.4 Btu/hr-ft-0F Research Papers on Fluid Temperature Distributation in Oil Riordan Manufacturing Production PlanResearch Process Part OneBionic Assembly System: A New Concept of SelfInfluences of Socio-Economic Status of Married MalesBringing Democracy to AfricaPETSTEL analysis of IndiaOpen Architechture a white paperMind TravelDefinition of Export Quotas

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