Friday, August 21, 2020
The Emergence of a Unique Cultural Life in the South America - Essay Example The quantity of the individuals who relocated was as far as millions. For the Asians and the Europeans who moved to South America needed to go over the sea. A significant number of the individuals who moved to America favored dwelling in the Western side of America and a few pieces of the North Eastern side. Be that as it may, others felt more pulled in to move toward the Southern side of America (Cobb 75). These individuals incorporate; Greeks, Italians, Cubans, Jews, and Asians among numerous others. Be that as it may, the quantity of the outsiders to South America was not exactly the quantity of Southern African Americans who lived in destitution. In South America, there was a great deal of destitution and the wages were too low to even think about attracting migrants. There were not very many open doors for the migrants since dark Americans and a couple of the nearby whites are the once who worked in the horticultural divisions as workers and representatives in the material busin ess separately. By 1860, just five percent of the populace was made of the settlers not at all like in the North and East pieces of America whereby the level of the populace made up by the foreigners was fourteen. As a matter of fact, toward the South American government, that was extremely baffling thinking about that the administration attempted however much as could reasonably be expected to draw in more outsiders (Cobb 99). After the happening to outsiders to South America, a few elements affected the way of life of the area in an affecting manner. One of the variables is bigotry. Among the Asian outsiders, the most noteworthy number was made of Chinese individuals. There were not many Chinese ladies when contrasted with Chinese men. In the long run, the greater part of the Chinese men wedded dark American ladies who were dark in appearance. In somewhere in the range of hardly any cases, Chinese men wedded the nearby whites in South America. The kids conceived because of the int ermarriage were neither white nor dark. White schools couldn't enlist the Chinese youngsters to their schools since they didn't have the foggiest idea about the most ideal approach to order the kids (Edward 97). Because of intermarriages, new gatherings of individuals came up who were progressively unique in their lifestyle. Language is another factor that prompts the one of a kind culture in South America. Merging of various societies and various ways of life in the locale made the way of life remarkable. Despite the fact that others attempted to duplicate and adapt to various societies, new societies were created. The blacks had the option to develop staples, for example, corn and cassava. Asians thought of a method of disposing of the toxic parts found in the groceries. The blacks needed to adjust the way of life of the Asians in a manner to profit them (Edward 101). Regularly, when various sorts of individuals involve a spot, it happens that one isn't restricted in their way of life. Along these lines, there was a great deal of advancing in various societies so as to improve life. Various religions, which existed in South America, caused a great deal in the way of life. Since there were religions, which functioned admirably with a specific gathering of individuals, this influenced the way of life of the individuals. A few gatherings of individuals didn't esteem others relying upon their religions and numerous categories. This lead to clashes in light of the fact that various chapels had their own specific manner of doing and indicating their here was a period that protestants wouldn't fret the congregation to go to since the protestant houses of worship had basic practices. In the long run, there being sub division in the holy places and various religions, abberations emerged in this way various temples were intended for various gatherings (Edward 185). By the late nineteenth century, indiscipline in places of worship began on the grounds that the admirers began being against one another. This caused inner indiscipline in the district. Each congregation accepted that its confidence was the most right and
Sunday, July 12, 2020
Read Every Day 7 Ways to Put a Little Literature in Your Inbox As I accumulate side jobs like its my job, I find more and more days pass by where I dont really sit down and read. Although I try to listen to audiobooks during my commute, I wanted another way to make sure I got a little literature in my brain every day. Thats when I discovered the existence of newsletters that send a short piece of literature right to your inbox. Most of us are constantly checking our email anyway, so why not make sure one of those emails will be a poem, a short story, or essay? These email newsletters tend to be short, something you can read in a few minutes while you sip your coffee or tea. Theyve let me add a few solid reading minutes to even my busier mornings. Plus, getting a poem in my email every day helps me make sure Im actually reading poetry! So you can bring a little more reading into your inbox, here is a list of a few sources for literary email goodness: Poetry The Poetry Foundations Poem a Day feed allows you to subscribe via your preferred reader. A new poem is posted every day, with a mix of poetry from canonical and contemporary poets. Poets.orgs Poem-a-Day email is as easy as it gets. They send an email once a day that includes the text of the poem right in your email! Typically, its contemporary poetry on weekdays with throwback classics on the weekend. Prose The Season of Stories runs from October 11-December 30th and sends you a short story or essay straight to your inbox. Ive really been enjoying them so far. Daily Science Fiction will shoot a science fiction story to your inbox every day if you sign up for their newsletter. Daily Lit will send you 15-minute installments of a book of your choice each day. Theres a vast library of books, both free and for purchase, to choose from. You can also check out the serials and short stories they publish to fit this time frame. Every Day Fiction sends you a short short story each day. Their tagline is bite sized stories for a busy world, which promises content that will slip seamlessly into your day. Mixed Bag The Writers Almanac newsletter includes short poetry or prose depending on the day. Theres also bonus literary history so you can brush up on your bookish trivia. These are just a few of the many options to find a daily email that will encourage you to read a little every day. Happy reading!
Wednesday, May 20, 2020
Introduction Today, medical interventions have made it possible to save or prolong lives, but should the process of dying be left to nature? (Brogden, 2001). Phrases such as, Ã¢â¬Å"killing is always considered murder,Ã¢â¬ and Ã¢â¬Å"while life is present, so is hopeÃ¢â¬ are not enough to contract with the present medical knowledge in the Canadian health care system, which is proficient of giving injured patients a chance to live, which in the past would not have been possible (Brogden, 2001). According to Brogden, a number of economic and ethical questions arise concerning the increasing elderly population. This is the reason why the Canadian society ought to endeavor to come to a decision on what is right and ethical when it comes to facing death.Ã¢â¬ ¦show more contentÃ¢â¬ ¦On the other hand, voluntary euthanasia is described as a situation in which the critically ill patient requests from someone else to help them die. They may either influence someone to assist them in s uicide, or refuse life-saving medical treatment (Ramabele, 2004). Euthanasia and the Elderly Population When it comes to peopleÃ¢â¬â¢s attitudes towards euthanasia, age has a very strong impact. According to Brogden, elderly, terminally ill individuals are considered vulnerable. They might be short of the ability and understanding of lessening the pain of their symptoms, and could experience apprehension regarding the future and what the consequences of their illness are (Blank et al, 2001). The elderly individualÃ¢â¬â¢s decision making about euthanasia may just be because of confusion, depression, dementia, or a number of other symptoms, however, these could all be relieved with suitable treatment and support (Blank et al, 2001). However, great pressure is experienced by elderly people to request euthanasia because many of them already feel a burden to their families and caregivers (Brogden, 2001). Individuals may argue that although medical technology can preserve their life, the financial burden and pain that is endured could be so immense that it would be better off for the family, society, and even the patient them self if they choose to die (BlackShow MoreRelated Argument in Favor of Euthanasia Essay2098 Words Ã |Ã 9 PagesDebate about the morality and legality of voluntary euthanasia has been a phenomenon since the second half of the 20th century. The ancient Greeks and Romans did not believe that life needed to be preserved at any cost and were tolerant of suicide in cases where no relief could be offered to the dying or when a person no longer cared for their life (Young). In the 4th century BC, the Hippocratic Oath was written by Hippocrates, the father of medicine. One part of the Oath states, Ã¢â¬Å"I will not giveRead MoreArgument Of Favor Of Active Voluntary Euthanasia1781 Words Ã |Ã 8 PagesBenny Mutoni Ethics Society Argument in favor of Active Voluntary Euthanasia In this paper, I will discuss euthanasia and physician-assisted suicide and whether there are circumstances under which the two are ever ethically permissible. I will also be examining active and passive euthanasia and how philosophers view both differently. I will cite the text Ã¢â¬Å"Doing Ethics: Moral Reasoning and Contemporary IssuesÃ¢â¬ , philosophers like James Rachel, and cases such as Dax Cowart and Brittany MaynardRead MoreArgumentative Essay On Euthanasia1302 Words Ã |Ã 6 Pagesbehind Euthanasia In an ethics class I took in high school, I have learned about many controversial topics. One that caught my attention specifically was euthanasia or the Ã¢â¬Å"right to dieÃ¢â¬ as some call it. There are many types of Euthanasia, including active and passive. In class we debated the difference between the two and why passive euthanasia is legal and active is not. Active euthanasia is defined as Ã¢â¬Å"a person directly and deliberately causing the patient s death.Ã¢â¬ (Forms of euthanasia) PassiveRead MoreShould Euthanasia Be Legalized?907 Words Ã |Ã 4 Pagesactive euthanasia, which is a highly contentious issue in the United States. Voluntary active euthanasia is currently illegal in the United States. However, I believe that patients with terminal illnesses experiencing a lot of pain and misery should have the right to die the way they choose, with dignity, instead of being subjected to agony. People should be able to choose voluntary active euthanasia, if ever need be, w hich is why I believe that despite current policy, voluntary active euthanasia shouldRead MoreOpinions on Euthanasia and Assisted Suicide1347 Words Ã |Ã 5 PagesÃ¯ » ¿Opinions of euthanasia and assisted suicide vary by country to country, and only a few nations permit euthanasia in the case of terminally ill patients (van der Heide et. al., 2007, p. 1957). The public discourse surrounding the ethical, and subsequently legal status of euthanasia is frequently heated and somewhat polarized, because the debate cuts to the very heart of notions of human rights and ethics. Unfortunately, this only tends to further obscure the issue at hand, which is in reality a fairlyRead MoreThe Morality Of Euthanasia By James Rachels1086 Words Ã |Ã 5 PagesID: 3339147 Active Euthanasia Does James Rachels in Ã¢â¬Å"The Morality of EuthanasiaÃ¢â¬ successfully argue that in at least some cases active euthanasia is morally acceptable? Explain his view and respond to it. In this essay, we are going to analyze the main ideas included in Ã¢â¬Å"The Morality of EuthanasiaÃ¢â¬ by James Rachels to provide a response to the following question: Does James Rachels in Ã¢â¬Å"The Morality of EuthanasiaÃ¢â¬ successfully argue that in at least some cases active euthanasia is morally acceptableRead MoreThe Ups And Downs Of Euthanasia1288 Words Ã |Ã 6 PagesMiÃ¢â¬â¢esha Straughn Dr. Willis 12 October 2017 ENG 101/102 Mini Term The Ups and Downs of Euthanasia Losing a loved one is an experience that no one wants to go through. Moms, dads, aunts, uncles, and the like are all an integral part of life. However, what if one of these loved ones were terminally ill and losing strength day by day? Would one want to watch them suffer, clinging on to the last bit of life that they have, or would he want to help end the suffering in a peaceful manner? These are someRead MoreThe Argument Of Active And Passive Euthanasia1240 Words Ã |Ã 5 Pages# 3 This essay will aim to focus on the arguments that author, James RachelÃ¢â¬â¢s presents in his article, Active and Passive Euthanasia,Ã¢â¬ In his article RachelÃ¢â¬â¢s argues that both passive and active euthanasia are morally permissible and the doctors that is supported by the American Medical Association(AMA) is believed to be unsound. In this paper I will offer a thorough analysis of RachelÃ¢â¬â¢s essay then so offer a critique in opposition of his arguments. In conclusion I will refute these oppositionsRead MoreEuthanasia Essay1561 Words Ã |Ã 7 Pagesethical issue of euthanasia, or mercy killing, concerns whether it is morally permissible for a third party, such as a physician, to end the life of a terminally ill patient who is in intense pain. The word euthanasia comes from the Greek words eu (Ã¢â¬ËwellÃ¢â¬â¢) and thanatos (Ã¢â¬ËdeathÃ¢â¬â¢). It means a painless and gentle death. But in modern usage, it has come to imply that someoneÃ¢â¬â¢s life is ended for compassionate reasons by some passive or active steps taken by another person. The euthanasia controversy isRead MoreFor Euthanasia Persuasive Essay1663 Words Ã |Ã 7 Pagespain and suffering. Euthanasia is a word that most people avoid because it is very controversial. But why? Euthanasia is a way of ending the prolonging of suffering, while leaving life in peace. Euthanasia is derived from the Greeks where Eu means good and Thanatos means death. When these phrases are combined the word euthanasia is created; meaning Ã¢â¬Å"good deathÃ¢â¬ (6.) There are three types of euthanasia although only two are authentic forms. The first type is active euthanasia. It is described as
Wednesday, May 6, 2020
When faced with the debate between the relationship between slavery and racism, scholars often use two arguments that attempt to provide an answer of whether or not slavery produced racism or racism was a necessary precursor to slavery. Some authors address the relationship between slavery and racism by exploring the economics behind slavery while relating it back to the development of chattel slavery and racism. Others explore how the views Europeans had on Africans prior to the mass enslavement and argue that these interpretations came from racial differences. This led to not only slavery, but the growth of racism seen not just in early America but that is deep seeded in many people even today. When reviewing the works of many authors,Ã¢â¬ ¦show more contentÃ¢â¬ ¦Although, E. Morgan discusses how early colonist displayed racial tensions towards the indigenous tribes that were in Virginia, his larger argument was that the racism towards Africans and African Americans stemmed from the larger hostilities towards members of the lower class structures and the economy. Free and enslaved Africans and African Americans were almost destined to be a part of the lower class. Slavery helped this destiny as many children who were mulatto or black deemed slaves, transposed into an economic gain for the slave owner. However, unequal taxation by the state of African American men and women also prevented the raise in social status. Black Majority by Wood, also explores how the economy and the enslavement of Africans created the strong racial tensions. Wood, like E. Morgan, discusses the decision of using African American or African slave labor was an economic and a seemingly sensible choice. Africans or African American laborers were ideal because they could be held for an indefinite time, they could not report abuse back to their families, they were not involved in any immediate diplomatic relations for the colonist like the indigenous tribes, and they were cheaper to tra nsport unlike the white European laborers. According to Wood, it was the rampant enslavement of Africans and African Americans that produced racism in the Americas. Wood, like E. Morgan discusses how the growingShow MoreRelatedCadbury Corporate Governance Essay1236 Words Ã |Ã 5 Pagesframework by which the various stakeholder interests are balanced, or, as the IFC (International Finance Corporation) states, the relationships among the management, Board of Directors, controlling shareholders, minority shareholders and other stakeholders. The OECD Principles of Corporate Governance states that: Corporate governance involves a set of relationships between a companyÃ¢â¬â¢s management, its board, its shareholders and other stakeholders. Corporate governance also provides the structureRead MoreRole Of The Systems Approach For The Water1199 Words Ã |Ã 5 PagesThe Role of the Systems Approach for the Water Ã¢â¬â Food Ã¢â¬â Energy Nexus The role of the systems approach when dealing with the water, food, and energy nexus is to understand and depict the interconnections between all parts, to ensure the parts are divided equally, and that the sum of all parts equals the whole. By focusing on just one part, for instance water - trying to make the heating of water and the extraction of water better, you can actually be causing more issues at the expense of the energyRead MoreThe Hierarchy Of Gender Is An Issue That The Entire World Has Faced For Many Years954 Words Ã |Ã 4 Pages The hierarchy of gender is an issue that the entire world has faced for many years. In the United States, there is a large problem with women being represented in politics. This can be traced back to how children are placed into different hierarchies of males being masculine and females being feminine through their clothes, toys, and more. However, the issue is also caused by the mediaÃ¢â¬â¢s portray of female politicians in comparison to m ale politicians. The mediaÃ¢â¬â¢s reporting of the 2016 presidentialRead More The Great Debaters: The Wiley College Debate Team Essay1444 Words Ã |Ã 6 PagesIntroduction Conflict is inevitable in any personal relationship or among members of any group. While we encounter many types of conflict in our lifetime, we often look for ways to avoid conflict. So, why do we run away from dealing with our conflict? It is often because many of us fear the conflict will escalate into a situation we will not be able to sustain. Ã¢â¬Å"As conflicts escalate, they go through certain incremental transformations. Although these transformations occur separately on eachRead MoreHuman Communication: Non Verbal Communication1231 Words Ã |Ã 5 Pagesare giving an emphasis. However, emphasis in body language is simply giving a larger, physical presence to a word or phrase. When it comes to connecting to an audience nobody delivers better than former President Bill Clinton. A perfect example of this skill would be during the nineteen ninety-two presidential debate between Bill Clinton and George Bush. During the second debate, an audience member asked a question on the recession. George BushÃ¢â¬â¢s response was more defensive and confusing than a definitiveRead MoreModern Technology1463 Words Ã |Ã 6 Pages The debate of modern technology is one that reaches out to almost everyone in the modern era living in the United States, since it is a first world country, everybody living in the country at one point has interacted with a piece of modern technology. The evolution of technology in the last two decades has been exponentially fast, changing evolution of almost an entire generation in the way that they view things and interact with the world around them. Things such as virtual reality haveRead MoreThe Creation Of A Nation942 Words Ã |Ã 4 Pagesit had times where it really struggled. The fear of monarchy, the debate over slavery and the issues pertaining to their relationships with foreign countries, coupled with feuds between the founding brothers somehow resulted in the success of the nation. Although, America had gained their independence, the states feared the return of a monarchy while the government itself feared anarchy. This is seen greatly in the dinner between Jefferson, Hamilton and Madison and the effects of it and John AdamÃ¢â¬â¢sRead MoreAnalysis Of The Movie The Ugly Truth 892 Words Ã |Ã 4 Pagesbe controlling and physically unappealing. At the climax, Mike and Abby both become tempted to make love with each other. The features of old comedy are buffoonery, obscene language, and frank sexual talk. The Ugly Truth exemplifies such features when an anchorman, Larry, experiencing adversity with his wife, Georgia, on the job. The protagonist, Abby, motivates him by saying he has Ã¢â¬Å"balls the size of VolkswagensÃ¢â¬ . Later in the movie, Larry describes Georgia as Ã¢â¬Å"angry and bitterÃ¢â¬ and she respondsRead MoreThe Relationship Between Inflation And Unemployment1662 Words Ã |Ã 7 PagesThe relationship between inflation and unemployment is a topic, which has been debated by economists for decades. It is this debate that has made the opinions about it evolve. In this essay, the controversial topic will be discussed by viewing different economistsÃ¢â¬â¢ opinions on that according to time sequencing. Inflation is an increase in price levels within an economy. Basically it means that you will have to pay more for the same goods. Unemployment is even more straightforward. It means thatRead MoreDefoe Roxana Analysis723 Words Ã |Ã 3 Pagesdrastically different. In former novels, when faced with a moment of devastation, the character divided from their previous self, and in turn gained control. From there, the character is faced with yet another unfavorable situation, but this time they are able to overcome it in their new powerful state. On the contrary, Roxana divided from her previous self, but still faced destruction and tragedy in the end. Maddox also examines closely the relationship between Roxana and Amy, and how their characters
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Thursday, April 23, 2020
Approved by: Chair of Committee, Committee Members, Robert A. Wattenbarger Goong Chen Christine Ehlig-Economides Bryan Maggard Stephen Holditch Head of Department, May 2009 Major Subject: Petroleum Engineering iii ABSTRACT Rate Transient Analysis in Shale Gas Reservoirs with Transient Linear Behavior. (May 2009) Rasheed Olusehun Bello, B. Sc. , University of Lagos, Nigeria; M. Sc. , University of Saskatchewan, Canada Chair of Advisory Committee: Dr. Robert Wattenbarger Many hydraulically fractured shale gas horizontal wells in the Barnett shale have been observed to exhibit transient linear behavior. This transient linear behavior is characterized by a one-half slope on a log-log plot of rate against time. This transient linear flow regime is believed to be caused by transient drainage of low permeability matrix blocks into adjoining fractures. This transient flow regime is the only flow regime available for analysis in many wells. The hydraulically fractured shale gas reservoir system was described in this work by a linear dual porosity model. We will write a custom essay sample on Rate Transient Analysis in Shale Gas Reservoirs with Transient Linear Behavior or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page This consisted of a bounded rectangular reservoir with slab matrix blocks draining into adjoining fractures and subsequently to a horizontal well in the centre. The horizontal well fully penetrates the rectangular reservoir. Convergence skin is incorporated into the linear model to account for the presence of the horizontal wellbore. Five flow regions were identified with this model. Region 1 is due to transient flow only in the fractures. Region 2 is bilinear flow and occurs when the matrix drainage begins simultaneously with the transient flow in the fractures. Region 3 is the response iv for a homogeneous reservoir. Region 4 is dominated by transient matrix drainage and is the transient flow regime of interest. Region 5 is the boundary dominated transient response. New working equations were developed and presented for analysis of Regions 1 to 4. No equation was presented for Region 5 as it requires a combination of material balance and productivity index equations beyond the scope of this work. It is concluded that the transient linear region observed in field data occurs in Region 4 Ã¢â¬â drainage of the matrix. A procedure is presented for analysis. The only parameter that can be determined with available data is the matrix drainage area, Acm. It was also demonstrated in this work that the effect of skin under constant rate and constant bottomhole pressure conditions is not similar for a linear reservoir. The constant rate case is the usual parallel lines with an offset but the constant bottomhole pressure shows a gradual diminishing effect of skin. A new analytical equation was presented to describe the constant bottomhole pressure effect of skin in a linear reservoir. It was also demonstrated that different shape factor formulations (Warren and Root, Zimmerman and Kazemi) result in similar Region 4 transient linear response provided that the appropriate f(s) modifications consistent with ? Ac calculations are conducted. It was also demonstrated that different matrix geometry exhibit the same Region 4 transient linear response when the area-volume ratios are similar. v DEDICATION I dedicate my work to all those who have lovingly supported me throughout life and all its travails. vi ACKNOWLEDGEMENTS First, I want to give praises to Almighty Allah for sparing my life, continuously granting me His blessings and allowing me to successfully conclude this phase of my life. I want to acknowledge my supervisor, Dr. Robert. A. Wattenbarger for being a father, mentor, supervisor and friend to me. I am honored to have worked with him. I am also eternally grateful to him. I want to acknowledge the suggestions and contributions of my committee members, Dr. Christine Ehlig-Economides , Dr. Bryan Maggard Ã¢â¬â whose classes are among my favorites and invaluable- and Dr. Goong Chen. The research problem is described and the project objectives are presented. Chapter II presents an extensive literature review. The dual porosity model and its applications to liquids and gas are reviewed. Horizontal well applications are also reviewed. Chapter III describes the linear model to be used in this work. Validation of the linear model is also presented. Chapter IV presents new analysis equations developed using the linear model. Chapter V discusses the transient linear regime in detail and discusses the effects of shape factors and area-volume ratio. Chapter VI describes the constant bottomhole pressure effect of skin in linear reservoirs Chapter VII presents development of new type curves with application to sample field data. Chapter VIII presents conclusions and recommendations. 9 CHAPTER II LITERATURE REVIEW 2. 1 Introduction Initial studies of fractured reservoirs were concerned with applications to well test analysis of reservoir flow of liquids (constant rate, pressure buildup and drawdown). Subsequent research considered production data analysis (constant bottomhole pressure) and extension of existing models to gas flow. Most of the literature is devoted to radial reservoir models. In this chapter, review of literature will be conducted in three sections. The first section discusses the dual porosity model and its application to flow of slightly compressible fluids. The second section discusses the application of the dual porosity model to gas flow. The final section discusses the application of the dual porosity model to analysis of naturally fractured reservoirs with horizontal wells. 2. 2 Dual Porosity Model (Slightly Compressible Fluids) Naturally fractured reservoirs (tight gas, shale gas and coal gas) have been described by the dual porosity model. The dual porosity model was first formulated by Barenblatt et al. 17 and later extended to well test analysis by Warren and Root. 18 The Warren and Root model forms the basis of modern day analysis of naturally fractured reservoirs. In the Warren and Root model, the naturally fractured reservoir is modeled by uniform homogeneous matrix blocks separated by fractures as shown in Fig. 2. 1. The matrix blocks provide storage of the fluid to be produced while the fractures provide the 10 permeability. When a producing well is present, the fluid flows from the matrix to the fractures and to the well. There have been two types of approach in applying the dual porosity model based on how flow of the fluid from the matrix to the fractures is modeled Ã¢â¬â pseudosteady state and transient. Fig. 2. 1 Dual Porosity Model. 18 2. 2. 1 Pseudosteadystate Matrix-Fracture Transfer Models An equation for interporosity flow from the matrix to the fractures at a mathematical point under pseudosteadystate (quasisteadystate or semisteadystate) conditions was presented by Warren and Root. 18 11 q =? km Ã µ (p m ? pf ) Where q is the drainage rate per unit volume, ? is the Warren and Root shape factor, pm is the matrix pressure at a mathematical point. Two new parameters which are used to characterize naturally fractured reservoirs were presented by Warren and Root18 the interporosity flow parameter, ? (a measure of the flow capacity of the system) and the storativity, ? (a measure of the storage capacity of the fractures). Warren and Root18 were the first to apply Laplace transformation to obtain Ã¢â¬Å"f(s)Ã¢â¬ and solve for the dimensionless pressure distribution. A method of analyzing pressure buildup data for the infinite radial reservoir case was presented. Buildup plots were found to exhibit parallel lines on a semilog plot separated by an Sshaped transition period. The first line represents flow in the fracture system only while the second line represents flow in the total system (matrix and fractures). Kazemi et al. 19 investigated the suitability of applying the Warren and Root model to interpret interference results. They presented a model which extends the Warren and Root model to interference testing. They applied the Laplace transformation to obtain Ã¢â¬Å"f(s)Ã¢â¬ and solve for the dimensionless pressure distribution. They also numerically solved the model equations by finite-difference methods and included vertical pressure gradients. It was concluded that an equivalent homogeneous model was not appropriate at early times but could be used at later times. It was also concluded that the Warren and Root model yielded similar results as their numerical solution and was thus appropriate for analyzing naturally fractured reservoirs. 12 Odeh20 developed an infinite radial reservoir model for the behavior of naturally fractured reservoir. The model incorporates some limiting assumptions. The Laplace transformation is also utilized. Two parallel straight lines were not observed on a semilog plot contrary to Warren and RootÃ¢â¬â¢s results. It was concluded that buildup and drawdown plots of naturally fractured reservoir transient responses are similar to those of homogeneous reservoirs. Mavor and Cinco-Ley21 present solutions for the constant rate case in an infinite radial reservoir with and without wellbore storage and skin; and a bounded radial reservoir. Solutions are also presented for the first time for a constant pressure inner boundary with skin in an infinite radial reservoir. Da Prat et al. 22 extended the Warren and Root18 solutions to constant pressure inner boundary conditions and bounded outer boundary cases for the radial reservoir. They also present type curves for analysis. The results do not appear to represent realistic field cases. Bui et al. 23 present type curves for transient pressure analysis of partially penetrating wells in naturally fractured reservoirs by combining the Warren and Root model with the solution for these wells in homogeneous reservoirs. 2. 2. 2 Transient Matrix-Fracture Transfer Models Kazemi24 used a slab matrix model with horizontal fractures and unsteady state matrixfracture flow to represent single-phase flow in the fractured reservoir. The assumptions include homogeneous behavior and isotropic matrix and fracture properties. The well is 13 centrally located in a bounded radial reservoir. A numerical reservoir simulator was used. It was concluded that the results were similar to the Warren and Root model when applied to a drawdown test in which the boundaries have not been detected. Two parallel straight lines were obtained on a semilog plot. The first straight line may be obscured by wellbore storage effects and the second straight line may lead to overestimating ? when boundary effects have been detected. De Swaan25 presented a model which approximates the matrix blocks by regular solids (slab and spheres) and utilizes heat flow theory to describe the pressure distribution. It was assumed that the pressure in the fractures around the matrix blocks is variable and the source term is described through a convolution term. Approximate linesource solutions for early and late time are presented. The late time solutions are similar to those for early time except that modified hydraulic diffusivity terms dependent on fracture and matrix properties are included. The results are two parallel lines representing the early and late time approximations. The late time solution matches Kazemi24 for the slab case. De SwaanÃ¢â¬â¢s model does not properly represent the transition period. Najurieta26 presented a transient model for analyzing pressure transient data based on De SwaanÃ¢â¬â¢s25 theory. Two types of fractured reservoir were studied- stratum (slabs) and blocks (approximated by spheres). The model predicted results similar to Kazemi. 24 Serra et al. 27 present methods for analyzing pressure transient data. The slab model used is similar to De Swaan25 and Najurieta. 26 The model considers unsteady state 14 matrix fracture transfer and is for an infinite reservoir. Three flow regimes were identified. Flow Regime 1 and 3 are the Warren and Root18 early and late time semilog lines. A new flow Regime 2 was also identified with half the slope of the late time semilog line. Chen et al. 28 present methods for analyzing drawdown and buildup data for a constant rate producing well centrally located in a closed radial reservoir. The slab model similar to De Swaan25 and Kazemi24 is used. Five flow regimes are presented. Flow regimes 1, 2 and 3 are associated with an infinite reservoir and are described in Serra et al. 27 Flow regime 1 occurs when there is a transient only in the fracture system. Flow regime 2 occurs when the transient occurs in the matrix and fractures. Flow regime 3 is a combination of transient flow in the fractures and Ã¢â¬Å"pseudosteady stateÃ¢â¬ in the matrix. Pseudosteadystate in the matrix occurs when the no-flow boundary represented by the symmetry center line in the matrix affects the response. Two new flow regimes associated with a bounded reservoir are also presented. Flow regime 4 reflects unsteady linear flow in the matrix system and pseudosteadystate in the fractures.. Flow Regime 5 occurs when the response is affected by all the boundaries (pseudosteady-state). Streltsova29 applied a Ã¢â¬Å"gradient modelÃ¢â¬ (transient matrix-fracture transfer flow) with slab-shaped matrix blocks to an infinite reservoir. The model predicted results which differ from the Warren and Root model in early time but converge to similar values in late time. The model also predicted a linear transitional response on a semi-log plot between the early and late time pressure responses which has a slope equal to half 15 that of the early and late time lines. This linear transitional response was also shown to differ from the S-shaped inflection predicted by the Warren and Root model. Cinco Ley and Samaniego30 utilize models similar to De Swaan25 and Najurieta26 and present solutions for slab and sphere matrix cases. They utilize new dimensionless variables Ã¢â¬â dimensionless matrix hydraulic diffusivity, and dimensionless fracture area. They describe three flow regimes observed on a semilog plot Ã¢â¬â fracture storage dominated flow, Ã¢â¬Å"matrix transient linearÃ¢â¬ dominated flow and a matrix pseudosteadystate flow. The Ã¢â¬Å"matrix transient linearÃ¢â¬ dominated flow period is observed as a line with one-half the slopes of the other two lines. 7,29 It should be noted that the Ã¢â¬Å"matrix transient linearÃ¢â¬ period yields a straight line on a semilog plot indicating radial flow and might be a misnomer. The fracture storage dominated flow is due to fluid expansion in the fractures. The Ã¢â¬Å"matrix transient linearÃ¢â¬ period is due to fluid expansion in the matrix. The matrix pseudosteadystate period occurs when the matrix is under pseu dosteadystate flow and the reservoir pressure is dominated by the total storativity of the system (matrix + fractures). It was concluded that matrix geometry might be identified with their methods provided the pressure data is smooth. Lai et al. 31 utilize a one-sixth of a cube matrix geometry transient model to develop well test equations for finite and infinite cases including wellbore storage and skin. Their model was verified with a numerical simulator employing the Multiple Interacting Continua (MINC) method. Ozkan et al. 12 present analysis of flow regimes associated with flow of a well at constant pressure in a closed radial reservoir. The rectangular slab model similar to De 16 Swaan25 and Kazemi24 is used. Five flow regimes are presented. Flow regimes 1, 2 and 3 are described in Serra et al. 7 Two new regimes are presented- Flow regime 4 reflects unsteady linear flow in the matrix system and occurs when the outer boundary influences the well response and the matrix boundary has no influence. Flow Regime 5 occurs when the response is affected by all the boundaries. Houze et al. 32 present type curves for analysis of pressure transient response in an infinite naturally fractured reservoir with an infinite c onductivity vertical fracture. Stewart and Ascharsobbi33 present an equation for interporosity skin which can be introduced into the pseudosteadystate and transient models. The effect of interporosity skin is to delay flow from the matrix to the fractures. This equation is given by s ma = 2k mi h s hm k s where kmi is the intrinsic matrix permeability, hs is the thickness of the interporosity skin layer, hm is the matrix block dimension and ks is the permeability of the interporosity skin layer. It should be noted that all the transient models previously described were developed for the radial reservoir cases (infinite or bounded). El-Banbi16 was the first to present transient dual porosity solutions for the linear reservoir case. New solutions were presented for a naturally fractured reservoir using a dual porosity, linear reservoir model. Solutions are presented for a combination of different inner boundary (constant pressure, constant rate, with or without skin and 17 wellbore storage) and outer boundary conditions (infinite, closed, constant pressure). This model will be used in this work. 2. 3 Dual Porosity Model (Gas) Kucuk and Sawyer34,35presented a model for transient matrix-fracture transfer for the gas case. Previous work had been concerned mainly with modeling slightly compressible (liquid) flow. They considered cylindrical and spherical matrix blocks cases. They also incorporate the pseudopressure definitions for gases. Techniques for analyzing buildup data are also presented for shale gas reservoirs. Their model results plotted on a dimensionless basis matched Warren and Root18 and Kazemi24 for very large matrix blocks at early time but differ at later times. They also conclude from their tests that naturally fractured reservoirs do not always exhibit the Warren and Root behavior (two parallel lines). Carlson and Mercer15 coupled FickÃ¢â¬â¢s law for diffusion within the matrix and desorption in their transient radial reservoir model for shale gas. Modifications include use of the pressure-squared forms valid for gas at low pressures to linearize the diffusivity equation. They provide a Laplace space equation for the gas cumulative production from their model and use it to history match a sample well. They also show that semi-infinite behavior (portions of the matrix remain at initial pressure and is unaffected by production from the fractures) occurs in shale gas reservoirs regardless of matrix geometry. They present an equation for predicting the end of this semi-infinite behavior. 18 Gatens et al. 6 analyzed production data from about 898 Devonian shale wells in four areas. They present three methods of analyzing production data Ã¢â¬â type curves, analytical model and empirical equations. The empirical equation correlates cumulative production data at a certain time with cumulative production at other times. This avoids the need to determine reservoir properties. Reasonable matches with actual data were presented. The ana lytical model is used along with an automatic history matching algorithm and a model selection procedure to determine statistically the best fit with actual data. Watson et al. 37 present a procedure that involves selection of the most appropriate production model from a list of models including the dual porosity model using statistics. The analytical slab matrix model presented by Serra et al. 27 is utilized. Reservoir parameters are estimated through a history matching procedure that involves minimizing an objective function comparing measured and estimated cumulative production. They incorporate the use of a normalized time in the analytical model to account for changing gas properties with pressure. Reasonable history matches were obtained with sample field cases but forecast was slightly underestimated. Spivey and Semmelbeck38 present an iterative method for predicting production from dewatered coal and fractured gas shale reservoirs. The model used is a well producing at constant bottomhole pressure centered in a closed radial reservoir. A slab matrix is incorporated into these solutions. These solutions are extended to the gas case by using an adjusted time and adjusted pressure. Their method also uses a total compressibility term accounting for desorption. 19 2. Horizontal Wells in Naturally Fractured Reservoirs There have been different traditional approaches to modeling horizontal wells in homogeneous reservoirs. Horizontal wells are normally modeled as infinite conductivity (pressure is uniform along the wellbore). It is not practical, as Gringarten et al. 39 demonstrated with infinite conductivity fractures, to compute the wellbore pressure from the infinite-conductivity model because of the computational work involved. Gringarten et al. 39 suggested computing the pressure drop from the uniform flux model (flowrate is the same for each individual segment along a wellbore) at a value of xD = 0. 32. This value was the point at which the uniform flux model yields the same results as the infinite conductivity model. This computation has also been incorporated into horizontal well models. 40-46 The mathematical problem to be solved for the anisotropic case is usually given by kx ? 2 p ? 2 p ? p ? 2 p + k y 2 + k z 2 = ? Ã µct 2 ? t ? x ? y ? z Several authors have used a model of a line source well in a semi-infinite45,47 or infinite reservoir. 40-44,48-50 Others41-44,48,51 have used a line source well in a closed rectangular reservoir. The infinite model has no-flow boundaries at the top and bottom. The semi-infinite reservoir model has three no-flow boundaries (top, bottom and left). The closed reservoir model has all four no-flow boundaries. 20 It should be noted that in these models, the well is usually not completely penetrating but the models by Ozkan 41-44 and Odeh and Babu51 provide this possibility once the appropriate well and reservoir dimensions are specified. The differential equation and boundary conditions have been mostly solved by the Newman product method and source functions. 0-45 These concepts for the homogeneous reservoir case have been extended to model horizontal wells in naturally fractured reservoirs. Ozkan41-44 presents Laplace space solutions for horizontal wells in a reservoir for infinite and closed rectangular boundary cases in terms of f(s). The line source approach previously described is utilized. As demonstrated by Ozkan, there is a possibility of applying this to the naturally fra ctured reservoir by substituting the appropriate f(s) for a selected matrix geometry. Carvalho and Rosa52 present solutions for an infinite conductivity horizontal well in a semi-infinite reservoir. The reservoir is homogeneous and isotropic. The horizontal well is modeled as a line source. The solutions for the homogeneous case were then extended to the dual porosity case by substituting s*f(s) for s in Laplace space for the pressure derivative (homogeneous). Wellbore storage and skin are incorporated into their model using Laplace space. Aguilera and Ng53 present analytical equations for pressure transient analysis. Their model is a horizontal well in a semi-infinite, anisotropic, naturally fractured reservoir. Transient and pseudosteadystate interporosity flow is considered. Six flow periods are identified Ã¢â¬âFirst radial flow (at early times, from fractures), Transition 21 period, Second radial flow in vertical plane, First linear flow, Pseudoradial flow and Late linear with expressions for determining skin provided. Ng and Aguilera54 present analytical solutions using a line source and then compute pressure drop on a point away from the well axis to account for the radius of the actual well. A method for determining the numerical Laplace transform is presented. This method was then used to compute the dual porosity response (pseudosteady state). Their solutions were compared to other solutions. Thompson et al. 55 present an algorithm for computing horizontal well response in a bounded dual porosity reservoir. Their model is a horizontal well in a closed rectangular reservoir. Their procedure involves converting a known analytic solution to Laplace space numerically point by point and then inverting using the Stehfest algorithm. 56 This is similar to the procedure presented by Ohaeri and Vo46 who use a numerical Laplace space algorithm57 but also present alternative equations determined by parameter ranges which result in computational efficiency. Du and Stewart58 describe situations which can yield linear flow behavior Ã¢â¬â a multi-layered reservoir (one layer has a very high permeability relative to the other); naturally fractured reservoir (flow from matrix into horizontal well intersecting fractures); and areal anisotropy (vertical fractures aligned predominantly in one direction). Their model is that of a horizontal well in a homogeneous, infinite acting reservoir. Three flow regimes are identified Ã¢â¬â radial vertical flow, linear flow opposite completed section and pseudoradial flow at late time. A bilinear flow behavior was also identified. 22 The model presented in this work has the advantage of being simpler than the horizontal well models. The model will be presented in Chapter III. It also allows the direct use of Laplace space techniques not easily seen with these horizontal well models. Review of literature also shows that the transient linear flow regime has not been investigated in the manner presented in this work. 23 CHAPTER III MATHEMATICAL MODEL 3. 1 Introduction A schematic of the model to be used in this work is shown in Fig. . 1. A rectangular grid is imposed on the microseismic results as shown in Fig. 3. 1. The model is shown in detail with representative cube matrix blocks in Fig. 3. 2. The features of the model to be used in this work are described below. Ã¢â¬ ¢ A closed rectangular geometry reservoir containing a network of natural and hydraulic fractures (as in Mayerhofer et al. 14). The fractures do not drain beyond the boundaries of this rectangular g eometry. Ã¢â¬ ¢ Ã¢â¬ ¢ Ã¢â¬ ¢ Ã¢â¬ ¢ The perforated length of the well , xe is the same as the width of the reservoir.