thesis comprehensive evaluation

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The thesis project must be an empirical research project that makes a scholarly contribution to the current body of knowledge in some area of psychology. The student may not submit an IRB/IACUC proposal or begin collecting data until after the committee approves the proposal  unless  the pre-proposal process (see below) is completed and the committee grants approval to do so.

The student writes the proposal under the supervision of the advisor. The expectation is that the thesis proposal will result from an iterative process where, in order to develop a high quality document, the advisor edits drafts of the proposal that the student prepares. During preparation of the proposal, the student should consult committee members only if he or she needs their expertise. The proposal is to specify clearly, what the student proposes to do for the thesis project so that the student and the committee can discuss the details and arrive at definite decisions and agreement about the feasibility and quality of the proposed research.

Once the advisor provides approval to do so, the student distributes the completed proposal to all committee members for review. The thesis proposal defense meeting (typically 2 hours) is scheduled, not less than one week after the student distributes the proposal to members of the committee. The student should not make changes to the proposal after he or she distributes it to the committee.

Members of the committee read the thesis proposal and complete the Written Document Scoring Rubric prior to attending the proposal defense meeting. During the proposal meeting, the student makes a brief presentation during which he or she should: demonstrate foundational knowledge, skills, and abilities relevant to the project; interact professionally with the audience; competently field questions about the project and the written document and; effectively use presentation software. Once the student has answered all questions, the committee will ask the student to leave the room while the members of the committee (a) discuss the document and the student’s presentation, (b) complete the Oral Presentation and Overall Rating Scoring Rubrics, and (c) decide whether to approve the proposal, approve the proposal with specified revisions discussed in the meeting, or reject the proposal. After the thesis proposal meeting is over, the chair of the thesis committee should submit a copy of the proposal and the completed Scoring Rubrics from the committee members to the Program Director.

In all cases, the committee will provide the student formative feedback regarding the quality of the written document and oral presentation will be provided to aid the student in preparing the written thesis and completing the oral defense of the thesis, which serves as the program’s comprehensive assessment. If the committee rejects the proposal, they will make specific recommendations for remediation and the student may need to make substantial changes to the document, schedule another proposal meeting, or both in order for the committee to approve the proposal. Once the committee approves the thesis proposal, the committee members should complete new Scoring Rubrics and the chair of the thesis committee should submit a copy of the proposal and the new Scoring Rubrics from the committee members to the Program Director.

The middle of the third semester is the target date for completing and defending the thesis proposal. However, each student should consult with his or her advisor to determine (a) whether individual circumstances suggest that a later proposal date is appropriate and (b) the extent to which later proposal approval could impact completion of the thesis and the student’s anticipated graduation date.

Pre-Proposal Process : A student must complete the pre-proposal process if he or she (a) intends to use a pre-existing data set or (b) needs to attain IRB/IACUC approval and/or, (c) needs to begin data collection before a full proposal of suitable quality can be completed. In such cases, the student will work with the advisor to develop a pre-proposal document that the thesis committee will review. The major issues to be addressed in the pre-proposal document are those related to the proposed method and analyses: however, a clear hypothesis and rationale also must be provided so that the proposed method and analyses can be evaluated within context. The student or any member of the committee may request meeting to discuss the pre-proposal document but a meet is not required. If committee approval is granted, the student may submit an IRB/IACUC proposal (if necessary) and/or begin collecting data (if necessary) at that time.   The pre-proposal is NOT a replacement for the thesis proposal; students who complete the pre-proposal process also must prepare a thesis proposal that the committee ultimately approves .

Once the data are collected, the student analyzes the data and writes the thesis under the supervision of the advisor. As with the proposal, several drafts of the written thesis are usually required. The expectation is that the thesis will result from an iterative process where, in order to develop a high quality document, the advisor edits drafts of the proposal that the student prepares. While analyzing the data and writing the thesis, the student should consult the committee members only if he or she needs their expertise.

Once the advisor provides approval to do so, the student distributes the complete written thesis to all committee members for review. The thesis defense meeting (typically 2 hours), which serves as the program’s Comprehensive Assessment, is scheduled not less than one week after the student distributes the thesis. The student must not edit the thesis document after distributing it to the committee.

Members of the committee read the thesis and complete the Written Document Scoring Rubric prior to attending the thesis defense meeting. During the meeting, the student makes a brief presentation during which he or she should: demonstrate foundational knowledge, skills, and abilities relevant to the project; interact professionally with the audience; competently field questions about the project and the written document and; effectively use presentation software. Once the student has answered all questions, the committee will ask the student to leave the room while the members of the committee (a) discuss the document and the student’s presentation, (b) complete the Oral Presentation and Overall Rating Scoring Rubrics, and (c) and decide whether the student should pass or fail the Comprehensive Assessment, and (d) decide whether to approve the thesis as written (very rare!), approve the thesis with specified revisions discussed during the meeting (common), or reject the thesis. After the defense meeting is over, the chair of the thesis committee should submit the completed Scoring Rubrics from the committee members and a completed Comprehensive Assessment Results form to the Program Director.

If the committee rejects the thesis, they will make specific recommendations for remediation and the student will need to make changes to the document, until it is acceptable. Once the committee approves the thesis, the committee members should complete new Written Document and Overall Rating Scoring Rubrics and the chair of the thesis committee should submit these Rubrics to the Program Director.

In the event a student fails the comprehensive assessment, the student may request a re-assessment. Unless there are extenuating circumstances, the re-assessment must occur within six months of the date of failure. Only one re-assessment will be allowed. Cases involving extenuating circumstances must be raised or supported by the graduate program faculty and presented in writing to the dean of the relevant college for approval. Members of the committee must complete new Oral Presentation and Overall Rating Scoring Rubrics based on the student’s performance during the re-assessment and the chair of the thesis committee should submit the these Scoring Rubrics and a new completed Comprehensive Assessment Results form to the Program Director. If a student fails the second comprehensive assessment, the Graduate School will terminate his or her graduate.

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Think of yourself as a member of a jury, listening to a lawyer who is presenting an opening argument. You'll want to know very soon whether the lawyer believes the accused to be guilty or not guilty, and how the lawyer plans to convince you. Readers of academic essays are like jury members: before they have read too far, they want to know what the essay argues as well as how the writer plans to make the argument. After reading your thesis statement, the reader should think, "This essay is going to try to convince me of something. I'm not convinced yet, but I'm interested to see how I might be."

An effective thesis cannot be answered with a simple "yes" or "no." A thesis is not a topic; nor is it a fact; nor is it an opinion. "Reasons for the fall of communism" is a topic. "Communism collapsed in Eastern Europe" is a fact known by educated people. "The fall of communism is the best thing that ever happened in Europe" is an opinion. (Superlatives like "the best" almost always lead to trouble. It's impossible to weigh every "thing" that ever happened in Europe. And what about the fall of Hitler? Couldn't that be "the best thing"?)

A good thesis has two parts. It should tell what you plan to argue, and it should "telegraph" how you plan to argue—that is, what particular support for your claim is going where in your essay.

Steps in Constructing a Thesis

First, analyze your primary sources.  Look for tension, interest, ambiguity, controversy, and/or complication. Does the author contradict himself or herself? Is a point made and later reversed? What are the deeper implications of the author's argument? Figuring out the why to one or more of these questions, or to related questions, will put you on the path to developing a working thesis. (Without the why, you probably have only come up with an observation—that there are, for instance, many different metaphors in such-and-such a poem—which is not a thesis.)

Once you have a working thesis, write it down.  There is nothing as frustrating as hitting on a great idea for a thesis, then forgetting it when you lose concentration. And by writing down your thesis you will be forced to think of it clearly, logically, and concisely. You probably will not be able to write out a final-draft version of your thesis the first time you try, but you'll get yourself on the right track by writing down what you have.

Keep your thesis prominent in your introduction.  A good, standard place for your thesis statement is at the end of an introductory paragraph, especially in shorter (5-15 page) essays. Readers are used to finding theses there, so they automatically pay more attention when they read the last sentence of your introduction. Although this is not required in all academic essays, it is a good rule of thumb.

Anticipate the counterarguments.  Once you have a working thesis, you should think about what might be said against it. This will help you to refine your thesis, and it will also make you think of the arguments that you'll need to refute later on in your essay. (Every argument has a counterargument. If yours doesn't, then it's not an argument—it may be a fact, or an opinion, but it is not an argument.)

This statement is on its way to being a thesis. However, it is too easy to imagine possible counterarguments. For example, a political observer might believe that Dukakis lost because he suffered from a "soft-on-crime" image. If you complicate your thesis by anticipating the counterargument, you'll strengthen your argument, as shown in the sentence below.

Some Caveats and Some Examples

A thesis is never a question.  Readers of academic essays expect to have questions discussed, explored, or even answered. A question ("Why did communism collapse in Eastern Europe?") is not an argument, and without an argument, a thesis is dead in the water.

A thesis is never a list.  "For political, economic, social and cultural reasons, communism collapsed in Eastern Europe" does a good job of "telegraphing" the reader what to expect in the essay—a section about political reasons, a section about economic reasons, a section about social reasons, and a section about cultural reasons. However, political, economic, social and cultural reasons are pretty much the only possible reasons why communism could collapse. This sentence lacks tension and doesn't advance an argument. Everyone knows that politics, economics, and culture are important.

A thesis should never be vague, combative or confrontational.  An ineffective thesis would be, "Communism collapsed in Eastern Europe because communism is evil." This is hard to argue (evil from whose perspective? what does evil mean?) and it is likely to mark you as moralistic and judgmental rather than rational and thorough. It also may spark a defensive reaction from readers sympathetic to communism. If readers strongly disagree with you right off the bat, they may stop reading.

An effective thesis has a definable, arguable claim.  "While cultural forces contributed to the collapse of communism in Eastern Europe, the disintegration of economies played the key role in driving its decline" is an effective thesis sentence that "telegraphs," so that the reader expects the essay to have a section about cultural forces and another about the disintegration of economies. This thesis makes a definite, arguable claim: that the disintegration of economies played a more important role than cultural forces in defeating communism in Eastern Europe. The reader would react to this statement by thinking, "Perhaps what the author says is true, but I am not convinced. I want to read further to see how the author argues this claim."

A thesis should be as clear and specific as possible.  Avoid overused, general terms and abstractions. For example, "Communism collapsed in Eastern Europe because of the ruling elite's inability to address the economic concerns of the people" is more powerful than "Communism collapsed due to societal discontent."

Copyright 1999, Maxine Rodburg and The Tutors of the Writing Center at Harvard University

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Application of fuzzy comprehensive evaluation to evaluate the effect of water flooding development

• Original Paper - Production Engineering
• Open access
• Published: 13 January 2018
• Volume 8 , pages 1455–1463, ( 2018 )

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• Ping Zhang 1 &
• Guoqing Feng 1  

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Fuzzy comprehensive evaluation (FCE) is a synthetic appraisement method based on fuzzy mathematics, and evaluation result is practical and reliable, therefore, which is widely used in petroleum, construction and many other fields. This paper applies it to the evaluation of water flooding effect of oilfield. This paper introduces the principle of FCE method and the evaluation steps. The method is applied to the evaluation of water flooding development effect, which is helpful to improve the analysis level of oil and gas field development. Compared with the traditional method, this proposed method can reflect the difference of the evaluation units. Meanwhile, the weight vector is gotten by entropy method and analytic hierarchy process (AHP), which making the evaluation results more convincing. Taking W oilfield as an example, the ten factors (e.g., reserves controlled degree of water flooding, reserves producing degree of water flooding, recovery percent of recoverable reserves, water cut, water storage rate, oil recovery rate of residual recoverable reserves, cumulative water injection, maintenance of formation pressure, comprehensive decline rate, water flooding recovery) were evaluated by proposed FCE method. Then the membership matrix is established, and the weight vector is calculated by the entropy method and the AHP. Finally, the evaluation results of the two methods are obtained by fuzzy transformation and are consistent with the actual water flooding effect. Thus, the FEC method can be used as method to accurately evaluate the effect of oil field water flooding.

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Introduction

FCE is a comprehensive evaluation method based on fuzzy mathematics. Quantitative evaluation is converted to qualitative evaluation by FCE based on the membership degree theory of fuzzy mathematics. It evaluates the change of membership degree and judges things from multiple indexes. On the one hand, it takes into account the level of the object, making the evaluation criteria and the impact of fuzzy factors can be reflected. On the other hand, it can give full play to people’s experience, making the evaluation results more objective and real. FCE can be combined with qualitative and quantitative factors, which expands the amount of information and evaluates credibility of conclusion. In addition, it also can be better to solve the fuzzy and difficult to quantify the problem. So it is suitable for solving a variety of non-deterministic problems. The following introduces the development of fuzzy comprehensive evaluation method.

To express the uncertainty of things, Zadeh ( 1965 ) put forward the concept of fuzzy set theory, which marks the birth of the new discipline of fuzzy mathematics. Subsequently, Zadeh ( 1974 ) proposed the concept of linguistic variables and explored the meaning of it. The AHP was developed by Saaty ( 1977 ) and originally applied to the marketing sector. Dolan ( 1989 ) firstly applied this method to health economics research. The concept of fuzzy language is one of the most important developments in fuzzy set theory. The concept of multisets and fuzzy multisets was proposed by Miyamoto ( 2000 ). Zheng and Tian ( 2009 ) used entropy method and analytic hierarchy process to obtain weight, which makes the result more reliable. Torra ( 2010 ) firstly defined a hesitant fuzzy set. Hesitant fuzzy set is different from classical fuzzy set, and can be composed of a plurality of real numbers.

Fuzzy comprehensive evaluation method was proposed to predict the remaining oil distribution by Hou et al. ( 2011 ). It is seen that this method can predict whether there is remaining oil in the pore space or not with satisfactory accuracy, which is above 75%. Zheng et al. ( 2011 ) established the reservoir evaluation index system by fuzzy comprehensive evaluation method based on water flooding reservoir characteristics and influential factors.

You et al. ( 2014 ) analyzed the comprehensive classification reservoir’s producing conditions during the ultra-high water cut developing phase based on multilevel fuzzy comprehensive evaluation mathematics method. Moreover, they established a quantitative evaluation method from geological and developmental factors, which solved the problem of analyzing remaining oil in different kinds of reservoirs and pointed out the quantitative characterization of remaining oil in the ultra-high water cut oilfield.

Wen et al. ( 2017 ) developed the index system evaluating water flooding development effect of oilfield at ultra-high water cut stage based on Pearson correlation analysis and gray clustering-rough set quantitative evaluation index.

Above all, FCE method is widely used in medical, construction, environmental quality supervision, traffic management, image processing, market forecast and many other fields. Recently, this method is more and more applied to the oil field, which is used to evaluate the distribution of permeability. After research, it is applied to the evaluation of water flooding effect in this paper.

The evaluation of oilfield development effect runs through the whole process of oil field development and provides the basis for the development of technology policy. In other word, it can offer a reference for formulating clear potential direction and reasonable regulation and control measures in oilfield development. Therefore, it is particularly important to evaluate the effect of water flooding in oil field. In this paper, the FCE method is used to evaluate the effect of water flooding in oilfield.

The principle of fuzzy comprehensive evaluation

FCE method is the application of fuzzy transformation and maximum degree of membership principle. Firstly, the fuzzy set is used to represent the various factors related to the evaluation object. Next, it is used to calculate the evaluation matrix and weight of evaluation factors. Finally, fuzzy linear transformation is used to get the evaluation results of fuzzy sets. This method can be applicable for solving the problem of multi factor complexity and uncertainty.

Evaluation index set and evaluation set

Given two finite fields, in which U represents a comprehensive evaluation index set, V represents the evaluation set (Sun 2008 ).

where \(u_{i} \left( {i = 1,2, \ldots ,n} \right)\) represents each evaluation factor, n is an integer.

where \(v_{i} \left( {i = 1,2, \ldots ,m} \right)\) represents each evaluation comment, m is an integer.

Evaluation matrix

The membership matrix is the degree of membership of an index to a comment. If the membership of the i th index \(U_{i}\) and the j th comments \(V_{j}\) is symbol as \(r_{ij}\) , then the i th index of the membership is expressed as:

\(R_{i}\) is a single factor evaluation vector, in which the value of \(r_{i1} ,r_{i2} , \ldots ,r_{im}\) is determined by the classical ridge distribution function Eq.  4 . Then the membership value is normalized to get the single factor evaluation vector. And all the single factor matrices constitute the evaluation matrix R (Chen and Zhang 2001 ).

Weight matrix

Each evaluation factor \(u_{i}\) determines \(x_{i}\) , indicating the importance of the evaluation results. A set \(X\) called a weight set or a weight vector is composed of \(x_{i}\) .

There are many methods to calculate the weight, for example, entropy method and analytic hierarchy process (AHP).

• Entropy method

Entropy is a measure way to the degree of unordered system. It can be used to measure the amount of available information through known data and determine the weights in the fuzzy evaluation. That is to say, the weight of each index is determined by the difference degree of each index value.

The detailed steps to calculate the weight of entropy method are as follows (Zheng and Tian 2009 ):

Original data matrix normalization. The original data matrix of m evaluation index and n evaluation comment is \(R = \left( {r_{ij} } \right)_{m \times n}\) , and the normalized matrix is \(A = \left( {a_{ij} } \right)_{m \times n}\) . In terms of the index of excellence, the normalized formula is:

And for the small ones, the normalized formula is:

Defined entropy. In the assessment of m indicators and n evaluation comment, the entropy of the i th index is:

where \(f_{ij} = a_{ij} /\sum\nolimits_{j = 1}^{n} {r_{ij} }\)

Defined entropy weight. After the entropy of the i th index is defined, the entropy weight of the i th index can be obtained:

• Analytic hierarchy process (AHP)

AHP is a simple and convenient method to quantitative analysis of non-quantitative events. It is in accordance with the decomposition, comparison, comprehensive way of thinking through regarding the research object as a decision-making system and has become an important tool to the system analysis. According to the relationship between the components and membership, the multilevel structure is built by AHP. Based on the hierarchical structure model, we can obtain the judgment matrix. The maximum eigenvalue and the eigenvector of the judgment matrix X are calculated by using the power method (Wen et al. 2017 ; Gerbacia and Hanaa 2001 ).

Firstly, the factor set \(U = \left( {u_{1} ,u_{2} , \ldots ,u_{n} } \right)\) is determined, and then the judgment matrix \(P = \left[ {P_{ij} } \right]_{m \times n}\) is constructed by the following method, which \(P_{ij}\) reflects the relationship between the two factors. And its values are shown in Table  1 (Ahmad et al. 2011 ).

After determining the judgment matrix P , the maximum eigenvalue and its corresponding feature vector are calculated, which is the order of importance of each evaluation factor. It also calls the weight coefficient of each evaluation factor. Using the power method calculates the largest eigenvalue of the judgment matrix P and the corresponding eigenvector.

Initial vector \(Z_{0} = \left( {\begin{array}{*{20}l} {0,} \hfill & {0,} \hfill & \ldots \hfill & 0 \hfill \\ \end{array} } \right)\) , then the power method iteration format (Chen and Zhang 2001 ):

Take \(x_{i}\) as the evaluation coefficient of the importance degree of the factor \(U_{i}\) , it can be normalized so that \(\sum\nolimits_{i = 1}^{n} {x_{i} = 1}\)

Fuzzy transformation

The fuzzy transformation (Chen and Zhang 2001 ) is:

In fact, fuzzy transformation Y is the synthesis of weight vector X and fuzzy evaluation matrix R . In practical applications, it is generally done as follows:

In the fuzzy transformation, X is a fuzzy subset of U and evaluation result of Y is a fuzzy subset of V , which is the basic principle of comprehensive evaluation. Generally, Y is a comprehensive evaluation of the results. In \(Y = \left( {y_{1} ,y_{2} , \ldots ,y_{m} } \right)\) , \(y_{i}\) is the membership degree of the evaluation factors corresponding to the i th fuzzy comment. According to the principle of maximum membership degree, the evaluation result is:

Evaluation method and procedures

Using the FCE method, the main steps of the comprehensive evaluation for the water flooding development effect of water flooding reservoir are shown in Fig.  1 .

Block diagram of single level fuzzy comprehensive evaluation

The model mainly includes three factors: factor set, evaluation set and weight set, namely. Firstly, the factor set is a set of indicators that affect the evaluation results of water flooding development, denoted as \(U = \left( {u_{1} ,u_{2} , \ldots ,u_{m} } \right)\) . In order to make the evaluation result simple and clear, using 5 levels of evaluation set, that is (excellent, good, general, poor, very poor), denoted as \(v = \left( {v_{1} ,v_{2} , \ldots ,v_{m} } \right)\) . Secondly, the evaluation set of the i th factor \(P = \left[ {P_{ij} } \right]_{m \times n}\) is called the single factor evaluation vector or membership degree, denoted as \(R_{i} = \left( {r_{1} ,r_{2} ,r_{3} ,r_{4} ,r_{5} } \right)\) , n factors of the single factor evaluation vector combination to form a matrix, called the evaluation matrix R . Finally, the evaluation results can be obtained by fuzzy transformation of judgment matrix R and weight vector X , which is calculated by entropy method or AHP.

Influence factor

Water cut is an important index to evaluate the effect of oil field development, which not only affects the stability of oil field, but also directly affects the final recovery rate. The water storage rate, water flooding index and the recovery degree are the important indexes which reflect the development effect of the water injection field. It is directly related to the water injection rate and the total water cut.

Water storage rate

The water storage rate is the difference between water injection and water production in the development field of water injection, which is mainly characterized by the level of the utilization rate of water injection. The higher the value of the water storage rate, the higher the degree of utilization of the injected water, the better the development effect. According to the definition of the water storage rate, the calculation formula (Ma and Zhang 2016 ) for the water storage rate is:

And the expression of injection production ratio is:

Due to water cut is:

From the above formula, the relationship between the water storage rate and the water cut is plotted as shown in Fig.  2 .

The relationship curve of water storage rate and water cut

Water flooding index

Water flooding index is defined as the amount of water stored in the ground for each ton of oil produced. The greater the water drive index, the greater the amount of water needed. According to the definition, the formula (Ma and Zhang 2016 ) is:

Expression of injection production ratio can be obtained:

By water cut:

According to the above formula, the relationship between water flooding index and water cut is plotted based on different Z values as shown in Fig.  3 .

The relationship curve of water flooding index and water cut

Recovery degree

The recovery degree is the percentage ratio of the cumulative oil production and using geological reserves, which reflects the recovery of the oil field reserves. Using the semiempirical formula derived from the Tong ( 1978 ) to determine the relationship between water cut and recovery degree in water injection development oilfield (Liang and Liu 2016 ):

According to the above formula, the relationship between recovery degree and water cut is plotted based on the different values of the water storage rate, as shown in Fig.  4 .

The relationship curve of recovery degree and water cut

There are many indexes evaluating the effect of water flooding development at present. In the index system of these factors, each index of the complex relationship and some indicators on development effect cannot give accurate evaluation. So the FCE method can be used to solve fuzzy, difficult to quantify and uncertainty problems, and the evaluation factors are more comprehensive and the evaluation results are more reliable.

W oilfield is lithological reservoirs with layered structure, has good reservoir properties but serious heterogeneity. Since it was developed in December 1977, it has experienced the adjustment of the layer system including first infilling and second infilling, local area well network encryption and improvement, well net comprehensive adjustment and other major adjustments. At present, it has entered a special high water cut period.

Evaluation index

Different development stages of oil field development indicators are not the same, different reservoir development stages need to establish the corresponding development evaluation system. Taking W oilfield as an example, this paper selects the representative and the most important indicators to evaluate water flooding development effect. The comprehensive evaluation index system of water injection reservoir is composed of three parts, which are injection production well network condition index, water injection condition index and development condition index.

According to the actual situation of the oil field, a set of comprehensive evaluation index system was established. Ten representative indexes were selected in this paper, the evaluation indexes and parameters of W oil field are shown in Table  2 . These indicators constitute a set of factors \(U = \left\{ {u_{1} ,u_{2} , \ldots ,u_{10} } \right\} =\) {Reserves controlled degree of water flooding, reserves producing degree of water flooding, recovery percent of recoverable reserves, water cut, water storage rate, oil recovery rate of residual recoverable reserves, cumulative water injection, maintenance of formation pressure, comprehensive decline rate, water flooding recovery} (Wen et al. 2017 ).

On the basis of the actual geological characteristics and developed characteristics of the reservoir, comprehensive evaluation of evaluation index classification standard was proposed. This paper adopts the 5 grade evaluation criteria, namely the fuzzy comment set is \(V = \left\{ {v_{1} ,v_{2} ,v_{3} ,v_{4} ,v_{5} } \right\} = \left\{ {{\text{Excellent}},{\text{Good}},{\text{General}},{\text{Poor}},{\text{Very}}\,{\text{poor}}} \right\}\)

In the light of Oilfield development level classification industry standard issued by Chinese Oil and Natural Gas Corp and related references, the range of evaluation criteria for development effects of each index is obtained in W oilfield. Reservoir level classification criteria and evaluation factors are shown in Table  3 .

From Tables  2 and 3 , the effect of water flooding is evaluated only by single factor and evaluation result is shown in Table  4 . Obviously, the evaluation results of different factors are inconsistent, so it is not accurate enough using the single index to judge the water flooding effect of the oilfield. Thus, it is necessary to make a comprehensive evaluation of multiple factors.

Single factor evaluation results of each index shown in Table  5 are calculated by Eq.  4 ; thus, the evaluation matrix R is obtained. This method can minimize the impact of human subjective factors, making evaluation results more scientific and reasonable.

Evaluation matrix: \(R = \left( {\begin{array}{*{20}l} {0.724} \hfill & {0.239} \hfill & {0.037} \hfill & 0 \hfill & 0 \hfill \\ {0.052} \hfill & {0.172} \hfill & {0.224} \hfill & {0.263} \hfill & {0.288} \hfill \\ {0.123} \hfill & {0.288} \hfill & {0.274} \hfill & {0.234} \hfill & {0.080} \hfill \\ 0 \hfill & 0 \hfill & {0.103} \hfill & {0.301} \hfill & {0.296} \hfill \\ 0 \hfill & 0 \hfill & {0.074} \hfill & {0.401} \hfill & {0.525} \hfill \\ {0.074} \hfill & {0.226} \hfill & {0.273} \hfill & {0.294} \hfill & {0.133} \hfill \\ {0.108} \hfill & {0.294} \hfill & {0.283} \hfill & {0.237} \hfill & {0.078} \hfill \\ {0.109} \hfill & {0.250} \hfill & {0.256} \hfill & {0.258} \hfill & {0.126} \hfill \\ {0.105} \hfill & {0.261} \hfill & {0.261} \hfill & {0.258} \hfill & {0.115} \hfill \\ {0.429} \hfill & {0.276} \hfill & {0.182} \hfill & {0.094} \hfill & {0.019} \hfill \\ \end{array} } \right)\)

Index weight

Via Eqs.  7 – 10 , using MATLAB programming calculate the weights of the indicators. The weight of the vector X :

We obtain the judgment matrix P by water flooding index evaluation standard shown in Table  1 and calculate the maximum eigenvalue and its corresponding eigenvector by Eq.  11 . The feature vector is each evaluation factor weight vector X ; the calculation result is:

Fuzzy Evaluation Results and Analysis

The weight vectors calculated by the entropy method and AHP are added to Eqs.  12 and 13 , which is to get the final result of the FCE. They are (0.229, 0.188, 0.184, 0.210, 0.190) and (0.235, 0.203 0.178, 0.230, 0.155), respectively. Based on the principle of the maximum membership degree, the results of the two methods are identical. We can conclude that the water flooding development effect is “excellent.”

Combined with the single factor evaluation result of each index and the actual production characteristics of the oil reservoir, we can draw the conclusion that it should take a series of measures to adjust and improve the water flooding control degree, producing degree of water flooding and swept volume of water flooding, and further increase the recovery of water flooding in the W oilfield development process. As the plane heterogeneity and vertical heterogeneity lead to water cut rising fast and low water injection efficiency. Therefore, in the following mining, we should further improve water flooding reserves producing degree of the non-main oil layers, updip pinch-out site of the main layers and subdivision out of thin and poor layers. Furthermore, we should further optimize the injection production system and promote the utilization rate of water injection in extra high water cut stage to improve the effect of water flooding development.

Conclusions

The relationship between water storage rate, water drive index, extraction degree and water cut was calculated by the newly proposed formula, and the relationship curves were plotted, which has a guiding significance for the water drive adjustment of oil field.

The fuzzy comprehensive evaluation method is used to evaluate the development of oil field and has a strong theoretical foundation. It can calculate many uncertain or only qualitative evaluation factors through fuzzy transformation and obtain the quantitative evaluation results, which are objective, reasonable, accurate and reliable.

Comparing the entropy method and the analytic hierarchy process, although the weight vector is not equal, the final evaluation result is consistent. The evaluation result is “excellent.” According to the evaluation result, the main problems and adjustment suggestions of oil field development are pointed out. It indicates the direction of oilfield development and adjustment.

Abbreviations

Fuzzy comprehensive evaluation

Analytic hierarchy process

Evaluation index set

Evaluation set

Single factor evaluation vector

Ridge distribution function

Weight vector

Judgment matrix

Feature vector

Maximum eigenvalue, \(k = 1,2, \ldots .\)

Fuzzy operation

Comprehensive results of evaluation

Cumulative water injection (10 4 t)

Cumulative water production (10 4 t)

Cumulative oil production (10 4 t)

Water storage rate (f)

Injection production ratio (f)

Crude oil volume factor (f)

Crude oil density (g/cm 3 )

Water flooding index (f)

Ultimate oil recovery (%)

Recovery percent (%)

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Zhang, P., Feng, G. Application of fuzzy comprehensive evaluation to evaluate the effect of water flooding development. J Petrol Explor Prod Technol 8 , 1455–1463 (2018). https://doi.org/10.1007/s13202-018-0430-y

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Received : 16 July 2017

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Issue Date : December 2018

DOI : https://doi.org/10.1007/s13202-018-0430-y

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