Abstract

Knowing the injection profile of each injector in a reservoir is of major importance for analyzing residual oil distribution, which is the foundation of IOR project design. However, in practice, it is impossible to acquire real-time injection profiles for each well when we need it. In this paper, a new method using fuzzy mathematical theory is introduced, to predict injection profiles for wells with outdated or no related information by analyzing those injectors whose injection profiles are well characterized. Three pivotal factors were selected as an evaluation factor set: sand-body type, communication with surrounding oil wells and well spacing. Based on the statistical results for those wells with wellcharacterized injection profiles, three standard diagrams were constructed based on the relationship between the relative water absorption of each layer and each evaluation factor.

An analytical model of fuzzy mathematics for the prediction was then constructed. Fuzzy subsets were based on those standard diagrams, and a weighting set was obtained by trial and error. To verify this proposed method, some injection profiles were predicted from two blocks in the Daqing oilfield. Their average accuracy was shown to be above 75%. The results from this method have been applied successfully to analyze residual oil distribution in a block and to designperforation projects. An example from infill well projects has been successfully carried out in one block, improving oil recovery by 4.5%.

Introduction

During the analysis of remaining oil, a key factor is to beat out the water absorbing capacity of each subzone in every water injection well. At present, many water injection wells have no test data or have farness test duration, so the water absorbing capacity of each subzone could not be reflected factually. Each subzone of water injection well is a fuzzy system. Because of the effect of reservoir depositional character and development factor as well as the effective factors are very complex, and they could not be expressed by quantitative mathematical relational expression, so fuzzy comprehensive judging method is suitable to be used in evaluating the water absorbing capacity of reservoir.

Principle of Fuzzy Comprehensive

Every influential factor is called an appraisal object. Appraisal results are denoted by a group of fuzzy sets on remarks. This group of sets is called remark set. Recorded as V={v1, v2, v3,..., vm }. The set constituted by all the factors that have some effect on appraisal result is called factor set. Recorded as U={u1, u2, u3,..., um}. The evaluation based on ui is called single factor evaluation. Recorded as ri= {ri1, ri2, ri3,..., rim} i=1,2,...n. This single factor evaluation can only reflect one aspect and could not reflect the total instance. But n factors have n single factor evaluation vector, they are composed to be a fuzzy matrix that called judging matrix: R=(rij)n_m, suppose a fuzzy vector: X= {x1,x2,x3,...,xn} 0<xi<1 i=1,2,...n, it iscalled weighting set X. The value of weighting set X is calculated by analytical hierarchy process after the essentiality sequence of each factor's physical significance.

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