Nearly all commercial hydraulic fracture design models are based on the assumption that a single fracture is initiated and propagated identically and symmetrically about the wellbore, i.e., the fracture growth and proppant transport occurs symmetrically with respect to the well. However, asymmetrical fractures have been observed in hundreds of hydraulic fracturing treatments and reported to be a more realistic outcome of hydraulic fracturing. The asymmetry ratio (length of short fracture wing divided by length of long wing) influenced the production rate adversely. In the worst case, the production rate could be reduced to that of an unfractured well. Several authors observed asymmetrically propagated hydraulic fractures in which one wing could be ten times longer than the other. Most pressure transient analysis techniques of hydraulically fractured wells assume the fracture is symmetric about the well axis for the sake of simplicity in developing mathematical solution. This study extends the work by Rodriguez to evaluate fracture asymmetry of finite-conductivity fracture wells producing at a constant-rate. The analysis presented by Rodriguez only involves the slopes of the straight lines that characterize the bilinear, linear and radial flow from the conventional Cartesian and semilog plots of pressure drop versus time. This study also uses the Tiab’s direct synthesis (TDS) technique to analyze the linear and bilinear flow regimes in order to find the asymmetry factor of the fractured well. With the fracture conductivity estimated from the bilinear flow region, dimensionless fracture conductivity and the asymmetry ratio are calculated. A technique for estimating the fracture asymmetry ratio from a graph is presented. An equation relating the asymmetry ratio and dimensionless fracture conductivity is also presented. This equation assumes that the linear and/or bilinear flow regime is observed. However, using the TDS technique, the asymmetry ratio can be estimated even in the absence of bilinear or linear flow period. It is concluded that the relative position of the well in the fracture, i.e., the asymmetry condition, is an important consideration for the fracture characterization. A log-log plot of pressure derivative can be used to estimate the fracture asymmetry in a well intersected with a finite-conductivity asymmetric fracture. The analysis using pressure derivative plot does not necessarily require the radial flow period data to calculate the asymmetric factor.
This paper provides an analytical solution for a well near a linear leaky boundary, in otherwise infinite laterally composite systems. The leaky boundary is viewed as an infinitesimal damaged discontinuity (linear skin discontinuity) located at the interface between two adjacent media. The zone thickness may or may not be equal, and the infinitesimal damaged zone width is a restatement to the assumption of low fault conductivity and storativity. The problem was solved using the two-dimensional diffusion equation with successive integral transformations, and the one dimensional green's function. Both solutions, uniform and non-uniform diffusivity cases merge exactly at early and late time. Solutions presented in this study have been validated by comparing a number of its simplified forms with those available in the literature. Confirmation of the solution is also demonstrated by investigating three limiting cases:a well near a sealing boundary,well near undamaged linear discontinuity in a composite system, andwell near a constant pressure linear boundary. As shown in this paper, a single leaky fault can give appearance of naturally fractured reservoir on a pressure transient response for a unit-mobility ratio case and a linear flow regime may also develop for a low diffusivity contrast. Further investigation of the correlating skin parameter ‘sa’ representing the product (Sf * ad) proves that Yaxley's definition addressed to the fault (a) is equivalent to the term (1/Sa) derived in this work. Consequently, computing the discontinuity damage leads to an indirect measurement of the fault conductivity. Pressure and pressure derivative type curves have also been generated showing the effect of all the parameters affecting the wellbore responses. Making the use of the flexibility of the final solution, we have also investigated the pressure response of a linear boundary in an infinite naturally fractured composite reservoir. The step-by-step procedure for calculating reservoir parameters is also developed in this study. The Tiab's Direct Synthesis (TDS) technique is applied to interpret pressure derivative behavior of a vertical well near a linear leaky boundary in laterally composite systems. Lastly, for a practical implication, the procedure developed is illustrated with one simulated example and one field case.
This paper presents an analysis method of the transient pressure behavior of dual lateral wells. Conventionally lateral wells have been analyzed using horizontal well analysis techniques. As we will show in this paper, that if the phase angle between the two lateral sections differ from p, they can not be treated as horizontal well and such practices any result erroneous reservoir properties. An infinite conductivity solution for dual lateral wells was developed by coupling both; the infinite conductivity horizontal well model and the superposition concepts. From the sensitivity analysis study, it was found that infinite conductivity solution for dual lateral wells is affected by the horizontal anisotropy, phasing of the lateral sections, dimensionless horizontal separation, mechanical skin, wellbore storage. It is less affected by the dimensionless vertical separation and the contrast between the dimensionless lateral lengths. Transient pressure behavior of dual lateral wells appears to be more pronounced in the cases:for a phase angle decreasing,for a horizontal separation decreasing, andfor a horizontal anisotropy increasing. The effect of the phase angle decreases while increasing the dimensionless lateral lengths and horizontal separation. The effect of the horizontal anisotropy on the pressure behavior is more pronounced for high phase angles. The wellbore storage dominated flow period tends to be more affected for small dimensionless lateral lengths, LD. The effect of unequal lateral lengths and vertical separation are pronounced only at early times. The intermediate time pseudoradial flow period displayed by dual lateral wells is more distinguishable from the wellbore responses in the cases of a large phase angle and a high value of the horizontal separation. It is worthwhile to note that the responses of dual lateral wells having a phase angle, ß=p, may be viewed as an equivalent single horizontal well. Also Tiab's Direct Synthesis (TDS) technique methodolgy for dual lateral wells has been developed, which adds to the analysis of such wells. Few examples are solved in a step-by-step manner, which demonstrate the use of the method developed. Introduction The productivity improvement expected from horizontal wells is usually proportional to the length of the well. As the length of the horizontal well increases, drilling and well control become extremely difficult. In addition, transportation of a large volume of fluid along a long horizontal borehole results in considerable wellbore pressure losses affecting the productivity. In term of the well coverage, dual lateral wells are expected to provide an excellent alternative to the long horizontal wells. A thorough treatment of the well itself based on accurate computational methods for analyzing and predicting the well performance is needed for better understanding the dual lateral pressure behavior. Practically, the main characteristic features of the responses is that the dual lateral wells may be viewed and analyzed as an equivalent single horizontal well. However, this approach is a great simplification and is suitable only for certain phase angles and anisotropy ratios. Therefore, this approximation is restricted to a specific reservoir-well configuration and its use may introduce significant error in estimating reservoir parameters. For this purpose, we present a semi analytical dual lateral model based on that of the horizontal wells. According to our knowledge, there does not exist such a model to date. Literature review Over the last decade, a considerable amount of work has been published on various aspects of multilateral wells. Most of these works have been presented on the performance of multilateral wells as means of new technology to improve productivity. But only few of them treat the transient pressure behavior of multilateral wells. Karakas, Yokohama and Arima(1) have presented an interpretation of several transient tests conducted in multilateral wells. Using a numerical solution, they indicated that most multiple drain hole systems can be approximated by an equivalent single layer, single drain hole systems.
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