There are a number of considerations to be made in the process of designing a fracturing stimulation treatment. The reservoir deliverability, well producing systems, fracture mechanics, fracturing fluid characteristics, proppant transport mechanism, operational constraints and economics should be considered and integrated in order to obtain the most cost-effective design and to maximize the benefit of a well stimulation treatment. The main purpose of this work is to develop an analytical scheme which mathematically couples each elements as described above. The criteria used to determine the optimum size of the treatment are:optimize reservoir deliverability,maximize propped fracture penetration,optimize pumping parameters,minimize treatment cost, andmaximize economic returns of the well. Firstly, an analytical inverse algorithm has been derived based on 2-D PKNC (Perkins, Kern, Nordgren and Carter) and KZGD (Khristianovic, Zheltov, Geertsma and de Klerk) formulations. It allows us to calculate the fluid and proppant volume needed for a desired fracture geometry and conductivity. Secondly, a technique to search for optimal pumping parameters and to maximize the proppant coverage for a given hydraulic penetration is developed. This allows us to optimize the propped geometry taking into account the operational constraints. Thirdly, a coupling algorithm is developed to link the reservoir producibility, well producing systems and the optimized fracture geometry. This enables us to optimize the wellhead deliverability based on the balance between the reservoir and the fracture characteristics. Finally, the overall economic analysis is performed to calculate the net present value for various design options. The most cost-effective treatment design can then be determined based on the point of diminishing return on the well's net present value. Introduction Hydraulic fracturing has been recognized to be an effective means for enhancing well productivity and recoverable reserves, especially for low permeability reservoirs. Over the years, a significant amount of effort has been directed to the understanding of the physics involved in such complicated processes. As a result, new techniques have been developed to enhance our abilities to optimize the fracturing stimulation treatment. The fracture design procedures currently practiced in the industry include:the prediction of well producibility from various fracture penetrations and conductivities;parametric studies on the fracture geometry requirements;the selection of appropriate types of fracturing materials; andthe determination of fracture design criteria based on maximum economic returns of the well. Various reservoir simulators, hydraulic fracture propagation simulators and economic models are often run on a trial-and-error basis until the desired design criteria are met. This is a time-consuming and ineffective exercise. Ideally, the reservoir deliverability, well producing systems, fracture mechanics, fracturing fluid characteristics, proppant transport mechanism, operational constraints and economics should be considered and integrated in order to obtain the most cost-effective design. The following outlines the key design parameters for each of the elements under consideration. P. 485^

A systematic approach is presented for generating transient inflow performance relationship curves for finite conductivity vertically fractured wells. A semi-analytical model was developed to simulate dimensionless wellbore pressure drop and dimensionless pressure loss through the fracture vs. dimensionless time at constant-rate of production for wells intercepted by a finite-conductivity vertical fracture. Flowing bottom hole pressure can be predicted at any time period using these dimensionless variables. System average pressure at any stage of production can be obtained through material balance calculations. A straight line reference curve was observed at all times provided that the real gas pseudo-pressure function is used to plot m(pwf(t))/m(p¯R(t)) vs. qg(t)/qgmax (t). The advantage of normalizing the dimensionless variable in termas of pseudo-pressure function is that only one straight line relationship is obtained throughout the entire production life of the reservoir. This provides a more simple means for performance prediction purposes. The major contribution of this paper is the provision of a valuable tocl to study the sensitivity of fracture design parameters on ultimate well performance. The economic benefits of this approach can be substantial.

This work shows that discrete fracture network modeling is very desirable for the characterization of naturally fractured reservoirs but it is only a highly subjective starting point. Thus, calibration against short and long term pressure transient tests is most crucial. This paper shows how the dynamic behavior of a discrete fracture network model of Margarita gas field compared against pressure transient measurements in a sidetrack delineation-well. The performance comparison of a very fine-grid reservoir model, which included the discrete fracture network information, versus a much coarser upscaled grid model is also documented. Introduction Geological reservoir characterization is the most crucial first step in construction of a credible reservoir flow model for naturally fractured reservoirs. The most notable approaches for constructing a geological model of a reservoir include classical deterministic methods, where geologists make the best interpretation from existing data and build a model of the reservoir. In the last several years, however, deterministic approaches have been complemented by quantitative geostatistical approaches such as multipoint statistics (MPS) and discrete fracture network (DFN) modeling.1,2,3 The MPS generates a depositional and lithofacies model of a reservoir by incorporating geological architecture and properties of the rock fabric and is touted as a very promising stepping stone in construction of viable numerical reservoir flow models.1 However, for reservoir modeling purposes, the flow units and fracture flow paths must be included in the depositional model.4 The DFN modeling is often used to accomplish the latter. Both the deterministic and geostatistical techniques, however, are highly subjective and, while such fundamental geological modeling techniques are often the necessary starting points, any revisions toward the construction of the ultimate reservoir flow model would depend on calibration against reservoir performance as well as carefully designed flow tests.5 In fact, an ultimate reliability standard for viability of any reservoir characterization model is calibration against dynamic data from several wells. This implies that reservoir characterization life cycle is an iterative process as new static and dynamic data become available. Experience in naturally fractured reservoirs (NFR) has indicated that low permeability formations often produce fluids through open fractures, which intersect the wellbores. This paper illustrates fluid flow through individual fractures intercepted by a vertical well, initially estimated using a parallel plate method, finding that contribution of each fracture need to be calibrated to a production test. The composite summation of individual fractures along the wellbore allowed the construction of a synthetic PLT profile. A horizontal sidetrack from the vertical well was planned to improve the well's productivity. A discrete fracture network (DFN) model, generated around the area of influence of the well, was used to identify the best direction for the sidetrack interval (perpendicular to the most open main fracture planes) and to predict the type of the fractures to be intercepted. After the sidetrack was drilled, fracture types (hierarchy by aperture) were identified and classified using an ultra sonic borehole image tool. The DFN fracture model was calibrated against a pressure buildup test conducted in the sidetrack well, using dual-porosity numerical simulation over a very fine grid model. The calibration studies showed that the aperture-based effective transmissivity was significantly greater than the actual well test transmissivity while the estimated fracture storativity was significantly lower than the actual well test value. Dynamic upscaling of the fine-grid model was performed to evaluate whether the upscaled models would preserve the well/reservoir behavior of the fine-grid models. Margarita Field General Characteristics The Margarita structure is located in the southern Bolivian Subandean, on the structural trend of the Suaruro Range, 35 km to the west of Villamontes town.6–8 The Margarita Field lies in the Caipipendi Block (Fig. 1) operated by Repsol-YPF with 37.5% equity. Partners are BG International (37.5%) and Pan American BP (25%). The field is located in the northern part of an elongated anticline oriented NNE-SSW, and is 30 km long and 9 km wide. The closure of the field consists of several compartments separated by reverse faults.

Streamline-based flow simulation for the purpose of ranking large-scale geologic realizations continues to receive significant attention. However, the procedures and the analyses for ranking are not straightforward and therefore actual case examples are very limited. This paper describes a field example showing a very practical process for dynamically ranking various geologic realizations using uniform well patterns. This mature field has a 60-year primary recovery history but still has potential for additional development. The ranking process is further complicated by the presence of a gas cap and a water zone. A major difficulty with dynamic ranking of geological models is that the recovery may be as much a function of the flow-physics as the geologic variability. Accounting for gravity, fluid contacts, changing streamlines, and fractional flow effects may be important to the ranking study. Even the choice of well locations, rates, boundary conditions, and patterns will affect the ranking. The uniform patterns used in this study are not representative of actual well patterns or injected fluids rates. The waterflood efficiency, however, can still be used as a basis of comparison. A novel map based presentation of the ranking simulations provides valuable understanding of the effect of the geologic model on recovery uncertainty. The use of regular well patterns is different from the common approach of using existing wells with pseudo boundary conditions. The uniform spacing ensures complete coverage of the area-of-interest and not just the areas where the model is already conditioned to existing data. This method tests the variability of the models away from existing wells as these areas will have longer-term effect on performance and affect the decision regarding future infill wells and recovery methods. Another important aspect of this paper is a demonstration of how modern tools and analysis techniques are greatly improving the ability to understand complex reservoirs and thus make improved decisions regarding optimum development. Efficient analysis and visualization of the data and interpretations is important for a detailed understanding of the reservoir. Motivation for Study The methodologies described here resulted from several major considerations:evaluate the impact of geologic uncertainties on production performance within a one month window during which a conventional history match is performed;use existing commercial software to prevent long delay time in project completion,present the results in a manner which visually relay the results to a wide audience, anddevelop a methodology which provides more information than a simple cumulative distribution of field recovery. Anyone involved in reservoir simulation realizes there are several potential sources of errors or uncertainties when doing a reservoir study:numerical error (from the approximate solution of non-linear partial differential equations),error from the approximations in the underlying equations (e.g. 3-phase approximation of Darcy's law)errors or uncertainties in data interpretation (e.g. converting log signals to reservoir properties),ignored data (e.g. not using the seismic data in reservoir property distribution),unknown or uncertain data (e.g. only a small portion of the reservoir is sampled) andincorrect averaging of data (e.g. averaging log measurements over a flow unit). All of these errors or uncertainties lead to uncertainties in forecasts of future production. Recognition of these uncertainties has lead to a desire to incorporate the resulting uncertain rate and recovery forecasts into a corporate risk analysis methodology1–9.

Methods for analyzing buildup data following a short flow period are presented, discussed, and illustrated. A new type curve for uniform-flux and infiniteconductivity vertically fractured wells is presented. By matching buildup data with this new type curve, we can determine the dimensionless flowing time before shut-in. A method for converting buildup data to equivalent drawdown data is discussed. This method can be used to combine buildup and drawdown data to obtain a longer band of data for type-curve matching. This method can be used for constant-rate production, constant-pressure production, and for the case where both pressure and rate vary during production.

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Summary An application of geostatistical modeling in the context of a full field reservoir model study of the Northeast Nash waterflood is described. A methodology for preparing a geostatistical description of the field and the rationale for selecting a stochastic description instead of a deterministic description are presented. Modifications to the geostatistically generated geology during the history match process are discussed. Introduction Oil production from the Northeast Nash Misener sand began in 1985, and a waterflood began in the field in early 1992. Basic reservoir data and the location of the field are shown in Table 1 and Figure 1, respectively. The field was initially an undersaturated black oil reservoir that was depleted below the bubble point and then subjected to a waterflood. Several production wells had experienced water breakthrough, yet it appeared that significant parts of the field were unswept. A reservoir model study was undertaken to accomplish two objectives:Acquire a better understanding of reservoir performance, particularly those factors contributing to early water breakthrough.Determine the optimum strategy for economically maximizing recovery from the field. The study which achieved the above objectives also serves as an example of geostatistical modeling within the context of a full field reservoir model study. In the study, two different mapping algorithms (deterministic vs. stochastic) were used to generate a suite of geologic maps for the Nash reservoir. Reservoir simulation models were initialized using both the deterministic and stochastic geologic models. A description of the models and the rationale for selecting the stochastic geologic model are given. Following the selection of a reservoir model is a discussion of the history match and prediction process. MODEL INITIALIZATION RESERVOIR CHARACTERIZATION Qualitative Geologic Description The geology of the Misener formation has been described by Amsden and Klapper, and Francis. A qualitative description of the geology of the Northeast Nash field was prepared by the Northeast Nash Technical Committee (16 November 1990). According to their report, the Northeast Nash field is located on the northern shelf of the Anadarko Basin. Regionally, the sediments dip southerly towards the center of the basin at approximately 50 feet per mile.