Geostatistics has been used to improve the reservoir characterization process for the last fifteen years. This article briefly discusses the accomplishments so far, and discusses the future challenges. What Is a Reservoir Characterization Process? Reservoir characterization is a process of integrating various qualities and quantities of data in a consistent manner to describe reservoir properties of interest at inter well locations. Appropriate weight should be given to the quality and the scale of the data, and data should be integrated such that we can predict the future performance of the reservoir. Our goal in reservoir characterization is not to seek the truth about reservoir; instead, to build a reasonable reservoir model which is adequate to predict the future performance. The model will not only be dependent on the type of data available, but it should also be dependent on the type of flow process we are trying to simulate. More complex the flow process (e.g., CO2 process), more detailed will be the reservoir description; more simple the flow process (e.g., dry gas reservoir), simpler will be the reservoir description. Reservoir description process is not new; since the first oil discovery, oil companies have used all the available data techniques to describe the reservoir so that the next well to be drilled will be based on more information than a prior well. However, several changes have taken place in the last fifteen years. Some of these changes are listed below:We have better and faster computers so that we can handle more complex algorithms, and can generate detailed reservoir descriptions in a reasonable amount of time. PC revolution has brought the computer power to small players, making it feasible for even small operators to harness the power of detailed reservoir description processes.Several new algorithms have been developed in the last fifteen years which allow integration of various types of data in an easier fashion.As the reservoirs get more mature, there is more need to describe the reservoir in more details so as to locate the remaining hydrocarbons.There is an increasing recognition that representation of heterogeneities is as important as representing correct physics in the flow simulators. What Is Geostatistics? Geostatistics is based on a simple principle that geological data are spatially correlated. This spatial correlation is quantified and is utlilized to determine the weights assigned to the nearby samples to estimate the value at the unsampled location. Geostatistics has been used in mining industry for several years. Its use in petroleum industry is of relatively recent origin. To address the unique problems encountered in petroleum engineering, several new geostastical techniques have been established in the past several years. Some of these techniques are discussed below. Accomplishments to Date Several papers have been published in the literature to demonstrate the application of geostatistics. It will be impossible to list all the successes of various geostatistical techniques. Instead, an effort is made to highlight the accomplishments which are widely used and embraced by oil companies.

This paper presents a comprehensive study on the productivity and flow efficiency of horizontal wells completed with slotted-liners or perforations. The study is based on a semi-analytical model that couples the flow equations in the reservoir and wellbore. The reservoir model takes into account the 3D convergence of flow around perforations and slots. The wellbore flow model considers the pressure losses inside the horizontal well and the effect of axial influx at the perforations and slots. A new, experimental apparent friction factor correlation is used for horizontal wellbore flow computations with perforations and slots. The model is capable of incorporating the effects of selective completion and non-uniform skin distribution. The results of this study indicate that software based on detailed semi-analytical models can provide a powerful tool to design, predict, and optimize horizontal well completions. It is also shown that horizontal wells deserve genuine guidelines to optimize their completions. For example, horizontal wells are shown to require significantly lower slot and perforation densities to accomplish optimum PI compare to vertical wells. Similarly, in horizontal wells, the effect of slot or perforation phasing becomes more important as the anisotropy of the formation increases. Introduction Horizontal wells are one of the most important strategic tools in petroleum exploitation.1 As a result of the advances in drilling and completion technologies in the last two decades, the efficiency and economy of horizontal wells have significantly increased. Today, horizontal well technology is applied more often and in many different types of formations. The state of the art applications of horizontal well technology require better completion designs to optimize production rates, long-term economics, and ultimate producible reserves. Horizontal well completions can be categorized as natural completion, sand-control completion, and stimulation completion. Natural completion includes open-hole, slotted-linear, and cased and perforated completions. Sand-screens, prepacked screens, and gravel packing are the completions used for sand-control. Stimulation completion includes completion with hydraulic fracturing and fracturing with gravel packing (fracpack or stimpack). All of these completion methods have been used in practice under different reservoir conditions.2,3,4 In a horizontal well, depending upon the completion method, fluid may enter the wellbore at various locations and at various rates along the well length. Fig. 1 illustrates the interplay between the pressure and flux distribution along the wellbore through the completion openings. The complex interaction between the wellbore hydraulics and reservoir flow performance depends strongly on the distribution of influx along the well surface and it determines the overall productivity of the well. Therefore, the optimization of well completion to improve the performance of horizontal wells is a complex but very practical and important problem. The complexities of the numerical simulation of horizontal well completions make analytical models extremely attractive. However, the inherent difficulties of the analytical solutions caused by the complex flow geometries, excessive number of perforations or slots, and non-uniform distribution of flux along the horizontal well calls for the challenging task of developing efficient computational algorithms.

Advances in drilling and fracturing technologies in Woodford Shale have attracted the operators to drill horizontal wells with long laterals (up to 5,000 ft), and to fracture using multiple stages (up to 22) using large amounts of slickwater and sand.It has been observed that exploitation of shale plays relies on the ability to contact as much of the reservoir as possible using fracturing techniques by creating a network of interconnecting fractures between laterals placed as close as 660 ft apart. As the spacing gets closer, the operators have a vested interest in knowing the optimal spacing of infill wells. Ideally, an infill well should have as little interference with the existing wells as possible.In this paper, we examine fracture data, and daily gas and water production data of 179 horizontal gas wells over five years in the Arkoma Basin to quantify the impact of interference between wells on their performance. We quantify the lost gas production from the surrounding wells; calculate the probability of interference as a function of distance and age of the surrounding well; determine the preferential direction of interference, and develop a new measure of spacing to understand the relationship between performance of the well and its surrounding wells. Finally, we provide recommendations regarding the spacing of infill wells.

Geostatistics is an increasingly important tool for developing an integrated reservoir description. Though Applied Geostatistics for Reservoir Characterization is written to illustrate the importance of geostatistics in improving the reservoir characterization process, it does not require any prior knowledge of statistics or advanced mathematics. Emphasis is placed on intuitive understanding of procedure rather than on mathematical details. Each chapter has an associated appendix in which additional mathematical details are provided. Several numerical and field examples, as well as a large number of illustrations, are provided to explain the strengths and weaknesses of different methods. Media Resources (http://go.spe.org/AGRCmedia)

Summary We present a method to integrate log, core, and well-test pressure data to describe reservoir heterogeneities. The conditional simulation method of simulated annealing is used to incorporate diverse sources of data. We use analytical solutions for radially heterogeneous reservoirs to define an equivalent radial permeability and a corresponding region of investigation. By numerical experimentation on drawdown well-test simulations in heterogeneous permeability fields, we determine that a weighted-area-based geometric average of the gridblock permeabilities within the region of investigation best defines the equivalent radial permeability. This information, along with the spatial statistics from core/log data, is coded into the overall objective function of the simulated annealing algorithm to yield a consistent reservoir description. Introduction Integration of all available data in describing a reservoir will yield a more accurate prediction of reservoir performance. The conventional approach to reservoir description by use of geostatistics can readily accommodate the use of static (core and log) data, specifically permeability and porosity data. The statistics of the sample data can be defined, and the support volume is a function of the size of the retrieved core or the depth of investigation of the logging instrument. Permeability and porosity values can be upscaled to represent gridblocks for the purpose of reservoir simulation studies. Well-test interpretation techniques provide useful information on a scale larger than core or log data. On this scale, we can determine faults, drainage boundaries, and an average reservoir permeability. On a smaller scale, we can determine wellbore damage and whether the system is single or dual porosity. Conventional geostatistical methods are unable to incorporate well-test data. The support volume represented by a well-test permeability needs to be determined, as well as a procedure that relates the well-test derived permeability to the distribution of small-scale permeabilities within the reservoir. We present a methodology to include well-test data for the description of small-scale heterogeneities.

Summary The effect of pipe diameter on liquid-loading initiation has been investigated experimentally with pipes having internal diameters of 5.1- (2-) and 10.2-cm (4-in.). Two-phase-flow parameters, such as pressure gradient and liquid holdup, were measured. Flow characteristics were determined by visual observation with a high-speed video camera. Critical gas-flow rate for liquid-loading initiation was identified, and comparisons between the two pipe diameters were presented. The critical superficial-gas velocity corresponding to the minimum pressure gradient was found to be faster for the smaller diameter. When the comparison was carried out in terms of mass-flow rates, critical flow rate for liquid loading in a 5.1-cm (2-in.) pipe was less than that in a 10.2-cm (4-in.) pipe. This verifies the use of velocity strings to extend the production life of the gas wells. Additionally, comparison of the data with available mechanistic-model prediction showed significant discrepancies. Possible reasons for these discrepancies are discussed.

In this paper, we present a field example where a streamline simulator was used to rank multi-million cell geostatistical reservoir descriptions and to find the optimum level of vertical upscaling for finite-difference simulation. During geostatitstical reservoir characterization, it is a common practice to generate a large number of realizations of the reservoir model to assess the uncertainty in reservoir descriptions and performance predictions. However, only a small fraction of these models can be considered for comprehensive flow simulations because of the high computational costs. A viable alternative is to rank these multiple ‘plausible’ reservoir models based on an appropriate performance criterion that adequately reflects the interaction between heterogeneity and the reservoir flow mechanisms. In this study, we explore the use of ranking based on streamline time of flight connectivity derived from a streamline simulator. The time of flight reflects fluid front propagation at various times and its connectivity at a given time provides us with a direct measure of volumetric sweep efficiency for arbitrary heterogeneity and well configuration. The volumetric sweep efficiency is the simplest measure that reflects the interaction between heterogeneity and the flow field. It is a dynamic measure that can be easily updated to account for changing injection/production conditions. We show that the proposed connectivity criterion can also be used to evaluate the effects of vertical upscaling in the dynamic performance and to determine the optimal level of upscaling for numerical simulation purposes. Our field study involves a Middle Eastern carbonate reservoir under a moderate to strong aquifer influx. The reservoir is on primary depletion and has no injectors. Multiple geostatistical reservoir descriptions were generated using a hierarchical approach whereby the larger level of uncertainty is defined first followed by smaller levels. The aquifer is modeled with a constant pressure boundary and for each time update, the location of the boundary was modified to account for the water encroachment. Using the field-wide sweep efficiency as a performance measure, the realizations were ranked, and used for flow simulation to assess risks associated with various development strategies. Subsequently, three selected realizations were upscaled for the purpose of comprehensive history matching and performance prediction. Background With the wide-spread use of geostatistics, it has now become a common practice to generate a large number of realizations of the reservoir model to assess the uncertainty in reservoir descriptions and performance predictions. Most commonly, these multiple realizations account for spatial variations in petrophysical properties within the reservoir and thus, represent a very limited aspect of uncertainty. For reliable risk assessment, we need to generate realizations that capture a much wider domain of uncertainty such as structural, stratigraphic, as well as petrophysical variations. From a practical point of view, we want to quantify the uncertainty and at the same time keep the number of realizations manageable. In this study, we will adopt an approach that is based on hierarchical principles. Thus, the uncertainty having the most potential impact is identified first. For example, with limited well control, the structural uncertainty derived from the seismic interpretations can have the most impact on the flow performance. Or, for faulted reservoirs, the uncertainty with respect to locations of faults can have the most impact. Then, the next level of uncertainty is identified and so on. The last level of uncertainty is the multiple geostatistical realizations of reservoir properties for a given set of input parameters. The petrophysical uncertainties generally tend to have a much lower impact on the reservoir performance compared to factors affecting large-scale fluid movements.

The fluids in horizontal wells can exhibit complicated flow behaviors, in part due to interaction between the main flow and the influxes along the wellbore, and due to completion geometries. An existing small-scale test facility at Tulsa University Fluid Flow Projects (TUFFP) was used to simulate the flow in a horizontal well completed with either circular perforations or slotted liners. Single phase liquid flow experiments were conducted with Reynolds numbers ranging approximately from 5000 to 65,000 and influx to main flow rate ratios ranging from 1/50 to 1/1000. For both the perforation and slot cases, three different completion densities and three different completion phasings are considered. Based on the experimental data, new friction factor correlations for horizontal well with multiple perforation completion or multiple slots completion were developed using the principles of conservation of mass and momentum.