A fully implicit, three-dimensional simulator with local grid refinement around the wellbore is developed to solve reservoir and horizontal well flow equations simultaneously, for single-phase liquid and gas cases. The model consists of conservation of mass and Darcy’s law in the reservoir, and mass and momentum conservation in the wellbore for isothermal conditions. Establishing the continuity of pressure and preserving mass balance at the sandface satisfy the coupling requirements. The proposed simulator is tested against and verified with the results obtained from a commercial code ECLIPSE-100™, and available public domain simulators and semi-analytical models. The proposed model can be used for multiple purposes such as well productivity prediction, transient analyses, well length optimization, completion design and optimization, and production logging interpretation. Different completion scenarios and reservoir anisotropy are simulated and their effects on the productivity of the horizontal wells are discussed. Completion cases include open-hole and partial completions. During the production logging of a horizontal well, the coil tubing reduces the wellbore cross sectional area and may cause substantial changes in the wellbore flow behavior. Depending on the well and coil tubing diameters, a significant difference between the actual production rates and the rates obtained from a production log can be observed.
With the widespread applications of horizontal wells and its successful performance in the last decade, a number of relevant questions has been raised with respect to the optimization of horizontal well design. Considering the high costs involved and the technical challenges that are faced by the industry under various scenarios such as offshore environment, unconsolidated sands and heavy oil production, questions related to the optimization protocols to be followed have become progressively more important and more difficult to answer. Thus, the task of optimizing horizontal well design requires an investigation of the parameters that affect the productivity and ultimately the behavior of both reservoir and horizontal well domains, as well as the risks and costs involved in each alternative. Based on a fully implicit, three-dimensional numerical model coupling reservoir and horizontal well flow dynamics, a detailed study of the parameters that affect the behavior of flux distribution and productivity along horizontal wells has been performed. The parameters analyzed include permeability, initial gas saturation, anisotropy ratio, well location, fluid viscosity, flow rate, well length, and well diameter. A tool that permits to compare and select the potential options in terms of the gain in productivity per additional unit of well length and diameter is also introduced. Validation of the numerical model used in this study is performed using production-logging data and the examples of results of the application of the optimization protocol developed are reported for some of the Petrobras offshore fields. Introduction Different analytical and numerical models have been used to predict flow behavior and performance of horizontal wells. Basically, there are two different approaches to address the coupling issue between the two domains, namely, reservoir and wellbore and the effect of the hydraulics within the well. First approach involves the use of an infinite conductivity representation that treats the wellbore as an infinite conductivity medium and neglects the wellbore hydraulics. Although this idealization overpredicts the productivity, it is applicable in low productivity systems or in systems in which the pressure losses in the wellbore are negligible when compared to the pressure drop observed in the porous media1. However, for long wells, high flow rates, slim holes, high viscosity fluids, and multiphase conditions, the wellbore hydraulics play an important role in the production behavior of horizontal wells and should not be neglected. The second approach represents the actual behavior better, as it considers the wellbore domain as a finite conductivity medium by incorporating in the formulation the effects of friction, acceleration, gravity and influx coming from the reservoir. Unlike the results obtained with the infinite conductivity assumption, flux along the well has been shown to be not uniform or symmetrically distributed, as a larger volume of fluid enters near the downstream end of the wellbore in most of the cases studied. Therefore, the region near the heel of the well, would be under higher drawdown and more prone to water and gas coning. In general, all kinds of coning detrimentally affects both the short-term performance of the well as well as the ultimate recovery of the reserves.
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractA fully implicit, three-dimensional simulator with local hybrid grid refinement around the wellbore is developed to solve reservoir and horizontal well flow equations simultaneously for liquid-gas flow systems. The model implements the conservation of mass equations in the reservoir and conservation of mass and momentum in the wellbore for isothermal conditions. Establishing the continuity of pressure and preserving mass balance at the sandface satisfy the coupling requirements between the two computational domains. The hydrodynamic model for the wellbore is based on the homogeneous flow assumption. The model is used to simulate the transient pressure and flow rate behaviors of reservoir and horizontal wellbore. The traditional approach of decoupling of wellbore flow from reservoir flow does not capture the horizontal well pressure and flow rate transients at early times since the interaction between the reservoir and wellbore is inherently neglected. Simulation runs with the proposed model reveal the realistic characteristics of horizontal wellbore storage and unloading. By conducting a series of parametric study, effects of permeability, formation thickness, well length, fluid compressibility, reservoir anisotropy, and selective completion strategies on the coupled reservoir and horizontal well flow dynamics are investigated.
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractA fully implicit numerical model coupling reservoir and multifractured horizontal well flow dynamics has been developed to investigate the flow behavior and predict the productivity of such systems. The simulator solves simultaneously for pressure distribution within the reservoir and horizontal well domains, while taking into account the friction losses along the wellbore for laminar and turbulent flow conditions. Fractures with distinct properties are placed perpendicular to the wellbore axis and can intersect the well at arbitrary locations. The model is unconditionally stable and can be used to analyze the early transient period as well pseudo-and steady-state conditions. The use of multifractured horizontal wells has been gaining popularity in tight reservoir systems; however, the existing design protocols do not consider wellbore hydraulics that can have a governing role in the performance of the system. The appropriate design of a multifractured well has a definite impact on its performance. The numerical model presented in this paper can be utilized as a design tool towards the optimization of the number, position and penetration lengths of the fractures connected to a horizontal well.The calculated influx and pressure distributions along the wellbore show that solutions can deviate dramatically from the actual behavior if infinite conductivity idealization is used to represent flow dynamics in the horizontal well, and this discrepancy becomes more pronounced with an increase in reservoir permeability. Parametric studies are conducted to evaluate the influence of the number of the fractures in the flow behavior and productivity of the system. The observations and analyses presented in this paper will provide the much needed guidance to engineers who face the daunting task of designing a cost-effective optimum fracturing scheme in horizontal wells completed in formations with different flow characteristics.
A fully implicit, three-dimensional simulator with local hybrid grid refinement around the wellbore solving reservoir and horizontal well flow equations simultaneously for liquid-gas flow systems is used to investigate the effects of permeability, gas saturation, well length, well diameter, reservoir anisotropy and perforation/slot phase angle on the well productivity behavior. In addition, the effect of the coil-tubing diameter on the two-phase production logging measurements is studied. The model implements the conservation of mass equations in the reservoir and conservation of mass and momentum in the wellbore for isothermal conditions. The establishment of the continuity of pressure and preservation of mass balance at the sandface satisfy the coupling requirements between the two computational domains. The hydrodynamic model for the wellbore is based on the homogeneous flow assumption. In this paper, we show that the indiscriminate use of single-phase flow models to predict the productivity of horizontal wells producing under multi-phase flow conditions can lead to significant errors and the magnitude of the discrepancy increases with reservoir permeability and gas saturation. Also, for multiphase flow conditions, pressure drop along the wellbore plays a crucial role in the asymmetrical flux distribution profile and should not be ignored. The seriousness of the problem is considerably aggravated in long wells, slim holes, high permeabilities and high gas saturation systems. In some completion designs, the simulations have shown that 70% of the production comes from the first 1/6 of the total well length. In other examples, the last third of the well length contributes with less then 2% of the total production. It has been shown that in anisotropic systems, a more uniform flux distribution is obtained with openings aligned orthogonal to the larger permeability direction. Regarding to production logging applications, a significant deviation on the measurements and actual behavior can be observed, depending especially on the ratio between well and coil tubing diameter. The proposed model can be a useful tool in generating the appropriate corrections for the undesirable effects of the coil tubing on production logging measurements. Introduction Although a number of numerical and analytical tools have been developed to investigate the flow behavior and predict the performance of horizontal wells, several issues that can significantly affect performance predictions have not been addressed properly. One issue is the improper treatment of wellbore flow and reservoir-wellbore interaction. The earlier studies assuming constant pressure along the horizontal wellbore treated the horizontal well as an infinite conductivity medium. However, as discussed by Ozkan et al.1, the infinite-conductivity idealization is applicable only in low productivity systems in which the pressure loss in the wellbore is negligible compared to the pressure decrease encountered during a drawdown. Utilizing a simplified steady-state wellbore model, they also showed that pressure losses in the wellbore affect the productivity of a horizontal well significantly when the wellbore pressure losses and drawdown are of the similar orders of magnitude. Furthermore, unlike the results obtained with the infinite-conductivity assumption, the flux distribution along the wellbore has been shown to be asymmetrical, with greater amount of fluid entering near the downstream end of the wellbore. Therefore, especially for long wells, high flow rates, slim holes, high viscosity fluids, and multiphase conditions the wellbore hydraulics can play an important role in the production behavior of a horizontal well and they should not be neglected.
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