This paper presents a discussion of the pressure-transient responses of horizontal wells in anticlinal structures and curved and undulating wells in slab reservoirs. It confirms that, in the absence of a gas cap, conventional horizontal-well models may be used to approximate the flow characteristics of the systems in which the trajectory of the well does not conform to the curvature of the producing structure. If a gas cap is present, however, the unconformity of the well trajectory and producing layer manifests itself, especially on derivative characteristics when the gas saturation increases around the well. In general, the most significant deviations from the conventional horizontal-well behavior are observed during the buildup periods following long drawdowns. In these cases, the pressure-transient analysis is complicated and requires detailed numerical modeling of the well trajectory and reservoir geometry in the vertical plane. Numerical Simulation of Horizontal-Well Responses In this paper, we have used two finite-difference formulations of transient flow for a horizontal well (see Appendix A). The first formulation was for single-phase flow, and the second formulation was for two-phase flow of oil and gas (the relative permeabilities used in this work are presented in Appendix B). In the latter, we have neglected gas solubility in oil for simplicity. (Solution gas
The common approach of using refined grids and small time steps usually does not provide accurate and efficient numerical models to simulate horizontal-well pressure-transient tests. In most cases, this approach requires impracticably long computational times or creates artifacts on pressure and derivative responses that may be confused with the characteristics of certain flow regimes. The results of this study indicate that the conventional well index should be used with log-distributed grid and time steps to obtain closer match to the analytical solution at early times. There is, however, a limit to grid refinement beyond which the results do not improve. This paper introduces the transient well index that allows the use of larger grids while improving the accuracy of simulations especially at early times. Introduction The need for numerical simulation of transient pressure behavior of horizontal wells often arises in the interpretation of complex structures and calibrating the static data used in reservoir models. Several techniques1,2 have been proposed in the literature to improve the grid system requirements in modeling pressure-transient responses of vertical wells. These references have implied the extension of the same techniques to horizontal wells but no conclusive information has been presented. We first document the effect of grid size selection and the representation of horizontal wellbore within the grid blocks. Next, we present guidelines to determine the grid size and discuss modifications of the Peaceman's probe radius formula1 to improve the simulation of horizontal well pressure-transient responses. These techniques include the use of the appropriate well indices and transmissibility modifiers for transient flow in horizontal wells. The transient numerical well index (TNWI) presented in this paper is shown to be essential to reproduce the characteristics of the early-time pressure-transient characteristics of horizontal wells. We demonstrate that with the correct choice of the equivalent well grid radius, the proposed techniques considerably improve the simulation of the early time responses without requiring significant grid refinement. The techniques proposed can be easily implemented in the conventional simulation codes to simulate both short-term and long-term performances of horizontal wells. Background Several studies have searched for techniques to improve the numerical simulation of well tests. These studies included comparison of bottom-hole flowing pressure calculation methods using well-known steady-state productivity index versus the less common transient productivity index equations. In a related subject, the reservoir simulation literature focuses on the implementation of local grid refinement near the wellbore as the main method to improve the accuracy of the bottomhole pressure calculations. While the use of transient well index for numerical well test analysis has been discussed in the literature, these studies, in general, were for vertical wells. In this paper, however, we are specifically interested in transient well index for horizontal well applications. Below is an account of the relevant literature.
Careful gathering and analysis of outcrop analogue data is a valuable data source for enhancing the understanding of analogue hydrocarbon reservoirs. However, information from outcrops is commonly limited to static descriptions, i.e. reservoir body dimension and geometry.
In a first ever joint venture initiative, Qatar Petroleum has joined forces with Total in an effort to improve acid stimulation programs. Acid stimulation in carbonates can greatly increase well productivity. Near-wellbore impairment or formation damage is typically analysed by a term called skin factor. It is this 'skin' that is removed during an acidizing operation in a well. Typically, reducing the skin factor by a factor of 5 can increase a well's productivity by up to 50 percent (Furui et al. 2003). Acid stimulations performed in Qatar on 23 offshore wells in 2008-2009, increased oil production by 100 percent while at the same time reducing the water cut by 10 percent. In this joint venture project conducted by researchers and engineers from Total and Qatar Petroleum, the study is divided into three phases which also includes knowledge transfer and training. Phase 1 consists of core-flooding under reservoir conditions using standard acid recipes on outcrop and field cores. In Phase 2, improved or novel acidizing systems will be tested using a dual core setup, allowing the study of acid diversion from high permeability zones to low permeability zones. The objective here is not only to improve acidizing efficiency but also to mitigate the water production from heavily watered-out zones. Modeling activities will be undertaken to design acid stimulation treatments using results from the laboratory experiments. Phase 3 involves knowledge sharing and training on mud cake removal treatments. Mud cake is the damage caused to the near-wellbore, i.e., the interface between the reservoir matrix and the well, during the drilling of open hole wells. The knowledge gained will be implemented in both onshore and offshore fields as part of acid stimulation field trials.
In greenfield developments, production test data is often the only data available (other than analogues) that can be used to constrain dynamic reservoir behaviour. However, often the integration of production well-test data and its interpretation into the static and dynamic reservoir models is limited to the incorporation of the calculated Kh and skin values. A well-test of a gas bearing carbonate formation of a well drilled as part of a gas development drilling campaign is used. In addition, a care is taken to include well-test results into the static and dynamic reservoir models. This is because relatively coarse-gridded simulation models cannot reproduce detailed well inflow behaviour due to the lack of discretization. As a result, the assumption of directly using well properties (kh and skin) determined from analytical well-test analysis in coarse gridded simulation models may not hold for all physical environments, particularly in the near-wellbore behaviour. Well-tests can be matched with detailed fine gridded single well models, which then should be used to upscale the well properties for coarser grids. The study illustrates how these "pseudo-well properties" can change as a function of full field simulation grid size and permeability thickness product (kh). In addition, this is done with out incorporation of the viscous stripping effect and the detailed geological features such as small fractures, warmholes on the condensate behaviour of different grid sizes. Introduction One of the challenges in building static and dynamic reservoir models is the aspect of upscaling. The right balance is sought between the preservation of geological resolution, accurately representing of physical behaviour and the required computational time to generate dynamic simulations. However, where in the process of upscaling due attention often is paid to the correct preservation of the geological properties, less attention is paid to the impact of grid coarsening on the calculated near-wellbore behaviour. This paper describes a workflow that was developed to address this issue and the findings of a case study that investigated the impact of matching well performance observed in production tests as a function of the grid size. In addition, this workflow may lead to a significant improvement in the prediction of future well productivity particulary in the near-wellbore flow. The workflow and the possible impact of this well-test interpretation approach on production forecasts will be illustrated using well-test results from a gas-bearing carbonate formation wells. These wells are drilled and production tested as part of a gas development drilling campaign located in the North Field. In this paper, the study focuses on the inclusions of the detailed flow behaviour recorded during well-test in a coarser full field model. Study Workflow As well-test transient pressure responses cannot be adequately replicated in a coarse full-field model, an intermediate step was introduced in the modelling workflow wherein, a finely gridded sector model is extracted from the full-field geological model. The minimum wellblock size required to resolve a certain level of detail from well-test can be found based on the radius of investigation (Rinv) of the pressure responses at different times during well-test as shown in Figure 1. It can be seen that 50m wellblock size is needed as minimum to simulate the early time pressure transient responses.
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