Modelling of gas-condensate flow around complex well geometries and cleanup efficiency in heterogeneous systems
Ebrahim Alajmi, Saad
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Two phase flow of gas and condensate fluids in porous media is different from that of conventional Gas-Oil fluid systems. Such reservoirs are characterized by their complex phase and flow behaviors that significantly affect the well performance. The presence of retrograde fluid, when the pressure drops below dew point, and the dependency of the gas and condensate relative permeability (kr) on the velocity and interfacial tension (IFT) makes numerical modeling and performance prediction of gas condensate systems a real challenge, especially for complex well geometries such as hydraulically fractured wells (HFWs). The current research work is divided into three elements. The first one is devoted to study the flow behaviour around Single and Multi-layer hydraulically fractured wells (HFWs) in gas condensate reservoirs. Here, several in-house simulators have been developed for single-phase and two-phase gas condensate flow. The two phase in-house simulators correctly account for the phase change and the dependency of relative permeability to velocity and interfacial tension, due to inertia (reduction in kr as velocity increases) and coupling (improvement in kr as velocity increases and/or IFT decrease). The integrity of the in-house simulators have been verified by comparing some of their results with those obtained using the fine grid option of the ECLIPSE (E300) commercial reservoir simulator under the same prevailing flow conditions. Benefiting from, the 2 and 3-D in-house simulators a large data bank has been generated covering a wide range of variations of pertinent geometrical and flow parameters. Then, a new formula is proposed for estimation of an effective wellbore radius of an equivalent open-hole (EOH) radial 1-D system replicating flow around the 2 and 3-D HFW systems. The proposed formulation is general, in the sense that if the total gas fractional flow (GTR) is unity, then it correctly converts to that suitable for single phase gas system under Non-Darcy flow conditions and when Reynolds number is small to that under Darcy flow conditions. The second part of this thesis is devoted to study the optimization of hydraulic fracture geometry in gas condensate reservoirs. In this part of the study, a general optimum fracture design formulation is proposed based on the effective proppant number concept. In this new formula the maximum productivity index and optimum penetration ratio can be calculated for a certain proppant number, both accounted for the coupling and inertia effects. Here an effective proppant number formula is proposed (i.e. correcting the absolute proppant number for the effect of coupling and inertia). The proposed formula is general as it correctly converts to that suitable for single-phase Darcy and Non-Darcy flow. Furthermore, using the effective proppant number formula proposed here, the well-known Unified Fracture Design (UFD, Economides and Valko formula) has been modified to account for gas condensate flow conditions, i.e. coupling and inertia effects. The third part of this research work presents a thorough and extensive evaluation of the impact of the pertinent parameters on the clean-up efficiency process, which is often considered as one of the main reasons for the under-performance of hydraulic fracturing treatments, in gas reservoirs. In fact, most available clean up efficiency literature studies are concentrated on evaluating the impact of a single pertinent parameter at a time. That is, none of these studies have investigated the variation of all pertinent parameters simultaneously over a wide practical range of their variations, which may help in better understanding of the clean-up process and may provide practical guidelines to successful hydraulic fracturing jobs. Accordingly, this work embarked on a much more expanded study following statistical approaches. First, the key parameters which have significant impact on the gas production loss (GPL) are identified and then a 2-level full factorial statistical experimental design method has been used to sample a reasonably wide range of variation of pertinent parameters covering many practical cases for a total of 12 parameters. Since over 36,000 simulation runs were required, to cover the range of variation of all parameters, the simulation process has been simplified using a computer code, which was developed to automatically link different stages of these simulations. The analysis of the simulation runs using two response surface models (with and without interaction of parameters) demonstrates the relative importance of the pertinent parameters after different production time periods and provide a practical guidelines to a successful hydraulic fracturing job. In conclusion, this research cover the following main elements of HFW research, 1) – To propose simple numerical modelling methods for gas and gas condensate flow around single and multi-Layer HFWs, 2) – To propose a general Optimum Fracture Design method for gas and gas condensate reservoirs, which correctly account for the effects of coupling and inertia. 3) – To provide a thorough and extensive evaluation of the impact of pertinent parameters on clean-up efficiency of hydraulically fractured gas well.