The design of steam injection projects requires a knowledge of the quality and pressure of steam at the sandface before it enters the formation. In order to make such predictions, the multiphase flow and energy balance equations must be solved simultaneously. There are very few multiphase correlations in the literature that could be applied to the down flow of steam. A mathematical model was developed for multiphase, non-isothermal down flow of steam in pipes. Several correlations were tested against limited experimental data. A method was also developed to adjust one of the correlations to fit available experimental data. The results of this investigation indicate the limitations of existing correlations and show the need for more experimental data. Introduction Wellbore heat loss and pressure drop for steam injection wells are often ignored and most thermal reservoir simulators as· same the sandface condition of the steam to be the same as that at the surface. This may be a good approximation for shallow wells, but for deep steam injection wells wellbore heat loss is often substantial. One of the first workers to consider this problem was Ramey(l). He was primarily concerned with wellbore heat loss during the injection of hot water. Ramey developed a model with the following assumptions:The physical properties of the fluid and the formation are independent of depth and temperature.Heat transfer in the wellbore rapidly reaches steady state, while heat transfer to the formation occurs under transient conditions.The over-all heat transfer coefficient, U, is independent of depth.The frictional losses and kinetic energy effects are negligible. Satter(2) improved Ramey's analytical model by making the over-all heat transfer coefficient, U, dependent on depth and the fluid properties a function of temperature. Holst and Flock(3) further improved the models proposed by Ramey and Satter to include friction losses and kinetic energy effects. Pacheco and Farouq Ali(4), as well as Herrera et al(5), presented comprehensive models, but only considered single-phase fluid flow in the tubing. In this paper, a mathematical model is presented that also accounts for two-phase flow in the tubing. Our objective is to see if available two-phase flow correlations, possibly with some minor modifications, are applicable to the down flow of wet steam. Mathematical Model Assuming constant rate of injection (flow rate in the tubing), the conservation of mass, the conservation of energy and the mechanical energy balance equations may be combined to yield the following two simultaneous ordinary differential equations(4.6). (Equation in full paper) Method of Solution The method of solution chosen to simultaneously solve equations 1 and 2 is the Fourth Order Runge Kutta Method(l3). The convergence of the method was tested to obtain the maximum ∆z that could be used without incurring appreciable truncation error. A ∆z of 100 ft was found to be adequate. The computer model consists of a main program and six subroutines. A flow chart of the main program is shown in Table 1.
Summary Several oil wells in a Saudi Arabian field have shown a significant decline in oil productivity in recent years. A few have "died" prematurely, while others have become intermittent producers. The oil productivity decline is aggravated by water encroachment and has occurred with relatively low water rates and without any significant drop in reservoir pressure. These wells have low productivity indices (PIs), resulting in relatively low flowing bottomhole pressures (FBHPs). This paper presents the results of an investigative case study to determine the causes of productivity decline in these wells. A multidisciplinary team was set up with engineers and scientists from reservoir management, production engineering, and the R&D Center for the investigative study. The team focused on multiple aspects, including reservoir and production engineering as well as a comprehensive laboratory and field investigation. The results of this study indicate that one of the main causes of productivity decline in these wells is related to asphaltene precipitation and the subsequent formation of tight emulsions downhole. The emulsions block the pore throats and cause formation damage, which leads to productivity decline. Another factor that further aggravates the productivity of these wells is poor rock quality in the area. Possible causes of formation damage by inorganic scaling and leakage and mixing of gas from a deeper reservoir have been eliminated. Well-test analyses on some of the affected wells show that the formation-damage mechanism in the affected area is further aggravated by poor reservoir rock quality. The time-lapse pressure-transient analysis also indicates a deterioration of skin and productivity with time. On the basis of these findings, a special solvent treatment was recommended and designed as a pilot trial for one of the dead wells. The treatment included squeezing xylene and demulsifier to dissolve the asphaltenes and break the tight emulsions around the wellbore area. The treatment resulted in only a slight improvement in the PI, and the well died after a few days. Currently, a stimulation treatment with acid and demulsifier is being implemented in selected wells. The results of the field trials are described here. Introduction Several wells in the northwestern part of a Saudi Arabian field have shown a decline in productivity in recent years. A few wells have died prematurely at relatively low water cuts, some as low as 25%, which is atypical for wells in this area. It has been noticed that the oil productivity decline is aggravated when wells become wet. The decline has occurred with water rates remaining mostly stable and without any significant drop in reservoir pressure. A location map of affected wells is shown in Fig. 1. Oil and water production rates are plotted in Figs. 2 through 4 for three affected wells. The oil production rates declined from ~ 10,000 to 12,000 B/D to less than 1,000 B/D during a period of approximately 4 to 5 years. Water rates remain generally low, less than 2,000 B/D. It can also be observed that the oil rate decline is substantial as soon as water breaks through in the well. This study was initiated with the objectives of finding the causes of productivity decline in these wells and of finding effective ways to mitigate the problem. A multidisciplinary team was set up with members from reservoir and production engineering and the R&D Center. Several potential causes of productivity decline in these wells were investigated, including the precipitation of asphaltenes, emulsion blocking, mixing of hydrocarbons from a deeper reservoir, inorganic scale precipitation, aquifer-brine and injected-water compatibility, and regional geology, including rock quality, drilling fluid damage, and distance of wells from the gas/ oil separation plant (GOSP). This paper presents extensive experimental work, reservoir-engineering and pressure-transient analysis studies, and results of a field trial. Experimental Investigation Asphaltene Precipitation. Asphaltenes comprise the heaviest polar fraction of crude oils. Asphaltenes exist in the form of colloidal dispersions and are stabilized in solution by resins and aromatics that act as peptizing agents. Asphaltene precipitation and deposition may occur deep inside the reservoir, near the wellbore, and/or in processing facilities.1–4 It was evident from preliminary analyses of wellhead samples that some form of asphaltene precipitation was taking place in the affected wells. All these wells showed tight emulsions, and asphaltenes were observed in the bailer samples. Asphaltene precipitation is a function of pressure, temperature, live crude oil composition, and, to a lesser extent, oil/water interactions. Asphaltenes have a tendency to precipitate as the pressure is reduced, especially near the bubblepoint. However, precipitation can occur even at pressures higher than the bubblepoint, depending on the crude. Normally, this reduction in pressure occurs in the wellbore, where it might not be such a problem because the precipitated asphaltenes may be dragged to the GOSP and redissolve as the pressure reduces further.1,3 However, if the pressure reduction occurs inside the reservoir, for example near the wellbore, it may result in asphaltene precipitation within the effective pore space. This may lead to an increase in skin and, subsequently, more precipitation. Ultimately, this may result in the reduction of oil rates and lead to the death of the well. Asphaltenes are also known to stabilize emulsions.5–8 Tight emulsions can lead to emulsion blocking, a phenomenon that also reduces productivity in oil wells.
Waterflood optimization via rate control is receiving increased interest because of rapid developments in the smart well completions and i-field technology. The use of inflow control valves (ICV) allows us to optimize the production/injection rates of various segments along the wellbore, thereby maximizing sweep efficiency and delaying water breakthrough. A major challenge for practical field implementation of this technology is dealing with geologic uncertainty. In practice, the reservoir geology is known only in a probabilistic sense; hence, the optimization of smart wells should be carried out in a stochastic framework to account for geologic uncertainty. We propose a practical and efficient approach for computing optimal injection and production rates accounting for geological uncertainty. The approach relies on equalizing arrival time of the waterfront at all producers using multiple geologic realizations. The main objective is to improve sweep efficiency and thereby improve oil production and recovery. We account for geologic uncertainty using two optimization schemes. The first one is to formulate the objective function in a stochastic form which relies on a combination of expected value and standard deviation combined with a risk attitude coefficient. The second one is to minimize the worst case scenario using a min-max problem formulation. The optimization is performed under operational and facility constraints using a sequential quadratic programming approach. A major advantage of our approach is the analytical computation of the gradient and Hessian of the objective function which makes it computationally efficient and suitable for large field cases. Multiple examples are presented to support the robustness and efficiency of the proposed optimization scheme. These include 2D synthetic examples for validation and a 3D field-scale application. The role of geologic uncertainty in the outcome of the optimization is demonstrated both during the early stage and also, later stages of waterflooding when substantial production history is available. Introduction The recent increase in oil demand worldwide combined with the decreasing number of new discoveries has underscored the need to efficiently produce existing oil fields. The maturity of most of the existing large fields requires prudent reservoir management and development strategies to maximize recovery. With this goal in mind, the use of smart/complex wells and completions are becoming increasingly common place. Among the various improved recovery schemes, waterflooding is by far the most widely used (Craig 1971; Lake et al., 1992). In spite of its many appealing characteristics, the presence of heterogeneity such as high permeability streaks might yield unfavorable results, causing premature breakthrough, poor sweep and consequently reduce oil production and recovery (Sudaryanto and Yortsos 2001; Brouwer and Jansen 2004; Alhuthali et al., 2007). Various methods have been suggested to mitigate this problem. Among these is smart well completion where the production or the injection section is divided into several intervals (Arenas and Dolle 2003; Glandt 2005). The flow rate at each interval can be independently controlled by inflow control valves (ICVs), making it possible to manage the flood front in highly heterogeneous reservoirs.
Summary Waterflood optimization by means of rate control is receiving considerable attention because of increasing deployments of smart well completions and i-field technology. The use of inflow control valves (ICVs) allows us to optimize the production/injection rates of various segments along the wellbore, thereby maximizing sweep efficiency and delaying water breakthrough. Field-scale rate-optimization problems, however, involve highly complex reservoir models, production and facility constraints, and a large number of unknowns. In this paper, we propose an approach that is computationally efficient and suitable for large field cases. It is based on our previous work (Alhuthali et al. 2007, 2008), which relies on equalizing arrival time of the waterfront at all producers to maximize the sweep efficiency. We use streamlines to efficiently and analytically compute the sensitivity of the arrival times with respect to well rates. We also account for geologic uncertainty by means of a stochastic optimization framework using multiple realizations. Analytical forms for gradients and Hessian of the objective functions are derived, making our optimization computationally efficient for large-scale applications. Finally, optimization is performed under operational and facility constraints using a sequential quadratic programming approach. We demonstrate our approach using two field-scale examples. The first is a synthetic example called "Brugge" field, a benchmark case based on a North Sea Brent-type field. The production optimization of this field is carried out as part of a closed-loop process where the production history is matched prior to the production optimization. The production optimization is performed over multiple realizations for 20 years and involves 30 wells equipped with three ICVs per well. The second example is a super-giant Middle Eastern field that has more than 50 years of historical oil production. The optimization is performed for 20 years on a portion of this field that contains nearly 300 wells consisting of conventional vertical and horizontal wells and smart horizontal wells. In both examples, multiple field-related constraints are imposed, such as the maximum well injection and production rates, the maximum allowable drawdown, restriction on high-water-cut wells, and voidage replacement for pressure maintenance. The results clearly demonstrate the viability of our approach and the benefits of optimal rate control, with a considerable increase in cumulative oil production and a substantial decrease in the associated water production.
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