Wormholes are believed to be generated during the process of cold production and are responsible for enhanced production rates. Understanding the wormhole patterns generated inside the reservoir formation is critical to improve the recovery efficiency and to model the fluid flow behaviour in the cold production process. In this paper, we have proposed that the wormhole growth can be described by the Diffusion-Limited Aggregation (DLA) model, which naturally relates to a broad variety of branchinggrowth patterns through the physics of the processes. The physical processes that were described using fractal models include the following: the growth of a drainage network; the formation of cavities; the dissolution of porous materials; and, the growth of random dendrites in the thin films. The DLA model has important implications in petroleum geology and engineering. Based on the experimental results published in the literature, which were specifically designed to investigate the wormhole dynamics by a Computed-Tomography X-Ray scanner, the wormhole diameter distribution along the wormhole path has been analyzed using the Area Version of Gaussian Function. Then, the material balance method has been applied to the sand production data to determine the possible range of the wormhole structure around the wellbore, assuming that the sand particles are solely produced along the paths of wormholes. Finally, a numerical method has been developed to analyze the field sand production data. The studies have shown that the fractal wormhole model can be used to diagnose the characteristics of the wormhole structures, and that it can be applied to optimize well placement in cold heavy oil production. The model will greatly enhance the analyses of the inflow performance and the pressure response of wells in wormholed reservoirs. Results acquired from this study can also be implemented in field scale numerical simulations for the cold flow process. Introduction Cold production is a non-thermal process in which sand is aggressively produced to reach a higher oil production rate. In the cold flow process, sand and oil are produced together under primary conditions and oil production rates can typically increase by a factor of 10 or more(1–5). For example, primary oil production rates of 8 – 12 m3/d are roughly 10 times greater than those calculated for the radial flow in the Celtic field using Darcy's law(2). The unusual sand production in cold production was observed in several oil fields. Records have indicated that the production of about 708 m3 of sand in the first four months, and in nearly all the wells in S.E. Pauls Valley Field, Oklahoma, produced 10 – 50% sand initially, declining a few months later to 0.1 – 2%, regardless of completion method(5). The cumulative gross fluid production of about 9,000 m3 with an associated sand production of 200 m3 within a period of 1,000 days was observed in the Lindbergh and Frog Lake Fields, Alberta(1).

While water production is an inevitable consequence in bottom water reservoirs, it is usually desirable to defer the onset or the rise of water coning as long as possible. Numerous mechanical and chemical methods have been applied to achieve this goal over recent decades. This paper presents new insights into improving oil production and reducing water production by considering flow barriers below horizontal well trajectories in formation regions with low permeabilities, especially natural ones such as shale bodies. A 3D numerical simulation that applies the Computer Modelling Group's (CMG) STARS Simulator as a cost-effective way to investigate the effects of barriers on horizontal well performance in a bottom water reservoir has been conducted. More specifically, the effects of permeability, dimension, and position of barriers have been comprehensively analyzed when a horizontal well is implemented as a producer. The simulation results have shown that if barriers exist below a horizontal producer, water cut can be postponed and reduced greatly, and cumulative oil production can be increased. Cumulative water production can be decreased dramatically as well. To broaden the applicability of this new insight, some of the possible field implementing technologies, including fractured horizontal wells, small-scale CO2 injection, and solvent injection, are qualitatively simulated to determine their applicability for developing heavy oil in bottom water reservoirs using horizontal wells with the presence of barriers. The simulation results have shown that much better well performance can be reached with the help of barriers when these technologies are integrated systematically. This new strategy shows a rather promising and economic way to develop bottom water reservoirs where the natural driving energy of the aquifer could benefit the oil production process. The results and understanding acquired from this study offer insights into the development of bottom water reservoirs. Introduction Water coning is a critical issue for conventional vertical well production in bottom water reservoirs. Generally speaking, the fluid production process creates a low-pressure region around the wellbore in the reservoir. This differential pressure causes the oilwater interface to deform into a cone shape, at which time the less viscous water phase is produced in preference to the more viscous oil phase. Consequently, the producing Water-Oil Ratio (WOR) increases quickly and readily reaches an uneconomic level. Darcy's law is still the fundamental principle behind this phenomenon. In the past, many researchers have conducted experimental, analytical, and numerical studies on water coning behaviour in vertical wells. Muskat and Wyckoff(1) published one of the early studies related to water coning in 1935. They observed that water coning is a rate-sensitive process and determined the critical oil rate, which is the maximum water-free production rate, by neglecting the shape of the cone. Later on, researchers(2, 3) directed their studies toward the calculation of the critical oil rate. Guo and Lee(4) indicated that the critical rate does not occur at zero wellbore penetration, as may intuitively be expected, but at a wellbore penetration of about one-third of the total oil-zone thickness for an isotropic reservoir.

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The length of the etched fracture is rather limited utilizing traditional acid fracturing techniques, especially in a high-temperature carbonate reservoir. Although the propped fractures may have a deeper penetration, they have such drawbacks as low fracture conductivity, unintended proppant bridging, and subsequent proppant flow back. This paper presents the development of a new acid fracturing technique, Nitric Acid Powder (NAP) acid fracturing, to improve the acid penetration and fracture conductivity. The NAP acid fracturing technique has been applied in several oil fields in China. It has been shown that the NAP acid fracturing technique has the advantages of both hydraulic fracturing and acid fracturing, such as long effective penetration, high fracture conductivity, low cost, and easy field operation. We have developed a comprehensive mathematical model for the NAP acid fracturing technique to facilitate the optimization of the field treatment design. The model presented considers fracture growth, acid transport and reaction, leak-off, etched width of the fracture, and so on. The study has shown that the NAP acid fracturing technique could reach a very high stimulation ratio, even in a high-temperature carbonate reservoir. Therefore, it is an innovative and promising technique for well stimulation in carbonate reservoirs. Introduction Carbonate formations generally have a low permeability and can be highly fissured. Long fractures in acid fracturing treatments are essential to maximize production. Acid must react with the walls of the fracture to form a channel that remains open after the treatment. Flow channels can be formed as a result of an uneven reaction with the rock surface or preferential reaction with minerals heterogeneously distributed in the formation. If the formation temperature is very high, the reaction rate will be fast. If this occurs, the acid treatment will tend to remain in the near wellbore vicinity, resulting in short penetration. Acid fracturing techniques are the primary preference in carbonate formations. Operationally, acid fracturing is less complicated because no propping agents are used, which eliminates the risk of a screen-out and subsequent problems of proppant flowback and cleanout from the wellbore. Generally, acid-etched fractures have high conductivity, although they are quite limited in penetration, whereas the propped fractures have limited conductivity with deeper fracture penetration. The techniques to overcome the limitations of conductivity and penetration for the carbonate formation have been studied continuously to enhance the acid fracturing technology. Equilibrium acid fracturing was developed by Tinker(1) to maximize the contact time of acid with the fracture face to get a high fracture conductivity in cool dolomite formations, which react slowly with acid. Maximum acid contact time is essential to create highly conductive etched channels on the fracture faces. After the designed fracture length is created, the injection is continued at certain rates to maintain the equilibrium with the fluid leak-off rate from the created fracture faces. This technique was proven to be effective in stimulating the relatively cool dolomite. Closed acid fracturing techniques(2) were designed to obtain high conductivity, especially for the formations with extra high fracture close stress.