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Summary The performance of acid-fractured wells depends on the conductivity distribution along the acid-penetration length, which is a function of reservoir properties, treatment design, and execution. The previously published models for fractured-well performance assume constant fracture conductivity, which cannot be achieved in acid-fracturing operations. This work proposes a design optimization method where acid-fracture and reservoir models are integrated. Fracture-conductivity distribution along the fracture surface is considered in the optimization process. In the new integrated model, the acid transport and reaction are joined to the fracture-propagation and heat-transfer models. The dissolution patterns along fracture surfaces are generated, and this is converted to a conductivity distribution. To predict the fractured-well productivity, the reservoir model is built using the input reservoir properties, as well as the calculated acid-fracture geometry and conductivity distribution. The acid-fracturing parameters that lead to the optimal fracture productivity are determined with this integrated model. This method shows that there is an optimal productivity that can be obtained for a given acid treatment volume and reservoir properties. Design parameters such as flow rate, viscosity, acid concentration, acid treatment volume, and pad and overflush volumes can be selected to achieve optimal well performance. Reservoir permeability has an important impact on how acid-fracture jobs should be designed. At low-reservoir permeability, a more evenly distributed conductivity and a long acid-penetration length are preferred. This can be accomplished by injecting a retarded acid system at moderate- to high-flow rate. However, excessive fracture-height growth should be prevented by carefully designing the injection rate and viscosity. For high-permeability reservoirs, higher conductivity along a shorter acid-penetration length is targeted. This can be obtained by selecting a more-reactive acid system such as straight acid and injecting at moderate rates, or by lowering the injection rate of retarded acids. A minimum amount of pad should be used in this case. Still, the flow rate should be highly sufficient to keep the fracture open during acid injection. We also show how acid concentration and fluid stages can be designed to optimize productivity and presents a procedure for selecting the acid treatment volume. A theoretical model, which integrates acid fracturing and reservoir flow, is used to implement the guidelines on optimizing acid-fracture design parameters. In this paper we provide a scientific approach to determine acid treatment volume that yields optimal outcomes for acid fracturing.

In naturally fractured carbonates, the efficiency of acid fracturing stimulation can be hindered due to the decreased effective length and conductivity of created fractures, and acid loss into natural fractures is one of the main reasons for the reduced efficiency. At the same time, acid that leaks into natural fractures creates additional conductivity that may enhance production from the stimulated well. A model was developed to predict the acid fracturing performance in naturally fractured carbonate reservoir by taking into account the etching of both hydraulically induced and naturally occurring fractures to estimate fracture conductivity and well productivity. The model uses a domain that contains a well and a rectangular reservoir. The well is intersected by a bi-wing vertical hydraulic fracture which is intersected by transverse natural fractures. The model simulates acid injection into the fracture system, acid-rock reaction, and width increase for both hydraulic and natural fractures. At the end of the acid injection, the conductivity of the fracture system is estimated, and the well stimulation efficiency is evaluated by calculating productivity increase and skin factor. This is done by simulating the production flow into the hydraulic and natural fractures using a coupled reservoir model without the need of an external reservoir simulator. In contrast to previously published acid fracturing models which calculate leakoff using the Carter's model, in this study, we developed a model that calculates the leakoff during acid injection by simulating the flow through porous media using a reservoir model, which includes both hydraulic and natural fractures. In contrast to the Carter's leakoff model which assumes that fractures are spaced far enough so that no interaction among the fractures occurs, the new approach allows the natural fractures to interact with each other as acid leaks off and pressure changes in the reservoir surrounding the fractures. The new approach does not impose limitations on fracture spacing, and leakoff rate of individual natural fractures is a function of fracture spacing and location. The other feature of the new model is that the leakoff flow rate does not necessarily decrease with time, unlike what Carter's leakoff model predicts. It was observed that leakoff rate from natural fractures may increase initially as the natural fractures are stimulated. The effects of natural fracture geometry and spacing, reservoir permeability, and treatment conditions on acid leakoff, fracture conductivity and well productivity are analyzed. The role of natural fractures on stimulation efficiency is evaluated by comparing the results with the cases where no natural fractures are present in the reservoir. The model enables a better prediction of acid fracturing performance in naturally fractured carbonate reservoirs, and also simulates more realistic leakoff behavior compared to the conventional leakoff model, which improves the accuracy of the results.

Summary Most wells in carbonate reservoirs are stimulated. Because of their low cost and simpler operations, acid-stimulation methods are usually preferred if they are sufficient. Matrix acidizing can effectively stimulate carbonate reservoirs, often resulting in skin factors on the order of −3 to −4. In low confining stress and hard rocks, acid fracturing can yield better results than matrix acidizing. However, acid fracturing is less effective in high permeability, high confining stress, or soft rocks. There is a combination of parameters, among them permeability, confining stress, and rock geomechanical properties, that can be used as criteria to decide whether matrix acidizing or acid fracturing is the best acid-stimulation technique for a given scenario. This study compares the productivity of matrix-acidized and acid-fractured wells in carbonate reservoirs. The criterion used to decide the preferred method is the largest productivity obtained using the same volume of acid for both operations. The productivity of the acid-fractured wells is estimated using a fully coupled acid-fracturing simulator, which integrates the geomechanics (fracture propagation), pad and acid transport, heat transfer, temperature effect on reaction rate, effect of wormhole propagation on acid leakoff, and finally calculates the well productivity by simulating the flow in the reservoir toward the acid fracture. Using this simulator, the acid-fracturing operation is optimized, resulting in the operational conditions (injection rate, type of fluid, amount of pad, and so forth) that lead to the best possible acid fracture that can be created with a given amount of acid. The productivity of the matrix-acidized wells is estimated using the most recent wormhole-propagation models scaled up to field conditions. Results are presented for different types of rock and reservoir scenarios, such as shallow and deep reservoirs, soft and hard limestones, chalks, and dolomites. Most of the presented results considered vertical wells. A theoretical extension to horizontal wells is also presented using analytical considerations. For each type of reservoir rock and confining stress, there is a cutoff permeability less than which acid fracturing results in a more productive well; at higher than this cutoff permeability, matrix acidizing should be preferred. This result agrees with the general industry practice, and the estimated productivity agrees with the results obtained in the field. However, the value of the cutoff permeability changes for each case, and simple equations for calculating it are presented. For example, for harder rocks or shallower reservoirs, acid fracturing is more efficient up to higher permeabilities than in softer rocks or at deeper depths. This method provides an engineered criterion to decide the best acid-stimulation method for a given carbonate reservoir. The decision criterion is presented for several different scenarios. A simplified concise analytical decision criterion is also presented: a single dimensionless number that incorporates all pertinent reservoir properties and determines which stimulation method yields the most productive well, without needing any simulations.