Acid fracture operations in carbonate formations are used to create highly conductive channels from the reservoir to the wellbore. Conductivity in calcite formations is expected to be highest near the wellbore, where most of the etching occurs. The near wellbore fracture etched-width profile can be estimated from the measured temperature distribution. Temperature data can be obtained from fiber optic distributed temperature sensing (DTS) installed behind casings to monitor fracturing operations.
Heat transfer is commonly coupled in acid fracture models to account for temperature's effects on acid reactivity with carbonate minerals. Temperature profiles are usually evaluated during simulations of fracture fluid injection, but seldom during fracture closure. Since most of the acid is spent during injection, many models have assumed that the remaining acid reacts proportionally along the fracture length. Because of this assumption, neither acid spending nor temperature is usually simulated during fracture closure.
In this study, a fully integrated temperature model was developed wherein both the acid reaction and heat transfer were simulated while the fracture was closing. At each time step, transient heat convection, conduction, and generation were calculated along the wellbore, reservoir, and fracture dimensions. Modeling temperature during this transient period provides a significant understanding of the fracture etched-width distribution. During shut-in, cold fracture fluids are heated, mainly because of heat flow from the formation to the fracture. The amount of fluid stored in the fracture determines how fast the fluid is heated. Wider fracture segments contain larger amounts of cold fracture fluids, resulting in it taking longer to reach the reservoir temperature. Because of this phenomenon, near a wellbore, the vertical fracture etched-width profile can be determined from the temperature distribution. Also, minerals' spatial distributions along the wellbore's lateral can be estimated in multistage acid fracturing. This is done by minimizing the difference between the observed and modeled temperatures.
This evaluation of etched width profiles at the fracture entrance provides an estimation of fracture-conductive channel locations. Moreover, it has significantly improved the understanding of mineralogy distribution in multi-layer formations. This information will be particularly useful when designing acid fracturing jobs in nearby wells or revisiting the same wellbore for further stimulation.
Aljawad, Murtada Saleh (KFUPM University and Texas A&M University) | Schwalbert, Mateus Palharini (Petrobras and Texas A&M University) | Zhu, Ding (Texas A&M University) | Hill, Alfred Daniel (Texas A&M University)
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 is joined to the fracture propagation and heat transfer models. The dissolution patterns along fracture surfaces are generated, and that 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 optimum fracture productivity are determined with this integrated model.
This method shows that there is an optimum 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, pad, and overflush volumes, can be selected to achieve the optimum 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 long acid penetration length is 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 lowering injection rate of retarded acids. Minimum amount of pad should be used in this case. Still, the flow rate should be high enough to keep the fracture open during acid injection. This paper also shows 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. This paper provides a scientific approach to determine acid treatment volume that yields the optimal outcomes of acid fracturing.
Modeling acid fracturing operations in carbonate formations is performed to evaluate the possible improvement in well productivity. Models are developed to mainly estimate the acid penetration length and the fracture surfaces etched-width profile. Variable combinations of these two parameters produce a significant difference in the fracture productivity. To better estimate these parameters, a reliable fracture propagation model should be coupled with the acid reaction/transport model. Simulating weak acids or dolomite formations reactivity requires the inclusion of a heat transfer model. The model provided in this study couples these factors as fractures propagate to finally obtain the fracture conductivity distribution along its length.
The fracture propagation model continuously updates the domain for the acid model. A transient acid convection and diffusion equation is solved and the fracture etched-width profile is calculated. An iterative procedure is implemented in a temperature dependent kinetic model which is stopped when both the temperature and acid solutions converge. When injection stops, acid etching and the fluids temperature are updated as the fracture closes. As the final etching profile is drawn, conductivity is calculated using a correlation that considers formation heterogeneity.
Coupling fracture propagation shows a significant difference on the acid model solutions compared to that assuming constant fracture geometry. For extremely high Peclet number that represents a very retarded acid system, a constant drop in the etched-width value until reaching zero at the fracture tip is theoretically obtainable. For lower Peclet numbers, the etching profile is shown to be sharply declining towards the fracture end. This is in contrast with the non-coupled approach from which a uniform etching profile is obtained at moderate to high Peclet numbers. It is also observed that the simulation of acid injection in non-coupled, constant fracture geometry always overestimates the acid penetration distance. The etched-width distribution and the acid penetration length are temperature sensitive, especially in dolomite formations. Temperature coupling shows that the maximum etching in dolomite formations occurs away from the fracture entrance as acid reactivity increases. It also shows that the cooling effects of the first stage pad fluid on improving the acid penetration distance is limited.
Simulating acid fracturing operations assuming constant final fracture geometry and an average single temperature is time efficient but results in inaccurate solution. This paper quantifies the effects of integrating fracture propagating and heat transfer models on the acid etching pattern from which, a better estimate of the fracture productivity is expected.