We aim at the development of a general modelling workflow for design and optimization of the well flowback and startup operation on hydraulically fractured wells. Fracture flowback model developed earlier by the authors is extended to take into account several new fluid mechanics factors accompanying flowback, namely, viscoplastic rheology of unbroken cross-linked gel and coupled "fracture-reservoir" numerical submodel for influx from rock formation. We also developed models and implemented new geomechanical factors, namely, (i) fracture closure in gaps between proppant pillars and in proppant-free cavity in the vicinity of the well taking into account formation creep; (ii) propagation of plastic deformations due to tensile rock failure from the fracture face into the fluid-saturated reservoir. We carried out parametric calculations to study the dynamics of fracture conductivity during flowback and its effect on well production for the set of parameters typical of oil wells in Achimov formation of Western Siberia, Russia. The first set of calculations is carried out using the flowback model in the reservoir linear flow regime. It is obtained that the typical length of hydraulic fracture zone, in which tensile rock failure at the fracture walls occurs, is insignificant. In the range of rock permeability in between 0.01 mD and 1 D, we studied the effect of non-dimensional governing parameters as well as bottomhole pressure drop dynamics on oil production. We obtained a map of pressure drop regimes (fast, moderate or slow) leading to maximum cumulative oil production. The second set of parametric calculations is carried out using integrated well production modelling workflow, in which the flowback model acts as a missing link in between hydraulic fracturing and reservoir commercial simulators. We evaluated quantitatively effects of initial fracture aperture, proppant diameter, yield stress of fracturing fluid, pressure drop rate and proppant material type (ceramic and sand) on long-term well production beyond formation linear regime. The third set of parametric calculations is carried out using the flowback model history-matched to field data related to production of four multistage hydraulically fractured oil wells in Achimov formation of Western Siberia, Russia. On the basis of the matched model we evaluated geomechanics effects on fracture conductivity degradation. We also performed sensitivity analysis in the framework of the history-matched model to study the impact of geomechanics and fluid rheology parameters on flowback efficiency.

The study provides insights into the development of a data-driven model for hydraulic fracturing design optimization. We make a specific focus on practical aspects of testing the model in the field. Database for hydraulic fracturing treatments is built on the data from 22 oilfields in Western Siberia, Russia. The database contains about 5500 points with formation, well and fracturing process parameters, the target feature for model is a cumulative fluid production for 3 months. System and method for searching offset (similar) wells is also developed, tested and validated. Authors developed the model for predicting cumulative production that is used for futher hydraulic fracturing design optimization.

Summary One of the main factors affecting the efficiency of hydrocarbon production during the field development is waterflooding pattern used for the formation pressure maintenance. It is common practice when production wells that have been worked for depletion are converted to the injection. However, since hydraulic fracturing was previously performed on the majority of production wells, the injection under high pressure can cause risks associated with spontaneous fracture growth. This can lead to the water breakthrough and decreasing of production efficiency. The purpose of this work is modeling of fracture growth pressure on the injection well using poroelasticity approach. Thus, a physico-mathematical model of the problem for determining the pressure at which the fracture will grow on the injection well is built. Solving a problem involves sequential finding of the pressure field in a development element using Laplace equation, and then the stress field using an equilibrium equation. The solutions were obtained by usage of analytical and numerical approaches including Fourier transform and finite-difference scheme. Verification of the obtained solution was carried out by validating the model on a finite element solution. The criterion of fracture growth was also derived, according to which the fracture propagation occurs when the minimum horizontal stress at the tip of the fracture is exceeded. The influence of the parameters of the reservoir and the development on the value of the critical pressure was evaluated, namely, it was shown that an increase of Biot coefficient leads to an increase of fracture growth pressure and an increase of Poisson’s ratio decreases the critical pressure. It was found that an increase of the distance between the wells in the line leads to the decrease of the pressure at which water-induced fracture starts to grow, while an increase in the distance in a row along the vertical increases this pressure. It should be pointed out that the most common way to control the growth of water-induced fractures is combined hydrodynamic and geomechanical modeling, but this method is very time consuming and computationally expensive. In this connection, a quick method for estimating the fracture initiation pressure was proposed. The presented model can be used to control the growth of water-induced fracture, namely, to determine the regimes of fracture growth, to regulate the waterflood regimes (pressure and flow control), and to optimize the field development system without using combined hydrodynamic and full geomechanical modeling.

The paper considers a semi-analytical model for the water-injection well critical pressure estimation at which the fracture will initiate. The model is based on the Biot`s theory of poroelasticity and the algorithm based on the Fourier transforms and the finite difference method was used to solve the problem. The solution involves a sequential calculation of changes in the reservoir pressure distribution and changes in rock stresses using plane-stress approach for a periodic development element. For the cases when the assumption of the homogeneity of the elastic, strength and formation reservoir properties is unacceptable three-dimensional geomechanical modeling algorithm is used, taking into account the actual geological parameters of the formations and the results of hydrodynamic modeling using historical data. In addition, a semi-analytical model for the water-induced fracture breakthrough interval (in height) estimation is proposed. The model includes the following parameters: formation pressure, injection speed, fluid viscosity and injection time. The model is based on the net pressure calculation for a rectangular hydraulic fracture in the leakage dominant regime (Perkins–Kern–Nordgren model). The model uses a 1D geomechanical model and reservoir properties as an input data. The breakthrough interval is calculated iteratively with the assumption of the fracture height at each step. The additional net pressure is calculated using the distribution of permeability and formation elastic properties. If this pressure exceeds the compressive rock stresses in the neighboring layers, then the water-induced fracture will grow vertically into the neighboring layers. The iteration continues until the vertical growth stops. The resulting techniques can be used for waterflooding process control and development system optimization.

Due to the frequent application of hydraulic fracturing technology (HF) on oil and gas fields, there is a large amount of statistical information about the operations carried out. It is possible to make a conclusion about the efficiency of the hydraulic fracturing, consider the design changes and make recommendations on the basis of results of data processing. However this task becomes complicated because conduction of pressure transient analysis on fracking wells reveals that the values of the fracture parameters, in particular the half-length, significantly differ from those planned for design. This paper is devoted to the investigation of the possible reasons of this discrepancy by using dimensionless variables, which allows analyzing of information about the performed fracturing operations. The nondimensionalization of the basic equations using for the hydraulic fracture modeling made it possible to obtain the dependence of the dimensionless half-length of the fracture on the dimensionless volume of the injected liquid, and also to obtain an empirical formula for estimating the half-length of the fracture. Also, the analysis provides a possibility to exclude the influence of different factors that could make a significant contribution to the existing discrepancy. As a result of the analysis, limitation of PTA models, related, for example, to the non-uniform fracture conductivity and the lack of interflow between layers with different properties, as well as the fracture design errors associated with incorrect closing ratios are identified among the most probable causes of the fracture length difference.