Abstract
The object of this study is the propagation of hydroacoustic disturbances in a gas-lift well, where the main state variables are pressure and volumetric flow rate. The problem solved is the development of a numerical method for hydroacoustic problems, in which unknown initial distributions or harmonic input parameters are reconstructed from pressure and flow-rate data. A two-dimensional axisymmetric formulation was developed with longitudinal and radial flow-rate components. For the inverse problem, a quadratic objective functional was introduced, and adjoint-based gradient relations were obtained using the Lagrange method. A finite-difference scheme based on integral conservation relations was constructed for discontinuous coefficients and gas-lift boundary conditions. Numerical validation was performed on a one-dimensional gas-lift well model under harmonic input action with amplitudes A = 0.5 and A = 0.8. The pressure and flow-rate curves showed stable disturbance propagation from inlet to outlet boundary, while amplitude and phase changes reflected hydraulic resistance. The inverse procedure was verified using synthetic data. The prescribed parameters A = 0.8, ω = 30.0, and φ = 0.2 were reconstructed from different initial approximations within numerical precision. The frequency sweep detected the minimum of the objective functional at ω = 30.0. Stability verification gave CFL = 0.075. Grid refinement confirmed a decrease in pressure and flow-rate errors. Under noisy synthetic data, reconstruction accuracy decreased; at 5% noise, the amplitude error was about 10.65%, while frequency and phase errors remained small. The proposed method can be used to analyze pressure and flow-rate dynamics and identify gas-lift process parameters