Modeling the Formation of Hydrates in gas Wells in Their Thermal Interaction With Rocks

Generalization of the algorithm of determining mass flow rate by measuring pressure in gas transportation systems

“…The formation and deposition of hydrates in pipelines is studied using quasi-stationary mathematical model [1][2][3][4][5][6][7][8]. In this model imperfect gas flow in pipes is described in the frame work of tube hydraulic and dynamics of hydrate formationin the frame work of the generalized Stefan problem in which temperature of gas-hydrate phase transition depends on gas flow pressure.…”

“…In addition to the phenomenological constants, the model includes technological parameters, for example, mass flow rate of gas which is constant at stationary flow, that can also be determined from these measurements. This inverse problem of determining the coefficients of differential equations via some additional information about behavior of the solution is the subject of this paper, where upon the algorithms of determining the parameters of ordinary differential equations created in [8,10,11] are generalized for the hydrate formation model proposed in [1][2][3][4][5][6][7][8]. An essential feature of this model is the determination of pipe cross-section that changes with time along with the calculation of gas temperature and pressure distribution via solving the Cauchy problem for equation which describes how dimensionless cross-section S changes over time:…”

“…Now we will set forth an algorithm for determining mass flow rate of gas from pressure measurements at the outlet, when cross-section varies along the length and in time due to the formation (dissociating) of hydrate layer. First note that the model proposed in [1][2][3][4][5][6][7][8] is sensitive to the input data due to its nature (nonisothermiс process, real properties of the gas, cross-section of pipe that changes with time, heat exchange with environment). These items are discussed in detail in monographs [8,11,12].…”

“…8. Determine the temperature distribution in surrounding ground solving the initial boundary value problem for equation of heat conduction using the enthalpy method[6].At each time step points 3 -9 are repeated. The calculations were carried out with the following initial data:…”

“…The change of cross-section along pipeline and in time at6 The change of cross-section along pipeline and in time for conjugated formulation: 1 -7 у  p…”