Probabilistic forecast of sand pressure based on the results of one-dimensional geomechanical modeling

The paper presents a study on the influence of uncertainty in the initial data on geomechanical and strength properties of rock, as well as the horizontal reservoir stress, on the results of numerical estimation of the wellbore pressure required to prevent sand production. A model of the near-well rock mass is constructed from geophysical well logging data and laboratory core studies to solve this problem. The rock mass is considered a layered, multifacial, linear elastic medium. The hypothesis of subvertical principal stress was used for stress reconstruction. A method based on point measurements, specifically hydraulic fracturing data, is used to analyze horizontal stress profiles and reconstruct the stress distribution in a layered medium.

The uncertainty in the input data for the elastic and strength properties of the medium and the horizontal reservoir stresses is varied. These parameters are randomized within the range of uncertainty corresponding to the actual variation in the properties of rocks belonging to a specific geomechanical facies. The pressure allowing sand production is determined for various combinations of initial parameters using the Monte Carlo method within the framework of a simple model. The statistical approach makes it possible to determine the probability density function for sand production pressure with a given value of a certain parameter. Note that the prediction of the critical pressure is mostly sensitive to the magnitude of maximum horizontal stress.

The results of applying this approach allow us to accurately account for uncertainties in the initial data used to create geomechanical models. Using the example of the sand problem, we estimate the real ambiguity in determining the pressure at which irreversible rock destruction begins in the borehole surrounding rock masses during hydrocarbon deposit development.

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