*2.1. Geomechanical Modeling*

Many researchers [33–43] find a notably high influence of fine fractions (<50 μm) on the well operation (mainly plugging screens), as a result, the material associated with the formation of sand arches was worked out, but significant results were not achieved in by analyzing the literature (except for the connection of the aforementioned arches with the process of the natural decrease in the number of suspended particles in the first few days of well operation).

Some investigations look at the use of chemical compositions for the selective retention of fine fractions; however, no field test results have been conducted [14,15,44–48].

Interdependences were investigated within the framework of a field with high viscosity oil, currently under development between the following parameters: the number of suspended particles, the influence of the sand production process on the operation of

individual wells and the study of the effectiveness of screens of certain standard sizes and structures [49,50]. It was found that with different production rates and water-cuts, the interdependence of the number of suspended particles on certain parameters may or may not be observed, as, for example, with the flow rate: its increase or decrease does not affect the number of suspended particles in the fluid flow, which is unexpected (since the fluid flow with a higher speed should entrain more rock particles from the formation). It was found that for wells with a liquid flow rate of <100 m3/day, there is a significant dependence for the number of suspended particles on water cut (for wells with a flow rate >100 m3/day, there is no dependence). The effect of water cut on the process of formation destruction has been noted numerous times, which is some confirmation of the fact that phase flow is one of the key parameters that should be taken into account when working with a poorly cemented reservoir.

The authors analyzed the operating experience of one of the facilities and constructed a distribution of the well stock, categorizing wells as either "complicated" or "uncomplicated" according to the following criteria: flow rates (Figure 2), water cut (Figure 3) and target bottomhole pressure (Figure 4). It can be seen from the graphs that operational complications (failures due to erosive wear or clogging with mechanical inclusions of downhole pumping equipment are mostly observed in the well stock with a flow rate of less than 100 m3/day and a water cut of less than 50%).

Coupling of wells is not always applicable due to the differentials in the tubing diameter, equipment and other factors, which influence the sanding process. The number of wells for consideration for the first category (0–50 m3/day) is three times fewer than the second. Making conclusions based on the beforementioned data seems questionable since a two-time increase in liquid flow rate leads to a rise in sanding. Nevertheless, a further increase in flow rate does not lead to complications in the well.

It is worth noting that many authors have found during their investigations that the amount of sand carried out increases along with an increase in water cut. Nevertheless, the graph above does not show this effect, since when the water cut is above 50%, there are no complicated wells at all.

**Figure 2.** Distribution of sand-prone well stock by fluid flow rate.

**Figure 3.** Distribution of sand-prone well stock by water cut.

**Figure 4.** Distribution of sand-prone well stock by bottomhole pressure.

With a decrease in bottomhole pressure (on average, a higher depression of the reservoir), a dependence of a higher level of sanding and complication can be observed.

This phenomenon is associated with the low bearing capacity of the flow and with high viscosity of the oil, which is explained by the lower sedimentation rate of the sand particles. Well operation is carried out according to the target bottomhole pressure control program, which is determined by the requirements of rational oilfield.

The trend towards lower drawdowns in the bottomhole formation zone is confirmed by the analysis of Figure 4, where it can be seen that the least number of failures and complications in the well stock with a target bottomhole pressure of more than 9 MPa, with the initial formation pressure—10.6 MPa.

Thus, the main issue of scientific and practical interest is the prediction of the onset of reservoir destruction and further determination of the critical bottomhole pressure (which leads to the production of sand together with the formation fluid) and, ultimately, to finding the optimal dynamics of bottomhole pressure lowering. There are two basic ways to solve this issue—practical modeling (laboratory tests) via sand retention tests (SRT) and Prepack tests and mathematical modeling. Physical modeling gives good results and provides a lot of information; however, preparing these experiments is time consuming, especially with bulk modeling included.

A literature review [16–19] makes it possible to recommend geomechanical modeling as a tool for assessing the stability of the bottomhole formation zone during operation in the conditions of weakly consolidated sandstones. The stability model is adapted to the data of caliper, imager, mini-frac and modular dynamic tests (MDT) studies. The model-building sequence for one-dimensional geomechanical modeling for PK formations is shown in Figure 5.

**Figure 5.** General scheme of geomechanical modeling. BSL—Broadband sonic logging, LOT—fractest, MDT—stress-test with bottomhole tester.

The 1D model of stability of the bottomhole formation zone according to the criteria of Mogi–Coulomb and Mohr–Coulomb is based on the current parameters of the formation and according to the data of the well operation:


The bottomhole pressure and the angular position around the circumference of the wellbore are the specified parameters in this model. Detailed algorithm for this modeling procedure is presented in [9].

The results of the calculations of the 1D model are used to determine the admissible value of depression, at which the fracture of the bottomhole formation zone will not occur. The next stage is a calculation of the optimal step for lowering the bottomhole pressure to value, when the well is brought to the target operating mode (at analogous fields— 0.3–0.5 MPa/day). A significant advantage of the proposed approach is the ability to assess the critical depression value even in the absence of core studies of the mechanical properties of the rock.

As a result, the following geomechanical modeling algorithm was developed:

