Non-stationary well production process in multilayered reservoir is considered. Fluid and rock matrix is deformable, bulk in a reservoir strata is not available. Wellbore fluid crossflow between layers during production shutting-in and start is leakage studied numerically. Predicted volume and time of such crossflow are comparable with parameters of well chemical treatment. The main conclusion of the research is the availability of wellbore crossflow usage for selective well treatment. Methods of variation of inflow volume in particular layer during non-stationary wellbore crossflow are considered.

Vertical fluid crossflows between different layers and reservoir in an oil formation play an important role in reservoir oil balance and processes of oil recovery. Even in the formation without layers link fluid crossflows are available through wellbore when reservoir pressure is different in various layers [1]. Production or injection stops of wells complied in different layers are accompanied by wellbore fluid crossflow even in a situation when reservoir pressure is uniform.

This effect was investigated also in conjunction with stratified reservoir analysis by pressure transient tests [2]. It was shown that simultaneous pressure and flow rate measurements gave possibility to determine parameters of reservoir layers.

Presented research is devoted to investigation of wellbore fluid crossflow during well production or injection stops. The results of numerical investigation show that volume and period of such crossflows is comparable to the parameters of well chemical treatments (for example acid treatment process). Influence of layer permeability ration, thickness flow rate variation is examined on crossflow direction, volume size and period.

Evolution of pressure distributions near well in isolated reservoir layers during well flow rate variation (including shutting-in) is studied. Simulating is undertaken under assumptions of small fluid and matrix deformation and without any hydraulic link of layers. Pressure distributions in particular layer governs by axial equation of pressure conductivity

Initial pressure distribution in layer is identical and described by Dupui formula (well production with constant flow rate)

here P_r - outside boundary condition, P_w - wellbore pressure, R, r_w, - outside boundary, well radius.

Flowrate drop is described by the following boundary condition on a well (r = r_w)

t > 0 with r = r_w

with r = R P_i= P_r

here Q_i – flow rate in i-th layer.

Numerical research begins from two-layered reservoir. Layers properties are assumed the following:

Well production before shutting-in was 86.4 m³/day, boundary pressures were equal 20 MPa and 18.6 MPa correspondingly.

Fig.1. Influence of layer permeability ratio k₂/k₁ with fixed k₂ = 10^-9sm²

Well injection shutting-in causes the opposite effect - wellbore crossflow from low to high permeability layers. On the reservoir with the same parameters crossflows are equal in magnitude but opposite in sign. Crossflow volume and period are the same after well injection shutting-in from flow rate 86.4 m³/day.

Numerical research was undertaken for three and four layered reservoirs. The general tendency of wellbore fluid crossflow from high to low permeable layers after production shutting-in and opposite after injection shutting-in retains exempt layers with intermediate permeability. For such layers flow direction depends on its permeability and may varies in crossflow period.

Injection rate drop to low but none zero value causes fluid inflow only in particular high permeability layers, low permeability layers do not take the fluid. So the result of present simulation would be useful to predict value of injection rate drop which causes fluid inflow only in several or single layers. This effect may be used for selective treatment of high permeable part of reservoir strata. Period of such treatment has the same value 1-3 days, fluid inflow is also the same as in common chemical technologies 0.5-2 m³ per production or perforated interval.

1. Modine A.D., Coats K.H., Wells M.W., A superposition method for representing wellbore crossflow in reservoir simulation, SPE reservoir Engineering, August 1992, pp. 335-342.
2. Ehlig-Economides C.A., Joseph J., A new test for determination of individual layer properties in a multilayered reservoir, SPE Formation Evaluation, September 1987, pp. 261-283.