The selective injection method of chemical reagents in stratified reservoirs

RS Software Lab, crossflows@netscape.net

A vertical fluid crossflow between different layers and reservoirs 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 crossflow is 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.

In this work we consider a well, which penetrated a multilayered reservoir and unsteady works. The task was solved in framework of homogeneous elastic liquid flow in a weakly deformed reservoir without formation crossflow. In a particular layer the pressure distribution obeys by axial equation of pressure conductivity:

(1),

here P - pressure, t - time, c = k/(m × m× b ) - conductivity coefficient, m - porosity, k - absolute permeability, m - reservoir fluid viscosity, b - reservoir elastic coefficient, index i denoted the layer number.

Initial pressure distribution in every layer is uniform and describes by Dupui formula (well production with constant flow rate)

here Pr - outside boundary condition, Pw - wellbore pressure, R, rw, - outside boundary, well radius.

The bottom hole pressure (r = rw) describes by the specification of flow rate change on a well

t > 0 with r = rw

(2)

with r = R Pi= Pr

here Qi - flow rate in i-th layer, Q(t) - flow rate change law.

Numerical algorithm of problem solution was tested by comparison of numerical results with data [2]. Flow rate graphs behaviour is identical.

We consider a problem solution of the fluid injection into injection well complied in three layers with parameters h1=h2=h3=3 m, m1=m2=m3=0,2, b 1=b 2=b 3=10-9m× s2/kg, m 1=m 2=m 3=10-3 Pa× s, k1=10-14m2, k2=8× 10-14m2 and k3=10-12m2. Reservoir pressures were equal Ðr=15 MPa. Initial injection rate was 252 m3/day, final flow rate varied from 252 to 0 m3/day. This regimes changes instantly.

Dependence of total fluid volume on difference between beginning injection rate and ending rate of liquid injection (during 12 hours) is shown on fig.1. Total fluid volume Vi that inflow (or outflow) in the i-number layer calculated as a time integral of flow rate in this layer during 12 hours from regime change. This graph shows that with small drop of injection rate is usual distribution of fluid volume over layer (proportionally with their hydro conductivity). With more drop of injection rate, the fluid volume that inflow in high-permeability layer increased, otherwise in low- permeability layer decreases. This is the reason of the critical injection rate value existence, which is characterised by fluid inflow only in high-permeability layer. Hence it is possible to regulate fluid volume inflow in selected part of a reservoir by changing of injection fluid rate over finitesimal time.

Fig.1. Dependence of total fluid volume in layers on difference between beginning injection rate and ending rate of liquid injection (during 12 hours)

1 - k1=10-14m2, 2 - k2=8× 10-14m2, 3 - k3=10-12m2

Now we consider a problem solution of the fluid injection into a production well complied in two layers with parameters k1=10-13 m2, k2=2× 10-14 m2, h1=h2=10 m. The well functions as following: before moment t=0 it worked as a production well with flow rate m3/day. In the moment t=0 the injection of fluid with flow rate Qin was start. The injection continued 1 day (first case) or 2 days (second case). Then well was shut-off. Total fluid volume Vi that inflow (or outflow) in the i-number layer calculated as time integral of flow rate in this layer during D t=10 days from regimen change with production to injection of fluid. It computed total fluid volumes that coming in layer with changing of Qin value over the range 0-13 m3/day.

In both cases total fluid volume rises linearly with injection flow rate increase Qin. The slope this dependence determines from corresponding layer parameters. For first case total fluid volume coming in low- permeability layer is equal to zero with injection flow rate Qcr=7.7 m3/day. Consequently, it is the critical value of injection rate when all injected fluid inflows only in low-permeability layer. If the injection flow rate obeys condition Qin<Qcr that reservoir fluid continues to flow from high-permeability layer and mixed with injection fluid coming in low-permeability layer. If Qin>Qcr that injection fluid inflow as in high-permeability as in low-permeability layers.

Comparison of the results of fluid injection in cases 1 and 2 shows that behaviour of fluid volume inflow in difference layers depends also from injection period. With increase injection time D t by 2 to 1 critical injection flow rate decreases from 7.7 to 3.85 m3/day.

The feed of fluid volume depends on concerted proportion of injection flow rate Qin and injection time D t. In this context it calculated the relation between injection flow rate Qin and injection time D t with other fixed parameters, which it came to 7.7 m3 fluid inject in low-permeability layer of the model reservoir. The result presented in fig.2.

Fig.2. Dependence between injection flow rate and injection period, which it came to 7.7 m3 fluid injection in low-permeability layer of model reservoir.

This graph shows that critical flow rate value is inversely proportional to the injection time, hence it defined by hyperbolic dependence. Consequently, the fact is established that maximum total fluid volume, which inflow only in low-permeability layer, is not dependent from injection period. The total fluid volume which inflow in low-permeability layer is constant value in all cases with injection flow rate selection Qin(D t) defined with presented procedure. This fluid volume value depends on layers parameters and beginning flow rate.

Therefore, this method can be used for selective treatment with reagents in low or high permeability layers. For example, if it is needed to inject the reagent in a low permeability layer during once shift (12 hours), than calculated injection flow rate will be Qin=15.4 m3/day. The reagent volume 7.7 m3 will inject only in low permeability layer, without influence on high permeability layer.

This work presents the example of proposed method to inject acid selectively in low permeability layer. Acid-rock reaction calculated our technique. Computations resulted that with traditional method of acid treatment the production more increase than with acid treatment by presented method, chiefly dependent on high permeability layer. If it is suppose that high permeability layer is water-saturated than water-oil ration in produced fluid increases in traditional injection method and decrease in presented method.

Conclusions

    1. The method for selective treatment by reagents in low or high permeability layer which based on regimen change of well is presented;

    2. For particular layer presented selective method allows to inject fixed reagent volume in low or high permeability layer, the value of this volume depends on layers parameters and initial flow rate;

    3. The example of proposed method is presented with acid selective injection in low permeability layer. The comparison of traditional and presented methods shows high efficiency of proposed method in case of water- saturated reservoir.

References

  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.

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