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Influence of pressure gradient on the relative phase permeability

UDK: 622.276.031:53
DOI: 10.24887/0028-2448-2017-5-32-35
Key words: capillary pressure, gradient of formation pressure, modelling of formation processes
Authors: A.M. Svalov (Oil and Gas Research Institute of RAS, RF, Moscow)

The article presents the analysis of the conditions necessary for formation pressure gradient influence on relative phase permeability.

In oil and gas mechanics it is traditionally accepted that the filtration characteristics of the reservoir rock, such as relative phase permeability and capillary pressure, do not depend on the pressure gradient because of the dominant influence of capillary forces in the distribution of moving phases over the pore space. Indeed, the capillary number defined as the dimensionless ratio of the formation pressure gradient in the product with the rock permeability coefficient to the value of the surface tension between the filtering phases in the main area of the developed fields (excluding, perhaps, the wellbore zones of the wells) is in the actual development conditions in the region of small values. From the physical standpoint, the capillary number is interpreted as the ratio of hydrodynamic and capillary forces and the small value of this number means that the capillary forces play the main role in the distribution of the wetting and non-wetting phase over the pore space of the rock.

At the same time, if we proceed from the physical meaning of the capillary number, it is necessary to take into account that in the course of field development conditions arise when the capillary forces approach zero values. In the hydrophilic reservoir, for example, with increasing watercut, the capillary curve will approach zero and this means that at this stage of watercut the ratio of hydrodynamic and capillary forces will increase and the effect of hydrodynamic forces, that is the formation pressure gradient, on the phase distribution over the pore space will also increase.

Thus, the analysis of the physical meaning of the capillary number presented in the work shows that there are stages of field development when an increase in the reservoir pressure gradient will affect the shape of the relative permeability curves. This result can be useful, in particular, in analyzing the conditions for the effective application of forced fluid extraction technology.

References

1. Efros D.A., Issledovanie fil'tratsii neodnorodnykh sistem (Research of the filtration of inhomogeneous systems), Moscow: Gostoptekhizdat Publ., 1963, 312 p.

2. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1982, 211 p.

3. Gimatudinov Sh.K., Fizika neftyanogo i gazovogo plasta (Physics of the oil and gas reservoir), Moscow: Nedra Publ., 1971, 312 p.

4. Lake L.W., Johns R., Rossen B., Pope G., Fundamentals of Enhanced Oil Recovery, Society of Petroleum Engineers, 2014, 496 p.

5. Tiab D., Donaldson E C., Petrophysics: theory and practice of measuring reservoir rock and fluid transport, Elsevier Inc., 2004, 926 p.

6. Svalov A.M., Problemy dobychi nefti i gaza. Kapillyarnye effekty v podzemnoy gidrodinamike: Novye rezul’taty (Problems of oil and gas production. Capillary effects in underground hydrodynamics: New results), Moscow: Librokom Publ., 2013, 112 p.

The article presents the analysis of the conditions necessary for formation pressure gradient influence on relative phase permeability.

In oil and gas mechanics it is traditionally accepted that the filtration characteristics of the reservoir rock, such as relative phase permeability and capillary pressure, do not depend on the pressure gradient because of the dominant influence of capillary forces in the distribution of moving phases over the pore space. Indeed, the capillary number defined as the dimensionless ratio of the formation pressure gradient in the product with the rock permeability coefficient to the value of the surface tension between the filtering phases in the main area of the developed fields (excluding, perhaps, the wellbore zones of the wells) is in the actual development conditions in the region of small values. From the physical standpoint, the capillary number is interpreted as the ratio of hydrodynamic and capillary forces and the small value of this number means that the capillary forces play the main role in the distribution of the wetting and non-wetting phase over the pore space of the rock.

At the same time, if we proceed from the physical meaning of the capillary number, it is necessary to take into account that in the course of field development conditions arise when the capillary forces approach zero values. In the hydrophilic reservoir, for example, with increasing watercut, the capillary curve will approach zero and this means that at this stage of watercut the ratio of hydrodynamic and capillary forces will increase and the effect of hydrodynamic forces, that is the formation pressure gradient, on the phase distribution over the pore space will also increase.

Thus, the analysis of the physical meaning of the capillary number presented in the work shows that there are stages of field development when an increase in the reservoir pressure gradient will affect the shape of the relative permeability curves. This result can be useful, in particular, in analyzing the conditions for the effective application of forced fluid extraction technology.

References

1. Efros D.A., Issledovanie fil'tratsii neodnorodnykh sistem (Research of the filtration of inhomogeneous systems), Moscow: Gostoptekhizdat Publ., 1963, 312 p.

2. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey i gazov v prirodnykh plastakh (Movement of liquids and gases in natural reservoirs), Moscow: Nedra Publ., 1982, 211 p.

3. Gimatudinov Sh.K., Fizika neftyanogo i gazovogo plasta (Physics of the oil and gas reservoir), Moscow: Nedra Publ., 1971, 312 p.

4. Lake L.W., Johns R., Rossen B., Pope G., Fundamentals of Enhanced Oil Recovery, Society of Petroleum Engineers, 2014, 496 p.

5. Tiab D., Donaldson E C., Petrophysics: theory and practice of measuring reservoir rock and fluid transport, Elsevier Inc., 2004, 926 p.

6. Svalov A.M., Problemy dobychi nefti i gaza. Kapillyarnye effekty v podzemnoy gidrodinamike: Novye rezul’taty (Problems of oil and gas production. Capillary effects in underground hydrodynamics: New results), Moscow: Librokom Publ., 2013, 112 p.



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