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Semi-analytical models for calculating well interference: limitations and applications

UDK: 622.276.031:532.585
DOI: 10.24887/0028-2448-2018-12-38-41
Key words: well interference, mathematical modeling, reservoir modeling, Capacitance Resistive Model, reservoir management, oilfield optimizatio
Authors: I.F. Khatmullin (Gazpromneft NTC LLC, RF, Sant-Petersburg), A.P. Tsanda (Moscow Institute of Physics and Technology, RF, Dolgoprudny), A.M. Andrianova (Gazpromneft NTC LLC, RF, Sant-Petersburg), S.A. Budenny (Moscow Institute of Physics and Technology, RF, Dolgoprudny), A.S. Margarit (Gazpromneft NTC LLC, RF, Sant-Petersburg), V.A. Lushpeev (Saint-Petersburg Branch of State Reserves),] M.V. Simonov (Gazpromneft NTC LLC, RF, Sant-Petersburg), D.S. Perets (Gazpromneft NTC LLC, RF, Sant-Petersburg)

For efficient oil and gas saturated reservoirs management (from waterflood induced fractures identification to water flooding system optimization of mature fields) it is often needed to promptly evaluate interwell hydrodynamics interaction. 3D reservoir simulation is of highly time consuming and it requires computational resources to evaluate required parameters, unlike semi-analytic models. In this paper, we describe various types of CRM-based (Capacitance Resistive Model) semi-analytic models, their features and restrictions, results of their practical application in well interference evaluation within a real field, and applicability criteria.

In this paper, we offer a new approach to hydrodynamic well interference evaluation based on the CR-model and its modifications, adapted for application on the real reservoir. A CR-model allows for determination physical parameters describing the fluid flow, requiring minimum resources and input data (flowrate, bottom-hole pressure, injection capacity, hole location, porosity and permeability). However, these models have notable applicability limitations, obstructing their implementation for work with field data. We made an analysis of application various types of CRM to field data, analyzed their efficiency for various problems and possibilities to avoid limitations that hamper the implementation of semi-analytic models for actual field data. We analyzed potential of various modifications of CR-models, differing by the amount of recorded events that affect the fluid flow, complexity and number of objective variables. Straightforward models exploit only flow rate and injection rate as input data. Ones that are less straightforward also use the bottom-hole pressure and, if needed, well shut down tracking. We estimated training speed with a training data sample for each modification till convergence and relative prediction error with test data are achieved. For this purpose we selected several cases with real field data with a variety of following parameters: number of wells, training time, number of a well’s startups and shutdowns, along with noise grade. Application area was evaluated for each modification of a CR-model.

References

1. Yousef A.A., Gentil P.H., Jensen J.L., Lake L.W., A capacitance model to infer interwell connectivity from production and injection rate fluctuations, SPE 95322-MS, 2006.

2. Sayarpour M., Zuluaga E., Kabir C.S., Lake L.W., The use of capacitance–resistance models for rapid estimation of waterflood performance and optimization, Journal of Petroleum Science and Engineering, 2009, V. 69(3-4), pp. 227–238.

3. Muskat M., The flow of homogeneous fluids through porous media, McGraw-Hill, New York, 1937.

4. Buzinov I.U., Umrikhin S.N., Issledovanie neftyanykh i gazovykh skvazhin i plastov (Investigation of oil and gas wells and reservoirs), Moscow: Nedra Publ., 1984, 269 p.

5. Savitzky A., Golay M.J., Smoothing and differentiation of data by simplified least squares procedures, Analytical chemistry, 1964, V. 36(8), pp. 1627–1639.

6. Kaviani D., Jensen J.L., Lake L.W., Estimation of interwell connectivity in the case of unmeasured fluctuating bottomhole pressures, Journal of Petroleum Science and Engineering, 2012, V. 90, pp. 79–95.


For efficient oil and gas saturated reservoirs management (from waterflood induced fractures identification to water flooding system optimization of mature fields) it is often needed to promptly evaluate interwell hydrodynamics interaction. 3D reservoir simulation is of highly time consuming and it requires computational resources to evaluate required parameters, unlike semi-analytic models. In this paper, we describe various types of CRM-based (Capacitance Resistive Model) semi-analytic models, their features and restrictions, results of their practical application in well interference evaluation within a real field, and applicability criteria.

In this paper, we offer a new approach to hydrodynamic well interference evaluation based on the CR-model and its modifications, adapted for application on the real reservoir. A CR-model allows for determination physical parameters describing the fluid flow, requiring minimum resources and input data (flowrate, bottom-hole pressure, injection capacity, hole location, porosity and permeability). However, these models have notable applicability limitations, obstructing their implementation for work with field data. We made an analysis of application various types of CRM to field data, analyzed their efficiency for various problems and possibilities to avoid limitations that hamper the implementation of semi-analytic models for actual field data. We analyzed potential of various modifications of CR-models, differing by the amount of recorded events that affect the fluid flow, complexity and number of objective variables. Straightforward models exploit only flow rate and injection rate as input data. Ones that are less straightforward also use the bottom-hole pressure and, if needed, well shut down tracking. We estimated training speed with a training data sample for each modification till convergence and relative prediction error with test data are achieved. For this purpose we selected several cases with real field data with a variety of following parameters: number of wells, training time, number of a well’s startups and shutdowns, along with noise grade. Application area was evaluated for each modification of a CR-model.

References

1. Yousef A.A., Gentil P.H., Jensen J.L., Lake L.W., A capacitance model to infer interwell connectivity from production and injection rate fluctuations, SPE 95322-MS, 2006.

2. Sayarpour M., Zuluaga E., Kabir C.S., Lake L.W., The use of capacitance–resistance models for rapid estimation of waterflood performance and optimization, Journal of Petroleum Science and Engineering, 2009, V. 69(3-4), pp. 227–238.

3. Muskat M., The flow of homogeneous fluids through porous media, McGraw-Hill, New York, 1937.

4. Buzinov I.U., Umrikhin S.N., Issledovanie neftyanykh i gazovykh skvazhin i plastov (Investigation of oil and gas wells and reservoirs), Moscow: Nedra Publ., 1984, 269 p.

5. Savitzky A., Golay M.J., Smoothing and differentiation of data by simplified least squares procedures, Analytical chemistry, 1964, V. 36(8), pp. 1627–1639.

6. Kaviani D., Jensen J.L., Lake L.W., Estimation of interwell connectivity in the case of unmeasured fluctuating bottomhole pressures, Journal of Petroleum Science and Engineering, 2012, V. 90, pp. 79–95.




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