# Dale Doty PhD

Mathematics Keplinger Hall 3205 918-631-2983

dale-doty@utulsa.edu

Ph.D., Michigan State University

M.S., Michigan State University

B.S., Michigan State University

Numerical Partial Differential Equations

Integral Boundary Methods

Artificial Life Techniques

Linear Algebra

Mathematical Modeling

Introduction to Advanced Mathematics

Calculus

The following may be selected publications rather than a comprehensive list.

## Journal Articles

The characteristic matrix of nonuniqueness for first-kind equations, in

*Integral Methods in Science and Engineering: Theoretical and Computational Advances,*Birkhauser, New York, 2015, pp. 111-118(with D. Doty).

Constanda, Christian et al. “Bilateral Estimates for the Solutions of Boundary Value Problems in Kirchhoff’s Theory of Thin Plates.”

*Applicable Anal.*91 (2012): 1661–1674. Print.

Constanda, Christian et al. “The Dirichlet Problem for a Plate on an Elastic Foundation.”

*Libertas Math.*30 (2010): 81–84. Print.

Amaya-Márquez, Marisol, Peggy S. M. Hill, John F. Barthell, L. Lisa Pham, Dale R. Doty and Harrington Wells. 2008. Learning and memory during foraging of the blue orchard bee,

*Osmia lignaria*Say (Hymenoptera: Megachilidae).

*Journal of the Kansas Entomological Society*, 81:315-327

Chudinovich, I., Constanda, C., Doty, D., Hamill, W. and Pomeranz, S., “The Dirichlet problem for the plane deformation of a thin plate on an elastic foundation”, Interval Methods in Science and Engineering: Techniques and Applications, Birkhauser, Boston, 2008, 83-88.

Constanda, Christian et al. “Nonclassical Dual Methods in Equilibrium Problems for Thin Elastic Plates.”

*Quart. J. Mech. Appl. Math.*59 (2006): 125–137. Print.

Chudinovich, I., Constanda, C., Doty, D. and Koshchii, A. “Non-classical dual methods in equilibrium problems for thin elastic plates”,

*Quart. J. Mech. Appl. Math.*59 (2006), 125-137.

Harry, F. A., Prado, M. G., Shiraz, S. A., Doty, D. R. "Two Phase Flow Modeling of Inducers",

*Journal of Energy Resources Technology*- June 2004.

Harun, A.F., Prado, M.G., Shirazi, S.A. and Doty, D.R., “Two-Phase Flow Modeling of Inducers,”

*ASME Journal of Energy Resources Technology, Vol. 126, No. 2, 2004, pp. 140–148.*

Harun, Amrin, Prado, M. G., Serrano, J.C. and Doty, D. R. “A Simple Model to Predict Natural Separation Efficiency in Pumped Wells," SPE 81826,

*SPE Production and Facilities Journal (February 2003).*

Lackner, Gernot, Doty, D.R., Shirazi, S.A., Schmidt, Z., “Effect of Viscosity on Downhole Gas Separation in a Rotary Gas Separator”, SPE 79076,

*SPE Production and Facilities, (Aug. 2002), 184–191.*

Lackner, G., Doty, D.R., Shirazi, S.A., and Schmidt, Z., “Effects of Viscosity on Downhole gas Separation in a Rotary Gas Separator,”

*SPE Production and Facilities, Vol. 17, No. 3, August 2002, pp. 184-191.*

Harun, A.F., Prado, M.G., Shirazi, S.A. and Doty, D.R. , “An Improved Model for Predicting Separation Efficiency of a Rotary Gas Separator in ESP Systems,”

*SPE Production and Facilities, Vol. 17, No. 2, May 2002, pp.78-83.*

Xu, J., Shirazi, S.A., Doty, D.R., Prado, M.G., and Blais, R.N., “Prediction of Turbulent Friction in Rod-Pumped Wells,”

*SPE Journal, Vol. 5, No. 2, June 2000, pp. 182–190.*

Tang, Y., Schmidt, Z., Blais, R. N., Doty, D. R., “Transient Dynamic Characteristics of the Gas-Lift Unloading Process”, SPE 57659, SPEJ (Sept. 1999).

Tengesdal, Jarl et al. “A Mechanistic Model for Predicting Pressure Drop in Vertical Upward Two-Phase Flow.” Ed. J. P. Brill.

*Journal of Energy Resources Technology*121.1 (1999): 1–9. Print.

Tang, Y., Schmidt, Z., Blais, R. N., Doty, D. R., "A Comprehensive Mechanistic Model for Transient Gas-Lift Unloading",

*SPEJ*(March 1999).

Gernot Lackner, Francisco J.S. Alhanati, Siamack A. Shirazi, Dale R. Doty, Zelimir Schmidt: “Numerical Simulation of the Gas-Liquid Flow in a Rotary Gas Separator,”

*ASME Journal of Energy Resources Technology,*(March, 1998) pp. 41-48.

Lackner, G., Alhanati, F.J.S., Shirazi, S.A., Doty, D.R., and Schmidt, Z., "Numerical Simulation of Gas-Liquid Flow Inside A Downhole Centrifuge,”

*ASME Journal of Energy Resources Technology, 1998, Vol. 120, pp. 41-48.*

Rastoin, S., Schmidt, Z., Doty, D.R.: "A Review of Multiphase Flow Through Chokes," ASME Jour. Eng. Res. Tech., (March 1997).

Nishikiory, N., Redner, R., Doty, D.R. and Schmidt, Z.: "An Improved Method for Gas Lift Allocation Optimization," SPE 19711,

*ASME Journal of Energy Resources Technology, (June 1995) 87–92.*

Sachdeva, R., Doty, D.R., Schmidt, Z.: "Performance of Electric Submersible Pumps in Gassy Wells," SPE 22767

*SPE Prod. & Facilities (February 1994) 55–60.*

Nicberding, M.A., Schmidt, Z., Blais, R.N., Doty, D.R., "Normalization of Nitrogen-Loaded Gas Lift Value Performance Data,"

*SPE Prod. & Facilities*(August 1993) 203-210.

Hepguler, G., Schmidt, Z., Blais, R.N., Doty, D.R.: "Dynamic Model of Gas-Lift Valve Performance,"

*JPT*(June 1993) 576-583.

Sagar, R., Doty, D.R. and Schmidt, Z.: "Predicting Temperature Profiles in a Flowing Well,"

*SPE Prod. Eng.,*November 1991.

Schmidt, Z., and Doty, D.R.: "System Analysis for Sucker Rod Pumping,"

*SPE Prod. Eng.*(May 1989) 125-129.

Miyoshi, M., Doty, D.R., Schmidt, Z.: "Slug Catcher Design for Dynamic Slugging in an Offshore Production Facility," SPE 14124,

*SPE Prod. Eng., (November 1988) 563–583.*

Hepguler, G., Schmidt, Z., Blais, R.N. and Doty, D.R.: "Instrumentation for Dynamical Modeling of Gas-Lift Valves," Advances in Test Measurement, Vol. 25, Instrument Society of America, (May 1988) 621-629.

Torre, A.J., Z. Schmidt, R.N. Blais, and D.R. Doty, "Casing Heading in Flowing Oil Wells," SPE Production Engineering, November 1987, 297-304.

Blais, R.N., Schmidt, Z., Doty, D.R. and Gutler, N.: "Test Facility for Measurement of Pressure Gradient in Large Diameter Vertical Pipes Carrying Two-Phase, Gas Liquid Flows,"

*Advances in Test Measurement,*Vol. 23, Instrument Society of America, (May 1986) 195-201.

Blais, R.N., Schmidt, Z., Doty, D.R., Jiao, B., and Biglarbigi, K.: "Test Facilities for Gas Lift Valves and Hydraulic Jet Pumps,"

*Advances in Test Measurement,*, Vol. 22, ISA, (May 1985), 525-530.

Z. Schmidt, D.R. Doty, K. Dutta-Roy, "Severe Slugging in Offshore Pipeline Riser-Pipe Systems," SPE 12334, SPEJ, January 1985.

Schmidt, Z. and D.R. Doty, "Hydrodynamic Model for Intermittent Gas Lifting," JPT, pp. 475-485, March 1984.

Doty, D.R. and Z. Schmidt, "An Improved Model for Sucker Rod Pumping," SPEJ, Vol. 23, No. 1, February 1983, 34-41.

Alhanati, F.J.S., Schmidt, Z., Doty, D.R.: "Continuous Gas Lift Instability: Diagnosis, Criteria and Solutions", SPE 26554 (Accepted pending revisions).

## Book Chapters

Constanda, C., Doty, D., Thomson, G. R., “Nonstandard Integral Equations for the Harmonic Oscillations of Thin Plates”, in

*Integral Methods in Science and Engineering: Progress in Numerical and Analytic Techniques, Birkhauser, Boston, 2013, 311-–328.*

Constanda, Christian et al. “Solution Estimates in Classical Bending of Plates.”

*Integral Methods in Science and Engineering*. 2: Computational Methods. Birkhauser, 2010. 113–120. Print.

Constanda, Christian et al. “Dual Methods for Sensor Testing of Industrial Containers. II. A Nonclassical Approach.”

*Computational Advances in Multi-Sensor Adaptive Processing*. IEEE, 2005. 74–76. Print.

Constanda, Christian, and Dale Doty. “The Characteristic Matrix of Nonuniqueness for First-Kind Equations.”

*Integral Methods in Science and Engineering: Theoretical and Computational Advances*. Birkhauser, 1900. 111–118. Print.

## Books

*Boundary Integral Equation Methods and Numerical Solutions: Thin Plates on an Elastic Foundation,*Springer, New York, 2015 (with D. Doty and W. Hamill).

Pomeranz, Shirley, Donna Farrior, and Dale Doty.

*Instructor’s Technology Resources and Solutions Guide; Student’s Technology Resources and Solutions Guide (Mathematica Solutions Manuals and CD-ROMs (Also Web Sites) to Accompany Text, Advanced Engineering Mathematics, by Robert Lopez)*. Pearson/Addison Wesley Publishers, 2002. Print.

Constanda, Christian, Dale Doty, and William Hamill.

*Boundary Integral Equation Methods and Numerical Solutions: Thin Plates on an Elastic Foundation*. Springer, 1900. Print.

## Technical Reports

Schmidt, Z., Doty, D.R., Report to American Petroleum Institute for the Recommended Procedure for The Testing of Gas Lift Valves, API R.P. IIV2, September, 1992.

Alhanatij, F.J.S., Schmidt, Z., Doty, D.R., "Continuous Gas Lift Stabilty," a report submitted to TUALP members, May, 1991.

Sagar, R., Schmidt, Z., Doty, D.R., "Gas-Lift Valve Performance Characterization," a report submitted to TUALP members, May, 1990.

Sachdeva, R., Doty, D.R., Schmidt, Z., "Final Report on Performance of Electric Submersible Pumps in Two-Phase Flow," a report submitted to TUALP member companies, Oct, 1989.

Pedersen, J., Doty, D.R., Schmidt, Z., "Report on Prediction of Liquid Holdup in Large Diameter Tubing," a report submitted to TUALP members, Oct, 1989.

Sachdeva, R., Doty, D.R., Schmidt, Z., "Preliminary report on performance of Electric Submersible Pumps in Two-Phase Flow," a report submitted to TUALP member companies, May 11, 1989.

Nishikiori, N., Schmidt, Z., Redner, R.A., Doty, D.R., "Gas Allocation Optimization for Continuous Flow Gas Lift Systems," a report submitted to TUALP member companies, May, 1989.

Liao, T., Z. Schmidt, D.R. Doty, and R.N. Blais, "Computer Simulation of Continuous Gas-Lift Installation Design," May 1988.

Nieberding, M., Z. Schmidt, D.R. Doty, and R.N. Blais, "Normalization of Nitrogen Loaded Gas Lift Valve Performance Data," January 1988.

Miyoshi, M., Doty, D.R., Schmidt, Z., "Offshore Pipeline Field Data Analysis," a report submitted to TUALP members, May 1985.

Biglarbigi, K., Schmidt, Z., Doty, D.R., Blais, R.N., "Gas Passage Performance of Continuous Flow Gas Lift Valves," a report submitted to TUALP members, Nov. 6, 1984.

Guler, N., Doty, D.R., Schmidt, Z., Blais, R.N., "Compressor Capacity for the TUALP Study of Two-Phase Flow in Large Diameter Tubing," a report submitted to TUALP member, July 1984.

Proposed LDF test, data analysis procedure, December, 1980.

Jiao, B., Schmidt, Z., Blais, R.N., Doty, D.R., "Jet Pump Performance when Handling Two-Phase Mixtures."

## Conference Proceedings

Chudinovich, Igor et al. “The Dirichlet Problem for the Plane Deformation of a Thin Plate on an Elastic Foundation.” The Ninth International Conference on Integral Methods in Science and Engineering (IMSE 2006) Proceedings, 2007. 83–88. Print.

Chudinovich, I., Constanda, C., Doty, D., Hamill, W. and Pomeranz, S., “On a boundary value problem for the plane deformation of a thin plate on an elastic foundation”,

*Proceedings of the Thirteenth International Symposium on Methods of Discrete Singularities in Problems of Mathematical Physics,*Khar’kov-Kherson, 2007, 358-361.

Constanda, Christian et al. “On a Boundary Value Problem for the Plane Deformation of a Thin Plate on an Elastic Foundation.”

*Proceedings of the Thirteenth International Symposium on Methods of Discrete Singularities in Problems of Mathematical Physics, Khar’Kov-Kherson*. 2007. 358–361. Print.

Harum, A. F., Prado, M. G. and Doty, D. R.: “Design Optimization of a Rotary Gas Separator in ESP Systems”, SPE 80890 - 2003 Production and Operations Symposium – Oklahoma City – March 2003.

Faustinelli, J. G., Doty, D. R., “Dynamic Flow Performance Modeling of a Gas-Lift Valve”, SPE 69406 – SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, March 2001.

Harun, Amrin, Prado, M. G., Serrano, J. C. and Doty, D. R. “A Mechanistic Model to Predict Natural Gas Separation Efficiency in Inclined Pumping Wells”. – SPE 67184 – 2001 Production and Operations Symposium – March 2001, Oklahoma City.

Harun, Amrin, Prado, M. G., Shirazi, S. A., Doty, D. “An Improved Model for Predicting Separation Efficiency of a Rotary Gas Separator in an ESP Systems”, SPE 63044 - SPE 2000 Annual Technical Conference and Exhibition – October 2000 – Dallas.

Harun, Amrin, Prado, M. G., Serrano, J. C., Doty, D. “A Simple Model to Predict Natural Gas Separation Efficiency in Pumped Wells ”, SPE 63045 - SPE 2000 Annual Technical Conference and Exhibition – October 2000 – Dallas.

Harun, Amrin, Prado, M. G., Shirazi, S. A., Doty, D., “Two Phase Flow Modeling of Inducers,” Proceedings of ETCE/OMAE2000 Joint Conference Energy for the New Millennium, February 14–17, 2000, New Orleans, LA

Cirilo, Roberto, Doty, D. R., “Gas-Liquid Flow through Electric Submersible Pumps”, SPE Gulf Coast Section - ESP Workshop in Houston, TX, April 1999.

Lackner, Gernot, Doty, D.R., Shirazi, S.A., Schmidt, Z., “Downhole Gas Separation in a Rotary Gas Separator,” SPE 52160, 1999 SPE Mid-Continent Operations Symposium, Oklahoma City, March 28-31, 1999.

Xu, J., Doty, D.R., Blais, R. N., Shahraki, A., Lea, J., “A Comprehensive Rod-Pumping Model and its Applications to Vertical and Deviated Wells,” SPE 52215, 1999 SPE Mid-Continent Operations Symposium, Oklahoma City, March 28-31, 1999.

Tang, Yula, Blais, R.N., Doty, D.R., Schmidt, Z., “A Mechanistic Model for Predicting Pressure Drop in Vertical Upward Two-Phase Flow,” ASME, February, 1999.

Xu, J., Shirazi, S.A., Doty, D.R., Schmidt, Z., Blais, R.N., “Prediction of Turbulent Friction in Rod Pumped Wells,” SPE paper 39800 presented at the 1998 Permian Basin Oil and Gas Recovery Conference in Midland, TX, March 25-27, 1998.

Gernot Lackner, Francisco J.S. Alhanati, Siamack A. Shirazi, Dale R. Doty, Zelimir Schmidt: “Numerical Simulation of the Gas-Liquid Flow in a Rotary Gas Separator,” ASME Paper presented in the Petroleum Production Technology Symposium at ETCE “98 in Houston, February 3-4, 1998.

Bertovic, D., D. R. Doty, R. N. Blais, A. Schmidt: "Calculating Accurate Gas-Lift Flow Rate Incorporating Temperature Effects,” SPE 37424, originally presented at 1997 SPE Production Operations Symposium in Oklahoma City, March 9-11, 1997.

Chokshi, R., Schmidt, Z., Doty, D. R.: “Expertimental Study and the Development of a Mechanistic Model for Two-Phase Flow Through Vertical Tubing, “SPE Paper 35676, presented at the Western Regional Meeting, Anchorage, Alaska, May 22-24, 1996.

Liao, T., Doty, D.R., Schmidt, Z.: “Investigation of Intermittent Gas-Lift by Mechanistic Modeling,” SPE 27852, presented at the 1995 SPE Production Operation Symposium, Oklahoma City, OK, April 2-4, 1995.

Alhanati, F.J.S., Sambaugi, S.R., Doty, D.R., Schmidt, Z.: "A Simple Model for the Efficiency of Rotary Separators," SPE 28525, presented at the 1994 SPE Annual Technical Conference and Exhibition, New Orleans, LA, September 25-28, 1994.

Tabouski, H., Doty, D.R., Schmidt, Z.: "Equation for Transient Gas Solubility Rates Improve Calculation of Volumetric and Work Efficiencies for Sucker Rod Pumps," SPE Paper 27852, presented at the Western Regional Meeting, Long Beach, CA, March 23-25, 1994.

Alhanati, F.J.S., Schmidt, Z., Doty, D.R., "Continuous Gas Lift Instability: Diagnosis, Criteria and Solutions," SPE Paper 26554, presented at the 1993 SPE Annual Technical Conference and Exhibition, Houston, TX, October 3-6, 1993.

Rastoin, S., Schmidt, Z., Doty, D.R., "A Review of Multiphase Flow Through Chokes," presented at the ASME International Symposium on Multiphase Flow in Wells and Pipelines, Anaheim, CA, November 8-13, 1992.

Acuna, H.G., Schmidt, Z., Doty, D.R., "Modeling of Gas Rates Through One Inch Nitrogen Charged Gas Lift Valves," SPE Paper 24839, presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, DC, October 4-7, 1992.

Sagar, R.K., Schmidt, Z., Doty, D.R., "A Mechanistic Model of a Nitrogen Charged Pressure Operated Gas Lift Valve," SPE Paper 24838 presented at the 1992 SPE Annual Technical Conference and Exhibition, Washington, DC, October 4-7, 1992.

Sachdeva, R., Doty, D.R., Schmidt, Z., "Performance of Axial Electric Submersible Pumps in a Gassy Well," presented at the SPE Rocky Mountain Regional Meeting, Casper, WY, May 18-21, 1992.

Chacin, J., Doty, D.R., Schmidt, Z., "Modeling and Optimization of Plunger Lift Assisted Intermittent Gas Lift Installations," SPE 23683, presented at the 1992 SPE Latin American Petroleum Engineering Conference.

Sachdeva, R., Doty, D.R., Schmidt, Z., "Performance of Electric Submersible Pumps in Gassy Wells," SPE 22767, presented at the 1991 SPE Annual Technical Conference and Exhibition, Dallas, TX, October 6-9, 1991.

Hepguler, G., Schmidt, Z., Doty, D.R., B lais, R.N., "Dynamic Model of Gas Lift Valve Performance," SPE 21637, presented at the Production Operations Symposium, Oklahoma City, OK, April 7-9, 1991.

Schmidt, Z., Doty, D.R., Agena, B., Liao, T., Brown, K.E., "New Developments to Improve Continuous-Flow Gas Lift Utilizing Personal Computers," paper SPE 20677, presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, LA, September 23-26, 1990.

Nieberding, H.A., Schmidt, Z., Blais, R.N., Doty, D.R., "Normalization of Nitrogen-Loaded Gas-Lift Valve Performance Data," paper SPE 20673, presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, LA, September 23-26, 1990.

Blais, R.N., Pedersen, J.G., Pedersen, B.K., Doty, D.R., Schmidt, Z., "Distinguishing Degree of Segregated and Dispersed Flow by Gamma Deusitometry," 36 International Instrumentation Symposium, Denver, Colorado, May 6-10, 1990.

Nishikiory, N., Redner, R., Doty, D.R., and Schmidt, Z., "An Improved Method for Gas Lift Allocation Optimization," paper SPE 19711, presented at the 1989 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, October 8-11, 1989.

Sagar, R., Doty, D.R., and Schmidt, Z., "Predicting Temperature Profiles in a Flowing Well," paper SPE 19702, presented at the 1989 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, October 8-11, 1989.

Pedersen, J., Pedersen, B., Doty, D.R., Blais, R.N., "Calibration of a Gamma-Ray Densitometer for Downhole void Fraction Measurement," 35th International Instrumentation Symposium, May 1, 1989.

Pedersen, J., Pedersen, B., Blais, R.N., Doty, D.R., "Flow Pattern Detection in Two-Phase, Gas-Liquid Vertical Flow by Gamma Densitometry," Bulletin of the American Physical Society, Vol. 34, Number 1, January 1989.

Hepguler, G., Z. Schmidt, R.N. Blais, and D.R. Doty, "Instrumentation for Dynamic Modeling of Gas-Lift Valves," Proceedings of ISA Aerospace Technology and Test Measurement Symposium, Albuquerque, New Mexico, May 2, 1988.

Schmidt, Z., Doty, D.R., "System Analysis for Sucker Rod Pumping," presented at the 1986 SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, October 6-8, 1986. (SPE 15426)

Blais, R.N., Schmidt, Z., Doty, D.R., Guler, N., "Test Facility for Measurement of Pressure Gradient in Large Diameter Vertical Pipes Carrying Two-Phase, Gas-Liquid Flows," 32nd Int. Instrumentation Symposium, Seattle, Washington, May 5-8, 1986.

Miyoshi, M., Schmidt, Z., Doty, D.R., "Slug Catcher Design for Dynamic Slugging in an Offshore Production Facility," presented at the SPE International Meeting of Petroleum Engineering, Beijing, Peoples Republic of China, March 17-20, 1986. (SPE 14124)

Vongvuthapornchai, S., Blais, R.N., Schmidt, Z., Doty, D.R., Brill, J.P., "Experimental Study of Pressure Wave Propagation in Two-Phase Mixtures," Fourth Adriatic Symposium of Oil Well Technology, Cavtat, Yugoslavia, October 14-17, 1985.

Torre, A.J., Schmidt, Z., Blais, R.N., and Doty, D.R., "Casing Heading in Flowing Oil Wells," presented at the SPE 1985 Production Operations Symposium, Oklahoma City, Oklahoma, March 10-12, 1985.

Z. Schmidt, D.R. Doty and D.R. Kunal, "Severe Slugging in Offshore Pipeline Riser-Pipe Systems," presented at Seminar on Offshore Natural Gas Technology, Dubrovnik-Yugoslavia, October 1984.

D.R. Doty, and Z. Schmidt, "An Improved Method for Sucker Rod Pumping," SPE 10249, presented at SPE Fall Meeting, San Antonio, Texas, October 1981.

## Others

Harun, A.F., Prado, M.G., Shirazi, S.A. and Doty, D.R., “An Improved Model for Predicting Separation Efficiency of a Rotary Gas Separator in ESP Systems,” SPE Paper 63031, paper prepared for presentation at the 2000 SPE Annual Technical Conference and Exhibition held in Dallas, Texas, 1–4 October 2000.

Harun, A.F.,Prado, M.G., Shirazi, S.A. and Doty, D.R., “Two-Phase Flow Modeling of Induces,” Paper No. ETCE00-PROD-10033, Proceedings of the ETCE 2000 / OMAE 2000 Joint Conference of ASME Petroleum Division, February 14-17, 2000, Houston.

Harun, A.F., Prado, M.G., Shirazi, S.A. and Doty, D.R., “Two-Phase Flow Modeling of Induces,” paper presented at the ETCE/OMAE 2000 Joint Conference of ASME Petroleum Division, Paper No. PROD-10033, February 14-17, 2000, Houston.

Harun, A.F., Prado, M.G., Shirazi, S.A., and Doty, D.R., “Improved Model for Predicting Separation Efficiency of a Rotary Gas Separator in ESP Systems, Proceedings – SPE Annual Technical Conference and Exibition, v PI, 2000, pp. 399-409.

Lackner, G., Doty, D.R., Shirazi, S.A., and Schmidt, Z., “Effect of Viscosity on Downhole Gas Separation in a Rotary Gas Separator,” SPE Paper 52160, in Proceedings of the SPE Mid-Continent Operations Symposium, Oklahoma City, March 1999.

Xu, J., Shirazi, S.A., Doty, D.R., Schmidt, Z., and Blais, R.N., “ Prediction of Turbulent Friction in Rod Pumped Wells,” in Proceeding of the 1998 SPE Permian Basin Oil and Gas Recovery Conference, SPE paper 39800, March 1998.

Bertovic, D., D. R. Doty, R. N. Blaix, A. Schmidt: "Calculating Accurate Gas-Lift Flow Rate Incorporating Temperature Effects, SPE 37424, JPT, issue on artificial lift (July, 1997), pp. 739-40.

MATH 3033 Introduction to Advanced Mathematics

MATH 4123 Linear Algebra and Matrix Theory

MATH 5013 Advanced Mathematical Modeling

MATH 7863 Special Topics in Mathematics

MATH 9986 Research and Dissertation