A novel laboratory method for simultaneous determination of relative permeability and capillary pressure from laboratory corefloods
Date
2023
Authors
Hemmati, Nassim
Editors
Advisors
Zeinijahromi, Abbas
Borazjani, Sara
Borazjani, Sara
Journal Title
Journal ISSN
Volume Title
Type:
Thesis
Citation
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Abstract
Hereby I present a PhD thesis by publications. The thesis includes eight journal papers, which have been already published or submitted, and two conference papers. The journals have high impact factor, Journal of Petroleum Science and Engineering – 4.757, Journal of Hydrology – 6.708, Journal of Fuel – 8.035, Journal of Geocience and Engineering – 4.757. The thesis designed a novel advanced laboratory method for simultaneous determination of relative phase permeability and capillary pressure from the same coreflood test. The novel steady-state-transient-test (SSTT) extends the classical steady state method by using the transient data between the sequential steady states along with steady-state data. The significance of this achievement is determined by relative phase permeability and capillary pressure being major model functions which determine two-phase flow in natural porous reservoirs. Besides, separate determination of relative permeability from corefloods and capillary pressure from other tests yields incompatibility of the data and significant errors in prediction of two-phase flow in porous media. The incomplete list of applications of SSTT method includes subterranean CO2 and H2 storage in subterranean reservoirs, enhanced geothermal projects, subterranean undersaturated flows in aquifers, oil and gas production from geological formations. Predictive modelling in all above mentioned cases is based on reliable model functions for relative permeability and capillary pressure. So, the importance of this topic of applied research is determined by widely spread two-phase flows in porous media, and by vital necessity to determine three curves of the phase relative permeabilities and capillary pressure from the same coreflood. Despite not being published, the idea of simultaneous determination of relative phase permeability and capillary pressure from steady-state two-phase tests with the use of transition data between the sequential injections with different water-cuts have been discussed in the community occasionally. Moreover, some in-house studies in Shell and Petrobras documented both steady state and transitional data. The problem was that very few transition points can be registered, and the data are extremely scattered. Consequently, the inverse problem for determining relative phase permeability and capillary pressure from steady state and transitional data become ill-posed. The following innovations developed in this thesis allows to resolve the above-mentioned shortcomings, (i) Formulating type-curves for transitional evaluation of pressure drop between the sequential injections; (ii) Planning and design of the laboratory SSTT to optimize injected velocity, sampling volumes and frequencies for given properties of rocks and fluids; (iii) Designing the inverse solution algorithm separately for the saturation interval between sequential injections; (iv) Defining the model for relative permeability and capillary pressure; and (v) Resolving inverse problem in such a way that the number of model coefficients does not exceed the number of degrees of freedom of the experimental data array. The item (i) was achieved by multiple numerical modelling prior to SSTT performance for concrete fluids and rocks. The relative permeability and capillary pressure for this massive sensitivity study is taken from the similar cases, for sister cores, based on the available literature data. Altogether, the thesis encompasses 6 well documented literature sources for steady state corefloods, and 10 original laboratory tests performed in laboratory of The University of Adelaide. In all those cases, three parametric exponential type curves have been observed. The scattered transitional data are approximated using those type curves, resulting in regularisation of the ill-posed inverse problem. The important part of type curve definition is introduction of the plot stabilisation period versus water-cut, allowing determining the transitional time interval depending on wettability for type curves. Stabilisation periods versus water-cut are reviewed by the asymptotic analysis of the transient solution near the end-point saturation. The innovation (ii) encompasses determination of the test parameters – flow velocity, frequencies and volumes of samples, number and values of water-cuts in SSTT – using the theoretical and operational criteria. The theoretical criteria include capillary number, assuring dominance of capillary forces over viscous forces on the pore level and capillary-viscous ratio as a similarity criterion on the core scale. Additional theoretical criteria include low gravity number, preventing separation of water and gas during flow in the core, and negligible relaxation time of capillary imbibition into low-permeable inclusions if compared with time of one pore volume injected. The operational criteria include accuracy of measurement of pressure, fractional flow, rates, minimum sampling time. Besides, three constants of the transitional type curves can be determined if at least three transition samples are collected, which is also the operational criteria. The innovation (iii) includes iterative procedure for solving the inverse problem at each interval between sequential water-cuts. In the case of water-wet cores where saturation and relative permeability for residual oil are directly measured at the final stage of water-cut 𝐹𝑛 = 1, the inverse solution is determined from residual saturation downwards where the initial guess for next interval is taken as a result of solution at the previous interval. In all laboratory data treated in this thesis (16 tests), the Kr and Pc data as calculated for different intervals allocated on the overall global curves. The innovation (iv) corresponds to the choice of either three-parametric van Genuchten approximation or Skjaeveland formula for capillary pressure depending on either available laboratory data or feasibility of the generation under the specific conditions of rocks and fluids. The basic criteria here is exceeding of the number of degrees of freedom by experimental data array of the number of model parameters. In particular, inserting bump flooding at the end of SSTT allows determining saturation and relative permeability for residual oil, reducing the number of unknows and allowing applications of four-parametric Skjaeveland formula. The designed SSTT method have been extended for water/gas, high-salinity water/oil, lowsalinity water/oil fluids in rocks with different wettability. The validity of the developed SSTT method and inverse solver is based on: (i) high match of the measured transient pressure drop data with the mathematical model; (ii) exact coincidence of the pressure drop and average saturation during steady states as measured in lab and obtained by modelling; (iii) coincidence of the saturation and relative permeability as obtained from two independent sources – by SSTT data tuning, and by beam intercept method; (iv) location of the Kr and Pc segments obtained for the intervals between two consequent water-cuts, on the same Kr and Pc curves for the overall interval of water-cut from zero to one.
School/Discipline
School of School of Chemical Engineering
Dissertation Note
Thesis (Ph.D.) -- University of Adelaide, School of Chemical Engineering, 2023
Provenance
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