Experimental Investigation of the Recovery of Gas and Oil by Spontaneous Water Imbibition

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Coupling mechanisms of displacement and imbibition in pore-fracture system of tight oil reservoir

Fracturing and water flooding have been popular technologies to achieve the effective development of tight oil reservoirs in recent years. However, in the late stage of production, the oil recovery rate declines with a rapid increase in the water cut. Water huff-puff could improve reservoir energy; however, the displacement and imbibition in the micro-nano pore throat and fracture systems are complex processes with unclear characteristics and position. Therefore, it is urgent to study the coupling mechanisms of oil-water displacement and imbibition in tight oil reservoirs. In this work, based on the phase field method of COMSOL Multiphysics software, we establish a two-dimensional microscopic numerical simulation model of the pore-fracture system, and carry out displacement-imbibition simulation programs of different injection media (water and surfactant) and injection methods (displacement, displacement-imbibition). By comparing the saturations and pressure distributions of different simulation programs, we analyze the changes in the oil-water interface, and summarize the action conditions of counter-current imbibition and pore throat limit. Finally, reasonable development suggestions are proposed for tight oil reservoirs.Cited as: Pi, Z., Peng, H., Jia, Z., Zhou, J, Cao, R. Coupling mechanisms of displacement and imbibition in pore-fracture system of tight oil reservoir. Capillarity, 2023, 7(1): 13-24. https://doi.org/10.46690/capi.2023.04.0

Simulation study of co-current spontaneous imbibition

Master's thesis in Petroleum engineeringSpontaneous imbibition is the main driving mechanism for obtaining high recovery from the naturally fractured reservoirs with low permeable matrix. The present thesis presents the results of a simulation study of one-dimensional, co-current spontaneous imbibition in a strongly water-wet sample. Experimental data used for this work was taken from Haugen et al. (2014, 2015). The circumstances of the experiments were characterized by one end face of the core to be open to brine (an inlet) and the other end face to be open to oil (an outlet). Under this Two-Ends-Open (TEO) boundary condition both co- and counter-current flow can take place at the same time, in other words, the inlet can be produced counter-currently and the outlet - co-currently. The simulation program IORCoreSim was used in this thesis to model the system. The water-oil flow was developed by using Corey relative permeability type and J-function capillary pressure correlation. The experiments were matched by establishing relative permeability and capillary pressure curves. After the match was obtained, the saturation functions were used to perform the sensitivity analysis. It was done by varying several parameters: mobility ratio by holding one of viscosities fixed while changing the other, then both viscosities at fixed mobility ratio, and furthermore capillary back pressure. The last two cases were performed at M=0.01 and M=11. With increased oil viscosity at fixed water viscosity, the imbibition rate was observed to be lower with decreasing co-current recovery, while counter-current recovery was increased. The breakthrough time was delayed. With increased water viscosity at fixed oil viscosity, the trends for inlet and outlet recovery were similar with increased imbibition time. The breakthrough time was also delayed. For fixed mobility ratio with varying both viscosities, the trend showed that increased viscosity ratio has no impact on total production and co-current recovery was reduced as M increased whereas counter-current increased. The capillary back pressure influenced essentially the system at M=11 when compared with M=0.01. Counter-current recovery decreased with increasing capillary back pressure at values beyond the threshold capillary pressure

Matrix/fracture transfer function during counter-current spontaneous imbibition in naturally fractured reservoirs

Naturally fractured reservoirs are abundant in the earth’s crust and host a substantial percentage of oil reserves globally. The main mechanism of oil recovery during waterflooding of these types of reservoirs is through spontaneous imbibition of water into the matrix and simultaneous counter-current flow of oil out of the matrix. Understanding the predominate recovery mechanism enhances reserves estimates, accurate simulation forecasts and overall sound development plans. Dual-porosity and dual-permeability simulations are used in the industry to simulate waterfloods in naturally fractured reservoirs. One of the key parameters in these simulations is the matrix-fracture transfer term, which is not well understood and modeled, especially in mixed-wet reservoirs. The same transfer term is used for primary, secondary and tertiary recovery processes, though it should change depending on the mechanisms of oil recovery. The key mechanism during primary recovery is depressurization, not spontaneous imbibition. The main goal of this research is to develop an accurate representation of the matrix-fracture transfer term in waterflooding for dual-porosity simulators. The analytical and semi-analytical solutions for 1D counter-current imbibition were studied for defining the exact solution in fractured porous media. Fine-grid, single-porosity numerical solutions were developed that are consistent with the 1D analytical solutions, in conjunction with coarse-grid single-porosity conceptual models. Both single-porosity models are used as reference against dual-porosity conceptual models to address the built-in matrix-fracture transfer terms through recovery of the matrix element. The error in simulation was defined as the difference in recoveries between the fine-grid single-porosity solution and the dual-porosity solutions. A detailed investigation of both rock and fluid inputs affecting transfer terms in dual-porosity was made in an effort to match the transient solution obtained from fine-grid single-porosity models. The inclusion of transient effect in dual-porosity requires optimizing the following inputs which are shape factor, capillary exponent and oil relative permeability exponent. Two main processes were proposed for optimization. Firstly, an accuracy-based Latin Hyper Cube sampling method was utilized that converged to the solution quickly. Secondly, utilizing a machine learning algorithm (specifically an Artificial Neural Net model) that predicts recovery accuracy based on the aforementioned chosen inputs. The machine learning model needed many iterations to converge to a solution.Petroleum and Geosystems Engineerin

Modeling two-phase flow of immiscible fluids in porous media: Buckley-Leverett theory with explicit coupling terms

Continuum models that describe two-phase flow of immiscible fluids in porous media often treat momentum exchange between the two phases by simply generalizing the single-phase Darcy law and introducing saturation-dependent permeabilities. Here we study models of creeping flows that include an explicit coupling between both phases via the addition of cross terms in the generalized Darcy law. Using an extension of the Buckley-Leverett theory, we analyze the impact of these cross terms on saturation profiles and pressure drops for different couples of fluids and closure relations of the effective parameters. We show that these cross terms in the macroscale models may significantly impact the flow compared to results obtained with the generalized Darcy laws without cross terms. Analytical solutions, validated against experimental data, suggest that the effect of this coupling on the dynamics of saturation fronts and the steady-state profiles is very sensitive to gravitational effects, the ratio of viscosity between the two phases, and the permeability. Our results indicate that the effects of momentum exchange on two-phase flow may increase with the permeability of the porous medium when the influence of the fluid-fluid interfaces become similar to that of the solid-fluid interfaces

Early- and Late-Time Prediction of Counter-Current Spontaneous Imbibition, Scaling Analysis and Estimation of the Capillary Diffusion Coefficient

Solutions are investigated for 1D linear counter-current spontaneous imbibition (COUSI). It is shown theoretically that all COUSI scaled solutions depend only on a normalized coefficient Λn (Sn) with mean 1 and no other parameters (regardless of wettability, saturation functions, viscosities, etc.). 5500 realistic functions Λn were generated using (mixed-wet and strongly water-wet) relative permeabilities, capillary pressure and mobility ratios. The variation in Λn appears limited, and the generated functions span most/all relevant cases. The scaled diffusion equation was solved for each case, and recovery vs time RF was analyzed. RF could be characterized by two (case specific) parameters RFtr and lr (the correlation overlapped the 5500 curves with mean R2=0.9989): Recovery follows exactly RF=T0.5n before water meets the no-flow boundary (early time) but continues (late time) with marginal error until RFtr (highest recovery reached as T0.5n) in an extended early-time regime. Recovery then approaches 1, with lr quantifying the decline in imbibition rate. RFtr was 0.05 to 0.2 higher than recovery when water reached the no-flow boundary (critical time). A new scaled time formulation Tn=t/τTch accounts for system length L and magnitude D¯¯¯¯ of the unscaled diffusion coefficient via τ=L2/D¯¯¯¯ , and Tch separately accounts for shape via Λn. Parameters describing Λn and recovery were correlated which permitted (1) predicting recovery (without solving the diffusion equation); (2) predicting diffusion coefficients explaining experimental recovery data; (3) explaining the challenging interaction between inputs such as wettability, saturation functions and viscosities with time scales, early- and late-time recovery behavior.publishedVersio

Numerical simulation of co-current and counter-current imbibition

Master's thesis in Petroleum engineeringSpontaneous imbibition (SI) is a very important mechanism for oil recovery in naturally fractured reservoirs. Several studies have indicated that counter-current oil production is much slower and give lower ultimate oil recovery than that of co-current production. This thesis presents an investigation of the relationship between co-current and counter-current relative permeabilities and their effect on production rates and ultimate oil recovery. SI into strongly water-wet low-permeability chalk has been investigated by numerical simulations using ECLIPSE 100. Two independent experimental studies have been considered, dividing this thesis into two parts. In part 1 counter-current relative permeability curves obtained by history matching experimental data by Standnes (2004) were used in co-current simulations. Unexpected results were found, in which simulations showed too fast oil recovery rates when counter-current relative permeabilities were included in the model. Further investigation showed inconsistency within experimental data and certain SI tests were considered unrepresentative. As further comparison would give inconsistent results, part 2 was introduced. For part 2, counter-current simulations were run with co-current relative permeability curves established by history matching experimental data by Bourbiaux and Kalaydjian (1990). Too fast oil recovery rates were observed. The half-recovery time was underestimated by approximately 50 %, which is in agreement with results found by Bourbiaux and Kalaydjian (1990). Exact prediction of counter-current experimental data was obtained by reducing both oil and water relative permeabilities including endpoints, by 50 % or by increasing the Corey exponents for oil and water by 45 %, however, with fixed endpoints. Since SI is described by a diffusion equation model, a relationship between the capillary diffusivity coefficient (CDC) and oil recovery curves for certain SI tests was investigated. A relationship is proposed were the oil recovery curve is expressed as a function of CDC value and curve shape (when plotted against normalized water saturation). The numerical investigation in this thesis underlines the importance of considering both co-current and counter-current conditions when evaluating the oil recovery potential on reservoir rocks experimentally, as inconsistencies may arise when results are scaled to reservoir conditions.submittedVersio

Numerical Investigation of Two-Phase Flow through a Fault

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Mathematical analysis, scaling and simulation of flow and transport during immiscible two-phase flow

Fluid flow and transport in fractured geological formations is of fundamental socio-economic importance, with applications ranging from oil recovery from the largest remaining hydrocarbon reserves to bioremediation techniques. Two mechanisms are particularly relevant for flow and transport, namely spontaneous imbibition (SI) and hydrodynamic dispersion. This thesis investigates the influence of SI and dispersion on flow and transport during immiscible two-phase flow. We make four main contributions. Firstly, we derive general, exact analytic solutions for SI that are valid for arbitrary petrophysical properties. This should finalize the decades-long search for analytical solutions for SI. Secondly, we derive the first non-dimensional time for SI that incorporates the influence of all parameters present in the two-phase Darcy formulation - a problem that was open for more than 90 years. Thirdly, we show how the growth of the dispersive zone depends on the flow regime and on adsorption. To that end we derive the first known set of analytical solutions for transport that fully accounts for the effects of capillarity, viscous forces and dispersion. Finally, we provide numerical tools to investigate the influence of heterogeneity by extending the higher order finite-element finite-volume method on unstructured grids to the case of transport and two-phase flow

Recent advances in spontaneous imbibition with different boundary conditions

Spontaneous imbibition plays an important role in many practical processes, such as oil recovery, hydrology, and environmental engineering. The development in spontaneous imbibition goes fast in the past few years. In this paper, we focus on boundary conditions of spontaneous imbibition, which has important effects on spontaneous imbibition rate and efficiency. We introduce the fundamental physical mechanism of spontaneous imbibition with different boundary conditions by capillary model. Then, the studies of spontaneous imbibition in core scale are reviewed. The feature of spontaneous imbibition with different boundary conditions is discussed and the relative permeability for co- and counter-current imbibition is analyzed. The scaling of imbibition data with different boundary condition is also discussed by combination of experimental and numerical methods. At last, the analytical model of spontaneous imbibition is discussed.Cited as: Meng, Q., Cai, J. Recent advances in spontaneous imbibition with different boundary conditions. Capillarity, 2018, 1(3): 19-26, doi: 10.26804/capi.2018.03.0