We present analytical solutions for capillary-controlled displacement in one dimension by use of fractional-flow theory. We show how to construct solutions with a spreadsheet that can be used for the analysis of experiments as well as matrix-block-scale recovery in field settings. The solutions can be understood as the capillary analog to the classical Buckley-Leverett solution (Buckley and Leverett 1942) for viscous-dominated flow, and are valid for cocurrent and countercurrent spontaneous imbibition (SI), as well as for arbitrary capillary pressure and relative permeability curves. They can be used to study the influence of wettability, predicting saturation profiles and production rates characteristic for water-wet and mixed-wet conditions. We compare our results with in-situ measurements of saturation profiles for SI in a water-wet medium. We show that the characteristic shape of the saturation profile is consistent with the expected form of the relative permeabilities. We discuss how measurements of imbibition profiles, in combination with other measurements, could be used to determine relative permeability and capillary pressure.
We present a new semianalytic method to solve the nonlinear pressure-diffusion equation at early time, before reservoir boundaries are encountered, and under constant bottomhole pressure (BHP), applicable to the analysis of unconventional reservoirs. We assume that the flow rate is inversely proportional to the square root of time since the beginning of production. The method is an extension of the semianalytic solution proposed by Schmid et al. (2011) for spontaneous imbibition; we replace the solution for saturation with one for pressure, while extending the functional form of the governing diffusion equation. The solution can accommodate arbitrary pressure-dependent nonlinear rock and fluid properties as well as production caused by desorption. The mathematical formulation is presented for a general nonlinear case and tested by use of synthetic data. Field production from the Barnett Shale is then used to estimate effective matrix permeability.
The model can be used to predict production if the rock and fluid properties are known, or can be used to constrain reservoir properties from production data. It is a complement to traditional pressure- or rate-transient analysis; if the response of a well for constant-pressure production can be determined, our method can be used to determine reservoir properties, without any approximations inherent in linearizing the flow equations.
We study Enhanced Oil Recovery (EOR) through Low Salinity (LS) waterflooding in a brown oil field. LS waterflooding is an emerging EOR technique in which water with reduced salinity is injected into a reservoir to improve oil recovery, as compared with conventional waterflooding, in which High Salinity (HS) brine or seawater are commonly used. The efficiency of this technique can be quantified at the well-scale by a Single Well Chemical Tracer Test (SWCTT), which is an in-situ method for measuring the Remaining Oil Saturation (ROS) after flooding the near-wellbore region with a displacing agent. Two SWCTTs were executed on a sandstone North African field. The tests were realized in sequence with seawater and LS water to evaluate the EOR potential at the well-scale.
Here, we propose the interpretation of these two SWCTTs. They were modeled through numerical simulations because of the presence of several non-idealities in the complex scenario considered. A recently-developed tracer simulator was employed to solve the reactive transport problem. This was used as a fast post-processing tool coupled with a conventional reservoir simulator. Model parameters were estimated within an inverse modeling framework, on the basis of an assisted history matching procedure that exploits the Metropolis Hastings Algorithm (MHA). Results were scaled up on a sector model of the field, and forecast scenarios that consider a field-scale implementation of this technique were defined.
The well-scale displacement efficiency gain associated with LS water, as compared with seawater, was evaluated. It was quantified as a ROS reduction of 8 saturation unit (s.u.), with a P10–P90 range of 3–15 s.u. Reservoir-scale simulations suggest that the associated ultimate oil recovery of the EOR pilot may be increased by 2% with LS water, with a P10–P90 range of 0.7–4.3%.
Overall, the LS EOR potential for a selected field was quantified through a robust and original workflow, based on SWCTT interpretation. This state-of-the-art procedure is now available for further applications. The simulated oil recovery improvement with LS water is promising, and leads the way to the implementation of an inter-well field trial.
This paper describes a simulation study of the low-salinity effect in sandstone reservoirs. The proposed mechanistic model allows differentiation of water composition effects and includes multi-ionic exchange and double layer expansion. The manifestation of these effects can be observed in coreflood experiments.
We define a set of chemical reactions, to describe the contribution of van der Waals forces, ligand exchange, and cation bridging to mobilization of residual oil. The reaction set is simplified by incorporating wettability weighting coefficients that reflect the contribution of different adsorbed ions to the wettability of the rock. Changes in wettability are accounted for by interpolation of the relative permeability and capillary pressure curves between the low and high salinity sets. We also construct and test simplified phenomenological models, one relating the change of the relative permeability to the concentration of a dissolved salinity tracer and another one to the concentration of a single adsorbed tracer.
The full mechanistic model, with multiple ion tracking, is in good qualitative agreement with experimental data reported in the literature. A very close agreement with the mechanistic model was obtained for a coreflood simulation using single tracer phenomenological models. The similarity of the results is explained by the fact that the most critical factor influencing the flow behavior was the function used to interpolate between the oil- and water-wet sets of saturation curves. Similar interpolation functions in different models lead to similar oil recovery predictions.
This study has developed a detailed chemical reaction model that captures both multicomponent ion exchange and double layer expansion effects, and can be used to improve understanding of low-salinity recovery mechanisms by analyzing their relative contributions. The approach of matching a tracer model to a detailed mechanistic model promises a route to the development of simplified, less computationally demanding proxy models for full field simulation studies.
Petvipusit, Kurt R. (Department of Earth Science and Engineering, Imperial College London) | Elsheikh, Ahmed H. (Institute of Petroleum Engineering, Heriot-Watt university, UK) | King, Peter R. (Department of Earth Science and Engineering, Imperial College London) | Blunt, Martin J. (Department of Earth Science and Engineering, Imperial College London)
The successful operation of CO2 sequestration relies on designing optimal injection strategies that maximise economic performance while guaranteeing long-term storage security. Solving this optimisation problem is computationally demanding. Hence, we propose an efficient surrogate-assisted optimisation technique with three novel aspects: (1) it relies on an ANOVA-like decomposition termed High-Dimensional Model Representation; (2) component-wise interactions are approximated with adaptive sparse grid interpolation; and (3) the surrogate is adaptively partitioned closer to the optimal solution within the optimisation iteration.
A High-Dimensional Model Representation (HDMR) represents the model output as a hierarchical sum of component functions with different input variables. This structure enables us to select influential lower-order functions that impact the model output for efficient reduced-order representation of the model. In this work, we build the surrogate based on the HDMR expansion and make use of Sobol indices to adaptively select the significant terms. Then, the selected lower-order terms are approximated by using the Adaptive Sparse Grid Interpolation (ASGI) approach. Once the HDMR is built, a global optimizer is run to decide: 1) the domain shrinking criteria; and 2) the centre point for the next HDMR building. Therefore, this proposed technique is called a walking Cut-AHDMR as it shrinks the search domain while balancing the trade-off between exploration and exploitation of the optimisation algorithm.
The proposed technique is evaluated on a benchmark function and on the PUNQ-S3 reservoir model. Based on our numerical results, the walking Cut-AHDMR is a promising approach: not only does it require substantially fewer forward runs in building the surrogate of high dimension but it also effectively guides the search towards the optimal solution. The proposed method provides an efficient tool to find optimal injection schedules that maximise economic values of CO2 injection in deep saline aquifers.
Augmented waterflooding is when a component is coinjected with water to modify the fractional-flow curve. Examples include polymer flooding, surfactant injection, low-salinity waterflooding, and carbonated-water injection (including applications related to carbon dioxide storage). The numerical simulation of these processes is a challenge for several reasons: The appropriate physical behavior needs to be incorporated consistently into empirical models of the fractional flow, whereas the solutions should minimize numerical dispersion, allowing the correct and accurate tracking of compositional variations.
Lower-order numerical simulations of these processes give excessive front smearing, requiring many thousands of gridblocks in one dimension to resolve the fronts adequately, rendering the predictions from 3D simulations dubious at best. These erroneous predictions are not caused by phase dispersion (the improper prediction of water velocity)--as in black-oil simulation, in which the effect is less significant--but occur because of the coupling of compositional dispersion with fractional flow. Small errors in composition alter the fractional flow, causing the development of incorrect wave speeds. The same effect is also seen in compositional simulation of gas injection.
We propose a simple method for streamline-based simulations that substantially reduces numerical dispersion. The method is rooted in the assumption of segregated flow within a gridblock. After comparing numerical and analytical results in one dimension, we implement the method into a 3Dstreamline-based simulator of polymer flooding that also incorporates a physically based model of the fluid rheology. We demonstrate that traditional simulation methods can vastly overestimate recovery, potentially leading to poor injection design and management decisions. We demonstrate the utility of our approach by suggesting optimal strategies for the design of polymer injection on the basis of our improved simulation technique.
We developed an injection strategy to recover moderately heavy oil and store carbon dioxide (CO2) simultaneously. Our compositional simulations are founded on pressure/volume/temperature-(PVT-) matched properties of oil found in an unconsolidated deltaic sandstone deposit in the Gulf of Paria, offshore Trinidad. In this region, oil density ranges between 940 and 1010 kg/m3 (9 to 18°API). We use countercurrent injection of gas and water to improve reservoir sweep and trap CO2 simultaneously; water is injected in the upper portion of the reservoir, and gas is injected in the lower portion. The two water-injection rates investigated, 100 and 200 m3/d, correspond to the water-gravity numbers 6.3 to 3.1 for our reservoir properties. We applied this injection strategy using vertical producers with two injection configurations: single vertical injector and a pair of horizontal parallel laterals in a simplified representation of the unconsolidated Forest sand found offshore Trinidad. Twelve simulation runs were conducted, varying injection-gas composition for miscible- and immiscible-gas drives, water-injection rate, and injection-well orientation. Our results show that water-over-gas injection can realize oil recoveries ranging from 17 to 30%. In each instance, more than 50% of injected CO2 remained in the reservoir, with less than 15% of the retained CO2 in the mobile phase.
Alyafei, Nayef (Imperial College London) | Gharbi, Oussama (Imperial College London) | Qaseminejad Raeini, Ali (Imperial College London) | Yang, Jianhui (Imperial College London) | Iglauer, Stefan (Curtin University) | Blunt, Martin J. (Imperial College)
Micro-CT scanning is a non-destructive technique that can provide three-dimensional images of rock pore space at a resolution of a few microns. . However, these greyscale images cannot be directly input into simulators to predict flow properties; they require image processing to segment the solid and void space in the rock. Dynamic and static single phase properties can then be computed using the images directly or on extracted equivalent network models. In this paper, we study the effect of imaging resolution (five different voxel sizes ranging from 6-20 μm) of Clashach and Doddington sandstone on predicted single phase properties (porosity and absolute permeability) and network properties. Experimental data is used to validate the predictions. The results suggest that the computed porosity was largely independent of resolution and in good agreement with the measured value, while image resolutions of a few microns are sufficient to determine the permeability of a high-permeability rock such as Doddington but may not be sufficient for lower permeability samples. The topologically representative networks are sensitive to resolution, adding additional smaller pores and throats as the resolution is increased. This latter reason was confirmed by a network extraction analysis that indicated the average throat radius was 6 µm, similar to the highest resolution used and insufficient to image all important features of the pore space properly.
We quantify the influence of the initial nonwetting-phase saturation and porosity on the residual nonwetting-phase saturation using data in the literature and our own experimental results on sandpacks and consolidated sandstones. These experiments were conducted at ambient or elevated pressure and temperature (ETP) conditions. The principal application of this work is for carbon capture and storage (CCS) where capillary trapping is a rapid and effective way to render the injected CO2 immobile, guaranteeing safe storage.
We introduce the concept of capillary-trapping capacity (Ctrap) which is the product of residual saturation and porosity that represents the fraction of the rock volume that can be occupied by a trapped nonwetting phase. We show that the measured trapping capacity reaches a maximum of approximately 11% for porosities of 22%, which suggests an optimal porosity for CO2 storage.
CCS is a method to reduce anthropogenic CO2 emissions and thereby mitigate potentially damaging climate change (Haszeldine 2009; IPCC 2005). In the CCS context, capillary trapping has been identified as a major mechanism to store CO2 in the subsurface reliably and rapidly (Juanes et al. 2006; Flett et al. 2004; Kumar et al. 2005; Qi et al. 2009; Hesse et al. 2008; Obi and Blunt 2006). This means that significant quantities of CO2 can be stored by capillary forces and it is not necessary to rely solely upon stratigraphic trapping.
Capillary trapping has been measured in oil/water, gas/water, and three-phase gas/water/oil systems (Agarwal 1967; Aissaoui 1983; Al-Mansoori et al. 2010; Chierici et al. 1963; Crowell et al. 1966; Delclaud 1991; Firoozabadi et al. 1987; Flett et al. 2004; Geffen et al. 1952; Iglauer et al. 2010; Irle and Bryant 2005; Jerauld 1997; Kantzas et al. 2001; Kleppe et al. 1997; Kralik et al. 2000; Land 1968a, b; Land 1971; Ma and Youngren 1994; McKay 1974; Mulyadi et al. 2000; Naar and Henderson 1961; Pentland et al. 2010a, b; Pentland et al. 2011; Plug 2007; Suekane et al. 2008a, b). While literature data have been mainly determined for gas/brine systems, CO2 is injected as a supercritical (sc) phase in CCS projects into reservoirs at depths of approximately 800 m or more. In the sc state, CO2 has a density similar to that of a liquid and a viscosity similar to that of a gas.
Current commercial simulators for polymer flooding often make physical assumptions that are not consistent with available experimental data and pore-scale modeling predictions. This may lead to overly optimistic recovery predictions for shear-thinning polymers, while the potential advantages of reducing flow rate or using shear-thickening agents are overlooked.
We develop a streamline-based simulator that overcomes these limitations and demonstrate how it can be used to design polymer-flooding projects. The simulator implements an iterative approach to solve the pressure field because the pressure depends on the aqueous-phase viscosity, which, in turn for non-Newtonian fluids, depends on shear stress and, hence, the pressure gradients. This is in contrast to the common approach in commercial simulators where this viscosity/pressure interdependence is ignored, leading to overestimation of sweep efficiency. Furthermore, in the simulator, non-Newtonian viscosities are defined to be cell-centered while current simulators use a face-centered approach, thereby overpredicting viscosities and the stability of the displacing fronts. In addition, we use a physically based rheological model where non-Newtonian viscosities in two-phase flow are taken at actual effective stresses instead of single-phase equivalents.
To validate the simulator, we construct 1D analytical solutions for waterflooding with a non-Newtonian fluid. We then compare our results to those from commercial simulators. We discuss the significance of current assumptions to demonstrate the effect of non-Newtonian behavior on sweep efficiency and recovery.