W.R. Rossen

New Capillary Number Definition for Displacement of Residual Nonwetting Phase in Natural Fractures

We propose a new capillary number for flow in fractures starting with a force balance on a trapped ganglion in a fracture. The new definition is validated with laboratory experiments using five distinctive model fractures. Capillary desaturation curves were generated experimentally using water-air forced imbibition. The residual saturation-capillary number relationship obtained from different fractures, which vary in aperture and roughness, can be represented approximately by a single curve in terms of the new definition of the capillary number. They do not fit a single trend using the conventional definition of the capillary number.

Influence of foam on the stability characteristics of immiscible flow in porous media

Accurate field-scale simulations of foam enhanced oil recovery are challenging, due to the sharp transition between gas and foam. Hence, unpredictable numerical and physical behavior is often observed, casting doubt on the validity of the simulation results. In this paper, a thorough stability analysis of the foam model is presented to validate the simulation results. We study the effect of a strongly non-monotonous total mobility function arising from foam models on the stability characteristics of the flow. To this end, we apply the linear stability analysis to nearly discontinuous relative permeability functions and compare the results with those of highly accurate numerical simulations. In addition, we present a qualitative analysis of the effect of different reservoir and fluid properties on the foam fingering behavior. In particular, we consider the effect of heterogeneity of the reservoir, injection rates, and foam quality. Relative permeability functions play an important role in the onset of fing...

Characteristic Fracture Spacing in Primary and Secondary Recovery for Naturally Fractured Reservoirs

Summary If the aperture distribution is broad enough in a naturally fractured reservoir, even one where the fracture network is highly inter-connected, most fractures can be eliminated without significantly affecting the flow through the fracture network (Gong and Rossen, 2016). During a waterflood or enhanced-oil-recovery (EOR) process, the production of oil depends on the supply of injected water or EOR agent. This suggests that the characteristic fracture spacing for the dual-porosity/dual-permeability simulation of waterflood or EOR in a naturally fractured reservoir should account not for all fractures but only the relatively small number of fractures carrying almost all the injected water or EOR agent (“primary,” as opposed to “secondary,” fractures). In contrast, in primary production even a relatively small fracture represents an effective path for oil to flow to a production well. This distinction means that the “shape factor” in dual-permeability reservoir simulators and the repeating unit in homogenization should depend on the process involved: specifically, it should be different for primary and secondary or tertiary recovery. We test this hypothesis in a simple representation of a fractured region with a non-uniform distribution of fracture flow conductivities. We compare oil production, flow patterns in the matrix, and the pattern of oil recovery with and without the “secondary” fractures that carry only a small portion of injected fluid. The role of secondary fractures depends on a dimensionless ratio of characteristic times for matrix and fracture flow (Peclet number), and the ratio of flow carried by the different fractures. In primary production, for a large Peclet number, treating all fractures equally is a better approximation than excluding secondary fractures; the shape factor should reflect both primary and secondary fractures. For a sufficiently small Peclet number, it is more accurate to exclude the secondary fractures. For waterflood or EOR, in most cases examined, the appropriate shape factor or repeating-unit size should reflect both primary and secondary fractures. If secondary fractures are much narrower than primary fractures, then it is more accurate to exclude them. Yet-narrower “tertiary fractures” are not always helpful for oil production, even if they are more permeable than matrix. They can behave as capillary barriers to imbibition, reducing oil recovery. We present a new definition of Peclet number for primary and secondary production in fractured reservoirs that provides a more accurate predictor of dominant recovery mechanism in fractured reservoirs than the previously published definition.

SAG Foam Flooding in Carbonate Rocks

Foam is used in gas-injection EOR processes to reduce the mobility of gas, resulting in greater volumetric sweep. SAG (Surfactant Alternating Gas) is a preferred method of injection as it results in greater injectivity in the field, but designing a successful process requires knowledge of foaming performance at very high foam qualities (gas fractional flows). Here the use of foam in low-permeability (~1 mD) Indiana Limestone cores for SAG foam applications is studied. Coreflood experiments were performed for a range of foam qualities at high pressure (100 bar), elevated temperature (55°C), high salinity (200,000 ppm) and in the presence of crude oil. The effectiveness of the foam was studied by differential pressure measurements along the core. Foam was still able to form under these stringent conditions, but it was a relatively weak foam (i.e. its ability to reduce gas mobility is modest). For one surfactant formulation, further analysis of the experimental results show that the foam would be able to maintain mobility control over the displaced phase, thus providing a stable displacement front, and that it can be used in a SAG foam process in these formations. For a second formulation the non-monotonic nature of the fractionalflow data require further investigation before scale-up to the field. In addition, further coreflood experiments were carried out using heterogeneous, vuggy Edwards White cores with even lower permeability (~0.5 mD). These experiments were performed to determine whether foaming is possible in heterogeneous media and especially to investigate the effects of disconnected vugs on the foaming performance. CT scans were taken during the period of foam injection to determine saturation profiles within the core. Foam was able to form inside these cores, but inside the vugs foam segregation was observed with liquid pockets visible in the bottom of the vugs and gas in the remainder. This segregation was only a local effect though, confined to the vug itself, and foam was able to persist in the rest of the core.

Discerning in situ performance of an eor agent in the midst of geological uncertainty

An enhanced-oil-recovery pilot test has multiple goals, among them to verify the properties of the EOR agent in situ. Given the complexity of EOR processes and the inherent uncertainty in the reservoir description, it is a challenge to discern the properties of the EOR agent in situ. We present a simple case study to illustrate this challenge: a polymer EOR process in a 2D layer-cake reservoir. The intended polymer design value is 21 cp in situ but we allow it might be ¼ that intended in the simulations. We test whether the signals of this difference at injection and production wells would be statistically significant in the midst of the geological uncertainty. We compare the deviation caused by loss of polymer viscosity to the scatter caused by the geological uncertainty at the 95% confidence level. Among the signals considered, the rate of rise in injection pressure with polymer injection and maximum injection pressure in the injector give the most reliable indications of whether a polymer viscosity was maintained in situ. Arrival time of the oil bank, minimum oil cut before oil bank arrival and polymer breakthrough time also give a statistically significant indication.