Zhenzihao Zhang

Bacterial collective behaviour emerges from the interplay of three distinct dynamical processes: quorum sensing (QS) mediates density-dependent gene regulation, chemotaxis directs movement along chemical gradients, and flocking aligns individual trajectories into coherent group motion. While each process has been studied extensively in isolation, no unified framework has integrated all three into a single mathematical model. Here, we present a deterministic coupled ordinary differential equation (ODE) and partial differential equation (PDE) framework that links QS-mediated phenotypic switching to Cucker–Smale flocking and Keller–Segel chemotaxis. Our mean-field reduction reveals a saddle-node bifurcation in the quorum-sensing-to-flocking transition: when the autoinducer concentration crosses a critical threshold, bacteria switch from fast, disordered, chemotactically driven planktonic motion (i.e., bacterial swimming, 2–2.5 μm/s (bulk)) to slow or fast, highly aligned, aggregation-prone swarm behaviour (5 ± 2 μm/s) and further to aggregation and biofilm-associated sessibility. Numerical simulations of the agent-based ODE model show that this switch drives spontaneous aggregation at chemoattractant sources, with flocking order peaking before the QS transition and collapsing as clusters form. A spatially resolved PDE–ODE hybrid confirms that autoinducer fields develop localized hotspots that coincide with bacterial aggregates, creating a positive feedback loop between density, signalling, and cohesion. Bifurcation analysis identifies a hysteresis region where small perturbations in basal autoinducer production can trigger hysteric transitions between planktonic and sessile states. These results provide a mechanistic basis for the well-documented but poorly understood motility–sessility switch in bacteria such as Pseudomonas aeruginosa and establish a quantitative platform for engineering synthetic microbial consortia with programmed collective behaviours.

The interpretation of post-fracture pressure decay (PFPD) data has long been a problem, with the advancement of hydraulic fracturing technology into zipper fracturing, the post-fracture pressure decay time has grown by multiple times. The post-fracture pressure decay now has sufficient time and data for analysis. In this study, we extend the fracture area estimation technique developed for diagnostic fracture injection test (DFIT) to PFPD scenario with multiple fractures, as a result of multiple clusters and more, as the major difference. The method was verified with ResFrac® simulation results, with the numerical simulator-generated results accurately overlapping the theory-calculated fracture total area. The developed method requires minimum principal horizontal stress, ie. Shmin, which is retrieved and extracted from DFIT test interpretation results. We then applied the developed technique to a pilot study to interpret two laterals’ 3 stages’ fracture areas and obtained reasonable estimations.

When considering multiphase flow scenarios, the interpretation of petrophysical properties poses significant challenges for production forecasts and reservoir modeling. The findings of the numerical modeling were therefore subject to uncertainty because characteristics like relative permeability and capillary pressure curve were hardly ever bound by interpretations. The uncertainty may result in inaccurate predictions of reservoir performance and skewed perceptions of the reservoir. Due to the difficulty in directly interpreting such property from the available field data and the expensive cost of coring, analyses or experimental measurements to determine relative permeability and capillary pressure were infrequently carried out. Such a gap would be filled by a straightforward yet rigorous method. In this study, we develop production projections for a wide range of three-phase compositional volatile oil reservoirs. Then, we used an artificial neural network to figure out how petrophysical characteristics and production data relate to one another. The artificial neural network model was adjusted, and the final trained model was tested blindly to determine how well it predicted permeability, multiphase relative permeability, and capillary pressure data. For the testing scenarios, consistency is seen between the predicted values and the original ones, despite some mispredictions being present. To provide production projections that can be compared to those from the reservoir model that include the initial petrophysical characteristic, the anticipated properties are then propagated into reservoir models. The comparison findings show that for 65/59/34 out of 74 testing scenarios, the reservoir model with artificial neural network-predicted features can anticipate oil/gas/water output with < 20% inaccuracy. With the developed artificial neural network tool, the reservoir engineers can evaluate the three-phase relative permeability surface from rate-transient data conveniently improving the accuracy of the relative permeability data implemented by history matching or from core experiments which sometimes are extremely expensive. The findings of this study can help for a better understanding of the relationships between three-phase rate-transient data and the relative permeability surface as well as the horizontal/vertical permeability.

The current practice for multi-fractured horizontal well development in low-permeability reservoirs is to complete the full length of the well with evenly spaced fracture stages. Given methods to evaluate along-well variability in reservoir quality and to predict stage-by-stage performance, it may be possible to reduce the number of stages completed in a well without a significant sacrifice in well performance. Provision and demonstration of these methods is the goal of the current two-part study. In Part 1 of this study, reservoir and completion quality were evaluated along the length of a horizontal well in the Montney Formation in western Canada. In the current (Part 2) study, the along-well reservoir property estimates are first used to forecast per-stage production variability, and then used to evaluate production performance of the well when fewer stages are completed in higher quality reservoir. A rigorous and fast semi-analytical model was used for forecasting, with constraints on fracture geometry obtained from numerical model history matching of the studied Montney well flowback data. It is concluded that a significant reduction in the number of stages from 50 (what was implemented) to less than 40 could have yielded most of the oil production obtained over the forecast period.

Straight-line analysis (SLA) methods, which are a sub-group of model-based techniques used for rate-transient analysis (RTA), have proven to be immensely useful for evaluating unconventional reservoirs. Transient data can be analyzed using SLA methods to extract reservoir/hydraulic fracture information, while boundary-dominated flow data can be interpreted for fluid-in-place estimates. Because transient flow periods may be extensive, it is also advantageous to evaluate the volume of hydrocarbons-in-place contacted over time to assist with reserves assessment. The new SLA method introduced herein enables reservoir/fracture properties and contacted fluid-in-place (CFIP) to be estimated from the same plot, which is an advantage over traditional SLA techniques. The new SLA method utilizes the Agarwal (2010) approach for CFIP estimation, extended to variable rate/pressure data for low permeability (unconventional) reservoirs. A log-log plot of CFIP versus material balance time (for liquids) or material balance pseudo-time (for gas) is created, which typically exhibits power-law behavior during transient flow, and reaches a constant value (original fluid-in-place, OFIP) during boundary-dominated flow. Although CFIP calculations do not assume a flow geometry, the SLA method requires this to extract reservoir/fracture information. Herein, transient linear flow is assumed, and used for the SLA method derivation, which allows the linear flow parameter (LFP) to be extracted from the y-intercept (at material balance time or material balance pseudo-time= 1 day) of a straight-line fit through transient data. OFIP can also be obtained from the stabilization level of the CFIP plot. Validation of the new SLA method for an undersaturated oil case is performed through application to synthetic data generated with an analytical model. Thenew SLA results in estimates of LFP and OFIP that are in excellent agreement with model input (within 2%). Further, the results are consistent with the traditional SLA methods used to estimate LFP(e.g. the square-root of time plot) and OFIP (e.g. the flowing material balance plot). Practical application of the new SLA method is demonstrated using field cases and experimental data. Field cases studied include online oil production from a multi-fractured horizontal well (MFHW) completed in a tight oil reservoir, and flowback water production from a second MFHW, also completed in a tight oil reservoir. Experimental (gas) data generated using a recently-introduced RTA core analysis technique, were also analyzed using the new SLA method. In all cases, the new SLA method results are in excellent agreement with traditional SLA methods. The new SLA method introduced herein is an easy-to-apply, fully-analytical RTA technique that can be used for both reservoir/fracture characterization and hydrocarbons-in-place assessment. This method should provide important, complementary information to traditionally-used methods, such as square-root of time and flowing material balance plots, which are commonly used by reservoir engineers for evaluating unconventional reservoirs.

This study developed a data-driven forecasting tool that predicts petrophysical properties from rate-transient data. Traditional estimations of petrophysical properties, such as relative permeability (RP) and capillary pressure (CP), strongly rely on coring and laboratory measurements. Coring and laboratory measurements are typically conducted only in a small fraction of wells. To contend with this constraint, in this study, we develop artificial neural network (ANN)-based tools that predict the three-phase RP relationship, CP relationship, and formation permeability in the horizontal and vertical directions using the production rate and pressure data for black-oil reservoirs. Petrophysical properties are related to rate-transient data as they govern the fluid flow in oil/gas reservoirs. An ANN has been proven capable of mimicking any functional relationship with a finite number of discontinuities. To generate an ANN representing the functional relationship between rate-transient data and petrophysical properties, an ANN structure pool is first generated and trained. Cases covering a wide spectrum of properties are then generated and put into training. Training of ANNs in the pool and comparisons among their performance yield the desired ANN structure that performs the most effectively among the ANNs in the pool. The developed tool is validated with blind tests and a synthetic field case. Reasonable predictions for the field cases are obtained. Within a fraction of second, the developed ANNs infer accurate characteristics of RP and CP for three phases as well as residual saturation, critical gas saturation, connate water saturation, and horizontal permeability with a small margin of error. The predicted RP and CP relationship can be generated and applied in history matching and reservoir modeling. Moreover, this tool can spare coring expenses and prolonged experiments in most of the field analysis. The developed ANNs predict the characteristics of three-phase RP and CP data, connate water saturation, residual oil saturation, and critical gas saturation using rate-transient data. For cases fulfilling the requirement of the tool, the proposed technique improves reservoir description while reducing expenses and time associated with coring and laboratory experiments at the same time.