A new workflow that uses the strain derived from geomechanical modeling of hydraulic fractures interacting with natural fractures is applied to an Eagle Ford well. The derived strain map is used to estimate the asymmetric half lengths that are input in any frac design software able to incorporate this new information. The simplistic symmetric and bi-wing design is revised by adjusting the leakoff coefficient, injection rate, and proppant concentration resulting in asymmetric half lengths that do not exceed the lengths of those provided by the strain map. Once the half lengths and orientation from the frac design match those provided by geomechanical simulation, the propped length and other key results provided by the frac design software may be used to optimize the well's completion. This process could be used iteratively to optimize desired metrics and could also be used to improve reservoir simulation. The derived strain map may be propagated in the stimulated geomechanical layer to form a strain volume which may in turn be used to estimate the stimulated permeability. In this paper, we used a radial function to relate the stimulated permeability to the strain within the maximum half lengths provided by the strain map. Two calibration constants are needed in the radial functions and could be estimated by history matching or pressure transient analysis. An adaptive Local Grid Refinement (LGR) and variable stimulated permeability provide a realistic representation of the stimulated reservoir volume (SRV). After history matching, the resulting pressure distribution allows an accurate selection of refrac or new well candidates, for optimizing well spacing, and for estimating an accurate EUR.

The flow behavior in nano-darcy shales neighbored by high conductivity induced natural fractures violates the assumptions behind Arps' decline models that have been successfully used in conventional reservoirs for decades. Current decline curve analysis models such as Logistic Growth Analyses, Power Law Exponential and Duong's model attempt to overcome the limitations of Arps' model. This study compares the capability of these models to match the past production of hundred shale oil wells from the Eagle Ford and investigate how the choice of residual function affects the estimate of model parameters and subsequently the well life, pressure depletion and ultimate recovery. Using the proposed residual functions increased the tendency of deterministic models to have bounded estimates of reserves. Results regarding well performance, EUR, drainage area and pressure depletion are obtained quickly and show realistic distributions supported by production hindcasts and commercial reservoir simulators. Overall, the PLE and Arps' hyperbolic models predicted the lowest/pessimistic and highest/optimistic remaining life/reserves respectively. The newly proposed residual functions were thereafter used with the Arps' hyperbolic and LGA models. We found that the use of rate-time residual functions increased the likelihood of the value of hyperbolic exponent being less than 1 by 87.5%. The proposed residual functions can be used to provide optimistic and conservative estimations of remaining reserves and remaining life using any of the above decline models for economic analysis. The key results provided by the modified DCA models help in long-term planning of operations necessary for optimal well completions and field development, accomplished in a fraction of the time currently required by other complex software and workflows.

Summary In this work, we developed a methodology that integrates decline-curve-analysis (DCA) models with an approximate Bayesian probabilistic method that is based on rejection sampling to quantify the uncertainty associated with DCA models. This methodology does not require the estimation of the likelihood, which simplifies the Bayesian inference greatly. In approximate Bayesian computation (ABC) with rejection sampling, the posterior distribution is approximated by substituting different values of the decline-equation parameters into the Arps’ DCA model and generating a large number of production-profile realizations. Summary statistics (mean, standard deviation) between the simulated and observed production data are then compared. On the basis of some optimum threshold value, the rejection-sampling technique is applied to either accept or discard the simulated production data. The resulting distribution is used to approximate the posterior. The 10th, 50th, and the 90th percentiles of the accepted data sets provide the P90, P50, and P10 estimates for reserves, respectively. History matching was performed to test the proposed Bayesian model and to check how well the simulation results match with the observed production data. Chosen for analysis were 57 gas wells from Johnson County (Barnett Shale) and 21 oil wells from Karnes County (Eagle Ford Shale) with production history of 90 and 45 months, respectively. Best-fit (deterministic) curves were computed with the least-squares regression method. Only two-thirds of available history was used for modeling, and the remaining one-third of the history was used for validating the methodology. The P50 history match trended well with the best-fit curve for majority of wells. The ABC P90–P50–P10 average cumulative production interval for wells in Johnson County was 1,263–1,410–1,528 MMcf, whereas the true average cumulative production per well was 1,425 MMcf. Similarly, for Karnes County, the ABC P90–P50–P10 average interval per well was 170,000/184,000/204,000 STB, whereas the true average cumulative production per well was 183,000 STB. This implies that the ABC bounds bracket the true reserve well. Approximately 42 and 98% of wells’ true cumulative production at the end of hindcast were greater than their P50 and P90 estimates, respectively. This implies that the P50 and P90 estimates were quite accurate even with short production history (approximately 2 years). The P10 estimates were less accurate but still acceptable with only 4% of wells’ true production higher than their P10 estimate. Therefore, estimates from the ABC methodology are well-calibrated. The proposed ABC methodology combined with rejection sampling provides a procedure that not only produces probabilistic forecasts but also quantifies reserves uncertainty in shale plays quickly and consistently. The ABC methodology can be coupled with any other deterministic DCA model.

Estimation of permeability in the Stimulated Reservoir Volume (SRV) is a vital input in any completion optimization workflow. One method to estimate the stimulated permeability in the SRV is to couple geomechanical modeling of the interaction between hydraulic and natural fractures with hydraulic fracture mechanics commonly used to design frac jobs. The proposed approach starts by deriving strain resulting from the integration of geological, geophysical and geomechanical modeling of interacting hydraulic and natural fractures. A unique feature of this approach is its ability to predict microseismicity, thus confirming the validity of the input natural fracture model and the geomechanical approach used to evaluate its interaction with the hydraulic fractures. The optimum validated geomechanical asymmetric half-lengths are then estimated from the derived strain map. These estimated geomechanical half lengths are used as a constraint in a frac design model which is able to incorporate this information and optimize stage treatments according to the variable SRV. The frac design parameters then need to be adjusted in order to approximately match the geomechanical half-lengths provided by the strain map.A new analytical asymmetric frac design model is developed, validated with existing commercial frac design software, and used in this study. The new asymmetric analytical frac design model is a pseudo 3D model that accounts for the variation in height in an iterative approach along with considering the asymmetric half lengths due to the lateral stress gradients in a heterogeneous reservoir. The new asymmetric analytical frac design model was compared to existing commercial frac design software and was found to provide similar estimations of frac heights but in a fraction of the time needed to run the commercial frac design software. The ability to combine these models and simultaneously solve for the optimum fracture height is provided by the constraints of the geomechanical half lengths derived from the strain map. In order to guide the engineer designing a frac job an optimum selection of the design parameters to get the target fracture geometry, this paper also presents a parametric analysis using experimental design of various fracing parameters used in our asymmetric hydraulic fracture model.In this study, the workflow was successfully applied to a complex Eagle Ford well. The frac design tool optimizes important parameters such as the injection rate, fluid viscosity, proppant type, proppant size, proppant specific gravity and leak-off coefficient in order to honor the interaction of natural and hydraulic fractures accounted for in geomechanics. The frac design model also provides vital information such as the proppant schedule to be pumped and the variation of propped length, width, and net pressure as a function of time. The results of this workflow are the fracture conductivity and proppant concentration along the fracture length and their interpolation between the stages so they can be exported to any reservoir...

Optimizing a well's hydraulic fracture design within a pad development environment is a multi-disciplinary effort and requires a 4-dimensional understanding of the reservoir. This paper presents a workflow that uses an integrated workflow that combines geology, and geomechanics to build a reservoir model which can be interrogated and updated with a geologically and geomechanically constrained grid-based 3D planar frac model and production simulation using a fast marching method. In this case, as applied to an Eagle Ford well to address concerns of completion optimization, production and depletion forecasting, well spacing and well interference. The workflow captures the variability of stresses and rock properties along the wellbore and around it by using multiple geologic and geomechanical approaches. The estimated variability of rock mechanical properties is used as input in a 3D planar frac simulator. An alternative approach to geoengineering a completion, using the differential stress derived from geomechanical simulation that overcomes the limitations of well centric methods, is also illustrated. The frac design results are used as inputs/constraints in a new reservoir simulator that was developed using the Fast Marching Method to estimate drainage area. This allows for a constrained, yet extremely fast estimate of the EUR and resulting pressure depletion, addressing the important concerns of well spacing optimization and prevention of frac hits and well interferences, all in a timely manner. The integrated approach facilitates adaptive frac design which honors in-situ conditions including stress field heterogeneity, stress shadow effects and the pressure depletion from nearby producing wells. The proposed workflow enables greater investment efficiency and promotes field development optimization.