By Saeid Karimi

One of the main complexities in reservoir simulations is lack of data. The extent of data on physical properties of the reservoir is often quite limited. This is partly due to imprecise measurements as well as insufficient sampling. Furthermore, hydraulic fracture models rely on parameters that may not be easily measurable, due to prohibitive costs, difficulty in sampling and measurement, or just time limits. An example of such a quantity is fracture toughness, which is usually denoted by and reported in units of or similar. Many hydraulic fracture models use fracture toughness as the fracture propagation criterion.

Another important parameter that can be challenging to estimate is the leak-off rate. Leak-off is the loss of fluid from the hydraulic fracture into the rock matrix due to a pressure difference. In reality, leak-off is a very complicated multi-component flow process. In hydraulic fracture modeling leak-off is typically modeled using Carter’s approximation. Carter’s leak-off rate can be estimated and calibrated based on reservoir properties, G-function analysis or other methods. Carter’s leak-off coefficient can be taken as

where leak-off rate coefficient is and is the pressure difference, permeability is denoted by , porosity shown by and is the total compressibility. Fluid viscosity is shown by . One should note the uncertainty and heterogeneity of each one of these quantities when it comes to hydraulic fracture simulations. For instance, permeability and porosity can change drastically from one layer to another. Hence, values of the leak-off coefficient can be highly heterogeneous as well. Additionally, the leak-off coefficient depends on the net fluid pressure , which varies from one point to another on the hydraulic fracture and also changes in time as the fracture propagates.

Microseismic data is a good indicator of the actual Stimulated Rock Volume (SRV). Based on microseismic data, one can calibrate or verify hydraulic fracture models and determine/calibrate some quantities such as the fracture toughness. In the figure below, simulated extent of the SRV, using FullRank Software’s own VirtuaFrac, is plotted against the recorded microseismic events during pumping of one stage. This data set is from a well in Texas. FullRank Software used the well logs, and frac design to simulate the propagation of hydraulic fractures in a layered heterogeneous formation. This means that parameters such as Young’s modulus, Poisson ratio, fracture toughness and leak-off coefficients are assumed to be heterogeneous with values derived from available well logs. Furthermore, leak-off coefficient is assumed to be pressure-dependent. Fracture toughness was determined using an empirical relation between the fracture toughness and the tensile strength of the rock. Then a scaling coefficient was then determined to match the model output to the microseismic data. This figure shows a convincing agreement between the calibrated model and the distribution of microseismic events. Only about 2.5% of all recorded events fall outside of the region suggested by the model.