To date no efforts were published to (numerically) compute the pressure transients following shut-in for a fracture that during pumping was propagating at an arbitrary, not necessarily constant velocity; and to use these computations to systematically understand the physics (type curves) of pressure decline after shut-in for both very rapidly growing and very slowly growing fractures during pumping; and to compare this with (existing or new) PTA analysis methods incorporating fracture closure. Paul van den Hoek came up with a new methodology to address the problem. The method enabled to handle the otherwise unaddressed problem of ‘fractured’ injector wells for both end of the fluid leak off spectrum and associated pressure transient analysis – i.e. for DFIT tests done for very low permeability reservoirs to Minifrac (MF) tests for medium to high permeability reservoirs, up until Injection Fall-off (IFO) tests done as part of waterfloods in low to high permeability reservoirs. An easy to use analytical model was formulated by generalization of IFO model developed for fractured waterflood injectors (high leak-off case). This work compares Van den Hoek method against ‘standard method’ which in our report is industry wide used well test program FEKETE for a number of hydraulic frac field cases. To identify each methods short comings and advantages. The identified advantages and disadvantages are highlighted and used as ready made reference for future work on the subject. To serve as easy-to-use overview of commonly used existing approaches of artificial/hydraulically fractured wells for both end of spectrum – (low leak off) Minifrac /DFIT and (high leak-off) Injection Fall Off tests, highlighting the physics involved, fundamental assumptions, and how they differ from each other subtly is covered.
Brief summary of Paul's unified method was done. Fracture Compliance Method was shortly discussed for each data set. Lastly, a basic model was developed to identify permeability based on Lamei and Soliman's BCA model.

It is well known in the oil & gas industry that mature oil fields with a water drive produce increasing volumes of oily produced water which require treatment and efficient disposal. It is a major concern of all waterflood operations now in the industry, to adopt cost effective and environmentally sound water disposal systems. Re-injection into the subsurface has been chosen to be a potentially attractive option from environmental regulations view point, but to become the preferred alternative for produced water disposal, re-injection (PWRI) must also be economical and should not incur excessive risk in form of injectivity decline and damage to the formation. In this study, a semi-analytical model of contaminated water injection under fracturing conditions, including the effects of damage mechanisms over time is developed, that couples the reservoir engineering and fracture mechanics aspects of the problem. The main features of this model are finite fracture conductivity, external filter-cake build-up on the fracture face, internal plugging at fracture tip by injected solids, backstress resulting from pore pressure inflation (poro-elastic stress), backstress resulting from formation cooling (thermo-elastic stress), and fracture propagation. The most important characteristic is that the fracture is of finite conductivity due to fracture fill up by total suspended solids and oils in injected water. This is what differentiates this model from conventional waterflood induced fracturing simulators. This model is an extension to Koning’s model for waterflood induced fracturing, where fracture is of infinite conductivity. This model is largely based on work of Hoek et al. for finite conductivity fracture. This model incorporates a rectangular fracture that fully penetrates a permeable layer bounded by impermeable layers on top and bottom. The fracture is surrounded by three elliptically shaped zones, formation damages caused are included which are critical for fracture propagation, and the primary objective is to predict long term fracture growth and well injectivity. The governing Equations for fracture propagation are based on four fundamental physical phenomena which are fluid leak-off from the fracture into the formation, fluid flow inside the fracture, poro-elastic and thermo-elastic backstress on the fracture face and fracture propagation into the formation. The novelty of the new simulator is the ability to model waterflood induced fracture including all kinds of damage mechanisms, and accurately predict fracture propagation quickly.

Water injection is a core element of geothermal, petroleum and waste water management industries where water is injected into the subsurface after treatment and filtration to comply with environmental regulations and water quality requirements. Some impurities still remain in the water even after the filtration process. It has been widely reported that water injection operations encounter severe injectivity decline which is of substantial concern for field management. Total dissolved and suspended solids in injection water are one of the significant reasons for injectivity decline. These solids are then filtered by the porous media and cause formation damage which can result in significant injectivity decline.
Major past studies have assumed typical filtration techniques (micro-filtration) where the size of remaining dispersed particles in the water are reduced to ~2 microns. Hence, the majority of the experimental studies have used suspended particles of ~1-5 microns to investigate injectivity decline. These studies show that initially internal filter cake starts to develop and after some transition time external filter cake is formed, after which injection face is almost completely plugged. However, not many studies have been performed with ultrafiltration where remaining dispersed particle size in injection water is reduced to nano size range.
In this study, injectivity decline by ultra-filtered water injection was investigated experimentally. To mimic ultra-filtered water, spherical silica nanoparticles of 120 nm diameter were used as dispersed particles in the injected water. First, stability study of nanoparticle colloid was carried out by varying nanoparticle concentration, brine compositions and pH. Hydrodynamic size and zeta potential measurements showed that there exists a salinity and pH range in which nanoparticle colloid remain within the expected size range.
Core flood experiments were conducted on Bentheimer sandstone core plugs. Pressure measurements along the core and influent/effluent analysis were used to study the transport and retention of nanoparticles in porous media. Experimental results showed about 50 to 70 percent less injectivity decline compared to micron size suspended particles. Furthermore, results showed that external filter cake does not form by nanoparticle flow through porous media if the injection fluid’s pH and salinity are kept within a defined range obtained from stability study. Only deep bed filtration takes place where three main retention mechanisms dominate i.e. surface deposition, plugging and entrainment.
Finally, a numerical model is presented in this study that describes deep bed filtration taking into account observed retention mechanisms. Model results are found to be in good agreement with experimental results.