WID

 

WID is a PC-based simulator developed at the University of Texas at Austin.  It can accommodate layered reservoirs, horizontal wells, and constant injection pressure boundary conditions.

 

The principles are as follows:

 

1. Determines the concentration of deposited particles around the injection well as a function of time and distance from the well.  This is done by solving the filtration equations in that region.  Information on the filtration coefficient is available in Pang and Sharma, 1994,[1] and Wennberg, 1998[2].
2. Calculate the altered permeability in the near-well zone due to retained particles.
3. Determine how this near-well damage changes the injectivity of the well.  This depends on the formation parameters as well as the completion geometry.
4. Calculate the transition time, i.e., the time where an external filter cake starts building on the wellbore.  Before the transition time, only internal filtration is considered.  After the transition time, only external damage is considered.  The default porosity for the external cake is 0.25 and permeability is calculated from particle size and the Cozeny equation. 

 

Other Features:

1. WID 3.1 can represent a constant half-length fracture with a constant width.  The conductivity is calculated assuming parallel plates.
2. Completion skin can be incorporated.
3. Surface properties are specified and downhole pressure is calculated.
4. Damage is calculated using particle deposition and the Cozeny equation (refer to Sharma et al., 1997[3]).  Changes in porosity and surface area are considered, as is the consequent tortuosity and reduction in permeability.  A damage factor is specified as is a filtration coefficient, l, (ds/dt=lvc where s is the deposited concentration, v is the velocity, and c is the suspended concentration).
5. The injectivity ratio is calculated and plotted.  This is the injectivity divided by the initial injectivity.  The half-life is indicated (the injectivity ratio has a value of 0.5).
6. “For fractured completions, we neglect injectivity decline due to internal filtration, i.e., damage to the rock matrix.  The injectivity curve, therefore, stays at a value of 1 until the transition time is reached.  Then the injectivity starts to decrease because the deposited particle layer at the fracture surface decreases the fracture conductivity.  Just before the fracture plugs completely, the injectivity declines very rapidly.”
7. The simulator defines a one-dimensional grid in the nearwell zone in which the filtration equation is solved and particle deposition is determined.

8.     The transition time is the time when the deposition mechanism changes from internal deposition to external cake build-up.  “In practice, this transition will be gradual, but WID considers it to take place abruptly in each layer.  Different layers can have different transition times. …By default, the transition time is reached when the porosity in the first few layers of grains is reduced to that of the formation porosity times the filter cake porosity.  This is the theoretical minimum value the formation porosity can achieve.  All subsequent particles are trapped as an external cake.”