RETINA Simulation™ has the BiCG-Stab standard iterative linear solver which is powered by several pre-conditioners including: 

  • -ILU0
  • -ILU1

The solver and all the pre-conditioners have been developed and tested by ESTD and are fully customized for reservoir simulation needs. Among them, the CPR method is the cutting-edge pre-conditioner in numerical sciences which is based on the AMG technique. Using the AMG technique along with the CPR method to solve the pressure equation is at the heart of RETINA Simulation™ powerful numerical solver. Especially considering the fact that using the CPR method without the AMG technique will present no industrial benefit. The linear solver of well-known commercial simulators that utilize the Nested-Factorization method as the pre-conditioner are almost the fastest solvers in the market which are mainly suited for models with a dominant directional behavior (mostly z direction) and make use of the nearly structured shape of corner point grids. Therefore using Nested Factorization for simulation of models with high heterogeneity and/or large number of non-neighbor connections (either of which usually occur in giant fractured reservoirs) can result in severe convergency problems. The AMG technology is one of the most recent strategies for solving matrices generated in elliptic partial differential equations that can produce suitable solutions for complicated problems. RETINA Simulation™ has its own customized AMG based solver which is fully tested on more than 50 sets of data from real-world fields, some SPE samples, and many synthetic models. This solver has the power of solving very complex, large and heterogonous models without linear convergency problems. This fact gives RETINA Simulation™ the power to solve models that are simply not solvable using known commercial simulators.   

One of the most valuable outcomes of using cutting-edge scientific methods and technologies in RETINA Simulation™ is that, RETINA Simulation™ can solve dual porosity/permeability models much faster and more reliable than known commercial simulators. 

RETINA Simulation™ usually has larger time steps with more realistic results in the case of dual porosity/permeability models. It can also solve these models with less time step cut back and has far less non-linear and linear convergency problems. The main reason for RETINA Simulation™ remarkable stability is its cutting-edge AMG based linear solver along with an improved non-linear iteration scheme. 

In order to tackle the complexity of the non-linear system with cross variable dependencies, RETINA Simulation™ uses a new and creative method to reduce the number of non-linear iterations. 

RETINA Simulation™ uses higher order terms in its Jacobian matrix in addition to the Newton’s basic linear terms to account for cross variable dependencies. This scheme leads to a smaller number of non-linear iterations compared to basic Newton iterations. The number of Newton iterations in RETINA Simulation™ non-linear solver is now comparable to other known commercial simulators with larger time-steps. All the aforementioned features allow RETINA Simulation™ numerical solver to be among the best solver technologies available to date. 

RETINA Simulation™ uses a 3-equation and 3-variable well model and solves well equations in saturated and under-saturated states just like ordinary cells which is not the case in known commercial simulators. RETINA Simulation™ solves well equations for the following set of variables:  

  • BHP, Sw and Sg for saturated wells
  • BHP, Sw and Rs for under-saturated wells

Whereas known commercial simulators always solve the well for three variables: BHP, Fw and Fg regardless of the state of the well. Therefore for under-saturated wells, Rs of well is not calculated and hence is not correct. Wrong Rs causes the wrong oil mobility especially for injection connections. This also causes the wrong reservoir volume rate calculation for under-saturated wells. omized AMG based solver which is fully tested on more than 50 sets of data from real-world fields, some SPE samples, and many synthetic models. This solver has the power of solving very complex, large and heterogonous models without linear convergency problems. This fact gives RETINA Simulation™ the power to solve models that are simply not solvable using known commercial simulators. 

RETINA Simulation™ utilizes a multi-threading algorithm that inserts no approximation in the solution and therefore is fully stable for large and complex models. This algorithm can utilize all or any user defined number of CPU cores efficiently. 

In RETINA parallel simulations, the solution does not change from the single core case and follows the exact same path. This however is not the case for other simulators that use domain-decomposition techniques. These techniques change the solution of the original system and therefore decrease the accuracy of the solution. This is the main reason why parallel accuracy of commercial simulators is decreased especially in cases with a large number of CPUs. 

A Discrete Fracture Network (DFN) model is a mathematical representation of fracture characteristics for hydraulically relevant fractures. We divided our DFN Workflow into the following four main components, illustrating our unique approach: 

  • Consistent Structural and Stratigraphic Model
  • Integrated Fracture Characterization
  • Static DFN Model Construction
  • DFN Dynamic Validation and Upscaling

The DFN feature allows RETINA Simulation™ to solve fully unstructured fractured grids (i.e. modeling fractures as 2D surfaces between 3D matrix cells). This feature is fully implemented and tested with several synthetic cases, however, due to the fact that DFN is not used in industry, real-world cases are not available for further testing. 

RETINA Simulation™ solves well equations fully implicitly and fully coupled with grid equations. This is the most stable scheme to solve the reservoir equations. However, unstable wells need a large number of non-linear iterations to converge. For these special cases, there is a better solution.

Well equations can be decoupled from the grid equations altogether before each Newton iteration and iterated separately to converge. All the equations are then coupled together and iterated again to reach the final solution. This is the default scheme used in known commercial simulators and causes a more stable well solution. In some rare cases however, this method causes some stability problems and increases computational cost. Therefore it's better to be an optional feature in the simulator. This facility is optional in RETINA Simulation™ so that the user can test its effectiveness without being forced to use it. 

Saturations will never go out of bound, cells with low oil saturation do not have an unrealistic Rs and combining oils with different Rs does not result in unrelistic free gas saturation when DRSDT is zero. All the above situations could happen in known commercial simulators. Known commercial simulators allow phase saturations to fall bellow zero or grow above one. This behavior is not realistic and should be avoided. The only way to make sure this numerical constraint is satisfied is to use algebraic constraints during non-linear iterations. RETINA Simulation™ applies these numerical constraints in all the possible cases so that no variable can take an unrealistic value. RETINA Simulation™ also controls the constraints to prevent any numerical inefficiencies. Under-saturated cells with very low oil saturation are very difficult to solve for Rs. Known commercial simulators solve this problem with a non-physical assumption. They solve these cells as saturated and therefore solve for Sg and not Rs. In some cases this can result in small values of free gas saturation below the WOC. It also causes the bubble point pressure of cells below WOC to be equal to their oil pressure which in turn leads to large values of Rs especially in highly under-saturated reservoirs. As it happens, these cells with large Rs can be located right next to other cells with regular (and hence much less) values of Rs. This can cause numerical instability in known commercial simulators. 

 RETINA Simulation™ however does not solve under-saturated cells with low oil saturation as saturated cells, but rather, treats them as regular under-saturated cells with some numerical enhancements. Therefore, cells have a correct value of Rs below WOC and no instability occurs in RETINA Simulation™ due to this issue. Moreover, RETINA Simulation™ solves these cells with almost no numerical difficulty. 

RETINA Simulation™ includes the following transfer functions: 


  • -Kazemi (1976)
  • -Gilman-Kazemi (1983)
  • -Quandalle and Sabathier (1989)

The following shape factor calculation formulas are implemented in RETINA Simulation™: 


  • -Warren and root
  • -Kazemi et al. (1976)
  • -Gilman, Kazemi (1983)
  • -Coats (1989)
  • -Chang (1993)
  • -Lim and Aziz (1995)

RETINA Simulation™ has magnificent ability to simulate unstructured and hybrid DFN models. Technically speaking, using RETINA Simulation™, engineers can model the volume around the wells using an unstructured DFN grid while using the conventional structured single or dual porosity grid for the rest of the reservoir volume. This ability comes in handy especially in case of wells stimulated using Hydraulic Fracturing. The current solution for predicting performance of unconventional reservoirs is to perform the following two simulations:  


1. Single well simulation using explicit DFN model to predict the well performance. The results of this simulation are usually used to design the Hydraulic Fracturing operation and predict the future performance of wells. An overall skin factor is also estimated for full field studies.  


2. Full field simulation with a conventional approach using a prevalent industrial simulator. The results are used to predict the overall (usually qualitative) performance of the field. Simulation is done using single or dual porosity approach according to rock properties of the field. In this simulation, hydraulically fractured wells are represented either by an overall skin or adjusting properties of cells surrounding each well.


The following shape factor calculation formulas are implemented in RETINA Simulation™: 


RETINA Simulation™ is able to combine the DFN model with the full field simulation to create a model that includes all the details needed to predict full field performance as well as single well results. RETINA Simulation™ has a toolbox that can generate unstructured or hybrid grids for the mentioned simulation approach. The overall full field study workflow for unconventional reservoirs is as follows: 


1. Importing conventional grid (static fine grid) for the model along with the well deviations. 


2. Entering hydraulic fracturing parameters for each well. (These parameters could be estimated using Hydraulic Fracturing Design module of RETINA Simulation™) 


3. Generating suitable grid for the reservoir and around wellbores according to well paths and fracture geometry. 


4. Transferring data from the conventional grid to the newly generated grid. 


5. Perform simulation using RETINA Simulation™ 


Running this kind of full field models has multiple numerical difficulties. The first issue is high heterogeneity of these models; and the second issue is high throughput nature of DFN models. Two dimensional fracture cells with small pore volume and high speed of flow are a great challenge for numerical solvers. These are the two main issues that prevent current industrial simulators from handling full field DFN models. By contrast, RETINA Simulation™ benefits from a modern and robust linear solver that is easily capable of handling the mentioned issues. Using RETINA Simulation™, DFN models are simulated smoothly and with large time-steps while other simulators face severe problems while simulating such models. 

All the usual group control facilities are available in RETINA Simulation™:  


  • 1. Multi-level hierarchical fully implicit production and injection group control  
  • 2. Re-injection and voidage replacement of the production group to injection wells
  • 3. Auto work-over and economic limit handling 
  • 4. Auto drilling and completion facilities 
  • 5. Limiting the drilling and work-over rigs 
  • 6. Drilling wells in sequential or prioritized queues  
  • 7. Group guide rate calculation formula   

Simulation graphs and 3D results can be animated in real-time during the simulation. Results are loaded automatically as they are written on disk in a smooth and efficient manner. 

Simulation can be paused at any time, which allows the user to change the data for the upcoming time steps. When the simulation is resumed, RETINA Simulation™ will load the new data for corresponding steps.