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Improving oil fields recovery through real-time water flooding optimization
Pamela Alessia Chiara Marescalco
Politecnico di Torino, Land, Environment and GeoTechnologies Engineering Department,
24, C.so Duca degli Abruzzi, 10129 Torino, Italy
SUMMARY
Increasing oil recovery from reservoirs is a strong urge. One of the most effective ways to get the result iswater flooding and that’s why its application is nowadays widely used in the petroleum industry. Obviously,water flooding efficiency strongly depends on reservoir properties; this makes simulating a water injectionprocess a priori an extremely important step of the reservoir production strategy. Simulation is commonlydone adopting a finite difference (FD) simulation approach.
This paper explores a different and complementary approach, represented by streamline-based simulation,coupled with a tool to optimize water flooding campaigns and to help quick decision making. Inthe present study, water flooding simulation is performed via two commercial software: an FD and astreamline-based simulator, to highlight advantages and disadvantages of both simulation techniques indescribing a water injection campaign and to exploit the two approaches’ uniqueness in parallel.
The final goal of iteratively converging to the optimal water flooding scheme, which is the core of thepresent work, is achieved through a customized Matlab script. The generated automatic procedure showsits effectiveness in improving oil recovery, expediting decision making and saving time and FD simulationruns. A three steps workflow is outlined to get the best water flooding scheme for the examples shownbelow. Copyright q 2008 John Wiley & Sons, Ltd.
Received 13 March 2008; Revised 1 September 2008; Accepted 8 November 2008
KEY WORDS: water displacement optimization; FD simulation; streamline simulation; Matlab automatedroutine; real-time decision making; quantitative and iterative adjustment of water rates tobe injected INTRODUCTION
In the last decades water flooding has been widely applied in the petroleum field, both in mature and in newly developed fields, and its attractiveness lies in supporting the entire field pressureduring depletion and in improving the final oil recovery [1–3]. The technique
consists in injecting water with the purpose of displacing and therefore producing oil, especially if the reservoir lacks an underlying aquifer able to counterbalance the depletion and to drive oil to the producer wells.
To really understand a water flooding process and to predict its efficiency, it is useful to simulate it a priori. This is usually done via finite difference (FD) simulation, which is able to describe any kind of existing reservoir very accurately, but unfortunately is not able to give enough details about the way the flow occurs throughout the field. Recent works [4, 5] have proposed a newly developed approach, based on streamline simulation, whose main attraction lies in providing information not obtainable from FD simulation and useful for the purpose of improving reservoir performances.In the present study, water flooding simulation is performed via two commercial software: an FDand a streamline-based simulator, to highlight advantages and disadvantages of both simulationtechniques in describing a water injection campaign and to exploit the two approaches’ uniquenessin parallel. If FD simulation is essential to checking the streamline simulation results, the streamlinebasedsimulator is, on the other hand, an ideal tool to perform a procedure able to optimizewater injection. Then, the core of the work and its innovative approach lies in exploiting the twosoftware features in conjunction with the application of a customized Matlab code developed inorder to elaborate all the streamline simulation outputs, to calculate the changes to be made to theproduction/injection constraints for the subsequent simulation run, so as to iteratively converge tothe optimal injection scheme for the reservoir under study. A three steps workflow is outlined toget the best water flooding scheme for the examples shown below.
FD APPROACH VERSUS STREAMLINE SIMULATION
ECLIPSE is a complete and complex simulator, whose attractiveness resides in being able todescribe any kind of reservoir, including geological complexity, formation features, and fluidproperties. The simulator is based on a time and spatial discretization and solves a three-dimensionalequation by assigning to all the parameters involved in the simulation a unique value, associated withthe entire cell, for every grid block. For models with a large number of cells, using FD relaxationcan be computationally heavy; therefore, a good balance must be kept between having sufficientaccuracy in describing the reservoir and keeping simulation time within reasonable limits [6].
3DSL, on the other side, solves two different equations on two different grids and this is usuallyfaster than FD simulation, especially for large models: the pressure equation is solved implicitlyon the background grid (or pressure grid), whereas the saturation equation is solved explicitly onthe streamline grid. This involves a minor effect of grid refinement on the results
of the simulation,time-step limitations not as severe, thanks to a better stability of the geometrical grid, numericaldiffusion easier to control, faster solutions with respect to FD approach [7].
Streamline simulation solves mono-dimensional equations along streamlines, which means itsolves multiple streamlines in parallel, and the fluid transport, which for FD approach occursbetween grid cells [8], occurs along streamlines: this gives an immediate answer in terms of howthe streamlines (connecting injector and producer wells—to say, well pairs) are distributed, sothat the fluid trajectories and their rates at the wells are known at every time step [9, 10]. Thanksto the available information, the distribution of injected water volumes can be modified, and amore effective production strategy can be planned to maximize oil recovery [4, 5]. Same as for FDsimulation, when using streamline-based simulation a good balance must be maintained betweenpressure updates and computational speed.
In conclusion, 3DSL is simpler from a reservoir description (includes both flow physics andpetro-physical/geological information) point of view, but it cannot take into account importantparameters such as capillary pressure or cross flow effects: moreover, fluid compressibility cannot beeasily taken into account and mass conservation errors may occur while mapping between pressuregrid and streamline grid therefore being incomplete or inadequate for most of real reservoirs. Everyfurther detail can be found in previous works [11]. THE IDEA OF THE STUDY
In this paper the use of the two software as complementary tools to optimize water injectionis shown: ECLIPSE appeared to be the most reliable software to simulate reservoir models andto be essential to verify 3DSL’s results accuracy upstream and downstream of the methodologydeveloped for this research, while 3DSL has been shown to be simpler and usually faster, providinginformation not obtainable by means of FD simulation, and which could be exploited to save atrial-and-error process trying to find the best injection scheme The idea of the study resulted from previous works [12].
The research presented here follows a three step workflow. In the first part of the study, thetwo software were used to simulate simple synthetic models. Once the results obtained from thetwo simulators were checked for consistency, a method was developed to exploit 3DSL’s features.The most interesting pieces of information available from 3DSL are the connections between wellpairs (injector-producer) and the rates at the wells and the connections. With this informatioavailable, the streamline simulator, coupled with Matlab, was involved into an automatic procedurethat reallocated water injected volumes in order to optimize water injection campaigns, for all the examined cases.This was gained by a customized Matlab script, written
for this specific purpose, which automaticallyinteracted with the streamline simulator, processed the input data supplied by the softwaregiving back new input rates to be used for the following simulation run. This was done for a fixednumber of runs to iteratively converge to the optimal injection scheme. From preliminary analyses[13] the procedure was shown to be effective
Eventually, in the third experimental phase, the last rates calculated from Matlab were inputinto ECLIPSE to check the procedure’s effectiveness and the added value in terms of oil recoveryimprovement.
THE AUTOMATED PROCEDURE AND THE EXPERIMENTAL METHOD
Let’s now focus on the second and main part of the experimental study which, as we said, consistedin writing a customized Matlab code. Streamline answers in terms of streamlines distribution(connecting injector and producer wells—or well pairs) and fluid rates at the wells are writtenat every time step in a 3DSL output file named ?.WAF, which is crucial for the entire codingdescribed below and for its application.
The endeavor of the Matlab customized code is the optimization of the displacement processthrough a gradual reallocation of injected water rates, carried out by increasing the water volumeinjected at the highly efficient connections and decreasing it at the poorly efficient connections.The term injection efficiency (for a well pair connection) stands for the ratio between offset oilproduced thanks to water displacement and the amount of water injected at a certain well. In ananalogue manner the injection efficiency of an injector well is the ratio between offset oil at allproducers connected to it and the total water injected at the same well. The approach used forthe current application was aimed at increasing the oil production through a better use of a givenwater volume available for injection. The Matlab code written for this purpose mainly works asfollows: the data needed for the procedure are read from 3DSL’s output ?.WAF file and loadedinto Matlab environment, then they are processed throughout the code; eventually new rates forthe next simulation run are output to 3DSL. This is all done automatically with an approach aimedat maximizing oil production through a more efficient use of a given water volume available forthe injection [13]. The code steps are here summarized [12]:
1st step consists in: establishing the number of iterations to be run for the procedure of ratereallocation and their duration; fixing the volume of water to be injected and the target liquid rate.
2nd step consists in: running a ‘do nothing’ 3DSL simulation in order to choose a properstarting time for the entire procedure of rate reallocation (usually the reallocation starts
whereas aproduction plateau starts).
3rd step consists in: reading (within the Matlab environment, by means of functions coded onpurpose) from the ?.WAF file: rates (total rate for each injector well, and partial rate for eachproduction well connected to the injector); time; name and number of injector or producer wellsand connections between them; number of existing connections in the model at any time step ofthe simulation.
4th step consists in: calculating the injection efficiency for each well pair, for each injector well,and for the field (average injection efficiency).
5th step consists in: calculating for each iteration and for each injector well a new rate:
Qnew i=(1+wi )·qoldi (1)
where i stands for the well, wi for the weight it has been assigned, and qoldi for the rate injectedat the well at the previous step.The average reference field injection efficiency (referred to as signed e) is a mean value:depending on its value, positive or negative weights are assigned to the efficient or inefficient connections.Once the maximum weight, minimum weight, minimum injection efficiency allowed, maximum injection efficiency awaited, and _ (which is the grade of the polynomial that interpolates the relation weight-efficiency) are fixed, the weights are evaluated as follows:
where wmin is the minimum weight at the least efficiency, wmax is the maximum weight at thehighest efficiency, emin is the least acceptable injection efficiency, emax is the highest awaitedinjection efficiency.6th step consists in: calculating new rates for each well pair connection and, consequently, foreach injector; calculating for each injector the differences between the last known rates and thenew ones; determining the new total volume of water injected as a summation of the new rates atthe injectors; checking that the constraints on the total water volume available (x) are satisfied by
Figure 1. Weighting functions (as from Equations (2) and (3)) for different values of exponent