Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q10/00—Administration; Management
  • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling

Definitions

• This invention relates generally to optimally allocating equipment for fracturing operations or oil-well stimulation operations by applying operations research methodologies. More particularly, the invention is a method for optimally allocating equipment to jobs at multiple geographic locations to maximize utilization of scarce and expensive equipment resources needed for fracturing operations.
• the optimal equipment allocation problem is formulated and solved using operations research and mathematical programming techniques.
• Fracturing consists of pumping complex water based fluids under high pressure into boreholes to make cracks in the geological formation. These cracks are held open by solid particles transported by the fluid and deposited in the cracks. Fracturing a well can typically improve the long-term oil flow from a well by a factor of two by increasing the local permeability of the geological formation. This is done by pumping special water based fluids containing small particles (sand) at high pressure (approximately 5 to 15,000 psi) into the well.
• the high pressure fractures the formation, ideally creating long cracks leading away from the borehole, which are kept open by the particles deposited in the cracks long after (years) the well stimulation.
• Control of fracture formation is critical to the success of the stimulation and is partly controlled by the rates at which the fluid is pumped into the well, as well as the design and dynamic control of the fluid properties.
• These pumping operations may last anywhere from 20 minutes to 12 hours in exceptional circumstances, but are typically from 1 to 2 hours.
• Equipment setup and takedown is time consuming and must be performed carefully given the potentially hazardous nature of the operations. This adds a total of 1 to 3 hours to the total on site time.
• Fracturing operations involve a variable number of pumping trucks (“pumpers") together with a control van and ancillary equipment for fluid and sand storage and blending.
• the most expensive pieces of equipment are the pumpers and the control van, with a pumper costing about several times as much as a control van. Given the expense of this equipment, there is only a small amount of it at any particular depot.
• Several depots may cooperate via equipment and job sharing. Jobs may be spread over a geographical area with many different geological formations. Clearly they are within a certain range suitable for trapping oil but may be heterogeneous with respect to specific requirements.
• Fracturing operations are a service industry. Jobs are typically requested some weeks in advance for a specific day, although there is wide variation in the actual details of client-provider interaction. These jobs are designed with the help of specific software simulating the details of the stimulation. However, managers typically have "comfort levels" for given operations so will send more equipment than is required by the job design, either to guard against equipment failure or to satisfy customer preferences or in case the design has to be changed at the job. Also the demand for fracturing services is not constant but depends on many macro-economic variables.
• the present invention optimally allocates the fracturing operation equipment (pumpers and control vans) to jobs in order to obtain the best return on investment possible for this capital equipment.
• the results of the optimal allocation are an improvement over any optimal allocation that can be obtained without using operations research tools.
• There is considerable flexibility in the present system in scheduling aspects at the initial client contact to matching equipment to job requirements, inter-Depot cooperation, and the comfort levels of the local managers.
• the optimal allocation of equipment may take place at current or increased demand levels.
• the present invention increases equipment utilization in fracturing operations carried out in one organizational area (called a fracturing Area) under current demand and under increased demand scenarios without losing significant market share.
• equipment allocated to Depots under supply-demand matching can be reduced with optimal allocation for little loss of market share.
• market share may be increased with the same amount of equipment.
• increase implies an increase relative to some pre-existing situation.
• market share means the number of jobs done relative to all jobs done by all companies within the fracturing Area. Changing management strategies, for example equipment sharing, also has major impact on increasing equipment utilization.
• the models described herein capture the main aspects of the optimal allocation problem.
• the models do this in two ways. Firstly, by making the management decisions for setting up the original Area explicit. Secondly, by illustrating the potential changes in equipment utilization possible by further management decisions helped by an optimal equipment allocation procedure using mathematical programming.
• the present invention comprises a computer implemented method for optimally allocating equipment to jobs at multiple geographic locations to maximize equipment utilization.
• the method comprises the steps of inputting the jobs to be completed within a specified time period, determining job requirements of each job specified in terms of an amount of equipment needed to perform each job, inputting supply equipment available for supplying to the jobs and optimally allocating the supply equipment to the jobs.
• the optimal allocation step comprises formulating an equipment allocation problem for allocating the supply equipment to each job based on the jobs to be completed, the job requirements and the supply equipment available, modeling the equipment allocation problem as an objective function and set of constraints and optimizing the objective function to generate an optimal solution for allocating the supply equipment to the jobs to be completed to maximize jobs performed within the specified time period.
• the jobs may comprise fracturing operations.
• the supply equipment may comprise pumpers and monitor vans.
• the amount of supply equipment to perform each job may be determined based on a maximum hydraulic horsepower, maximum pumping pressure and maximum rate needed for the fracturing operation for each job.
• the maximum hydraulic horsepower, maximum pumping pressure and maximum rate for each job is used to determine a number of pumpers needed for each job.
• the set of constraints may comprise that the pumping pressure capability of the supply equipment must be greater than or equal to a minimum pumping pressure needed for each job, at least one monitor van must be included in the supply equipment provided for each job and job duration must be less than or equal to a specified maximum working day duration.
• the present invention comprises computer executable software code stored on a computer readable medium, the code for optimally allocating equipment to jobs at multiple geographic locations to maximize equipment comprising code for inputting jobs to be completed within a specified time period, code for determining job requirements of each job specified in terms of an amount of equipment needed to perform each job, code for inputting supply equipment available for supplying to the jobs, code for formulating an equipment allocation problem for allocating supply equipment to each job based on the jobs to be completed, the job requirements and the supply equipment available, code for modeling the equipment allocation problem as an objective function and set of constraints, and code for optimizing the objective function to generate an optimal solution for allocating supply equipment to jobs to maximize jobs performed within the specified time period.
• the present invention also comprises a method for optimally solving a fracturing operation equipment allocation problem for a multiple number of fracturing jobs within a specified time period, in a computer program running on a computer processor, comprising the steps of obtaining fracturing problem data, determining variable parameters, determining problem constraints and generating an optimal solution.
• Generating an optimal solution comprises using an algebraic modeling language, building a fracturing problem model for optimally allocating fracturing equipment available to fracturing jobs, the model being expressed as an objective function and the problem constraints in terms of the variable parameters and problem data and then optimizing the objective function to generate an optimal solution for allocating the fracturing equipment to the fracturing jobs to maximize the number of fracturing jobs performed within a specified time period.
• the fracturing problem data may comprise data input by a user.
• the problem data comprises job location for one or more jobs to be done each day, job equipment requirements, job location specified relative to a depot location, distance between job locations, and supply equipment available for performing the job.
• the fracturing problem data may be varied and an optimal solution generated for the varied problem data.
• the supply equipment may comprise pumpers and monitor vans.
• the problem constraints may comprise time constraints or a prioritization of jobs.
• the prioritization of jobs may comprise scheduling jobs first that have been received first.
• the optimal solution generated maximizes number of fracturing jobs performed in a specified time period using the supply equipment available.
• Job equipment requirements may be increased to take into account equipment breakdown.
• the problem constraints may allow pumpers to be shared among jobs or time constraints for completing the fracturing jobs.
• the problem data varied may comprise increasing the job equipment requirements to simulate increased equipment demand.
• the job equipment requirements for each job may comprise maximum hydraulic horsepower, maximum pumping pressure and maximum rate for each job.
• the problem constraints may comprise that each job must be performed once, pumper total maximum hydraulic horsepower for each job must be greater than the maximum hydraulic horsepower required for each job, pumper total rate for each job must be greater than or equal to the maximum rate required for each job, pumper minimum pressure for each job must be greater than or equal to the maximum pumping pressure job required for each job, each pumper must be utilized and at least one monitor van is needed for each job.
• the optimal solution may comprise using a solver software program to solve for the variable problem parameters that satisfy the problem constraints and optimize the objective function.
• the order of determining the variable parameters may be prioritized prior to generating an optimal solution for the model.
• the method may further comprise determining fracturing job acceptance based on available equipment, determining an equipment sharing strategy for optimally sharing fracturing equipment between the fracturing jobs, increasing job requirements for each fracturing job based on manager comfort level and determining job scheduling and prioritization.
• Fig. 1 shows a typical fracturing area geography, job locations and depot locations.
• Fig. 2 is a table that shows customer job data for each job location depicted in Fig. 1 .
• Fig. 3 is a table showing the geology of the job area depicted in Fig. 1.
• Fig. 4 is a table showing the implied parameters of lognormal distributions describing the geology of Fig. 3.
• Fig. 5 is a table showing the depot locations and equipment levels.
• Fig. 6 is a table showing the equipment specifications with the capabilities of different pumper types.
• Fig. 7 is a table showing the resulting supply versus demand balance for the job requirements based on maximum hydraulic horsepower (HHP).
• Fig. 8 is a flow diagram for the optimal equipment allocation problem.
• Fig. 9 is a flow diagram for a fracturing operation optimal equipment problem.
• Fig. 10 is a flow diagram for additional what-if scenarios for a fracturing operation optimal equipment problem.
• Fig. 11 is a table showing the resulting percentage of pumper utilization for different equipment levels.
• Fig. 12 is a table showing the resulting percentage of job completions expressed in terms of their required HHP if there is no sharing of pumpers or monitor vans.
• Fig. 13 is a table showing the resulting percentage of pumper HHP utilized with different equipment levels if there is a sharing of pumpers only.
• Fig. 14 is a table showing the resulting percentage of job completions expressed in terms of their required HHP if there is a sharing of pumpers only.
• Fig. 15 is a table showing the resulting percentage of pumper HHP utilized with different equipment levels if there is a sharing of pumpers and monitor vans.
• Fig. 16 is a table showing the resulting percentage of job completions expressed in terms of required HHP if there is a sharing of pumpers and monitor vans.
• Fig. 17 is a table showing the resulting percentage of pumper utilization for different equipment levels based on increased demand with no sharing of equipment.
• Fig. 18 is a table showing the resulting percentage of job completions expressed in terms of required HHP based on the increased demand with no sharing of equipment.
• Fig. 19 is a table showing the resulting percentage of pumper HHP utilized with different equipment levels based on increased demand with a sharing of equipment.
• Fig. 20 is a table showing the resulting percentage of job completions expressed in terms of their required HHP based on the increased demand with a sharing of equipment.
• Fig. 21 is a table showing the percentage of pumper utilization for difference equipment levels based on current demand, increasing equipment by 25%, and sharing of pumpers only.
• Fig. 22 is a table showing the percentage of job completions expressed in terms of required HHP based on current demand, increasing equipment by 25%, and sharing of pumpers only.
• Fig. 23 is a table showing the percentage of pumper utilization for different equipment levels based on increased demand, increasing equipment by 25%, and sharing of pumpers only.
• Fig. 24 is a table showing the percentage of job completions expressed in terms of their required HHP based on the increased demand, increasing equipment by 25%, and sharing of pumpers only.
• Fig. 1 shows a typical fracturing area geography.
• the Area 10 consists of four Depots of equipment 1 1-14 (each indicated by an "X") serving a total of 20 customer locations.
• X the number of components that are spread around the four equipment Depots with five control vans (TCV's) and twenty-three pumpers.
• TCV's control vans
• a heterogeneous pumper fleet has three different pumper types. Not all Depots have all pumper types. Actual fracturing operations could possibly involve only single Depots for very small oilfields, or probably ⁇ 50% of what we have considered here. Detailed information is not available from the major companies.
• Equipment is used on 1 to 2 jobs each day depending on job length and location. Depot 11 serves six customer locations indicated by the six occurrences of the number 1.
• Each Depot 1 1 -14 is constructed by matching supply with demand independent of other Depots in the Area. Each Depot has enough equipment to be able to meet most of the job requests in terms of their size in maximum hydraulic horsepower (HHP) and in terms of the number of jobs. This matching is calculated below.
• the demand in the optimal equipment allocation problem consists of twenty customer locations (indicated by the numbers 1 -4) spread out over the Area 10.
• Each customer requests fracturing jobs independently of all the other customers according to a Poisson process.
• the requirements of the fracturing job are maximum hydraulic horsepower (HHP), maximum pumping pressure (Psi) and maximum rate (rale) at which fluid is pumped into each well.
• HHP maximum hydraulic horsepower
• Psi maximum pumping pressure
• RVe maximum rate at which fluid is pumped into each well.
• HHP rate x pressure/40.8 but the maxima of each will not necessarily occur at the same time.
• the distribution of these quantities will be taken as a joint lognormal distribution. This distribution is suitable for describing quantities that depend on the product of many factors which is certainly the case with oil well geology and oil recovery.
• the supply in the optimal equipment allocation problem consists of four Depots 11-14. Each Depot has a specific number of pumpers and control vans. There are three different types of pumpers with different capabilities in terms of HHP, Psi and rate.
• n L ⁇ average number of job requests from customer c to Depot d per day.
• N j set of jobs n requested by county c from Depot d. hhp,i p HHP available from pumper/? in Depot d.
• Fig. 2 is a table that shows customer job data for each job location for the twenty customers of Fig. 1. Job rates are per day and are Poisson distributed. Geology is defined in terms of one of four formation types present. X and Y coordinates are in miles relative to the location of the center Depot. The Depot serving the customer is shown in the last column of Fig. 2.
• Fig. 3 is a table showing the geology of the job area. Characteristics of each formation present in the geology are shown in terms of effect on job requirements. The requirements of the fracturing job are maximum hydraulic horsepower (HHP), maximum pumping pressure (Psi) and maximum rate (rate). Note that the mean and standard distribution of the marginal distributions are given, not the parameters of those distributions (which are uniquely determined by these values and given below). The correlation matrix is symmetric with the unit diagonal so only threr entries for each formation need to be specified. Note that there is no particular relationship between different formations.
• Fig. 4 is a table showing the implied parameters of lognormal distributions describing the geographical formations of Fig. 3. Parameter 1 is the mean of the log of the distribution and Parameter 2 is the standard distribution.
• Fig. 5 is a table showing the depot locations and equipment levels.
• the X and Y coordinates represent the miles relative to Depot 1.
• the equipment present at each level is also shown.
• Fig. 6 is a table showing the equipment specifications with the capabilities of different pumper types in terms of maximum HHP, pumping pressure and rate.
• Fig. 7 is a table showing the resulting supply versus demand balance for job requirements based on maximum HHP calculated using the equations above for the fracturing Area as depicted in Fig. 1.
• Operational data for a fracturing area such as that shown in Fig. 1 with organization and supply versus demand structure (as shown in Fig. 7) must be obtained so as to be able to model the operations and predict how the operations may be changed or would react to different circumstances.
• operational data is collected, there must be a way of validating it. There is a need to be able to find the accuracy of the collected data, and the size of the data population. It is unrealistic in most operational situations to suppose that it is possible to collect a complete dataset. Thus one needs to be able to define how much of the data have been sampled and, if possible, to identify what sort of a sample has been obtained. The collected data must also be checked before the collection is finished.
• the optimal equipment allocation for the fracturing operations problem is formulated as a Mixed Integer Problem and is formulated as shown in Table 1.
• Table 1 The objective is to maximize the total maximum hydraulic horsepower (HHP) of the jobs done. This objective is used rather than maximizing the utilization, as this is a more natural target and prevents pathological solutions, for example, with no equipment and all of it is always fully utilized.
• HHP total maximum hydraulic horsepower
• Fig. 8 is a flow diagram for the optimum equipment allocation problem 80.
• the current number of jobs to be completed in a specified time period are input 81.
• the job requirements of each job are determined and specified in terms of an amount of equipment to perform each job 82.
• An equipment allocation problem is formulated based on current jobs, job requirements and supply equipment available. 83.
• the equipment allocation problem is modeled as an objective function and a set of constraints 84.
• the objective function is then optimized 85.
• Fig. 9 is a flow diagram for a fracturing operation optimum equipment problem 90.
• Fracturing problem data is obtained 91.
• Variable parameters are determined 92.
• Problem constraints are determined 93.
• a fracturing problem model is build to maximize the desired objective function 94.
• the problem model is expressed as an objective function and set of problem constraints in terms of variable parameters and problem data 95.
• the objective function 95 is expressed as:
• ⁇ x(p, j, k) used ⁇ (p, j) T pump(p, " psi” ) x(p, k, j) ⁇ used2(p, j) job(j, " psi” ) Vy ⁇ do nothing k
• ⁇ x(p, k,j) sed2(p, j) k
• Equipment is always somewhere, either at home or on a job:
• Job 1 is a dummy job for staying at home and doing nothing.
• the formulation uses O(
• the constraints on time taken can be evaluated before the model is solved and the relevant variables fixed to reduce the solution space.
• the objective function and set of constraints 95 are a mixed integer programming problem. Equipment must be allocated to meet as much of the demand as possible each day. Equipment utilization will be increased if the same amount of work can be accomplished with less equipment or more work can be done with the same amount of equipment.
• the model 95 may be expressed in an algebraic modeling language, such as GAMS and may then be optimized 96 using a commercial software solver program.
• An MIP model for the allocation of equipment to jobs is formulated and then run through different scenarios to identify which management choices lead to higher utilization. Since the problem is expressed as a mixed integer problem (MIP), a MIP solver such as CPLEX may be used. This choice of the MIP solver defines the properties of some of the variable parameters 92.
• MIP mixed integer problem
• SIP Stochastic Integer Program
• the model 95 and optimal solutions generator may be repeatedly run using different scenarios to answer what-if questions posed.
• the present invention calculates equipment utilization in a chosen set of scenarios and decides from the set of "what if experiments which strategy or strategies to recommend.
• the present invention considers the following strategies: the amount and types of equipment present (pumpers and monitor vans) 101; equipment sharing between Depots 102; manager comfort levels 103; and job scheduling and prioritization 104. The invention evaluates how these choices affect equipment utilization and the number of jobs done.
• Manager comfort levels 103 describe the relationship between the quantity of equipment requested/required to do the job and the "extra" that the individual manager usually sends. This "extra” may in fact be necessary due to the probability of equipment failure or may simply be to reassure the client that no such failure will negatively impact ob completion. Of course, it is possible that the equipment is sent out so that it gets some regular use and not for the above reasons.
• the idea of a "comfort level” describes the extra equipment sent to jobs for both objectively measurable and subjective reasons. How much must be sent for objective reasons depends on joint equipment and job failure distributions.
• Job prioritization 104 is another strategy that can be incorporated into the optimal equipment allocation problem.
• Job priorities can model client importance or the preference of a manager for doing jobs in his own customer area as opposed to loaning equipment to another Depot manager.
• the optimal equipment allocation problem is similar to a bin covering problem (BCP).
• BCP bin covering problem
• Normally the bins are of unit size and each item is in [0,1].
• This problem is NP-hard.
• ILFD Iterated-Lowest-Fit-Decreasing
• DSKP dynamic and stochastic knapsack problems
• One type of DSKP is one with deadlines where randomly sized jobs with random rewards arrive according to some stochastic process and must be accepted or rejected at once. The aim is to fill as much of the knapsack as possible within a given time.
• the optimal policy for a DSKP is a threshold which decreases with time up to the deadline provided that a fairly lenient consistency condition is met for the size and reward distributions.
• this stochastic optimization problem is equivalent in some sense to an n-stage stochastic optimization program with recourse, where n is the number of items seen before the deadline.
• One feature of fracturing operations is that a pumper can be involved in more than one job on a single day. This can be thought of, turned around, as the sojourn time of the job at the pumper. Stochastic knapsack problems have been developed for this situation where jobs occupy capacity but only for a limited time. This has been particularly developed with respect to telecommunications networks but the applicability to the optimal equipment allocation problem may be limited because the number of job requests is so different (millions for the telecommunications network versus around 10 for the fracturing operation). Additional sets/indices, etc. are required to describe the different scenarios. The calculation of the distance matrices and some implementation issues which became relevant for reducing solution times are listed below:
• Priorities 105 are used to help specify the order of selection of variables for inclusion in the branch and bound tree by the solver. These were partly derived from known results about approximations to the problem.
• the optimal choice for a (0-1 ) knapsack problem is to accept items in order of decreasing value density.
• Dynamic sets are defined for indices and used in the formulation of the constraint equations, including the objective. This ensures that each of the problem instances solved contains only the range of indices used rather than the range needed by the largest problem to be handled.
• steps 91 through 96 are repeated to generate a new optimal model solution 96 for the new what-if scenario.
• MIP mixed integer programming
• this date may be changed either by the customer who, for example, has problems with the drilling (in the case of a new well), or by the service provider, because of another client who wants to change the service date and has a higher priority than the former client.
• Another aspect of scheduling is that some clients may be more important than others. Rescheduling may happen more than once before a job is finally done or canceled.
• the current equipment level is 23 pumpers and 4 monitor vans (TCV's).
• Total pumper HHP with 19 pumps is 33000, with 23 pumps is 43000 and with 27 pumps is 51000.
• Thirty simulated days were considered.
• no sharing of pumpers or monitor vans is assumed. If there is no sharing of pumpers or monitor vans between the four Depots shown in Fig. 1 , the resulting percentage of pumper utilization for different equipment levels is shown in Figure 11.
• pumpers are shared but monitor vans are not. If pumpers are shared but monitor vans are not shared between the four Depots shown in Fig. 1 , the resulting percentage of pumper HHP utilized with different equipment levels is shown in Fig.13.
• pumpers and monitor vans are shared. If there is a sharing of pumpers and monitor vans between the four Depots shown in Fig. 1, the resulting percentage of pumper HHP utilized with different equipment levels is shown in Fig. 15. If there is a sharing of pumpers and monitor vans between the four Depots shown in Fig. 1 , the resulting percentage of job completions expressed in terms of their required HHP is shown in Fig. 16.
• the current demand level is increased by twenty percent (20%). Decreased demand levels are not considered because the idea is to plan for an increase in market share.
• no sharing of pumpers or monitor vans is assumed. If there is no sharing of pumpers or monitor vans between the four Depots shown in Fig. 1, the resulting percentage of pumper utilization for different equipment levels based on the increased demand is shown in Fig. 17. If there is no sharing of pumpers or monitor vans between the four Depots shown in Fig. 1, the resulting percentage of job completions expressed in terms of their required HHP based on the increased demand is shown in Fig. 18.
• pumpers and monitor vans are shared. If there is a sharing of pumpers and monitor vans between the four Depots shown in Fig. 1, the resulting percentage of pumper HHP utilized with different equipment levels based on the increased demand is shown in Fig. 19. If there is a sharing of pumpers and monitor vans between the four Depots shown in Fig. 1, the resulting percentage of job completions expressed in terms of their required HHP based on the increased demand is shown in Fig. 20. Based on the results, it seems more effective to share monitor vans than to buy more. Sharing monitor vans results in more in total available at each site.
• the next set of scenarios attempt to factor in manager comfort levels. This is perhaps the most realistic scenario if pumpers may occasionally break down. No manager is going to send only exactly what is required to a job if the possibility of a pumper breaking down and being unrepairable on site is greater than, say, 5%. For typical jobs considered here 2 to 3 pumpers are required. This means that individual pumpers would need to be approximately 97.5% to 98.3% reliable. If this is not the case, sending more equipment is reasonable from a manager's point of view.
• the current demand level is as shown in Fig. 1.
• sharing of pumpers only is assumed. Twenty five percent (25%) more equipment is also assumed. If there is a sharing of pumpers only between the four Depots shown in Fig. 1 , the resulting percentage of pumper utilization for different equipment levels based on the current demand and sending 25% more equipment than needed is shown in Fig. 21.
• the current demand level is increased by twenty percent (20%).
• sharing of pumpers only is again assumed as is sending twenty five percent (25%) more equipment than needed. If there is a sharing of pumpers only between the four Depots shown in Fig. 1, the resulting percentage of pumper utilization for different equipment levels based on the increased demand and sending 25% more equipment than needed is shown in Fig. 23.

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