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Share-Based Compensation (Details 7) (USD $)
12 Months Ended 1 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2014
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Liability for unvested restricted share awards $ 38,300,000us-gaap_EmployeeRelatedLiabilitiesCurrent 45,800,000us-gaap_EmployeeRelatedLiabilitiesCurrent 38,300,000us-gaap_EmployeeRelatedLiabilitiesCurrent
Incentive Unit Award      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period 3 years    
Number of shares considered for determining cash payment for each award upon vesting 1cvi_SharebasedCompensationArrangementBySharebasedPaymentAwardNumberOfSharesConsideredForDeterminingCashPaymentForEachAwardUponVesting
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
   
Unrecognized compensation cost 6,800,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
  6,800,000us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
Weighted-average period for amortization of unrecognized compensation cost 1 year 10 months 24 days    
Compensation expense 2,400,000us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
   
Cash paid to settle liability-classified awards upon vesting 1,600,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilitiesPaid
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
   
Granted (in shares) 332,586us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
251,431us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
 
Incentive Unit Award | Tranche One      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Award vesting percentage 33.33%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
/ us-gaap_VestingAxis
= us-gaap_ShareBasedCompensationAwardTrancheOneMember
   
Incentive Unit Award | Tranche Two      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Award vesting percentage 33.33%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
/ us-gaap_VestingAxis
= us-gaap_ShareBasedCompensationAwardTrancheTwoMember
   
Incentive Unit Award | Tranche Three      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Award vesting percentage 33.33%us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
/ us-gaap_VestingAxis
= us-gaap_ShareBasedCompensationAwardTrancheThreeMember
   
Personnel Accruals | Incentive Unit Award      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Liability for unvested restricted share awards $ 800,000us-gaap_EmployeeRelatedLiabilitiesCurrent
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
/ us-gaap_BalanceSheetLocationAxis
= cvi_PersonnelAccrualsMember
  800,000us-gaap_EmployeeRelatedLiabilitiesCurrent
/ us-gaap_AwardTypeAxis
= cvi_IncentiveUnitAwardMember
/ us-gaap_BalanceSheetLocationAxis
= cvi_PersonnelAccrualsMember
Executive      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Period for determination of cash payment value 10cvi_SharebasedCompensationArrangementbySharebasedPaymentAwardPeriodforDeterminationofCashPaymentValue
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ExecutiveOfficerMember
   
Executive | Stock Appreciation Rights (SARs)      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period     3 years
Number of shares considered for determining cash payment for each award upon vesting     1cvi_SharebasedCompensationArrangementBySharebasedPaymentAwardNumberOfSharesConsideredForDeterminingCashPaymentForEachAwardUponVesting
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ExecutiveOfficerMember
Granted (in shares)     227,927us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_TitleOfIndividualAxis
= us-gaap_ExecutiveOfficerMember