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Net Income Per Limited Partnership Unit - Additional Information (Detail)
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Earnings Per Share [Line Items]    
Percentage of net income allocated general partner 1.00%dtrpi_PercentageOfNetIncomeAttributableGeneralPartner  
Weighted average number of units outstanding to general partner 8,751us-gaap_WeightedAverageLimitedPartnershipUnitsOutstanding 8,751us-gaap_WeightedAverageLimitedPartnershipUnitsOutstanding
General Partner [Member]    
Earnings Per Share [Line Items]    
Percentage of net income allocated general partner 1.00%dtrpi_PercentageOfNetIncomeAttributableGeneralPartner
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_GeneralPartnerMember
 
Percentage of net loss allocated general partner 24.00%dtrpi_PercentageOfNetLossAttributableGeneralPartner
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_GeneralPartnerMember
 
Percentage of additional losses allocated to general partner 1.00%dtrpi_AdditionalLossesAllocatedToGeneralPartnerPercentage
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_GeneralPartnerMember
 
Percentage of gain on sale and refinancing allocated to general partner 1.00%dtrpi_PercentageOfGainOnSaleAndRefinancingAllocatedToGeneralPartner
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_GeneralPartnerMember
 
Percentage of additional gain on sale and refinancing allocated to general partner 24.00%dtrpi_PercentageOfAdditionalGainOnSaleAndRefinancingAllocatedToGeneralPartner
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_GeneralPartnerMember
 
Limited Partners [Member]    
Earnings Per Share [Line Items]    
Percentage of net income allocated limited partners 99.00%dtrpi_PercentageOfNetIncomeAttributableLimitedPartners
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_LimitedPartnerMember
 
Percentage of net loss allocated limited partners 76.00%dtrpi_PercentageOfNetLossAttributableLimitedPartners
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_LimitedPartnerMember
 
Percentage of additional losses allocated to limited partners 99.00%dtrpi_AdditionalLossesAllocatedToLimitedPartnersPercentage
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_LimitedPartnerMember
 
Percentage of gain on sale and refinancing allocated to limited partners 99.00%dtrpi_PercentageOfGainOnSaleAndRefinancingAllocatedToLimitedPartners
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_LimitedPartnerMember
 
Percentage of additional gain on sale and refinancing allocated to limited partners 76.00%dtrpi_PercentageOfAdditionalGainOnSaleAndRefinancingAllocatedToLimitedPartners
/ us-gaap_PartnerTypeOfPartnersCapitalAccountAxis
= us-gaap_LimitedPartnerMember